Julie Amaury

Keywords: clés -Modélisation de la distribution des espèces, science des données, apprentissage profond, réseaux de neurones convolutifs, réduction de dimension, télédétection, sciences de la conservation, assemblages d'espèces, risque d Species distribution modelling, data science, deep learning, convolutional neural networks, dimensionality reduction, remote sensing, conservation science, species assemblages, extinction risk, orchids Primary publications Species Distribution Modelling, Deep learning, Image time-series, Sentinel-2, Convolutional Neural Networks, Remote Sensing, Macroecology, Spaceborne Ecology, Biogeography, Data Science spatial indicator, species assemblage, deep learning, species distribution modelling, IUCN status, orchids

extinction, orchidées

années de doctorat à Montpellier ont été intenses, mais menées dans un cadre privilégié tant sur le plan professionel que personnel. Commencer une thèse un 1er novembre 2020 de confinement peut paraître loin d'être idéal sur le papier. Pourtant, dès le début de cette aventure, j'ai eu la chance d'être extrêment bien encadré par mes directeurs Alexis Joly et François Munoz, ainsi que mes encadrants Maximilien Servajean et Pierre Bonnet. Je vous remercie sincèrement pour votre soutien continu. Avoir un créneau hebdomadaire pour discuter de nos avancées peut sembler anodin, mais s'est en fait avéré précieux et motivant pour garder le bon cap. Plus particulièrement, merci Alexis pour ta confiance, ta curiosité et perspicacité scientifique qui m'ont aiguillé tout au long de mes recherches. Merci François pour tes analyses qui ont toujours su apporter de la valeur à nos travaux. Tes venues à Montpellier ont été riches en apprentissages. Merci Maximilien pour ta réactivité supersonique, ton soutien scientifique mais pas que: finalement, devant n'importe quel point bloquant, tu as toujours su me rédiriger vers les ressources adaptées. Enfin, merci Pierre pour ton esprit critique, tes interprétations scientifiques et ton attention à tous les niveaux. Ta générosité pour s'assurer que les conditions et directions de travail soient idéales est inégalée.

Vient maintenant le moment de remercier toutes les personnes avec qui nous avons collaborer pour mener à bien cette thèse. Pour commencer, merci à Cathy Desseaux, Nathalie Brillouet et Nathalie Hodebert pour votre soutien administratif. Vous m'avez grandement facilité la vie de doctorant, notamment lors de mobilités, milles mercis. Merci à Alexander Zizka pour nous avoir donné accès à ses données d'occurrences d'orchidées. Merci à toi Laura Pollock pour m'avoir chaleureusement accueilli dans ton équipe à Montréal. Merci pour ton regard avisé sur nos travaux. J'ai ainsi eu l'opportunité de continuer mes recherches deux mois en immersion dans une culture nouvelle et j'en suis extrêmement reconnaissant. Je tiens également à remercier Christophe Fiorio, Ana Rodrigues et Dino Ienco pour votre écoute et vos suggestions lors des comités de suivi annuels. Merci à Patrick Valduriez, Ghislain Vieilledent, Grégoire Vincent et Joseph Salmon pour vos conseils. Merci à l'Inria pour le financement de cette thèse ainsi qu'aux bailleurs de projets européens GUARDEN et MAMBO. Enfin, merci aux membres de mon jury de thèse Catherine Graham, Daniele Silvestro, David Mouillot et Jesper Erenskjold Moeslund. C'est grâce à votre disponibilité que je pourrai défendre ma thèse dans un cadre scientifique excellent.

Bon, ça va dépasser une page c'est sûr, mais pas si grave. Évidemment merci à mes collègues rapidement devenus amis de l'Inria. Merci pour votre aide, pour nos pauses caféinées et pour nos sorties sportives en tout genre. Titouan, Benjamin D., Camille, Maximilien, César, Pierre L., Shamprikta, Théo, Diego, Benjamin B., Christophe, Antoine L., Raphael, Aïmi: on aura bien rigolé, et j'ai bien peur qu'on ait d'autres occasions à l'avenir. Merci à l'équipe PlantNet bien sûr! Matthias, Hugo, Antoine A., Hervé, Jean-Christophe, Maxime, Rémi, Vincent, Thomas: ça a été un plaisir de partager les couloirs avec vous. A mi-chemin j'ai rejoins l'UMR AMAP, merci encore Pierre pour cette opportunité. J'ai alors eu la chance de croiser la route de nombreux nouveaux camarades de boisson amère: Houssem, Laetitia, Paul, Dim & Dom, Camille S. et Camille

Résumé

Les modèles de distribution d'espèces (SDMs) ont pour but d'apprendre les préférences environnementales des espèces et de projeter leur distribution géographique. Les récentes percées dans le domaine de l'apprentissage profond, associées à l'explosion des données sur la biodiversité, ont conduit au développement d'une nouvelle génération de modèles appelés deep-SDMs. Dans cette thèse, nous explorons leur application pour la conservation de la biodiversité.

Tout d'abord, nous évaluons la contribution des séries temporelles d'images satellites en tant que covariables environnementales. La capture de la phénologie des habitats d'espèces s'est avérée précieuse, en particulier pour les espèces rares et dans les régions riches en espèces. Deuxièmement, nous entraînons un deep-SDM pour déduire les assemblages mondiaux d'espèces d'orchidées à l'échelle du kilomètre. Des indicateurs spatiaux de leur risque d'extinction sont ensuite cartographiés à l'aide de la liste rouge des espèces menacées de l'UICN (Union Internationale pour la Conservation de la Nature). En mettant en évidence des motifs spatiaux du risque d'extinction de taxons sous-évalués, ces indicateurs multi-échelles et basés sur de grands volumes de données peuvent informer la planification de la conservation. Troisièmement, nous utilisons des représentations d'espèces issues d'un deep-SDM pour prédire avec succès les statuts UICN des espèces, tout en permettant de projeter l'étude dans des conditions bioclimatiques futures. En effet, l'évaluation automatisée du risque d'extinction est un domaine de recherche actif pour compléter les évaluations manuelles. Notre méthode de classification bénéficie du pouvoir de généralisation des deep-SDMs. Il vise à atténuer la dépendance à l'information géographique dans les évaluations du risque d'extinction de la flore et ainsi pouvoir prédire l'évolution future de ces risques.

La modélisation de la distribution des espèces est une tâche extrêmement difficile en raison de leurs dépendances biotiques et abiotiques complexes. Les modèles d'apprentissage profond peuvent s'appuyer sur les informations clefs qui sont en corrélation avec les espèces observés, et ce même lorsque des covariables environnementales riches et de très grande dimension leur sont fournies. En outre, les données sur la biodiversité sont entravées par des biais (taxonomique, géographique, temporel, etc.) que les techniques d'apprentissage automatique peuvent aider à compenser. En conclusion, nous avons étudié trois directions dans lesquelles les deep-SDM peuvent contribuer à la production de supports d'aide à la décision pour la conservation. 1) Tirer parti des données satellitaires de grande dimension pour modéliser les distributions d'espèces, 2) utiliser le pouvoir de généralisation et l'inférence des deep-SDMs pour cartographier mondialement le risque d'extinction d'assemblages d'espèces, et enfin 3) encoder des variables de grande dimension et leurs interactions reflétant les préférences environnementales des espèces pour des tâches connexes telles que la classification des statuts UICN.

Publications

This thesis is based on three articles. These are listed below as primary publications. One of these articles (Chapter 3) has been published in the research topic Plant Biodiversity Science in the Era of Artificial Intelligence of Frontiers in Plant Science. A second one (Chapter 4) is under review in Ecological Informatics. The last article (Chapter 5) is being finalised for the special issue Predictive Biogeography of Ecography, where we have been invited to submit a full manuscript.

The articles listed in the secondary publications are related to, but not included in, this thesis. The first will be part of the book On the edge of sixth extinction in biodiversity hotspots : Facts, needs, solutions and opportunities in Thailand and adjacent countries. The second, the GeoLifeCLEF 2023 Dataset paper, is under review in Ecology.

INTRODUCTION Table of contents

INTRODUCTION

Context

Changes and challenges. Climate change is one of the proven drivers of the ongoing sixth mass extinction [START_REF] Barnosky | Has the Earth's sixth mass extinction already arrived?[END_REF][START_REF] Pacifici | Assessing species vulnerability to climate change[END_REF]. As a reminder, July 2023 was the hottest month ever recorded on Earth1 . Accompanied by a series of extreme weather events (heatwaves, wildfires, floods) and record sea surface temperatures, the weather of July 2023 has had catastrophic impacts2 . Against this background, it is fair to ask whether the manifestations of climate disruption are likely to provoke a strong political and social response. Many anthropogenic drivers explain the increasing extinction risk of species [START_REF] Sala | Global Biodiversity Scenarios for the Year 2100[END_REF]. Indeed, extinction rate is estimated to be up to a thousand times higher than historical background levels [START_REF] Pimm | The biodiversity of species and their rates of extinction, distribution, and protection[END_REF]. If species threatened with extinction collapse under the pressures they face, the rate could rise to 10,000 times the background rate. Besides climate, land-use change [START_REF] Foley | Global Consequences of Land Use[END_REF], chemical and industrial pollution, invasive species [START_REF] Gurevitch | Are invasive species a major cause of extinctions?[END_REF]) and international trade [START_REF] Lenzen | International trade drives biodiversity threats in developing nations[END_REF] are at the forefront. In addition to being taxon-specific, the causes are interrelated, difficult to measure in isolation and therefore difficult to understand. Measuring the multiple facets of biodiversity (taxonomic, genomic, phylogenetic, functional, ecosystemic, etc.) and its vulnerability is a challenging task [START_REF] Purvis | On the Expressive Power of Deep Neural Networks[END_REF]. At the taxon level, the research community considers that some species may go extinct before they have even been described [START_REF] Costello | Can We Name Earth's Species Before They Go Extinct?[END_REF]. Biodiversity scales are nested. Species loss is a major driver of ecosystem change, compromising the goods and services that directly and indirectly benefit humans [START_REF] Hooper | A global synthesis reveals biodiversity loss as a major driver of ecosystem change[END_REF].

A plural response. In the face of this incredibly complex biodiversity crisis, the response has no choice but to be multifaceted and collaborative [START_REF] Wheeler | Mapping the biosphere: exploring species to understand the origin, organization and sustainability of biodiversity[END_REF]. To be successful, the collaboration should be i) societal to raise awareness and embrace change, ii) political to lead and fund change at scale, and iii) scientific to advance understanding and levers. The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) delivered an impactful Global Assessment Report on Biodiversity and Ecosystem Services in 2019 (IPBES, 2019). This structure aims to improve the interface between science and policy on biodiversity and ecosystem services issues. While the quality and need for such synthesis work is manifest, uptake by policymakers still appears to be low [START_REF] Garcia | Strategy games to improve environmental policymaking[END_REF]). The most recent example occurred in the European Parliament, where the highly anticipated Nature Restoration Law was voted in favour, but only in a heavily watered-down version3 . Besides, science-based solutions do exist. Spatial ecology science is for instance producing new indicators on the health of biodiversity (see Section 2.2) that could help reporting progresses when integrated in international agreements like the post-2020 global biodiversity framework [START_REF] Jetz | Include biodiversity representation indicators in area-based conservation targets[END_REF]. The weak collective and political response to increasingly well-documented challenges can lead to frustration, eco-anxiety or eco-anger [START_REF] Stanley | From anger to action: Differential impacts of eco-anxiety, eco-depression, and eco-anger on climate action and wellbeing[END_REF]. While this is an alarming mental health issue, especially among the youngest [START_REF] Bennun | Review: Ecological awareness, anxiety, and actions among youth and their parents -a qualitative study of newspaper narratives[END_REF],

1.1. Context
the positive management of these strong emotional drivers to engage in action is a key process to restore wellbeing and nourish transformative change [START_REF] Díaz | Pervasive human-driven decline of life on Earth points to the need for transformative change[END_REF]. Action is meant here in a large and personal sense. It includes discussing these concerns with one's surroundings, vulgarising and disseminating current knowledge, producing scientific research, or engaging in politics and activism.

The role of research. In this context, research clearly has a crucial role to play. Understanding and mapping biodiversity and its threats across scales, but also providing answers (restoration and protection, environmental justice, responsible farming, mitigation of extreme events). Interdisciplinary science and nexus approaches are key to addressing the multidimensional challenges of the 21st century [START_REF] Allan | Futurecasting ecological research: the rise of technoecology[END_REF][START_REF] Haider | The undisciplinary journey: early-career perspectives in sustainability science[END_REF][START_REF] Liu | Nexus approaches to global sustainable development[END_REF][START_REF] Zarnetske | Towards connecting biodiversity and geodiversity across scales with satellite remote sensing[END_REF]. For example, promoting integrative studies from masters and graduate level is a promising direction to train qualified professionals 4 . Adopting novel success metrics to recognise and promote interdisciplinary projects is another avenue to consider [START_REF] Goring | Improving the culture of interdisciplinary collaboration in ecology by expanding measures of success[END_REF]. A major technical barrier to the study of biodiversity -and ecology more broadly -is scale. Studies carefully focused on a particular taxon and/or spatio-temporal context do indeed shape our knowledge of biodiversity, and will always be much needed. However, scaling up biodiversity assessment using the same methods is impossible in practice (time-consuming, expensive manual data collection and analysis using tailored methods). Current knowledge of biodiversity is biased i) geographically towards the poles, although species richness is concentrated in the tropics, ii) taxonomically towards well-documented, common or charismatic taxa (mammals, birds), iii) temporally towards recent years due to increasing resources and citizen data, and iv) functionally towards species with large spatial distributions, although most species have small ranges and are known from only a few localities [START_REF] Collen | The Tropical Biodiversity Data Gap: Addressing Disparity in Global Monitoring[END_REF][START_REF] Pimm | The biodiversity of species and their rates of extinction, distribution, and protection[END_REF]. A biased assessment of biodiversity would lead to unrepresentative -or at least equally biased -conservation, leaving facets of biodiversity vulnerable to pressures.

Data and biodiversity science. Advances in technology, data science and ecoinformatics are thankfully bringing new ways of collecting, pre-processing and analysing information [START_REF] Farley | Situating Ecology as a Big-Data Science: Current Advances, Challenges, and Solutions[END_REF][START_REF] Hampton | Rodent reservoirs of future zoonotic diseases[END_REF]. Using the common Four Vs definition of big data, it appears clear that ecology has become a data-intensive science [START_REF] Michener | Ecoinformatics: supporting ecology as a data-intensive science[END_REF], see Figure 1.1. i) Volume can be easily illustrated by Remote Sensing (RS). For example, the two satellites of the Sentinel-2 imaging mission generate 1.6 Tbytes of raw imagery per day5 . ii) Variety can be represented by the wide range of scientific projects across temporal, spatial and taxonomic scales. The multiple facets of biodiversity give a sense of how diverse ecological data can be. iii) Veracity includes the different levels of expertise in species identification, but also taxonomic and distributional inaccuracies, among others. iv) Velocity is probably the weakest dimension represented in ecology, but improvements are needed and promising, with two examples in iEcology [START_REF] Jarić | iEcology: harnessing large online resources to generate ecological insights[END_REF] and camera traps. However, the collection of vast amounts of data alone is not sufficient to address current conservation challenges (Pimm et al., 2015).

INTRODUCTION

Effective use of this wealth requires the successful extraction of valuable information, which is likely to be hampered by multiple biases (sampling, detection, taxonomy). This has the potential to reduce current gaps in biodiversity knowledge [START_REF] Hortal | Seven Shortfalls that Beset Large-Scale Knowledge of Biodiversity[END_REF]. In addition, efficient biodiversity conservation requires the integration of biodiversity modelling and conservation, two fields that are still largely independent [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF][START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. Extracting critical information is a key challenge for scientific progress in the age of big data. Distilling rich information and capturing relevant features for a given optimisation problem is a machine learning task. There is a clear need to bring data science and biodiversity closer together. Machine Learning (ML) and Deep Learning (DL) are increasingly being used to solve applications in ecology [START_REF] Christin | Applications for deep learning in ecology[END_REF], see Section 2.4 for a review in conservation. They provide the ability to handle the high-dimensional data that characterises biodiversity and to capture complex relationships between predictors and the desired response function [START_REF] Maxwell | Implementation of machine-learning classification in remote sensing: an applied review[END_REF]. Ecology produces global and ever-increasing amounts of data at ever finer resolutions (spatial, temporal and spectral). Unlike traditional models, deep learning can make the most of this opportunity by analysing these data jointly and across scales [START_REF] Zhu | Deep Learning in Remote Sensing: A Comprehensive Review and List of Resources[END_REF]. Exploiting machine learning models in frameworks that are flexible enough to deal with heterogeneous biodiversity data and uncertainties is a major challenge for computer scientists [START_REF] Farley | Situating Ecology as a Big-Data Science: Current Advances, Challenges, and Solutions[END_REF]. With the increasing sharing of data in open repositories, there is an unprecedented opportunity to co-evolve data science and biodiversity knowledge [START_REF] Soranno | It's Good to Share: Why Environmental Scientists' Ethics Are Out of Date[END_REF]. Finally, in a context where misinformation about climate change is on the rise [START_REF] Linden | Inoculating the Public against Misinformation about Climate Change[END_REF], the question of how information is presented takes on a particular importance. We will therefore pay attention to the appropriate representation of our results (maps, figures, scenarios, online tools, etc.).

Modelling species distributions and remote sensing. A common modelling framework has been used across our studies: Species Distribution Models (SDM), and more specifically models based on deep learning architectures, called deep Species Distribution Models (deep-SDM), Botella et al. (2018a). SDMs are statistical tools designed to shape the distribution of species from the association of species observations with environmental descriptors under modelling and ecological assumptions. The properties and challenges posed by this class of models are detailed in the state of the art section 2.3. The use of SDMs to guide conservation decisions has already led to successful actions. However, more dialogue between modellers and decision-makers is needed in the design of SDMs to make them fit for purpose [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF]. Remote sensing has revolutionised the monitoring of life on Earth, revealing the spatial and temporal aspects of biodiversity through assessments of ecosystem structure, composition and function [START_REF] Cavender-Bares | Species distribution modeling in the tropics: problems, potentialities, and the role of biological data for effective species conservation[END_REF]. To understand and safeguard biodiversity, it is essential to embrace an integrative approach to biodiversity science [START_REF] König | Biodiversity data integration-the significance of data resolution and domain[END_REF]. This involves extending our understanding of local-scale processes to much larger scales through the use of remote sensing. For example, plant spectral diversity can be monitored at large scales through remote sensing and has been shown to integrate functional and phylogenetic components of biodiversity [START_REF] Schweiger | Plant spectral diversity integrates functional and phylogenetic components of biodiversity and predicts ecosystem function[END_REF]. Remote sensing products provide globally consistent and continuous spatio-temporal data on factors influencing the distribution of organisms. This opens up the possibility of (3) Near real-time sensor networks that can deliver on-going data feeds at low latency and high velocity. (4) Field observations and experiments by scientists, across a wide variety of measurements, systems, and scales. This mapping of the four Vs to data types is illustrative; all four dimensions are present in all data types. Reproduced from [START_REF] Farley | Situating Ecology as a Big-Data Science: Current Advances, Challenges, and Solutions[END_REF] with permission from Oxford University Press.

improving the accuracy of SDMs for conservation purposes [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF]. Indeed, satellite missions deliver spatially-explicit environmental predictors that can help models accurately capture species' habitat characteristics and preferences [START_REF] He | Will remote sensing shape the next generation of species distribution models?[END_REF]. In addition, the increasing spatial resolution and temporal revisit frequency of satellites allows for the development of rapidly repeatable and scalable biodiversity indicators. SDMs based on deep learning can produce high resolution maps globally (1 km, see Chapter 4), or even very high resolution (50 m, [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF] when provided with appropriate remote sensing resources. Achieving such spatial resolution would ultimately allow conservation decisions to be informed by consistent and scale-appropriate indicators.

It is in this challenging societal and scientific context, at the intersection of data and biodiversity science, that my PhD project takes place. After presenting the overall organisation of the manuscript, we will now focus more specifically on the motivations behind my doctoral research.

Thesis motivation and contributions 1.2.1 Central research questions and organisation

Our overarching research objective is to take advantage of recent advances in deep learning to model plant species distributions and provide new decision support for conservation practitioners. With species distribution models based on deep learning at the heart of our project, we can identify three main research questions that have guided our work: INTRODUCTION 1. Leveraging the temporal revisit of recent satellite imagery missions, does characterising species habitat in time improve species distribution modelling? If so, where are the greatest gains?

2. Can deep learning help map the extinction risk of species at both high resolution and global scale? If so, how are threatened orchids distributed across scales?

3. Can deep-SDMs produce species features that are informative of the extinction risk status, and how do these predictions respond to a business-as-usual climate change scenario?

Manuscript organisation

This thesis is structured in six chapters. Chapter 1 is the current introduction, setting out the general context of this doctoral thesis, and continues below with our specific motivations and contributions. Chapter 2 provides an overview of the state of the art research that underpins our work: indicators for biodiversity conservation, species distribution models (especially those using deep learning), and insights for conservation planning based on predictive approaches. Then chapters 3-5 are our three original research papers.

Chapter 3 has been published in a peer-reviewed journal, chapter 4 is under review and chapter 5 is being finalised prior to submission. Finally, chapter 6 discusses our scientific findings and their limitations, concludes on our research contribution and suggests new directions.

Modelling species distribution from satellite time-series -Ch. 3

Describing species environment. In order to model accurately the distribution of species, it seems necessary to provide the best possible descriptors of their environment. While knowledge of the proximal features behind species' environmental preferences is still very limited, a legitimate approach is to describe the observed species' habitat as precisely as possible (see Section 2.3.1.4 for a review on SDM covariates). The Sentinel-2 (S2) mission now provides access to RGB+IR imagery with a spatial resolution of ten metres. This makes it one of the best sources of information, both free and available on a global scale, for describing species habitats. Such a data-intensive method is enabled by the ability of deep learning to generalise the potential niches of species without being over-parameterised and then over-reliant on the very high dimensional training data [START_REF] Poggio | Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review[END_REF].

Capturing habitat phenology. Modern remote sensing missions represent an unprecedented opportunity to collect images of species habitat at high spatial resolution, but also with high temporal revisit frequency. Providing not only the central value of environmental predictors as input to deep-SDMs, but also the two-dimensional spatial context around species observations has been proven valuable for shaping potential niches [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. What about the temporal dynamics of remotely sensed habitats?

We anticipate that the temporal dimension -still largely under-exploited by species distribution modellers -would contribute significantly to habitat qualification. Better habitat characterisation allows models to better explore and shape the environmental conditions that have allowed plant species to flourish. Ultimately, we expect that describing the phenology of habitats would lead to a thinner capture of species' environmental sensitivity.

Comparison and hypothesis. An analogous case is photogrammetry, where reliable information about physical objects is obtained from multiple images taken from different angles. In our case, we do not multiply the viewing angles, but rather the shots along a year. In both cases, multiplying the inputs along one of the dimensions of the measurement allows a richer description of the target. A first goal is then to comprehensively test this hypothesis i) with remote sensing data and ii) on a global scale and iii) on a particularly rich, diverse and sensitive taxon.

Objectives. The main objective of this first study is to test the global contribution of habitat phenology to the performance of deep-SDMs. This will require the collection and pre-processing of a remote sensing dataset with a spatial coverage and temporal revisit that, to our knowledge, has never been mobilised for modelling species distributions. We will also investigate for which species and where the addition of the temporal dimension is most beneficial for modelling distributions. On a global scale, an additional study will test the contributions of three SDM modalities: remote sensing imagery, bioclimatic variables and static variables (elevation, position, human footprint and ecoregions). The motivation behind this work is to assess, at a global scale and for a given study taxon, the trade-off between the processing cost of remote sensing and its predictive power compared to other readily available variables.

Contributions

1. A remote sensing dataset called DeepOrchidSeries is generated from a set of 1 million orchid observations for 14 thousand species distributed worldwide. Twelve-month image time-series from the Sentinel-2 mission are associated with each sighting. The four 10-metre resolution channels (RGB+IR) are sampled with an extent of 640 x 640 m centred on the observation.

2. An SDM based on a convolutional neural network architecture (Inception V3) is adapted to learn potential species niches from the satellite image time-series and with a tailored training procedure.

3. An ablation study tests the contribution of the temporal dimension of the input (capturing habitat phenology) to species distribution modelling.

4. As expected, the temporal dimension helps in modelling species distributions by allowing a better characterisation and differentiation of habitats. The macro-average performance with a time-series of satellite images as input is almost two times higher than with a random single view. Interestingly, hard predictions of rare species and in species-rich regions particularly benefit from the additional temporal context.

5. The contributions of three SDM modalities are compared on a global scale: bioclimatic variables, satellite image time-series and static variables (including altitude, position, human footprint and ecoregions). Prioritise conservation. Species around the world are increasingly threatened by extinction due to human activities. Conservation science is a mission-driven discipline that aims to prevent species from going extinct. All facets of biodiversity have intrinsic and potential value, and in a utopian world the entire tree of life would be protected or at least monitored [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. However, the costs of conservation and the socio-economic context leave no choice but to prioritise action on certain aspects of biodiversity (Juffe-Bignoli et al., 2016).

The dimensions of threat. Threat is a multidimensional concept that cannot be represented in a single way. The section 2.2.3 will focus on describing the literature on threat indicators. Existing threat maps mostly focus on pressures sources and processes with remotely sensed data, such as land use change, urbanisation or trade [START_REF] Harfoot | Using the IUCN Red List to map threats to terrestrial vertebrates at global scale[END_REF]. However, i) threat sources and mechanisms do not necessarily translate into threatened states and ii) these threatened states or stresses of biodiversity, such as population decline or niche shrinkage, are rarely mapped [START_REF] Balmford | Capturing the Many Dimensions of Threat: Comment on Salafsky et al[END_REF]. It is precisely these symptoms, these causes of concern, that the International Union for Conservation of Nature (IUCN) criteria are intended to measure for species and, more recently, for ecosystems. Species range knowledge. Mapping the concentration of threatened species therefore appears to be a useful input for decision making. According to [START_REF] Marco | Changing trends and persisting biases in three decades of conservation science[END_REF], the alignment between global conservation science and the distribution of biodiversity remains poor, especially for threatened species. Species assessments continue to show a clear geographical bias. Furthermore, spatial data to support extinction risk assessment with known ranges are extremely scarce for the plantae kingdom. Of the 150,300 species assessed by the IUCN, 82% have spatial data. However, this is mostly the case for comprehensively assessed taxonomic groups such as vertebrates or amphibians. In fact, the proportion of IUCN assessments supported by spatial data drops to one sixth for plant species 6 . Spatial data may also be incomplete, as IUCN acknowledges. Generalisation of species distributions through modelling can help to overcome the scarcity and bias of IUCN plant range data. We believe that this is a key modelling step towards the design of indicators that are truly representative of biodiversity patterns. Biodiversity indicators. There are three basic functions of indicators: simplification, quantification and communication [START_REF] Pinborg | An inventory of biodiversity indicators in Europe[END_REF]. Typically, indicators simplify complex phenomena to make them measurable and enable information to be communicated. Spatial indicators are naturally based on geospatial data, and this additional output dimension enables spatial analysis. Biodiversity indicators play a crucial role in facilitating communication about the current status and trends of biodiversity and the underlying relationships driving these changes.

Our proposal. We believe that scalable spatial indicators of the extinction risk of plant assemblages are needed to inform conservation decisions. What we map is i) the spatial concentration of threatened species as defined by IUCN and ii) the most critical status of species that may be present at a given location. The development of these indicators implies to fill the current spatial and taxonomic gaps in extinction risk assessments.

Objectives. Questions addressed in our study relate to the spatial distribution of plant 1.2. Thesis motivation and contributions extinction risk. How can we complement IUCN information to fill assessment gaps and provide global estimates at high resolution? Can we identify local, regional or global patterns in the designed indicators and where are the most affected countries? Another motivation for our work is to stimulate methodological research. Indeed, addressing such a global issue at high resolution requires technical expertise and the formulation of appropriate hypotheses that need to be carefully tested and challenged by the community. This is an illustration of the needed interdisciplinary context that we advocate in the introduction. Summary. To conclude, we believe that there is a strong need to map the concentration of potentially threatened species in under-assessed taxonomic groups. This fills a taxonomic, spatial, but also a target gap in the representation of threats. Such indicators would ultimately benefit conservation decision making. This study will hopefully contribute to and motivate the development of methodological research by interdisciplinary teams. We are confident that challenging and complementing these results would ultimately benefit conservation science.

Contributions 1. A deep-SDM is calibrated to predict species assemblages worldwide at kilometre resolution. Based on globally available information (bioclimatic, pedological, human footprint, ecoregions and position), the model is guaranteed to return the true species within its predicted assemblage with 97% confidence (conformal prediction).

2. Spatial indicators are developed from these predictions and from the IUCN Red List completed by a reference predictive model. They are defined as the proportion of threatened species (and each IUCN extinction risk category), the most critical IUCN status and the Shannon index. The interactive maps are available online at https://mapviewer.plantnet.org/?config=apps/store/orchidstatus.xml.

3. Summary spatial statistics are calculated at country level. The most threatened countries are compared with the most species-rich countries. Indicators are compared with current protected areas on the island of Sumatra.

4. The highest level of threat is observed in Madagascar and the surrounding islands. In Sumatra, we found a favourable alignment between protected areas and our indicators. However, when we enhance the existing IUCN assessments with predictions of species status, we find worrying levels of threatened species across the island and throughout the world.

INTRODUCTION assessed, such as mammals, birds or amphibians, and others barely assessed, such as invertebrates (2% assessed) or marine species (15% assessed). Overall, 7% of the world's described species have been assessed by IUCN. Despite important efforts to speed up manual assessments, the task is Herculean (e.g. 1,305,250 estimated number of described invertebrates). Limitations in Red List coverage remain numerous (taxonomic, but also spatial, temporal and thematic biases, [START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF].

Compensatory automatic methods. In addition, threatened but unassessed species are excluded from conservation efforts worldwide, but also from private sector protection and specific funding. In response to these massive concerns, research has developed compensatory automated assessment methods, see the state of the art section 2.4.2.

The motivations are numerous, with the need to update the Red List and the cost of assessment also coming into play [START_REF] Rondinini | Update or Outdate: Long-Term Viability of the IUCN Red List[END_REF].

Climate change and extinction risk. Climate change is expected to threaten up to one in six species with extinction under current atmospheric emissions trajectories [START_REF] Urban | Accelerating extinction risk from climate change[END_REF]. Overall, red listing has been shown to be a relevant warning to identify and protect species threatened by climate change [START_REF] Stanton | A third of the tropical African flora is potentially threatened with extinction[END_REF]. However, the consideration of climate change with appropriate hypotheses in red list assessment is still the fruit of active research and can massively influence assessment results [START_REF] Moat | Least concern to endangered: Applying climate change projections profoundly influences the extinction risk assessment for wild Arabica coffee[END_REF], see section 2.4.3.

Objectives. In our third study, our motivation lies in the intersection of these two research areas. We investigate the influence of climate change projections on automated Red List assessments based on SDM features. Our classification scheme benefits from the generalisation power of deep-SDMs. It aims to mitigate the over-reliance on geographic information in flora extinction risk assessments, thus allowing prediction of future extinction risk patterns. We test if a deep-SDM used as a dimension reduction algorithm can provide species features predictive of IUCN status. Our use of SDM to support red listing is novel and conditioned by species dispersal scenarios. In particular, we are interested in projections of threatened species across continents, across latitudinal gradients and across altitudes.

Contributions

1. A trained deep-SDM is used as a dimension reduction algorithm to encode species features that are predictive of IUCN extinction risk status and benefit from the niche generalisation power of SDMs. The method validation demonstrates competitive performances.

2. The business-as-usual emission rate scenario (RCP 8.5) along with two extreme dispersal scenario (null and unlimited) are adopted to model climate change until 2100. The response in threatened species predictions is declined by continents, latitude and elevation.

3. The proportion of threatened species is globally increasing, with alarming levels in Africa, Asia and South America. It is also predicted to peak around both Tropics and the Equator, in the lowlands and in the 800-1,500 m altitudinal range.

1.3. A suited case study family: Orchidaceae

A suited case study family: Orchidaceae

An hyperdiverse and threatened family. With c. 31,000 species8 worldwide, orchids are one of the largest families of flowering plants. This hyperdiverse family is also one of the most threatened, in part due to their complex life history strategies [START_REF] Cozzolino | Orchid diversity: an evolutionary consequence of deception?[END_REF][START_REF] Fay | Orchid conservation: how can we meet the challenges in the twenty-first century?[END_REF]. This, together with complex biotic interdependencies including with mycorrhizal fungi [START_REF] Mccormick | Mycorrhizal fungi affect orchid distribution and population dynamics[END_REF] and fire exposure, is considered to make their distributions particularly sensitive to climate change. Other major threats they face include habitat conversion and harvesting (horticulture, illegal trade). This family is therefore experiencing unprecedented challenges, surpassing those of many other plant groups.

A flagship ecological indicator... The specificity of orchids provide them good indicator properties of the health of their ecosystem [START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. In addition to their sensitivity to climate change, orchids have been shown to respond measurably to past and present environmental disturbances [START_REF] Kull | A comparative analysis of decline in the distribution ranges of orchid species in Estonia and the United Kingdom[END_REF]. The family is also involved in ecosystem functioning through their highly specific to generalist interactions with pollinators (sometimes resulting in high levels of co-evolution) and mycorrhizal associations [START_REF] Swarts | Terrestrial orchid conservation in the age of extinction[END_REF]. Finally, orchids are easy to monitor in the sense that once populations are established, they are easy to find every year. Orchids can therefore be considered as a suitable ecological indicator of the health of their ecosystem, as defined by (Jørgensen et al., 2016). Indeed, the family is i) easy to monitor, ii) sensitive to small-scale environmental changes with quantifiable and predictable responses, and iii) globally distributed. Moreover, the effectiveness of surrogate species for biodiversity planning has been tested and validated, at least for taxa within the same realm [START_REF] Rodrigues | Shortcuts for Biodiversity Conservation Planning: The Effectiveness of Surrogates[END_REF]. Through the prism of our orchid-based indicators, we do not pretend to accurately represent ecosystem health. The orchid family has some characteristics that are associated with ecosystem health and services, but naturally cannot capture all facets of ecosystem biodiversity.

But with scarce knowledge on spatial range and extinction risk. As of July 2023, the Red List has evaluated 1,970 orchids, representing 6.3% of the estimated 31,000 species. Although this is low, orchids are the vascular plant family with the third highest increase in evaluation effort over the last decade, behind Fabaceae and Cactaceae [START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF]. In terms of the availability of spatial data, less than 11% of the species assessed by IUCN (1,970) have recorded spatial ranges (210). In other words, less than 1% of described orchids have both an IUCN assessment and a described spatial range. This highlights the need to fill the gaps in assessment and range data before developing scalable biodiversity indicators to guide conservation.

Orchid conservation at all scales. As a beloved and charismatic family with a profile that can benefit plants on a large scale, orchid conservation receives attention from a wide range of actors. This has resulted in large orchid networks (Orchid Specialist Group, European Orchid Council, American Orchid Society, etc.) and numerous academic studies at global [START_REF] Cribb | Orchid conservation: a global perspective[END_REF][START_REF] Vitt | Global conservation prioritization for the Orchidaceae[END_REF] and national levels.

Here are examples from Costa Rica, Greece, France, Australia and China [START_REF] Crain | Biogeographical analyses to facilitate targeted conservation of orchid diversity hotspots in Costa Rica[END_REF]Tsiftsis INTRODUCTION & Tsiripidis, 2020;[START_REF] Vogt-Schilb | Recent declines and range changes of orchids in Western Europe (France, Belgium and Luxembourg)[END_REF][START_REF] Wraith | Quantifying anthropogenic threats to orchids using the IUCN Red List[END_REF][START_REF] Zhang | Distribution and conservation of orchid species richness in China[END_REF]. Moreover, [START_REF] Gale | Orchid conservation: bridging the gap between science and practice[END_REF] formulate eight recommendations to guide global orchid conservation, including the creation of orchid reserves that will benefit a wide range of other species, and more monitoring of all forms. Citizen science observations are also improving our understanding of the family distribution. However, knowledge gaps are still very important and lead to a difficult prioritisation work before implementing effective conservation [START_REF] Gale | Orchid conservation: bridging the gap between science and practice[END_REF][START_REF] Wraith | Orchid conservation and research: An analysis of gaps and priorities for globally Red Listed species[END_REF]. Here is the conclusion of Michael F. Fay from his study entitled "Orchid conservation: how can we meet the challenges in the twenty-first century?":

"The level of these threats [habitat destruction, climate change, harvest] now outstrips our abilities to combat them at a species-by-species basis for all species in such a large group as Orchidaceae; if we are to be successful in conserving orchids for the future, we will need to develop approaches that allow us to address the threats on a broader scale to complement focused approaches for the species that are identified as being at the highest risk." [START_REF] Fay | Orchid conservation: how can we meet the challenges in the twenty-first century?[END_REF] This author emphasises that species-specific research remains vital to understanding orchid biology, pollination, mycorrhizal associations, population genetics and demography. However, the threats are too severe to allow only this type of focused study if we aspire to conserve the incredible diversity of orchids.

(Michael F.
Our contribution to orchid conservation. Our research feeds into orchid conservation at several levels. We are helping to map their global diversity at the kilometre scale with the Shannon Index. With this unprecedented spatial resolution, we are also revealing global patterns of extinction risk for the family. In addition, we show how supplementing the IUCN Red List with automated assessments leads to drastically different risk levels and patterns. An interactive map allows users to explore regional or local gradients. Spatial statistics provide insights and priorities at the country level. Finally, we complement the IUCN Red List with our own predictive method that benefits from the generalisation power of deep-SDMs. Thanks to bioclimatic projections, we provide automated extinction risk assessments for 13,240 orchids, not only for the present, but also for four twenty-year periods up to 2100. We discuss projections of extinction risk levels per continent, as a function of latitude and as a function of altitude.

CHAPTER 2

STATE OF THE ART

Introduction

The background information that underpins our work is largely interdisciplinary. We decided to start this review of the state of the art by introducing the application targets behind our deep learning models in a first section 2.2 related to indicators for biodiversity conservation. This first section organises classical metrics and new approaches to quantify biodiversity. It is not intended to be exhaustive, but rather to provide an organised overview of i) the commonly used metrics that guide conservation measures, and ii) the original and ongoing research that attempts to fill current knowledge gaps. Whole facets of biodiversity such as ecosystem services and functions [START_REF] Burkhard | Mapping ecosystem services[END_REF][START_REF] Oliver | Biodiversity and Resilience of Ecosystem Functions[END_REF] or genetic diversity are not covered in this review, but should also be measured to guide conservation. In a second section 2.3, we will consider the state of the art in species distribution modelling. After an overview of SDMs, we will present recent models based on deep learning architectures. Indeed, deep-SDMs are the common building block of our three scientific contributions. Special attention will be given to the motivation for adopting deep learning successes in ecology and SDMs. The deep learning principles relevant to our work are also introduced and illustrated. Finally, the third section 2.4 provides insights for conservation planning, especially when they are based on predictive approaches. While such applications are now many and varied, we will focus on automated assessment of species extinction risk, prediction of climate change impacts on biodiversity, and optimisation of conservation resources.

Indicators for biodiversity conservation

Indicators simplify, quantify and communicate complex concepts. Spatial indicators exploit geospatial data and allow spatial analysis. Biodiversity indicators are essential for reporting the status, trends and drivers of biodiversity change. They allow conservation targets to be set and progress to be tracked against countries' commitments under international agreements. A wide range of conservation-oriented indicators are used to try to cover as many facets of biodiversity as possible. Multiplying indicators may seem contrary to their primary function of simplifying concepts. It remains necessary, however, as biodiversity cannot be reduced to a single measure of species, ecosystems or functions. The Biodiversity Indicators Partnership1 is a global initiative to coordinate the development and use of indicators for biodiversity-related conventions: IPBES, the Convention on Biological Diversity (CBD), the Sustainable Development Goals (SDG), national and regional agencies.

Here we present an overview of indicators for biodiversity conservation that we consider to be key reference points for situating our work. Our first focus is on indicators at the central and base level of species in section 2.2.1. Next, we will focus on higher level indicators of species communities and habitats in Section 2.2.2. Finally, we will present the active literature on the spatial indicators of biodiversity threats Section 2.2.3.

Indicator species of ecosystem health

One way of assessing the health of an ecosystem is to measure species or responses that are representative of its state or vigour [START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. These measures, or indicators, can be the presence or absence of species, biomass or species metabolism. Examples of indicators are the use of Posidonia oceanica (L.) Delile meadows to assess water quality (Pergent-Martini et al., 2005), the presence of freshwater fish and common birds in Europe to represent the quality of their respective habitats [START_REF] Vallecillo | A habitat quality indicator for common birds in Europe based on species distribution models[END_REF][START_REF] Yousefi | Using endemic freshwater fishes as proxies of their ecosystems to identify high priority rivers for conservation under climate change[END_REF] and finally butterfly assemblages to capture environmental heterogeneity (topography and moisture) [START_REF] Kremen | Assessing the Indicator Properties of Species Assemblages for Natural Areas Monitoring[END_REF]. Recent research suggests that, although work is needed to refine understanding of their response to specific disturbances, orchids have good indicator properties (presence and abundance, growth and symbionts) of ecosystem health [START_REF] Cribb | The conservation of Madagascar's orchids . A model for an integrated conservation project[END_REF][START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. Taking such properties into account, orchid-based indicators can be considered to have a wider scope than just qualifying their family, but also a degree of habitat quality. Again, however, we do not pretend to be able to fully capture ecosystem health through a single family of indicators. In practice, achieving this goal would require a large number of indicators and measurements.

Indicators at species level

The IUCN Red List of Threatened Species

Introduction and relevance

The International Union for Conservation of Nature (IUCN) maintains the most widespread and authoritative information on the extinction risk of species in the IUCN Red List of Threatened Species (RL), see [START_REF] Mace | Quantification of Extinction Risk: IUCN's System for Classifying Threatened Species[END_REF]. Its strength lies in the unified assessment process based on five criteria that include population size and dynamics, geographic range, and direct quantitative estimates of species' probability of extinction. For a comprehensive summary on IUCN criteria, the interested reader is invited to consult the Red List Criteria Summary Sheet available online2 and the official guidelines for more details (Commission et al., 2001). These criteria are the result of an iterative refinement process that began in the 1960s with emblematic species and converged on the current version, established in 2001 and revised in 2012. The Red List has gained political weight over the years and its conservation value is recognised by the community [START_REF] Rodrigues | The value of the IUCN Red List for conservation[END_REF]. [START_REF] Betts | A framework for evaluating the impact of the IUCN Red List of threatened species[END_REF] proposed a framework for measuring the impacts of red listing species. It allows conservation funding to be directed [START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF], but also restricts trade in species [START_REF] Challender | Identifying species likely threatened by international trade on the IUCN Red List can inform CITES trade measures[END_REF] and sets limits on the private sector [START_REF] Bennun | Review: Ecological awareness, anxiety, and actions among youth and their parents -a qualitative study of newspaper narratives[END_REF]. Many extinction risk assessment are led at the regional or national level.

Assessment process and categories

The IUCN Red List divides species into nine categories of extinction risk. By default, an accepted species that has never been evaluated falls into the Not Evaluated (NE) category. These species are not published on the IUCN Red List, but represent 93% of the world's described species. When an assessment is undertaken, the first step is to gather the information that supports the various criteria. Ideally, all criteria are assessed against official thresholds and the most critical status is retained (precautionary 2.2. Indicators for biodiversity conservation approach). In practice, information must be available to assess the risk of extinction of species against at least one of the five criteria. Otherwise, species inherit the status of Data Deficient (DD). With sufficient information, the assessment results in:

• Least Concern (LC) if the species is far from qualifying as threatened • Near Threatened (NT) if a threshold is close or likely to be reached in the near future • Vulnerable (VU), Endangered (EN), Critically endangered (CR) when a corresponding threshold is reached, resulting in a high, very high or extremely high risk of extinction in the wild, respectively.

Finally, a taxon may be Extinct in the Wild (EW) if it is known to occur only in a controlled environment, or Extinct (EX) if there is no reasonable doubt that the last individual has died. Classifying a species as extinct is i) a difficult task, as it requires an exhaustive survey of the species niche or habitat, and ii) a weighty task, as it halts any potential conservation and recovery of the species. The generalised Red List assessment process is outlined in Figure 2.1.

There are specific guidelines for adapting species assessments at regional and national levels (IUCN, 2012a). It is indeed important to complement global assessments at lower levels, where conservation decisions are often made and implemented. When regional assessments concern endemic species, they are equivalent to global assessments. It is estimated that 60% of plant species are endemic to a single region [START_REF] Bachman | Quantifying progress toward a conservation assessment for all plants[END_REF]). As regional assessments are abundant, they represent an important potential to extend the global coverage of the IUCN Red List [START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF]. Limitations to their integration, such as translation needs or manual entry, are being addressed by the community.

Area of Occupancy and Extent of Occurrence

Criterion B focuses mainly on the geographic range of species and is commonly used to assess the extinction risk of plants. It measures firstly two geographical descriptors, Area of Occupancy (AOO) and Extent of Occurrence (EOO). EOO is defined as "the area contained within the shortest continuous imaginary boundary which can be drawn to encompass all known, inferred or projected sites of present occurrence of a taxon, excluding cases of vagrancy". (Commission et al., 2001). It is not a measure of the size of a species' range, as already assumed [START_REF] Jetz | Ecological correlates and conservation implications of overestimating species geographic ranges[END_REF], but a measure of the species' spatial spread. AOO is defined as "the area within its EOO occupied by a taxon, excluding cases of vagrancy" (Commission et al., 2001). The cell size should be "appropriate to the relevant biological aspects of the taxon, the nature of threats and the available data". In practice, 2 x 2 km² cells are widely used. Two examples are shown in Figure 2.2. In addition to meeting the official thresholds for EOO and/or AOO, Criterion B requires two subcriteria out of three possible to be fully assessed. These are whether the species is (a) highly fragmented or has a limited number of locations, (b) in continuing decline, and (c) experiencing extreme fluctuations. An IUCN location is defined as "a geographically or ecologically distinct area in which a single threatening event can rapidly affect all individuals of the taxon present". While continuing decline (b) can usually be observed or inferred, a second subcriterion is often difficult to demonstrate. Indeed, subcriterion (c) on extreme fluctuations only concerns a limited range of species such as migratory birds, often leaving subcriterion (a) as the only and difficult remaining option. As the calculation of EOO and AOO can be easily coded, most attempts to automate the IUCN Red List assessment while respecting the official thresholds focus on this B criterion (see section 2.4.2).

Limitations and scientific debate

As an influential species conservation indicator, the RL and its assessment process are a source of scientific debate and research. Major criticisms have focused on the lack of flexibility or representativeness of the assessment process [START_REF] Akcakaya | Making Consistent IUCN Classifications under Uncertainty[END_REF][START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF][START_REF] Jarić | Potentially threatened: a Data Deficient flag for conservation management[END_REF]. In an attempt to improve the evaluation process, new or modified criteria are regularly proposed. For example, they may question the calculation of EOO and AOO [START_REF] Breiner | Improving the estimation of area of occupancy for IUCN Red List assessments by using a circular buffer approach[END_REF][START_REF] Joppa | Impact of alternative metrics on estimates of extent of occurrence for extinction risk assessment[END_REF][START_REF] Marsh | Mind the gap: Can downscaling Area of Occupancy overcome sampling gaps when assessing IUCN Red List status?[END_REF]. Studies also promote the inclusion of additional information in the assessment, be it species Area of Hability (AOH) [START_REF] Brooks | Measuring Terrestrial Area of Habitat (AOH) and Its Utility for the IUCN Red List[END_REF], environmental niche [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF], ecological traits [START_REF] Mattila | The use of ecological traits in extinction risk assessments: a case study on geometrid moths[END_REF] or genetic diversity [START_REF] Rivers | Do species conservation assessments capture genetic diversity?[END_REF]. Biases in RL coverage are well known: taxonomic, but also spatial towards the poles, temporal with 83% of assessments being outdated by 2025 [START_REF] Rondinini | Update or Outdate: Long-Term Viability of the IUCN Red List[END_REF] and functional: species with restricted distributions, small body sizes and low dispersal abilities are underrepresented [START_REF] Pimm | The biodiversity of species and their rates of extinction, distribution, and protection[END_REF]. In addition, assessing biodiversity through the RL is costly (Juffe-Bignoli et al., 2016). These concerns are legitimate. There is considerable value in identifying and attempting to tackle areas for improvement, even if the RL criteria do not set new standards. IUCN guidelines are regularly updated to incorporate new approaches. Misunderstandings of IUCN concepts can also occur [START_REF] Collen | Clarifying misconceptions of extinction risk assessment with the IUCN Red List[END_REF]. Although it can be frustrating, changing the RL assessment process could compromise its objectivity and authority [START_REF] Breiner | Revision of the Red List of fern and vascular plants -evaluation and application of statistical methods[END_REF]. Finally, new approaches are being developed to complement the RL, such as the Red List of Ecosystems (RLE), which will be introduced in section 2.2.2, and the Red List Index (RLI) introduced below. Short-term information is provided by other large-scale measures of changing nature, such as population size, number, and habitat extent. They can be easily linked to economic values and public concerns [START_REF] Balmford | Measuring the changing state of nature[END_REF].

Red List Indices

As the human impact on biodiversity was increasingly recognised, the need to quantify overall biodiversity loss in order to assess countries' commitments arose at the beginning of the century [START_REF] Butchart | Global Biodiversity: Indicators of Recent Declines[END_REF]. In response, IUCN and its partners developed the Red List Index [START_REF] Butchart | Improvements to the red list index[END_REF][START_REF] Butchart | Measuring global trends in the status of biodiversity: Red List Indices for birds[END_REF]. The RLI aggregates IUCN Red List information to provide information on trends in the status of biodiversity for sets of species. The IUCN categories are quantified from Least Concern (LC) (0) to Extinct (EX) ( 5). An RLI of 1 indicates that all species in the set are LC and an RLI of 0 indicates that all species are extinct. It was originally designed for groups that are extensively and repeatedly assessed, such as birds and mammals. When two different RL assessments are available in time, biodiversity loss can be quantified. The RLI targets genuine changes in threat status, not reassessments due to improved knowledge or changes in criteria. The RLI can be calculated for any subset of species. It can therefore be calculated for countries [START_REF] Rodrigues | Spatially explicit trends in the global conservation status of vertebrates[END_REF][START_REF] Saiz | Application of the Red List Index for conservation assessment of Spanish vascular plants[END_REF] or thematic groups of species such as bird and mammal pollinators [START_REF] Regan | Global trends in the status of bird and mammal pollinators[END_REF]. As an exhaustive RL assessment is far from being achieved for many taxonomic groups such as plants, a sampled RLI has also been developed (Brummitt et al., 2015). It is based on a representative sample of 1,500 species and can provide a representative picture of biodiversity change for under-assessed but threatened groups.

Ecological and evolutionary originality

Phylogenetic diversity

To protect the potential and inherent value of phylogenetic (evolutionary) diversity, new approaches have been praised [START_REF] Mace | Preserving the Tree of Life[END_REF][START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF][START_REF] Vitt | Global conservation prioritization for the Orchidaceae[END_REF]. Phylogenetic diversity is defined as "the evolutionary diversity represented by sets of taxa, where the most common metric (Faith's phylogenetic diversity) is the branch length of the minimum spanning tree connecting a set of species in a phylogeny" [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. The Evolutionarily Distinct and Globally Endangered (EDGE) metric contributes to identify and conserve such threatened species [START_REF] Gumbs | The EDGE2 protocol: Advancing the prioritisation of Evolutionarily Distinct and Globally Endangered species for practical conservation action[END_REF][START_REF] Isaac | Mammals on the EDGE: conservation priorities based on threat and phylogeny[END_REF]. Evolutionarily Distinctiveness (ED) scores are calculated by dividing the phylogenetic diversity of a clade among its members. Extinction risk is considered using numerical RL categories ranging from LC = 0 to CR = 4. By combining these two metrics, EDGE places emphasis on species with high evolutionary heritage but which are threatened with extinction. However, the approach requires that clade phylogenies have been established. It has been successfully implemented for mammals, amphibians, corals, birds, reptiles, sharks and rays, but many taxa remain to be considered.

Functional diversity

Another facet of biodiversity of great concern, but overlooked in current RL assessments, is functional diversity. It is defined as "the diversity of functional forms in a species set (or community) as measured by a variety of metrics using dendrograms or representations in multidimensional space" [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. Similar to the EDGE index, new metrics attempt to quantify the functional diversity of species and cross the result with the RL to give a sense of functional extinction risk priority. Recent examples are the Functionally Unique Specialized and Endangered (FUSE) index and the Ecologically Distinct and Globally Endangered (EcoDGE) index [START_REF] Griffin | Functionally unique, specialised, and endangered (FUSE) species: towards integrated metrics for the conservation prioritisation toolbox[END_REF][START_REF] Hidasi-Neto | Global and local evolutionary and ecological distinctiveness of terrestrial mammals: identifying priorities across scales[END_REF]. Finally, the latter authors also propose to combine both phylogenetic and functional diversity with extinction risk in a general index called EcoEDGE.

International agreements

At the international level, one of the most influential tools for protecting endangered species from excessive trade is the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES)3 . The Convention was originally drafted by IUCN members in the 1960s and was adopted by 80 countries in 1975. It aims to limit trade in charismatic animals and plants that are exploited alive and for derived products such as food, exotic leather goods, wooden musical instruments, timber, tourism and medicines. In addition, a significant number of species are threatened by complex trade systems where consumers in developed countries cause species to be threatened by goods produced in developing countries [START_REF] Lenzen | International trade drives biodiversity threats in developing nations[END_REF].

The European Union has also provided a framework for protection through the Birds and Habitats Directives (Commission et al., 2015). Thirteen years after the Birds Directive, the Habitats Directive was passed in 1992. It aims to protect over a thousand species, with the overall aim of "ensuring that these species and habitat types are maintained at or restored to a favourable conservation status within the EU" (Commission et al., 2015). A new impulse in 2017 aims to accelerate progress towards halting and reversing the loss of biodiversity and ecosystem services (Commission et al., 2017).

Species population level: The Living Planet Index

Definition

The Living Planet Index (LPI) is a highly visible biodiversity indicator whose alarming rates are often reported in the media. However, it is subject to many misinterpretations, probably because of its apparent simplicity, which contrasts with the highly complex nature of biodiversity. A misleading example from the Guardian: "Humanity has wiped out 60% of animal populations since 1970, report finds" 4 . What the LPI measures is the average change in the number of individuals in the animal populations surveyed. An accurate formulation of the global trend is between 1970 and 2018, there was an average decline in population size of 69% across the 31,821 populations studied. A population is defined as "a group of individuals of the same species living in the same geographical area. A species often has several or many populations, each living in a different area". This results in two populations of the same species, but with very different numbers of individuals, having the same contribution. Also, a common species with dozens of populations will be strongly represented, as opposed to a rare species with only one population. For more details and a clear example of the LPI calculation, the interested reader is invited to consult [START_REF] Loh | The Living Planet Index: using species population time series to track trends in biodiversity[END_REF][START_REF] Ritchie | Biodiversity[END_REF].

A biased species sample

The LPI is based on 31,821 populations of 5,230 species. This may seem a large sample, but in reality it is limited and highly biased to represent global biodiversity trends. First, the taxonomic bias: only vertebrates are included, with 16% of known bird species, 11% of mammals, 6% of fish and 3% of amphibians and reptiles. Entire taxonomic groups are overlooked: insects, fungi, corals or plants. Moreover, even represented groups are not evenly sampled in terms of IUCN extinction risk: threatened mammals and charismatic species are over-represented [START_REF] Collen | Monitoring change in vertebrate abundance: the Living Planet Index[END_REF]. Second, the spatial bias: the tropics are under-represented, even though they are both a biodiversity hotspot and a threat hotspot.

On the importance of results visualisation Figure 2.3 provides two contrasting views of the same information, the LPI. The top figure shows the averages per region over time and the bottom figure shows the overall trends per taxonomic group. Let's first focus on the two regions with the largest and smallest decreases in LPI. Latin America and the Caribbean experienced an average decline of 94% in its studied populations between 1970 and 2018. The main drivers are intense deforestation and the expansion of agricultural land. Europe and Central Asia have seen the smallest decrease in LPI, with an average decline of 18% since 1970. However, this low figure masks an additional bias in the data: in Europe, land-use change occurred well before 1970. Therefore, the 1970 reference represents already reduced populations and distorts the comparison with other regions. Details of the dynamics of each region are given in [START_REF] Ritchie | Biodiversity[END_REF]. Plots of overall LPI trends by taxonomic group (Figure 2.3 below) show a very different and more nuanced picture. Here, across all groups, we observe a roughly 50-50 split between declining and increasing populations. This apparent status quo is quite surprising compared to regional and world trends. It can be explained by small population increases and overwhelming decreases, which are not shown here, but may influence the calculation of the LPI geometric average. This more balanced view i) highlights the need to prioritise conservation action where it is most needed and ii) offers hope in the sense that populations are not doomed to collapse everywhere on Earth, as the LPI headline figures may suggest. Although it may seem secondary, the latter point is in fact essential if positive conservation action is to be taken. For example, some wild mammals are making a comeback in Europe [START_REF] Ritchie | Biodiversity[END_REF]. Finally, the Living Planet Report 2022, entitled Building a nature-positive society, provides an accurate global picture of the biodiversity crisis while clearly remaining solution-oriented.

STATE OF THE ART

These two contrasting views of the LPI illustrate the importance of data representation. Indeed, the aim of such an indicator is to guide and fund conservation where it is most needed. Result representations should therefore be varied and declined along different explanatory variables to accurately account for the multiple dimensions of the problem.

Community and habitat indicators

Biodiversity: components and measures

Biodiversity definition and diversity components

Michel Loreau provided a coherent definition of biodiversity in 2005:

"The Earth is home to an extraordinary biological diversity, which includes not only the species that inhabit our planet, but also the diversity of their genes, the multitude of ecological interactions among them and with their physical environment, and the variety of complex ecosystems that they form. This biodiversity, the product of more than 3 billion years of evolution, is a natural heritage and a vital resource on which humanity depends in many ways." [START_REF] Barbault | Actes de la conférence internationale Biodiversité, sciences et gouvernance[END_REF] Biodiversity is therefore not limited to species richness. However, here and throughout this thesis, species will be the level of study chosen. Given a pool of species, two key components influence perceived species diversity: species richness and species evenness (or equitability, [START_REF] Marcon | Mesures de la biodiversité[END_REF]. Richness is the number of different species, while evenness is their proportion. Consider two sets of species, A and B, with the same species richness. If set A contains a largely dominant species that leaves little room for other species, while set B contains equally balanced species, set B will appear more diverse. Most indices, such as Simpson's or Shannon's, assess both richness and evenness, see [START_REF] Marcon | Mesures de la biodiversité[END_REF] for a comprehensive review. These species-neutral diversity measures do not take into account the distance between classes. However, two species from the same genus are obviously closer than two species from different families. This idea is reflected in measures of phylogenetic and functional diversity. Disparity is the third component of diversity, measuring the degree of difference between species. Based on a broad literature review in disciplines concerned with diversity (beyond biodiversity), A. Stirling asserts that these three components (richness, evenness and disparity) cover all aspects of diversity [START_REF] Stirling | Machine learning in landscape ecological analysis: a review of recent approaches[END_REF].

A diversity measure: the Shannon index

The Shannon index is a classic measure of diversity. It is species-neutral in the sense that no specific species trait is taken into account in its calculation [START_REF] Marcon | Mesures de la biodiversité[END_REF]. Derived from information theory [START_REF] Shannon | A mathematical theory of communication[END_REF], the Shannon index is also known as the Shannon-Weaver or Shannon-Wiener index, or simply entropy:

H = - S s=1 p s ln(p s ) (2.1)
where S is the number of different species in the system under study and p s is the probability that a random species from the system belongs to species s (given by the species prevalence, assuming uniform detection). The Shannon index provides a measure of biodiversity as an information quantity.

Biodiversity types: α, β, γ Diversity is classically estimated at several nested levels. Whittaker calls them α, β and γ biodiversity types [START_REF] Whittaker | Vegetation of the Siskiyou Mountains, Oregon and California[END_REF]:

• α diversity is the local diversity measured within a bounded system. More precisely, it is the diversity within a uniform habitat of fixed size. • β diversity measures how different local systems are. This definition is still under discussion [START_REF] Moreno | A consistent terminology for quantifying species diversity?[END_REF]). • γ diversity is similar to alpha diversity, but this time the measure is over all the systems in the study.

The measures of α and β diversity depend on how finely the habitat is defined. Distinguishing many habitats reduces α diversity in favour of β diversity. It is therefore important to define an indicator that does not depend on this subdivision, hence γ diversity. Recent research suggests using deep learning to estimate species richness, α, β and γ diversity from environmental covariates, see (Andermann et al., 2022).

Habitat classifications

Compared to the authoritative IUCN Red List of Threatened Species, biodiversity indicators at higher levels, such as habitat or ecosystem, have a long way to go in terms of visibility and impact. Indeed, conservation science has long focused on the species level (considered more tangible), but biodiversity loss occurs at all levels [START_REF] Keith | Scientific Foundations for an IUCN Red List of Ecosystems[END_REF]. Advancing both knowledge and conservation at the ecosystem level is therefore a top priority. New initiatives in this direction are numerous and can benefit from remote sensing contributions.

Ecosystem is defined as "the living components (biotic complexes and assemblages of species), the non-living components (abiotic environment), the processes and interactions within and between the biotic and abiotic, and the physical space in which they operate" [START_REF] Nicholson | Scientific foundations for an ecosystem goal, milestones and indicators for the post-2020 global biodiversity framework[END_REF]. Habitats are inherently defined from a species perspective and, in simple terms, correspond to the ecosystem(s) in which species can subsist. The European Nature Information System (EUNIS) defines habitats more pragmatically as "a place where plants or animals normally live, characterised primarily by its physical features (topography, species morphology, soil characteristics, climate, water quality, etc.) and secondarily by the species that live there"5 .

The IUCN Habitats Classification Scheme and the Red List of Ecosystems When assessing the risk of species extinction, the IUCN requires species habitats to be reported according to a classification scheme (IUCN, 2012b). Crossed with global data on land cover (remotely sensed), climate and land use, this classification has allowed the creation of a global map of terrestrial habitat types [START_REF] Jung | A global map of terrestrial habitat types[END_REF]. However, the IUCN itself acknowledges that this classification scheme is not entirely satisfactory and that a review is needed6 . A spatial description of nature in terms of ecosystems rather than species habitats might have been preferable and was the origin of the Red List of Ecosystems (RLE).

The foundations of the RLE begin with the description of ecosystem risk assessments and the concept of ecosystem collapse [START_REF] Keith | Scientific Foundations for an IUCN Red List of Ecosystems[END_REF]. Based on five criteria, including the rate of ecosystem decline, distribution and degradation, the assessment process and threat categories mirror those of the IUCN Red List of threatened species. Improving the assessment of ecosystems will hopefully make it possible to prevent their collapse through restoration [START_REF] Valderrábano | Using ecosystem risk assessment science in ecosystem restoration: a guide to applying the Red List of Ecosystems to ecosystem restoration[END_REF]. The RLE also relies on a comprehensive and globally consistent typology of ecosystems, launched in 2020 and recently updated (IUCN, 2020;[START_REF] Keith | A function-based typology for Earth's ecosystems[END_REF]. The new typology is described as conceptually robust, scalable, spatially explicit and adapted to reflect functional responses to change and management. Research is underway to develop biodiversity indicators based on the RLE [START_REF] Rowland | Ecosystem indices to support global biodiversity conservation[END_REF].

The EUNIS Habitat Classification

The European Nature Information System (EUNIS) was developed in the 1990s and early 2000s for the European Environment Agency (EEA, [START_REF] Davies | EUNIS habitat classification revised 2004[END_REF]. It covers both marine and terrestrial habitats and is the largest comprehensive pan-European hierarchical habitat classification. The classification of terrestrial habitats is based on species composition and vegetation structure (phytosociological vegetation types), but also on the abiotic environment and geographical location. The classification is widely recognised as a key tool for monitoring progress towards the EU biodiversity targets. It is a common reference for habitat characterisation by vegetation science or satellite imagery and feeds both research and EU policy. Classification today relies on an expert-based system, mostly based on vegetation plots such as the European Vegetation Archive (EVA) [START_REF] Chytrý | European Vegetation Archive (EVA): an integrated database of European vegetation plots[END_REF][START_REF] Chytrý | EUNIS Habitat Classification: Expert system, characteristic species combinations and distribution maps of European habitats[END_REF], and new automated classification methods are under development. At the European level, the EEA is also supporting the development of (i) a set of thematic biodiversity indicators7 (one of which is Biodiversity -Ecosystems) and ii) the Mapping and Assessment of Ecosystems and their Services [START_REF] Maes | Mapping and Assessment of Ecosystems and their Services[END_REF].

Natura 2000

Natura 2000 is a network of natural and semi-natural sites in Europe, targeting breeding or resting sites for rare, threatened species and rare natural habitats. The sites are spread across the 27 EU countries (both on land and at sea) and the network is governed by the Birds and Habitats Directives (Commission et al., 2015(Commission et al., , 2017)). It is the EU's main response to the recommendations of the CBD. It currently covers 18% of the EU's land area and 8% of its marine territory 8 . It is important to note that Natura 2000 is not a strict network of protected areas where human activities are excluded (indeed, most of the sites are privately owned). Instead, EU countries must ensure that the sites are managed in a sustainable way, both ecologically and economically. Details and illustrations of the sites' objectives can be found in the book [START_REF] Sundseth | Natura 2000: protecting Europe's biodiversity[END_REF]. In this example, integrated data from different primary sources of observations (e.g. in situ, remote sensing) are combined within biodiversity models to produce layers of spatial and temporal variation in ecosystem extent and species distribution EBVs. This information is then integrated and summarised within reporting units to calculate an indicator of biodiversity change, used, for instance, for reporting progress towards an Aichi conservation target. EBVs and models can also be used to project changes in the indicator using scenarios. Reproduced from [START_REF] Navarro | Monitoring biodiversity change through effective global coordination[END_REF], CC-BY license.

Essential biodiversity variables

Essential Biodiversity Variables (EBV) have been introduced to promote the collection, sharing and use of biodiversity information [START_REF] Pereira | Descriptors of Posidonia oceanica meadows: use and application[END_REF]. EBVs are biological state variables. They provide a way to aggregate biodiversity observations from different methods, including citizen science and remote sensing [START_REF] Proença | Global biodiversity monitoring: from data sources to essential biodiversity variables[END_REF]. EBVs have been developed by the Group on Earth Observations Biodiversity Observation Network (GEO BON). Their aim is to support decision-makers by providing a general framework for biodiversity monitoring.https://geobon.org/ebvs/what-are-ebvs/ EBVs must be consistent over time [START_REF] Mihoub | Setting temporal baselines for biodiversity: the limits of available monitoring data for capturing the full impact of anthropogenic pressures[END_REF] and space, similar to Essential Climate Variables and Essential Ocean Variables. There are currently 6 EBV classes and 21 EBV names 9 . In the species populations class, the EBVs are species distributions and species abundances. Ecosystem phenology is an EBV from the class ecosystem functioning. EBVs STATE OF THE ART and BONs (a system of coordinated Biodiversity Observation Networks) are the two core components developed by GEO BON.

EBVs themselves can either be directly linked to the Aichi Targets and Sustainable Development Goals, or used as inputs to biodiversity models to derive indicators, see Figure 2.4. GEO BON is therefore developing a set of global biodiversity change indicators [START_REF] Bon | Global Biodiversity Change Indicators. Version 1.2[END_REF] to inform international agreements and reports such as the IPBES assessments. EBVs provide a common formalisation framework to qualify heterogeneous data, for example on species populations [START_REF] Jetz | Essential biodiversity variables for mapping and monitoring species populations[END_REF].

Community and habitat indicators have a spatial extent and can easily be mapped.

Our focus now will be on mapping the spatial dimensions of threats and how they can be integrated into conservation planning.

Spatial indicators of threat

Conservation planning is an inherently spatial process [START_REF] Evans | The Spatial Distribution of Threats to Species in Australia[END_REF]. Community and habitat indicators can be readily mapped and integrated into conservation planning. However, this is not the case for the species level indicators introduced in the previous section 2.2.1. These indicators must first be projected into geographic space. Following the dimensions of threat defined in [START_REF] Balmford | Capturing the Many Dimensions of Threat: Comment on Salafsky et al[END_REF], mapping species at risk of extinction amounts to representing stresses or unfavourable states and is the topic of the first section 2.2.3.1. Next, we are interested in mapping sources and mechanisms of threat (Section 2.2.3.2) and finally in integrating threat into conservation planning (Section 2.2.3.3).

Threatened species patterns

Spatial range of species Spatial ranges of species are often used to project species-level indicators into geographic space. Such ranges may be expert-based, simply inferred from species sightings, or modelled (see section 2.3). Only birds, mammals and amphibians have both comprehensive range maps and conservation status. Many studies have therefore focused on these taxonomic groups. However, these well-assessed groups are not always good surrogates for vulnerable species [START_REF] Hamilton | Increasing taxonomic diversity and spatial resolution clarifies opportunities for protecting US imperiled species[END_REF]. As spatial knowledge is still very scarce and poorly integrated [START_REF] Jetz | Integrating biodiversity distribution knowledge: toward a global map of life[END_REF], range generalisation is often necessary: "Given this pivotal role of species distribution information, it might be surprising to realize how poorly documented the geography of life on earth is, an impediment termed the Wallacean shortfall." [START_REF] Jetz | Integrating biodiversity distribution knowledge: toward a global map of life[END_REF] The Wallacean shortfall was named after Alfred Russel Wallace (1823Wallace ( -1913) ) by Lomolino et al. (2004) and refers to the paucity of information on the geography of nature.

Indicators for biodiversity conservation

In the following paragraphs, examples of studies are given where threatened species patterns have been mapped using known species ranges or SDM results. The aim is to illustrate a range of work comparable to the maps in our chapter 4 (maps that are not not reproduced here are linked to their online versions).

Global extinction probability

The Global Extinction Probability (GEP) is an approach that quantifies the contribution of potential local biodiversity loss events to global biodiversity loss [START_REF] Kuipers | Potential Consequences of Regional Species Loss for Global Species Richness: A Quantitative Approach for Estimating Global Extinction Probabilities[END_REF]. It is based on species range, IUCN status and species richness. The IUCN extinction risk categories are quantified according to a given scheme, e.g. LC= 0 to Critically endangered (CR)= 4. GEP is a relative measure that indicates, for a given area, whether many species are threatened with extinction and how dependent they are on that area. If there are many threatened species with very small ranges, or if there are endemic species, the GEP is likely to be higher than in other areas. [START_REF] Verones | Global extinction probabilities of terrestrial, freshwater, and marine species groups for use in Life Cycle Assessment[END_REF] calculated GEPs for 98,000 species in 20 species groups across marine, terrestrial and freshwater ecosystems (see their Figure 1). For taxonomic groups for which no IUCN range was available, polygons based on occurrence records (freshwater fishes) or SDM-based ranges (terrestrial vascular plants) were used [START_REF] Borgelt | Native range estimates for red-listed vascular plants[END_REF]. The GEP calculation can also inform biodiversity life cycle assessments. This is a method of estimating the potential environmental impacts of a product (or in this case, threat sources) over its entire life cycle (or over time, [START_REF] Winter | Including biodiversity in life cycle assessment -State of the art, gaps and research needs[END_REF].

Species threat abatement and restoration (STAR) metric

The STAR quantifies the extent to which mitigating threats and restoring habitats locally contributes to reducing extinction risk [START_REF] Mair | A metric for spatially explicit contributions to science-based species targets[END_REF]. The metric is scalable across species, threats and geographies, and is mapped at a grid cell resolution of 5 km (see their Figure 2). It consists of two complementary measures: STAR T , i.e. how much the reduction of a specific threat in a given location contributes to the reduction of the extinction risk of all studied species, and STAR R , which assesses the habitat restoration potential for a given species in a given location relative to its current habitat. The STAR calculation requires the species' IUCN extinction risk, threats, spatial range, current and restorable AOH. 5,359 species (2,055 amphibians, 1,957 birds and 1,347 mammals) were included in the analysis. From now on, only extensively assessed taxonomic groups can be included. Current and original AOH were calculated by matching species' IUCN ranges to synthetic land use and land cover maps from 2015 and 1992, respectively. It was also constrained to digital elevation maps with known IUCN elevation ranges. Finally, the recoverable AOH is calculated as the difference between the original and current AOH.

An SDM-based approach to inform under-assessed taxa in the United States [START_REF] Hamilton | Increasing taxonomic diversity and spatial resolution clarifies opportunities for protecting US imperiled species[END_REF] developed a novel spatial index at fine resolution (990 m) in the United States that highlights species with i) small modelled habitat ii) largely unprotected, i.e. with a large proportion of modelled habitat outside current protected areas. To do this, they used Random Forest (RF) models to shape suitable habitats for common, but under-assessed, taxa: vascular plants, terrestrial vertebrates, freshwater animals and pollinators. The suitability maps were then thresholded and validated by experts. The authors note that the spatial patterns of invertebrates and vascular plants are not well represented by the groups commonly used in biodiversity indicators (birds, mammals, amphibians), see Figure 2.5. These understudied groups are yet important contributors to ecosystem function, providing habitat, prey, pollination and nutrient cycling [START_REF] Hamilton | Increasing taxonomic diversity and spatial resolution clarifies opportunities for protecting US imperiled species[END_REF]. They also compared the spatial patterns of their indicator based on either modelled habitats or species range maps for vertebrates. Using modelled habitats resulted in much more nuanced conservation opportunities. The scientific approach taken by these authors is probably the closest to our work developed in chapter 4 on the extinction risk of orchid assemblages.

EDGE zones and Cactaceae maps

Based on the ED and EDGE scores for assessing Evolutionarily Distinct and Globally Endangered species (see section 2.2.1.2), the highest priority ED and EDGE zones were identified using species IUCN ranges [START_REF] Safi | Global patterns of evolutionary distinct and globally endangered amphibians and mammals[END_REF]. Two approaches were tested: one based on species richness and another based on randomisation, the maps being derived at rather coarse resolution (1°or 2°, see their Figure 1) to avoid commission errors. [START_REF] Goettsch | High proportion of cactus species threatened with extinction[END_REF] carried out a convincing study on the threats to the Cactaceae family. They showed that this group is one of the most threatened assessed to date, with 31% of the 1,478 species at risk. They also derived maps of the proportion and richness of threatened species based on ranges generated in ArcGIS and validated by experts, see Figure 2.6. [START_REF] Goettsch | High proportion of cactus species threatened with extinction[END_REF] with permission from Springer Nature.

Indicators for biodiversity conservation

Mapping sources and mechanisms of threat

It is the ever-increasing level of threats and our inability as a society to compensate for them that has led to the current biodiversity crisis. Understanding and addressing threats to nature is therefore essential to ensure that action is targeted where it is most needed, although the ultimate goal of conservation is to maintain biodiversity. Attempting to address the sources and mechanisms of threats requires clear mapping. Threat maps are defined as "spatial representations of the distribution, intensity or frequency of threats to biodiversity across a landscape or seascape" [START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF]. Using IUCN species or modelled ranges to model threats carries an implicit assumption: that species are threatened uniformly across their spatial range. Although this is often incorrect in practice, it is a convenient approximation that is found throughout the literature. In Australia, [START_REF] Evans | The Spatial Distribution of Threats to Species in Australia[END_REF] led a compelling study of 1,700 species of vascular and non-vascular plants, vertebrates and invertebrates considered nationally threatened. They used SDMs to map the likely distribution of threatened species across the country (see Section 2.3). They highlighted the three main threats: habitat loss, inappropriate fire regimes and introduced species. Their result can be appreciated in the map Figure 2.7 depicting the predominant threats to biodiversity across Australia. [START_REF] Harfoot | Using the IUCN Red List to map threats to terrestrial vertebrates at global scale[END_REF] used the IUCN Red List to map threats at a global scale based on 23,271 species representing terrestrial amphibians, birds and mammals. Species range maps were derived from BirdLife International, NatureServe and the IUCN. In addition, a probabilistic framework accounts for the fact that species are not uniformly threatened across their known ranges. This results in convincing global maps at a resolution of The distribution of the predominant threats to biodiversity across Australia. The "predominant threat" is the threat affecting the greatest number of species in each subcatchment. White indicates areas where no threatened species occur. Reproduced from [START_REF] Evans | The Spatial Distribution of Threats to Species in Australia[END_REF] with permission from Oxford University Press.

50 km × 50 km representing threats to terrestrial vertebrates. The maps can also be refined by threat (deforestation, pollution, agriculture, invasive species, hunting, climate change). In addition, [START_REF] Hampton | Rodent reservoirs of future zoonotic diseases[END_REF] used IUCN species ranges to produce impressive maps of current and future rodent disease reservoirs (see their Figure 2). Finally, much of Europe's native wildlife has disappeared. Therefore, rather than threat indicators based on remaining species, maps of cumulative drivers such as the terrestrial Human Footprint [START_REF] Venter | Global terrestrial Human Footprint maps for 1993 and 2009[END_REF], see Section 2.3.1.4) may better reflect the true extent of human impact in certain regions.

Threat integration in conservation planning

Trying to integrate threats with other aspects of conservation planning is a delicate task. Knowing where and why threats are occurring is valuable information for making conservation decisions, but it is not in itself sufficient. Ideally, threat maps should be developed with an understanding of how species respond to threat mitigation measures in order to properly inform conservation decisions [START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF]. In addition, social, political, economic and biodiversity outcomes need to be considered in order to allocate resources and avoid unintended consequences [START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF]. Figure 2.8 shows an example of how different aspects (here three threat maps and a conservation feature) can be combined to produce a synthetic decision support. Furthermore, in order to arrive at efficient decisions, the resource allocation process should be clearly structured, e.g. using a graph, and uncertainty accounting should be made explicit [START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF]. [START_REF] Tulloch | Incorporating uncertainty associated with habitat data in marine reserve design[END_REF]. Reproduced from [START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF] with permission from John Wiley and Sons.

As an ultimate goal, biodiversity outcomes should be central to conservation planning. Mapping and mitigating threats is a lever to conserve biodiversity. [START_REF] Jetz | Include biodiversity representation indicators in area-based conservation targets[END_REF] call for the inclusion of indicators reporting on biodiversity outcomes when assessing the effectiveness of area-based conservation targets. Indeed, international targets that are purely area-based can lead to the implementation of under-efficient Protected Areas (PA), [START_REF] Maxwell | Area-based conservation in the twenty-first century[END_REF]. Misleading observations could be made if a high proportion STATE OF THE ART of areas were protected but the network actually covered only a limited proportion of biodiversity. By linking PA implementation to biodiversity outcomes, this potential pitfall can be avoided. Similar to the 2°C climate target, a global biodiversity target based on species extinction is needed to galvanise biodiversity policy [START_REF] Rounsevell | A biodiversity target based on species extinctions[END_REF]. The inclusion of biodiversity indicators in area-based conservation targets would also encourage countries to protect their highly unequal share of biodiversity [START_REF] Jetz | Include biodiversity representation indicators in area-based conservation targets[END_REF]. This process will require increased international cooperation. Indeed, countries have uneven capacities to finance conservation, with some developing countries holding some of the greatest biodiversity [START_REF] Jetz | Include biodiversity representation indicators in area-based conservation targets[END_REF]. Spatial analysis of threatened species also requires adapted tools. The Spatial Portal developed by the Atlas of Living Australia is an example of a coherent response with advanced filtering tools available online [START_REF] Belbin | The Atlas of Living Australia: History, current state and future directions[END_REF]. Such an initiative, with a clear emphasis on the spatial analysis involved in conservation planning, is essential to improving biodiversity protection.

Throughout this section we have seen how important the spatial distribution of species is. Spatial ranges are needed to assess species extinction risk, but also to map habitats defined by species composition, or simply to map species and threats. We have also seen how scarce spatial knowledge currently is. Attempts to map biodiversity usually result either in the study of taxonomic groups that are extensively assessed as vertebrates, or in the use of surrogates and models to also study underassessed groups. In this second part of the state of the art, we will be interested in the modelling of species distributions and, in particular, in the class of models that employ deep learning to deal with big data on biodiversity.

"Scientific illustrations should speak to the senses without fatiguing the mind" In 1802, physical geographer Alexander von Humboldt and botanist Aimé Bonpland climbed Chimborazo, an equatorial volcano that was then thought to be the world's highest mountain. They documented the mountain's flora, from the tropical rainforest at its base to the highest lichens. Humboldt's Tableau Physique organises these observations in an innovative diagram showing Chimborazo in cross-section, with text detailing which species live at which elevation. This impressive study is a testament to man's desire to map the natural world. It also is a unique data source for assessing vegetation shifts in response to climate change, and is the oldest existing dataset on altitudinal ranges of tropical mountain vegetation. Today, interdisciplinary work between historians and ecologists allows the validity of such pioneering work to be adjusted [START_REF] Moret | Humboldt's Tableau Physique revisited[END_REF]. CC0 license, public domain.

Alexander von Humboldt

The study of species distribution is the fundamental goal of biogeography [START_REF] Wallace | On the zoological geography of the Malay Archipelago[END_REF]. It improves our understanding of the natural world. If one argues that it is not enough intrinsically, it also allows a better management of natural resources at the theoretical benefit of both nature conservation and society. Here we will review the core components of species distribution models before introducing a new class of models: SDMs based on deep learning architectures (deep-SDMs), which have occupied a key position throughout my research project.

Species distributions

In this section, a brief introduction on how species distributions are represented precedes a review of standard species observation data, models and covariates relevance. Finally, we will summarise the use of SDMs to inform conservation.

Mapping species geographic range

Representing the geographic distribution of species is an incredibly difficult task for a number of reasons: i) it requires extensive geolocated data on species presence and observations, ii) the spatial range of species is dynamic, iii) range generalisation is based on ecological hypotheses that necessarily simplify the myriad interdependencies of nature.

How to define species geographic range? As common as the notion of a species geographic range may be, it is difficult to find a consensus definition in the literature [START_REF] Brown | The geographic range: size, shape, boundaries, and internal structure[END_REF][START_REF] Gaston | How large is a species' geographic range?[END_REF]. Broadly speaking, it corresponds to the region occupied by a particular species and is influenced by both biotic and abiotic factors. The IUCN has developed two surrogate measures of the geographic range of species: the extent of occurrence, which recognises the inclusion of unsuitable regions, and the area of occupancy, which is intended to include only regions actually occupied by a taxon within its EOO. The difficulty in properly defining the species geographic ranges stems from their inherently dynamic nature and the inability to determine how generalised or strictly matching observations it should be. We will now further discuss the geographic ranges by introducing three high-level types commonly employed [START_REF] Beery | Species Distribution Modeling for Machine Learning Practitioners: A Review[END_REF].

Three common types of range maps

A simple representation of where species have been observed to occur is a first approximation of species geographic range. This raw display is hardly a geographic range, as observations are often punctual, but it can serve as a first surrogate to give a sense of species distribution. It is always possible to represent species in this way, as long as the observations have been georeferenced, e.g. in GBIF occurrence maps. Species observation data will be discussed further in the next Section 2.3.1.2.

A second possibility is to use statistical models to generalise the locations of sampled species with environmental data. SDMs obviously fall into this category and will be defined in Section 2.3.1.3. Finally, a third option is to rely on expert range maps. These are maps drawn by taxonomic experts with knowledge of terrain surveys, habitat preferences and species history. Importantly, this third type of representation is often the most trusted source of distribution information. However, expert maps are often scale dependent and tend to overestimate species with small ranges [START_REF] Hurlbert | Species richness, hotspots, and the scale dependence of range maps in ecology and conservation[END_REF]. They come in a wide variety of forms, from freehand drawing to maps resulting from data-intensive models and slightly refined by experts. Range maps from the RL and maps of iconic species are usually expert-based.

Species observation data

Definitions and examples Any attempt to map species distributions relies primarily on observation data. A variety of sampling protocols and resulting data types coexist. Presence-only occurrences report that a particular species has been observed at a particular place and time. No information is given about where the species was not observed. In contrast, presence-absence data provide both the presence and absence of the species observed in space. This massive difference leads to different types of models to make the most of each type of observation.

Other data types such as species abundance and species count exist and can feed species distribution modelling, but are not discussed further here (see [START_REF] Miller | The recent past and promising future for data integration methods to estimate species' distributions[END_REF] for a review). Another distinction for species observation data is the sampling protocol. standardised data is defined as "data collected using a standardised sampling design and a fixed protocol at known sampling locations" and is opposed to non-standardised data that is "not collected under a standardised protocol, where sampling locations and sampling effort are often unknown and the sampling protocol varies" [START_REF] Miller | The recent past and promising future for data integration methods to estimate species' distributions[END_REF]. The fixed sampling protocol in standardised data allows to partially mitigate the sampling biases introduced below. Examples of observation data and collection methods are listed in Table 2.1.

When it comes to mapping species distributions on a large scale, standardised data collection methods are too expensive to use. As a result, most large-scale distribution models heavily rely on presence-only and presence-absence data collected using nonstandardised approaches. However, the integration of observation data opens up the opportunity to merge rich spatial data sources with more focused and standardised datasets [START_REF] Miller | The recent past and promising future for data integration methods to estimate species' distributions[END_REF]. The GeoLifeCLEF 2023 dataset is an example dataset that aims to develop such integrated methods [START_REF] Botella | The GeoLifeCLEF 2023 Dataset to evaluate plant species distribution models at high spatial resolution across Europe[END_REF], see section 2.3.2.3).

Citizen science and new technologies

The recent surge in Citizen Science (CS) has generated massive amounts of opportunistic observations, which are ultimately collected on platforms such as the Global Biodiversity Information Facility (GBIF) portal10 . Figure 2 convenient ways to collect data, combined with increasing public engagement, including raising awareness from an early age [START_REF] Hobbs | Motivations and barriers in relation to community participation in biodiversity recording[END_REF]. Citizens can indeed be highly motivated to contribute to biodiversity knowledge and conservation. National taxon-specific networks of passionate citizens, NGOs and online platforms11 have largely contributed to the data explosion. Impressive advances in mobile phone cameras [START_REF] Graham | Using mobile phones to engage citizen scientists in research[END_REF] and automatic species identification [START_REF] Affouard | Pl@ntnet app in the era of deep learning[END_REF][START_REF] Unger | iNaturalist as an engaging tool for identifying organisms in outdoor activities[END_REF]) also play a big role. It is the use of deep learning that has enabled impressive species identification performance to be achieved.

Vegetation plots and specific datasets

Vegetation science has produced a variety of curated plant datasets with different focuses: taxonomic, geographic (e.g. national inventories), thematic, etc. For example, vegetation plots are an important source of standardised and presence-absence species observations. They are defined as "records of plant species composition, in plots of 1 m 2 to a few hundred m 2 , collected by phytosociologists" [START_REF] Zhongming | Linking in situ vegetation data to the EUNIS habitat classification: results for forest habitats[END_REF]. Global databases [START_REF] Bruelheide | Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants[END_REF][START_REF] Dengler | The Global Index of Vegetation-Plot Databases (GIVD): a new resource for vegetation science[END_REF] and integrative programmes at continental [START_REF] Chytrý | European Vegetation Archive (EVA): an integrated database of European vegetation plots[END_REF] and regional [START_REF] Schmidt | The West African Vegetation Database[END_REF] Gaps, uncertainty and biases in observation data Species observation data is conditioned by numerous gaps resulting from our limited biodiversity knowledge and non-standardised sampling protocols. First, biodiversity knowledge is conditioned by the taxonomic gap [START_REF] Hortal | Seven Shortfalls that Beset Large-Scale Knowledge of Biodiversity[END_REF]. Distribution, abundance, evolution, abiotic tolerance, species traits and biotic interactions are the other dimensions of the biodiversity shortfall. Together they limit our understanding of biodiversity. Large taxa such as insects or invertebrates, and geographical areas such as the tropics, are still largely undersampled (Cayuela et al., 2009;[START_REF] Feldman | Trends and gaps in the use of citizen science derived data as input for species distribution models: A quantitative review[END_REF].

Species observations are also subject to taxonomic, geographic and temporal uncertainties in their reporting [START_REF] Meyer | Multidimensional biases, gaps and uncertainties in global plant occurrence information[END_REF]. Uncertainty is therefore propagated in all modelling attempts based on uncertain observations. However, certain modelling techniques (boosted regression trees and maximum entropy approach) have been shown to be particularly robust to spatial error [START_REF] Graham | The influence of spatial errors in species occurrence data used in distribution models[END_REF].

Species observations are also conditioned by taxonomic, spatial and temporal sampling biases, as well as detection bias [START_REF] Boakes | Distorted views of biodiversity: spatial and temporal bias in species occurrence data[END_REF][START_REF] Troudet | Taxonomic bias in biodiversity data and societal preferences[END_REF]. Sampling biases result from unequal observation effort across species, space and time. Some places and species are sampled far more often than others. Biodiversity hotspots like the tropics are largely undersampled. Citizen science observations are classically concentrated at points and paths of interest, in spring or summer. Depending on the type of model, sampling biases can affect predictions to varying degrees. Standardised sampling protocols allow some compensation for sampling bias, e.g. through uniform or random sampling. Finally, detection bias also affects species observations [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF]. In a given place and time, species may be looked for but missed for various reasons: undetected presence, lack of expertise, fluctuating nature. Imperfect detection leads to omission errors (false negatives), which can damage the modelling process.

Models

Modelling species distributions involves learning a relationship between geolocated species observations and descriptors of the environment. Under precise ecological hypotheses, models can subsequently project the learned environmental preferences of species to spatially generalise their spatial distribution. In other words, SDMs are statistical tools that correlate species presence (and possibly absence) with environmental covariates. They can also be seen as a supervised learning problem, where the goal is to learn the function between species (labels) and their environment (qualified by some features).

Species distribution modelling is a very active area of research, boosted by new observational data, descriptive covariates and modelling techniques. We begin here with a formal definition of these models. The development of SDMs is underpinned by ecological concepts, methods and assumptions that are well summarised in [START_REF] Soberón | Niches and distributional areas: Concepts, methods, and assumptions[END_REF] and [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF]. Far from being able to do such a synthetic work in this section, we will next very briefly introduce the niche theory and the main assumptions of SDMs. We then describe the main properties, model classes and covariates of SDMs. Finally, we present their use in conservation planning. For a fluent overview on species distribution modelling, we refer the reader to the reference work of [START_REF] Elith | Species Distribution Models: Ecological Explanation and Prediction Across Space and Time[END_REF].

Formal definition

To simply define an SDM, we adapt the streamlined proposal from [START_REF] Beery | Species Distribution Modeling for Machine Learning Practitioners: A Review[END_REF] to a presence-only dataset of C different species and n observations. In practice, other nested steps can occur but most models can be summarised by these three core elements: 1) species observation data, 2) a method to encode observation locations, and 3) a function mapping location encodings to species predictions: 1) A dataset of species observations. (k i , y i )

n i=1 ⊂ K × Y K = [0, 180) × [0, 360) × [0, 1)
is the set of spatio-temporal locations including -but not restricted to-the dated locations of observations. Y = [[1, C]] is the set of species labels.

2) A location encoding function. h : K → X It is a simple function matching the geolocation of species observations with the chosen environmental features describing species habitat. X is commonly named the features space.

3) A model mapping environmental encodings to species. f θ : X → Y θ is a parameter vector. The objective is then to optimise θ thanks to the environmental contexts of the observations and the species observed, to exploit this relation and predict likely species in previously unobserved environmental contexts. This can be framed as a supervised learning problem on the dataset (h(k i ), y i ) n i=1 . The aim becomes to estimate θ to minimze the cost function over the n ′ ≤ n training set samples:

θ = argmin θ n ′ i=1 J h(k i ), y i (2.2)
where J is a loss function (e.g. binary cross-entropy, mean square error, etc.) proportional to the prediction error.

In practice, model outputs are often conditional probability distributions of observing each possible species given an environmental context, and a thresholding step is required to select the most likely species (see [START_REF] Liu | Selecting thresholds for the prediction of species occurrence with presence-only data[END_REF][START_REF] Liu | Selecting thresholds for the prediction of species occurrence with presence-only data[END_REF]. Model outputs are often interpreted as habitat suitability or relative probability of presence conditioned on one observation in the case of presence-only data.

Niche theory and assumptions

The modelling of species distributions has its theoretical origins in Hutchinson's fundamental and realised niche concepts [START_REF] Hutchinson | Cold spring harbor symposia on quantitative biology[END_REF]. The fundamental niche is defined as "a hypervolume where a species can persist indefinitely in the absence of competition" [START_REF] Hutchinson | Cold spring harbor symposia on quantitative biology[END_REF]. In turn, the realised niche of a species is defined as "that part of the fundamental niche in which the species is not absent because of competition" [START_REF] Hutchinson | Cold spring harbor symposia on quantitative biology[END_REF]. The realised niche definition was subsequently refined to take into account the environments made available by colonisation-extinction phenomena and the species' dispersal capacities (active resource exploration for animals and dispersal mechanisms for plants). A third and more recent niche proposal is the potential niche, defined as "the set of environments where a species could survive for a reasonable lifetime if there were no dispersal constraints" [START_REF] Jackson | Responses of plant populations and communities to environmental changes of the late Quaternary[END_REF]. There has been debate about what is modelled in SDMs, but no real consensus has been reached, partly due to the original ambiguities in niche concepts (Elith & Leathwick, 2009). The latter authors recommend "to retain a healthy scepticism about which components of the niche are represented by the predictions of an SDM". [START_REF] Araújo | Five (or so) challenges for species distribution modelling[END_REF] argue for a simpler biological definition, where SDMs target "the environmental conditions that allow a species to satisfy its minimum requirements so that the birth rate of a local population is equal to or greater than its death rate". Finally, the binary nature of niches has been superseded by a more continuous response function between the likely presence of species and their environment. The environment is indeed highly spatially correlated, and we can easily see that in practice there are no fixed niche boundaries. It is ultimately this response function that SDMs aim to capture by correlating species observation data with a representation of the environment.

In modelling species distributions, we rely on two key hypotheses:

1. Species are in equilibrium with their environment [START_REF] Araújo | Equilibrium of species' distributions with climate[END_REF]. In other words, species are assumed to be observed in environments that are suitable for them (climate, resources, anthropogenic disturbances, etc.). The models actually learn the environmental preferences of species from their observed geolocations.

2. Relevant environmental gradients have been provided (Elith & Leathwick, 2009). In effect, SDMs correlate species sightings with the provided environmental descriptors, assuming that they play a role in species preferences. Models rely on any descriptor provided, as long as it can help to capture species dispersal. With a reductio ad absurdum, it was shown that using paintings (with patterns completely unrelated to species observations) as covariates could lead to correct SDM performance measured with the usual metrics [START_REF] Fourcade | Paintings predict the distribution of species, or the challenge of selecting environmental predictors and evaluation statistics[END_REF]. This is mainly due to the spatial autocorrelation of paintings -as with all environmental covariates -and highlights the need to provide relevant environmental covariates for SDMs.

SDM properties

Inspired by the review from [START_REF] Beery | Species Distribution Modeling for Machine Learning Practitioners: A Review[END_REF], here are some of the main SDM properties.

• Presence-only & presence-absence models. As mentioned above, dealing with one or the other type of observation data classically leads to the adoption of different models. However, research aims to bridge this gap and benefit from both the massive presence-only data and the highly informative presence-absence observations [START_REF] Botella | The GeoLifeCLEF 2023 Dataset to evaluate plant species distribution models at high spatial resolution across Europe[END_REF]. When absences are not available, some methods use "pseudo-absence" or "background" points. These are artificial absence points that are often sampled at random in the study area or taking into account sampling bias [START_REF] Botella | Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection[END_REF][START_REF] Phillips | Sample selection bias and presence-only distribution models: implications for background and pseudo-absence data[END_REF].

• Single vs. multi-species models. This is a key distinction from the SDM literature. Early models focused on one species at a time, while the trend has now moved towards modelling subsets of taxa. Increasing computational resources have logically played a key role in this shift.

• Multi-species models: stacked vs. joint. Again, this distinction is key to understanding the field. Stacked SDMs (SSDM) use single-species models before stacking their outputs [START_REF] Schmitt | ssdm: An r package to predict distribution of species richness and composition based on stacked species distribution models[END_REF]. In contrast, Joint SDMs (JSDM) model multiple species in a single common step. Co-occurrence information and model parameters can be shared across species. Extensive data on more common species helps to shape the species environmental space and can ultimately benefit rare species modelling [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF][START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM)[END_REF][START_REF] Zhang | Improving prediction of rare species' distribution from community data[END_REF].

• Spatially explicit models. These models voluntarily include observations of geolocation within the model's covariates [START_REF] Domisch | Spatially explicit species distribution models: A missed opportunity in conservation planning?[END_REF]. Unlike niche models, species are no longer modelled in a purely environmental space, but within an environment where location is also explicit. [START_REF] Araújo | Five (or so) challenges for species distribution modelling[END_REF] specifies that niche models predict species potential habitats whereas spatially explicit models represent species potential geographical distributions. In practice, niche models implicitly incorporate spatial information through the spatial autocorrelation of environmental covariates.

• Bias mitigation methods. In response to the biases in observation data (see section 2.3.1.2), the community has developed a variety of methods to compensate for them. For example, sampling bias can be accounted for with Poisson point processes [START_REF] Botella | Jointly estimating spatial sampling effort and habitat suitability for multiple species from opportunistic presence-only data[END_REF] and imperfect detection is modelled in site occupancy models [START_REF] Bailey | Assessing effects of forecasted climate change on the diversity and distribution of European higher plants for 2050[END_REF].

• Uncertainty. The use of SDMs in conservation decisions requires the modelling of error and uncertainty (Elith & Leathwick, 2009). Classically, we distinguish between uncertainty in the data (observations and covariates) propagating through the models, and uncertainty in the modelling process itself [START_REF] Barry | Error and uncertainty in habitat models[END_REF]. [START_REF] Beale | Incorporating uncertainty in predictive species distribution modelling[END_REF] Suggest a review on this still understudied topic. [START_REF] Zurell | A standard protocol for reporting species distribution models[END_REF] propose a standard protocol for reporting SDM performance including uncertainty quantification. A convenient method to produce uncertainty estimates is to ensemble different models and examine the uncertainty around, for example, the median predictions [START_REF] Marmion | Evaluation of consensus methods in predictive species distribution modelling[END_REF].

Modelling species distribution

Model classes

Here is a brief description of the most commonly used models. For a more detailed overview, we refer the interested reader to [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF]. Classical methods, the widely used Maximum Entropy (MaxEnt) approach and ML methods are successively introduced. The aim is to capture potentially complex and non-linear relationships in a multi-dimensional environment. A recent study by [START_REF] Valavi | Predictive performance of presence-only species distribution models: a benchmark study with reproducible code[END_REF] benchmarks the performance of numerous presence-only models of all types.

• Classical statistical models. Traditional species distribution models are i) the Generalised Linear Model (GLM) from [START_REF] Nelder | Generalized linear models[END_REF], ii) its special case, logistic regression [START_REF] Pearce | An evaluation of alternative algorithms for fitting species distribution models using logistic regression[END_REF], and iii) the nonparametric alternative called the Generalised Additive Model (GAM), [START_REF] Yee | Generalized additive models in plant ecology[END_REF]. These methods use presence-absence data. GLMs are fitted using maximum likelihood and have the advantage of being both easy to implement and transparent. GAMs need fewer parameters to be adjusted and can express more complex functions without the risk of overfitting the training data. JSDM is an approach that considers species co-occurrence data in a multi-species SDM [START_REF] Wilkinson | A comparison of joint species distribution models for presence-absence data[END_REF]. It was democratised by [START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM)[END_REF] and is based on a hierarchical multivariate GLM similar to logistic regression (probit regression).

• The maximum entropy approach (MaxEnt). This is the most commonly used model to infer species distributions from presence-only data [START_REF] Phillips | Maximum entropy modeling of species geographic distributions[END_REF]. Described by its authors as "a general-purpose machine learning method", it is based on Shannon's fundamental concept of entropy [START_REF] Shannon | A mathematical theory of communication[END_REF]. We present MaxEnt apart from ML models only because of its importance in the field of SDM. Its rationale is to maximise the entropy of the unknown species probability distribution while satisfying a set of constraints derived from the observed presence and background points (i.e. the maximum entropy principle, [START_REF] Jaynes | Information theory and statistical mechanics[END_REF]. It is a single-species model. [START_REF] Elith | A statistical explanation of MaxEnt for ecologists: Statistical explanation of MaxEnt[END_REF] provided an alternative explanation of MaxEnt: the model minimises the relative entropy between two probability densities defined in environmental space: one estimated from the presence data and the other from the background -or landscape-points). The popularity of this method has been boosted by its ease of use and its ability to perform robust inference from limited occurrences [START_REF] Phillips | Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation[END_REF].

• Machine learning models. The complex interactions between species and environment defy conventional statistical assumptions, such as linear covariate dependence or independent and identically distributed (i.i.d.) sampling. For this reason, machine learning methods have been adopted to model species distributions for decades. Decision tree algorithms have been appreciated for their impressive predictive performance, with first random forests (Breiman, 2001a;[START_REF] Cutler | Random Forests for Classification in Ecology[END_REF] and soon after Boosted Regression Trees (BRT, [START_REF] Elith | A working guide to boosted regression trees[END_REF]. Support Vector Machines (SVM) have been used extensively since the early 2000s [START_REF] Drake | Modelling ecological niches with support vector machines[END_REF][START_REF] Schölkopf | Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond[END_REF] and, to a lesser extent, the k-Nearest Neighbours algorithm. Neural networks have also been used for a long time, well before the deep learning revolution (Özesmi & Özesmi, 1999). Deep learning has now brought new possibilities to improve multi-species distribution modelling, and this would be the specific topic of the Section 2.3.2. For more information, see the impressive review by [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]) and especially Table 1, which gives an overview of common supervised ML algorithms used in ecology.

The high predictive power of machine learning based models comes at the cost of model complexity and interpretability [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF]. Model inputs cannot be easily linked to and explain prediction patterns. However, ecologists value transparent models that they can understand, as this trust and interpretability is crucial for policy decisions (see section 2.3.1.5). In response, extensive research is underway on interpretable machine learning or explainable AI (xAI) and will be further discussed in Section 2.3.2.1 [START_REF] Murdoch | Definitions, methods, and applications in interpretable machine learning[END_REF]. Some xAI studies are specifically focused on the field of species distribution modelling [START_REF] Ryo | Explainable artificial intelligence enhances the ecological interpretability of black-box species distribution models[END_REF].

The challenge of evaluating SDMs is not addressed in this state of the art. However, it is partially covered in the chapters and in the final discussion. For a clear and concise review of SDM metrics, we again refer to the article by [START_REF] Beery | Species Distribution Modeling for Machine Learning Practitioners: A Review[END_REF] and [START_REF] Allouche | Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS)[END_REF] for presence-absence models. Before diving into deep-SDMs, we will now review common covariates and how SDMs can inform conservation, with a particular focus on IUCN assessments.

Covariates relevance

Providing relevant environmental covariates to enable models to estimate species' sound environmental preferences and sensitivities is a fundamental assumption underlying distributional modelling. [START_REF] Mod | Prioritizing multiple-use landscapes for conservation: methods for large multi-species planning problems[END_REF] conducted a review of covariates from published plant SDM studies (2010-2015; n = 200). They concluded that i) ecophysiologically relevant environmental variables were neglected in the majority of studies, resulting in incomplete niche quantification and limited predictive power, ii) some of the missing predictors are already available across scales (e.g. soil moisture), while others are not (e.g. soil pH and nutrients), and therefore more attention should be paid to their development. This reveals a first characteristic of environmental predictors: They can have direct or indirect effects on species, i.e. they can be arranged on a gradient from proximal to distal predictors [START_REF] Austin | Spatial prediction of species distribution: an interface between ecological theory and statistical modelling[END_REF][START_REF] Guisan | Predicting species distribution: offering more than simple habitat models[END_REF]. In addition, the latter authors classify environmental covariates as having three main types of influence on species: i) limiting factors, defined as factors that control the ecological physiology of species (e.g. temperature, water, soil composition), ii) disturbances, defined as any perturbation of environmental systems (natural or anthropogenic), and iii) resources, defined as all compounds that organisms can assimilate (e.g. energy and water). Another distinction concerns the format of covariates: they can be either continuous, e.g. temperature, or categorical, e.g. land cover. Most models are only adapted to handle continuous variables, so an adaptation step (or embedding) is needed to take advantage of categorical data.

Let's briefly review key environmental covariates. This is not intended to be an exhaustive list, but rather a synthetic entry point into SDM covariates.

• Climatic variables. They are the most widely used environmental covariates for two reasons: temperature and precipitation play a key role in the nature of ecosystems, and they are readily available at global and kilometre scale resolution [START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF]. They are derived from a dense network of weather stations 2.3. Modelling species distribution (between 9,000 and 60,000 for the 1970-2000 averages) whose observations are interpolated with covariates such as altitude, distance from the coast and satellite information. In addition, global climate models are used to generate future climate variables and project impacts on biodiversity (see Section 2.4.3).

• Pedological variables. Plant growth is naturally dependent on soil characteristics. For example, the presence of mycorrhizal fungi in the soil affects the distribution of orchids [START_REF] Mccormick | Mycorrhizal fungi affect orchid distribution and population dynamics[END_REF]. SoilGrids produces global soil information up to 250 m spatial resolution, including soil organic carbon content, total nitrogen and pH among others [START_REF] Poggio | SoilGrids 2.0: producing soil information for the globe with quantified spatial uncertainty[END_REF]. Again, this scale is achieved through machine learning based interpolation from 240,000 sites and over 400 global environmental covariates. In a study by [START_REF] Descombes | Spatial modelling of ecological indicator values improves predictions of plant distributions in complex landscapes[END_REF], combining CS data with edaphic and climatic conditions proved to be a cost-effective and relevant approach to model the distribution of Swiss plants.

• Remote sensing imagery. Remote sensing offers new opportunities to model species distributions. We have already motivated the use of remote sensing in the opening context of the manuscript section 1.1. We can add that, unlike climatic and pedological variables, RS imagery provides raw (non-interpolated) and extremely rich information on a global scale. Indeed, RS-derived covariates are used to interpolate station-based measurements around the world to reach the global scale.

In addition, the increasing spatial, temporal and spectral resolution of satellite imagery places RS in a central position for large-scale distribution modelling. Thus, the contribution of satellite imagery time-series to SDM performance is analysed in chapter 3. Finally, remote sensing is crucial for SDM covariates in at least two other ways. First, the spatial context around species habitats has proven valuable for mapping species distributions [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. As described in section 2.3.2, convolutional neural networks can capture valuable spatial patterns of the environment around species sightings. Second, remote sensing is the source of information for many derived covariates. These include vegetation indices, land cover and human footprints. However, there is an abundance of RS-derived environmental covariates, see for example the European catalogue EcoDataCube12 .

-Vegetation indices. From a computer vision perspective, they are essentially hand-crafted features of remotely sensed data that are used to qualify plant properties [START_REF] Beery | Species Distribution Modeling for Machine Learning Practitioners: A Review[END_REF]). The most famous example is the Normalised Difference Vegetation Index (NDVI). It is calculated from the red and nearinfrared spectral bands and quantifies the health and density of vegetation.

One motivation behind such an index is to make rich but heavy satellite data more manageable.

-Land use and land cover. These are two close concepts, with the difference that land cover qualifies the physical nature of a terrain, whereas land use is intended to represent its function. They are typically categorical data. The MODIS global kilometre-scale land cover map is a prime product example [START_REF] Friedl | Global land cover mapping from MODIS: algorithms and early results[END_REF]. While segmentation and classification have traditionally been performed with supervised algorithms, the addition of a self-supervised pre-training step holds promise to 1) achieve better performance and 2) reduce the need for labelled data [START_REF] Scheibenreif | Self-supervised vision transformers for land-cover segmentation and classification[END_REF].

-Human impact. Human settlements and activities exert strong pressure on biodiversity. For example, in a study of 4,867 terrestrial mammals, Di [START_REF] Marco | Human pressures predict species' geographic range size better than biological traits[END_REF] showed that climatic variables and human pressures were the most influential predictors of geographic range size, ahead of biological traits. However, quantifying human impacts is a complex task that requires the integration of different sources of information. The Human Footprint Index is the reference product at the kilometre scale [START_REF] Venter | Global terrestrial Human Footprint maps for 1993 and 2009[END_REF]. It is consistent for 1993 and 2009 to allow for change detection and uses both satellite imagery and systematic ground surveys. Variables include 1) built environment, 2) population density, 3) electrical infrastructure, 4) cropland, 5) pastureland, 6) roads, 7) railways and 8) navigable waterways. Cumulative scores combine these rasters with a biome normalisation [START_REF] Olson | Terrestrial Ecoregions of the World: A New Map of Life on EarthA new global map of terrestrial ecoregions provides an innovative tool for conserving biodiversity[END_REF].

In addition, recent work by [START_REF] Marconcini | Outlining where humans live, the World Settlement Footprint 2015[END_REF] combines open and free optical with radar satellite imagery to map human settlements globally at an unprecedented resolution of 10 m. Finally, human impact is not confined to land, with 41% of the world's marine ecosystems heavily impacted by multiple anthropogenic drivers [START_REF] Hakkenberg | Forest structure as a predictor of tree species diversity in the North Carolina Piedmont[END_REF].

To conclude on SDM covariates, here are two important insights for us.

1. First, the influence of covariates is scale and context dependent in addition to being taxon dependent. At broad scales, climate was consistently found to be the main determinant of species distribution [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF]. However, at finer scales, non-climate predictors such as land cover [START_REF] Luoto | The role of land cover in bioclimatic models depends on spatial resolution[END_REF] or remotely sensed imagery (Deneu et al., 2021a) provide increasingly valuable information. They are also context dependent. We present an example where the relative importance of covariates varies with altitude. In a study of 2,616 vascular plant species in the European Alps, Chauvier et al. ( 2021) indeed showed that:

• Climate, although overall the most influential driver of spatial patterns, had decreasing importance from low to high elevation due to increasing species endemism and climate homogeneity with elevation. • In compensation, the relative importance of soil and land cover increased with increasing altitude. • Land cover shows strong and local effects in the lowlands due to human influence.

These authors concluded that while disentangling covariate effects remains a challenge, including soil and land cover covariates in species distribution models can markedly benefit predictions. This brings us to our second point.

2.

The need for covariate selection depends on the model and the objective. Indeed, while traditional statistical models can be affected by the dimensionality of the covariates (curse of dimensionality, [START_REF] Giraud | Introduction to High-Dimensional Statistics[END_REF], the performance of machine learning based methods is not affected by inputs of very high dimensionality if properly parameterised. Therefore, the selection of uncorrelated inputs is usually required in traditional statistical models. However, thanks to modern technologies, the number of potentially relevant SDM covariates is very large. Including them all allows learning from their innovative properties as well as from their interactions. This should ultimately lead to a better capture of species' environmental preferences [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF]. This is a key motivation for the use of deep-SDMs, which will be further discussed in Section 2.3.2.1. Nonetheless, this flexibility often comes at the expense of interpretability. Consequently, the objective of the application should be clearly identified before selecting models and covariates.

SDMs to inform conservation

In the first Section 2.2, we have seen how beneficial species range can be to construct indicators for biodiversity conservation at all levels (extinction risk assessment, habitat classification, mapping threat sources, etc.). Here, we will first look at how SDMs are used to support the red listing of species according to IUCN criteria. We then discuss other ways in which SDMs can be used to inform conservation decisions.

Assisting IUCN Criteria Assessment with SDMs

As introduced in section 2.2.1.1, the IUCN extinction risk assessment is based on five criteria, which include population size and dynamics, geographic range, and direct estimates of the probability of species extinction. SDMs have been used to estimate variables from criterion B on geographical range: EOO [START_REF] Syfert | Using species distribution models to inform IUCN Red List assessments[END_REF], AOO [START_REF] Jiménez-Alfaro | Modeling the potential area of occupancy at fine resolution may reduce uncertainty in species range estimates[END_REF] or both [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF][START_REF] Moat | Least concern to endangered: Applying climate change projections profoundly influences the extinction risk assessment for wild Arabica coffee[END_REF]. However, there are drawbacks to this approach. SDMs may tend to overestimate true range size if suitable habitat remains unoccupied due to ecological and/or biogeographical constraints (landscape barriers, biological interactions, dispersal limitations, see [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF].

Similarly, species ranges may be underestimated if known occurrences only partially cover the realised niche of a species. The IUCN actually provides official guidelines to be followed when estimating criterion variables from SDMs [START_REF] Bland | Guidelines for the application of IUCN Red List of Ecosystems Categories and Criteria, version 1.1[END_REF].

Approaches such as the GeoCAT and ConR packages compute EOO and AOO directly from species observations, without generalising species niches [START_REF] Bachman | Supporting Red List threat assessments with GeoCAT: geospatial conservation assessment tool[END_REF][START_REF] Bachman | Rapid Least Concern: towards automating Red List assessments[END_REF][START_REF] Camacho | Red List and Vulnerability Assessment of the Páramo Vascular Flora in the Nevados Natural National Park (Colombia)[END_REF][START_REF] Dauby | ConR: An R package to assist large-scale multispecies preliminary conservation assessments using distribution data[END_REF][START_REF] Levin | Using publicly available data to conduct rapid assessments of extinction risk[END_REF]Stévart et al., 2019). [START_REF] Santini | Applying habitat and population-density models to land-cover time series to inform IUCN Red List assessments[END_REF] go a step further by estimating all five IUCN criteria from data on land cover change, species habitat preferences, population, and dispersal capacity. All these approaches respecting the official criteria thresholds for entering risk categories were called index-based methods by [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. They are in contrast to the prediction-based methods that directly learn a correspondence between species features and status (see Section 2.4.2 for an overview).

Overview of conservation opportunities

SDMs are used for a wide range of conservation decisions [START_REF] Sofaer | Development and Delivery of Species Distribution Models to Inform Decision-Making[END_REF]. For a comprehensive overview, we refer the interested reader to two references: [START_REF] Guisan | Predicting species distribution: offering more than simple habitat models[END_REF] and [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF]. We will only touch on some of the main applications. The prediction of climate change impacts through the modelling process can potentially benefit all of these applications (see Section 2.4.3). A first application is the management of biological invasions. In Mexico, for example, SDMs have been used to predict the potential impact of the invasive moth cactus on native cacti [START_REF] Soberón | The importance of Opuntia in Mexico and routes of invasion and impact of Cactoblastis cactorum (Lepidoptera: Pyralidae)[END_REF]. In addition, a recent study employing SDMs highlights the role of human-mediated long-distance dispersal in plant invasions [START_REF] Botella | Dynamic species distribution modeling reveals the pivotal role of human-mediated longdistance dispersal in plant invasion[END_REF]. SDM projections can also be used to identify critical habitats for threatened species. This was the case in Canada for the Ord's kangaroo rat [START_REF] Heinrichs | Assessing critical habitat: evaluating the relative contribution of habitats to population persistence[END_REF]. Optimising PA implementation is a complex process with multiple inputs, as highlighted in Section 2.2.3.3. SDMs allow multiple aspects of biodiversity (species richness, threatened species, ecological or evolutionary originality, etc.) to be mapped before these outputs are fed into the optimisation process (see Section 2.4.4 for an overview). A recent example is the identification of priority areas for endangered plant species in Asian headwaters [START_REF] Han | Integrated modeling to identify priority areas for the conservation of the endangered plant species in headwater areas of Asia[END_REF]. Other important applications include the translocation of species to survive pressures [START_REF] Chauvenet | Influence of climate, soil, and land cover on plant species distribution in the European Alps[END_REF] or natural disasters, and the orientation of prospective sampling based on model predictions of rare species (Le [START_REF] Lay | Prospective sampling based on model ensembles improves the detection of rare species[END_REF]. More indirect, but still instrumental, uses of SDMs for conservation planning include testing evolutionary hypotheses [START_REF] Graham | Integrating phylogenetics and environmental niche models to explore speciation mechanisms in dendrobatid frogs[END_REF] or identifying disease reservoirs [START_REF] Peterson | Ecologic niche modeling and potential reservoirs for Chagas disease, Mexico[END_REF].

We have now reviewed SDM principles and how these models can benefit conservation. As stated throughout the manuscript, deep learning brings new possibilities to the field by making the most of unprecedented amounts of data on biodiversity. This is the subject of the next section, which focuses on deep-SDMs.

Deep-SDMs

Motivations

Before introducing the concepts behind the efficiency of deep learning, we will first go back in time and present how machine learning and deep learning emerged. Finally, the trade-off between model performance and interpretability will conclude this section.

A brief history of machine learning

Machine learning relies on modern statistical principles. Maximum likelihood estimation, for example, dates back to the early 1920s, as depicted in Figure 2.11. The core principle of classic statistics is the assumption of an ideal data generating model, e.g. a Gaussian distribution, which allows parameters and probabilities to be estimated. Then the advent of computers and robust numerical algorithms such as Markov Chain Monte Carlo allowed more complex statistical models to be developed. However, the inference of traditional statistical methods is conditioned on simple model assumptions, making it difficult to approach the complexity of the natural world (Breiman, 2001b).

In the 1980s, the increasing availability of computing resources allowed to refine the numerical solutions of classic statistical methods, but also to develop a new modelling paradigm where the formulation of the data generation process is abandoned [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. Instead, machine learning is trained on data to perform a supervised (mainly classification or regression) or unsupervised task (dimension reduction, clustering, etc.) with the goal of minimising a given loss function. The objective of supervised machine learning is to use a training data set to learn a response function that generalises well to unseen data. In fact, ML models are excellent approximators of any measurable function, given inputs and target outputs. [START_REF] Hornik | Multilayer feedforward networks are universal approximators[END_REF] showed that a neural network with enough neurons is a class of universal approximators. However, this comes at the cost of increasingly complex and over-parameterised methods that fit the training data but have become too specific and unrealistic to generalise to unseen data. This classic but undesirable phenomenon, called overfitting, has given rise to a number of compensatory regularisation techniques. Their aim is to avoid learning a response function that is only specific to the training data by limiting the complexity of the model. In addition, models are evaluated on unseen data (validation or test set, depending on the model), since the aim is to obtain a general, flexible function. The trade-off between model complexity and flexibility actually corresponds to the classical bias-variance trade-off discussed below, see Figure 2.12.

Deep learning is the branch of machine learning that deals with large amounts of data. It is distinct from ML because 1) it emerged later due to technical challenges, and 2) new principles governing model convergence have been identified. In practice, deep learning models are very large Neural Networks (NN), with hundreds to billions of parameters. These architectures were described in the 1980s and 1990s (see Figure 2.11), but computational resources and optimisation techniques were too limited to train such a model. Finally, deep learning took off in the last decade thanks to three major technical breakthroughs [START_REF] Botella | Méthodes statistiques pour la modélisation de la distribution spatiale des espèces végétales à partir de grandes masses d'observations incertaines issues de programmes de sciences citoyennes[END_REF]:

i) The creation of huge learning datasets such as ImageNet [START_REF] Deng | ImageNet: A large-scale hierarchical image database[END_REF] ii) The democratisation of Graphical Processing Unit (GPU) computing since [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF] iii) Many advances in NN optimisation techniques such as the use of the ReLU activation function to speed up training and combat vanishing gradients [START_REF] Nair | Rectified linear units improve restricted boltzmann machines[END_REF] or batch normalisation [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF].

On the reasons behind deep learning performances

Considering the classical bias-variance trade-off that rules statistical and machine learning models, deep learning appears to be a puzzle. Indeed, according to this principle, the optimal trade-off between model error (or bias, computed on training data) and model variance (computed on unseen validation data) lies at intermediate model complexity, see Figure 2.12 (a). This trade-off predicts that excessively large or expressive models [START_REF] Purvis | On the Expressive Power of Deep Neural Networks[END_REF] should overfit the training data and thus generalise poorly. However, the distinctive behaviour of deep learning models is precisely to overcome this trade-off and continue to generalise well as model complexity increases, see Figure 2.12 (b). Precise explanations of this phenomenon, often referred to as deep learning double descent, are still being debated by the research community [START_REF] Sejnowski | The unreasonable effectiveness of deep learning in artificial intelligence[END_REF]. An important distinction between in-distribution and out-of-distribution predictions is also acknowledged, with the latter logically experiencing higher generalisation error and uncertainty, see Figure 2.12.

(c) and (d). The field of domain adaptation focuses on improving these out-of-domain predictions, see [START_REF] Farahani | A brief review of domain adaptation[END_REF] for a review.

The commonly accepted reason is the combination of i) the efficient optimisation process based on Stochastic Gradient Descent (SGD), ii) DL expressivity resulting from the innumerable function compositions, and iii) the set of regularisation techniques applied. Regularisation prevent the model from learning an over-parameterised response function that reflects the training data. As a result, the number of parameters in a model is acknowledged to be a poor measure of its effective complexity, and various alternatives have been developed [START_REF] Birdal | Intrinsic dimension, persistent homology and generalization in neural networks[END_REF]. Regularisation techniques are numerous and intervene at different stages. For example, many ML algorithms produce ensemble predictions [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. The normalisation of layer inputs throughout the model, a widely used technique called batch normalisation [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF], not only helps convergence but also has a strong regularisation effect. Furthermore, as DL models rely on large data to avoid overfitting, a number of data augmentation techniques have been developed to increase the size and quality of training datasets (see [START_REF] Shorten | A survey on image data augmentation for deep learning[END_REF] for a survey on image data). In addition, dropout is a technique that consists of successively freezing random parts of the network during training [START_REF] Srivastava | Dropout: a simple way to prevent neural networks from overfitting[END_REF]. It can be interpreted as the indirect generation of many subnetworks that work together to regularise the output. Another well-known regularisation mechanism is the use of shrinkage penalties. These are additional terms in the loss function that bias the parameters updating to a certain value. L1, L2 and their combination elatic-net [START_REF] Zou | Regularization and variable selection via the elastic net[END_REF] are typical examples, pushing the parameter norm to zero and limiting weight updates from being too specific.

Still, the regularisation techniques do not fully explain why the DL generalisation performance continues to improve after the interpolation threshold (see Figure 2.12 b), i.e. after the model has reached its minimum bias. In the case of multi-class tasks, [START_REF] Poggio | Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review[END_REF] conjecture that i) SGD has a strong regularisation effect (see [START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF] for a review on gradient descent optimisation) and ii) the compositional nature of multi-class response functions plays a key role in DL success. In other words, deep neural networks are well suited to estimating complex response functions composed of many local and simpler functions that integrate lower-dimensional subsets of the input. In addition, deep learning seems to have an additional ability to share information between the classes involved, allowing well-represented classes to benefit classes with few samples.

A trade-off between performance and interpretability Predictions in ecology and species distribution modelling can inform decision making

Accuracy

Interpretability

Deep learning

MaxEnt

Ensemble trees (RF, BRT, etc.)

SVM Decision trees

Linear models (GLM, GAM, etc.) Figure 2.13: Schematic trade-off between accuracy and interpretability of models. Overall, interpretability is inversely proportional to achievable accuracy. In this figure, the relative positions of the models are partly derived from [START_REF] Valavi | Predictive performance of presence-only species distribution models: a benchmark study with reproducible code[END_REF]. However, they should not be considered as ground truth as they also reflect subjective views. Performance is application and scale dependent. [START_REF] Sofaer | Development and Delivery of Species Distribution Models to Inform Decision-Making[END_REF], see section 2.3.1.5. In this sense, model outputs are expected to be transparent, understandable or at least interpretable. However, while deep learning has higher predictive power than other ML methods, it suffers from low interpretability, as shown in Figure 2.13. We have seen in the previous paragraph that DL's impressive generalisation power is still not fully understood. DL's poor interpretability is related to this point, and progress in one direction should benefit the other. While certain ML algorithms provide metrics of feature importance, e.g. RF from Breiman (2001a), they do not provide simple effect estimates, nor do they provide measures of confidence such as confidence intervals or p values [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. This has led to the development of xAI, the subfield of machine learning that is interested in explaining how models rely on inputs to make their predictions [START_REF] Arrieta | Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI[END_REF], the ultimate goal being to understand how the model works. A popular option for interpreting predictions is to use the xAI unified framework called SHAP [START_REF] Lundberg | A unified approach to interpreting model predictions[END_REF]. The majority of xAI tools are post-hoc, i.e. they operate once the model has been trained. They can be either model agnostic (valid for any model) or model specific. To get a sense of the contribution of features, another option is to include/exclude or randomise groups of features and run independent trainings to see how performance is affected (e.g. [START_REF] Hampton | Rodent reservoirs of future zoonotic diseases[END_REF]. Lucas (2020) provides an overview of interpretable machine learning in ecology and [START_REF] Ryo | Explainable artificial intelligence enhances the ecological interpretability of black-box species distribution models[END_REF] focuses on xAI to interpret species distribution modelling. Finally, a promising research direction is the application of causal inference concepts to help interpret ML models and obtain proper effect estimates [START_REF] Gonzalez | A framework for the detection and attribution of biodiversity change[END_REF][START_REF] Zhao | Causal interpretations of black-box models[END_REF].

Deep learning for species distribution modelling

Traditional statistical SDMs typically assume a relatively simple relationship between the outcome (e.g. presence or abundance of a species) and environmental covariates. Given a site represented by different values of environmental covariates, the response function is classically modelled as the sum of univariate covariate functions and simple bivariate functions (typically products) representing pairwise covariate interaction effects (Botella et al., 2018a). The strength of these traditional models, such as GAMs or MaxEnt, is the ability to isolate and understand the influence of each covariate on the model prediction. However, the complexity of the biotic and abiotic interactions behind the presence of plants certainly cannot be reduced to such simple functions. In this context, ML models and especially deep learning offer the possibility to learn complex and non-linear dependencies between environmental patterns and species presence. Indeed, as developed in the previous paragraph, DL models show exceptional generalisation power for multi-class classification problems such as multi-species distribution modelling.

A common principle in the multi-species SDM literature is to share most of the parameters between all species studied (Leathwick et al., 2006). This idea allows both to limit the number of model parameters -which was a bottleneck before the advent of advanced computing resources and optimisation techniques -and to share a common representation space of reduced dimension between species. In the case of NN architectures (see next section 2.3.2.2), it consists of shared layers throughout the model. The final fully conected NN layer constrains the different species responses with parameters common to all species. This results in species responses that are 1) organised along common environmental concepts and 2) hopefully crystallise the environmental information responsible for their likely presence/absence. Another limitation of traditional models is their inability to capture the spatial patterns described by environmental variables. The rationale behind using Convolutional Neural Network (CNN) models to map species distributions is that spatial patterns (a water network, a forest edge, etc.) can have a significant impact on species occurrence. Such patterns cannot be inferred from point values of environmental covariates. Therefore, our choice is to build SDMs taking as input maps (2D arrays) for each environmental covariate. Captured with CNNs, such spatial and multidimensional patterns in environmental covariates have been shown to be informative about species distributions [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. CNNs are specific NN architectures originally developed for image analysis, see next section 2.3.2.2. They are theoretically able to capture patterns when applied to multi-dimensional spatial rasters, making them perfect candidates for modelling species distributions. CNNs have in fact found a variety of relevant applications in ecology, as reviewed in [START_REF] Brodrick | Uncovering Ecological Patterns with Convolutional Neural Networks[END_REF].

In conclusion, we believe that CNNs are especially appropriate for modelling species distributions because of their ability to 1) model complex and non-linear relationships between covariates, which are more likely to approximate the response of species to their environment, and 2) identify multidimensional and spatial patterns in environmental descriptor images (Botella et al., 2018a). Furthermore, the architecture of deep learning models can be easily adapted to combine different types of inputs. As a result, they are particularly suited to integrating and harnessing heterogeneous information, as illustrated in section 2.4.1 and finally discussed in the concluding chapter 6 of this manuscript.

Introduction

Convolutional neural networks are a class of deep learning models designed specifically for image processing. They can perform tasks such as image classification, segmentation and object detection thanks to their ability to capture shapes, edges, gradients and textures. Thanks to these capabilities, their use in ecology has exploded in recent years (see Figure 2 from [START_REF] Christin | Applications for deep learning in ecology[END_REF]. Their development responded to two technical bottlenecks that prevented Fully Connected (FC) networks from processing very high-dimensional inputs such as images. First, FC networks assign weights to each input dimension and connections to all neurons from one layer to another (see definitions in next paragraph), quickly resulting in millions of parameters to be updated via backpropagation. This leads to intractable optimisation problems, especially with the computational resources available at the time. For example, a linear layer with a 256 × 256 RGB image as input and a similar output format would require (256 × 256 × 3) 2 ≃ 3.87e + 10 (≃150Gb!) parameters. Second, FC models are sensitive to translation. This problem alone makes it impossible to use FC models to analyse 2D arrays. Indeed, images have an unstructured format where the relevant information (e.g. a bicycle to be detected) can have very different positions, orientations and scales. However, if FC models have learnt to recognise bikes of a certain size and in the centre of the image through the training set, they would not be able to recognise bikes in any other configuration (i.e. spanning other pixels). In 1989, LeCun solved both technical locks with the development of CNNs (LeCun et al., 1989). Combined with the increasing availability of training datasets, computing resources and modern optimisation techniques, these models have since become state of the art for image processing tasks [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF]. More recently, models based on attention mechanisms such as the vision transformers are overtaking purely convolutional models in image classification tasks (Dosovitskiy et al., 2020a). Opportunities in ecology and species distribution modelling opened up by new DL architectures will be discussed in the final chapter 6. Here, we will only review some of the basic principles of deep learning and CNN architecture. For a comprehensive introduction to the field, please refer to: i) the https://fleuret.org/dlc/ free and online deep learning course from François Fleuret for a complete introduction (CC BY-NC-SA license)

ii) The Little Book of Deep Learning [START_REF] Fleuret | The Little Book of Deep Learning[END_REF] for a more gentle and concise introduction by the same author (a book that you can even easily read on your phone!)

iii) [START_REF] Borowiec | Deep learning as a tool for ecology and evolution[END_REF] and [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF] reviews for an introduction of DL as a tool for ecology. Moreover, [START_REF] Desprez | Nine tips for ecologists using machine learning[END_REF] provide nine useful tips to help ecologists in implementing machine learning models.

CNN architecture

Here we present only some of the DL principles that we believe are essential for understanding and appreciating CNNs. First, the scalars of an input vector pass through layers of neurons. A neuron is a composition function made up of a linear combination of its inputs followed by a non-linear activation function. The weights assigned to each input are parameters of the model, which are optimised by the backpropagation step.

Classically, layers can be fully connected, i.e. composed of neurons with receiving fields covering all the outputs of the previous layer, or convolutional. Together with other operations such as pooling (aggregation) layers, which reduce the input dimension, they transform the input information through successive simple and parametric functions.

A convolutional layer is composed of a set of parametric kernels (or filters) spanning only local parts of their inputs with, like a neuron, a linear combination of its receptive field followed by an activation function, see the example Figure 2.14. They are applied Figure 2.14: Convolution example using a size 3 filter (padding of 1, step of 1). In this simple scheme there is no bias and the activation function is the identity function. Reproduced from [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF] with permission of the author.

successively to all input pixels like a sliding window. Each kernel has a user-specified size (typically ranging from 3 x 3 to 11 x 11 pixels) and is applied to the inputs with common parameters. The fact that the parameters of each kernel are common to all input values when successively applied with a sliding window is the innovation that allows to massively reduce the number of parameters and thus the number of images to be processed.

In a supervised learning task, the model output obtained after all model transformations is compared to the target reference. This is done by applying a loss function that reflects how different the two entities are. Next, a mechanism is needed to find the set of model parameters that minimises the loss function. In other words, once the loss value has been computed for a set of training samples, the influence of each parameter on the error needs to be traced back. This is done via chain rule calculus and consists of finding the gradient of the loss function with respect to the trainable network parameters [START_REF] Lecun | Cleannet: Transfer learning for scalable image classifier training with label noise[END_REF]. This mechanism is called backpropagation. Finally, the parameter values are updated as a function of (at least) the gradient and a learning rate setting the update step size. This process is highly iterative and is called stochastic gradient descent (SGD) when it is performed for each training batch [START_REF] Amari | Estimating alpha, beta, and gamma diversity through deep learning[END_REF]. One epoch corresponds to one iteration of this process over all the training set samples. Tens to hundreds of epochs are run to optimise the weights of the model.

Between epochs, the model is frequently used in prediction-only mode (no backpropagation, only the forward pass) on an unseen validation set to evaluate its generalisation power. The best model is selected depending on the model validation performance computed along different metrics. The reported model performance is computed on a third independent set called test set. In practice, for a large dataset, the training, validation and test sets are split randomly or with a custom strategy, with fixed proportions such as 90/5/5%. The partitioning can be designed to avoid performance bias that occurs when the three sets are not completely independent. For geospatial data, it is common to perform a spatial split to reduce the spatial autocorrelation between the covariates sampled in each set.

Limits

CNNs also have some limitations that need to be acknowledged. First, training a CNN requires the manual setting of many hyperparameters adjusting the learning process. They can be set via a grid search, i.e. an expensive performance test that evaluates the model's ability to generalise after it has been trained with different hyperparameter values each time. Still, setting hyperparameter values can be challenging because of the number of possible combinations. The influence of the hyperparameters on the model is crucial, from the split of the dataset to the regularisation techniques and the optimisation process. Second, even though convolutions have made it possible to drastically reduce the number of parameters to be trained compared to an FC model, CNNs remain deep learning methods that can quickly become computationally expensive to optimise. In particular, they require the use of GPUs to reduce training times to reasonable orders of magnitude. Although this resource is increasingly available, as mentioned above, it can still be a source of complication. In addition, CNNs suffer from still limited interpretability, see trade-off between performance and interpretability in section 2.3.2.1 and the discussion 6.2 for more details. Finally, for deep-SDMs, translation invariance has the added advantage of compensating for the geolocation uncertainty of the observations. However, it may not be advantageous if the observation is central and the covariates have a large spatial extent. Indeed, in this case, the central environmental information is likely to be more informative than the peripheral information. The use of a modern CNN architecture that exploits attentional mechanisms, i.e. an adaptable receptive field, could help to overcome this concern.

Resources and inference

Deep-SDMs demonstrate their capabilities through the use of large datasets and specialised tools. Analysis-ready datasets are rare, with the exception of the GeoLifeCLEF challenge. Here we first present available resources and then illustrate how models can be used for spatial inference.

Datasets

The GeoLifeCLEF challenge [START_REF] Botella | The GeoLifeCLEF 2023 Dataset to evaluate plant species distribution models at high spatial resolution across Europe[END_REF] is the only analysis-ready dataset for the development of deep-SDMs. The 2023 edition includes five million presence-only plant observations distributed across Europe, associated with high resolution rasters: remote sensing imagery, land cover, elevation, and coarse resolution data: climate, soil, and human footprint variables. The models are evaluated on 22,000 plots based on standardised surveys. Moreover, [START_REF] Gillespie | An image is worth a thousand species: combining neural networks, citizen science, and remote sensing to map biodiversity[END_REF] constituted an ambitious dataset of over half a million CS plant observations across California, paired with 1-metre resolution satellite imagery. The scripts to regenerate the dataset are available on the author's github. Another option is to manually associate environmental data with large datasets of species observations (see Section 2.3.1.2). In fact, this is how the datasets mentioned above were created. GBIF, for example, collects millions of geolocated observations. Finally, we can imagine using traditional analysis-ready datasets for multi-species SDMs such as [START_REF] Norberg | A comprehensive evaluation of predictive performance of 33 species distribution models at species and community levels[END_REF] or [START_REF] Elith | Presenceonly and presence-absence data for comparing species distribution modeling methods[END_REF] to fine-tune deep learning models. Fine-tuning is a transfer learning approach where the weights of a model trained on a large dataset are reused and partially retrained on a smaller dataset for a specific task.

Modelling frameworks

Deep learning models are typically developed using PyTorch or TensorFlow Python libraries. GPUs can be accessed locally, on a private remote server, or online with initiatives such as google colab [START_REF] Bisong | Building machine learning and deep learning models on google cloud platform: a comprehensive guide for beginners[END_REF]. More recently, a PyTorch library called TorchGeo [START_REF] Stewart | TorchGeo: deep learning with geospatial data[END_REF] provides new tools to ease the manipulation of geospatial data in deep learning. In the field of deep-SDMs, a new framework called Malpolon facilitates model training and is available on GitHub at https://github.com/plantnet/malpolon. Finally, online resources on deep learning for ecology, such as the https://ecostat.gitlab.io/ website, can be a great help in getting started with deep-SDMs.

Model examples and spatial inference

Under appropriate modelling hypotheses, deep-SDMs can be used to infer the spatial distribution of species. Here, we briefly review the studies that successfully measure and illustrate their spatial generalisation power. In particular, we refer to the various distribution maps drawn in the articles, with links to the online versions. Their spatial resolution varies from kilometres to metres.

• [START_REF] Harris | Generating realistic assemblages with a joint species distribution model[END_REF] illustrated early on that realistic species assemblages could be predicted using neural networks. Their model can take advantage of complex, non-linear relationships between species occurrences, biotic interactions (via co-occurrences) and the environment.

• Chen et al. ( 2017) concatenated NN-based embeddings of environmental covariates with bird species co-occurrence data to feed a competitive multi-species SDM.

The idea that justifies the separate modelling is that 1) species may share similar environmental preferences while exhibiting distinct inter-species associations, and 2) these two pieces of information have different spatial resolution.

• Botella et al. (2018a) showed that predictions of observed plant counts across France were closer to the ground truth using a CNN model than either MaxEnt or a FC model (see examples in their Figures 45).

• [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF] showed that deep-SDMs are particularly efficient for modelling species that are poorly represented in the training set (likely to be rare). With only one training occurrence in France, their CNN was able to produce a response function representative of the species distribution (model output was compared with independent observations, see their Figs. 67).

• [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF] illustrated with 1-metre resolution satellite imagery that deep-SDMs can capture landscape and habitat information at very fine scales. In particular, their Figure 7 shows coherent predictions of coastal species at 50 m resolution.

• [START_REF] Gillespie | An image is worth a thousand species: combining neural networks, citizen science, and remote sensing to map biodiversity[END_REF] showcase the interest of deep-SDMs with different high resolution (256 m) applications: prediction of keystone species (Fig. 2), but also detection of ecosystem changes from wildfires and urban biodiversity hotspots (Fig. 3).

• [START_REF] Brun | Rank-based deep learning from citizen-science data to model plant communities[END_REF] used a deep NN to jointly model the distributions of 2,477 plant species represented by 6.7 million Swiss observations. At a spatial resolution of 25 m, they estimated: species distributions, community composition, but also the seasonal variation of observation probability, i.e. a proxy for flowering phenology, see their Fig. 2.

• Finally, [START_REF] Bourhis | Explainable neural networks for trait-based multispecies distribution modelling-A case study with butterflies and moths[END_REF] propose a novel NN architecture that combines species trait information with environmental covariates. Applied to UK butterfly and moth datasets, they predict species occurrence probabilities (see their Fig. 3) and use a popular interpretation method [START_REF] Lundberg | A unified approach to interpreting model predictions[END_REF] to investigate the trait-mediated and species-specific model outputs.

The final section of this state of the art focuses on data-driven insights for applications in ecology and conservation. Building on the concepts introduced above (conservation indicators, SDMs and machine learning), we cover a selection of topics where the generalising power of Artificial Intelligence (AI) can make a difference to biodiversity conservation.

Insights for conservation planning

Insights for conservation planning

Our closing objective is to outline a number of areas where AI can benefit biodiversity conservation. Unlike previous efforts, the focus is on applications rather than concepts. Although some of these involve modelling species distributions, we do not limit this literature review to SDM-related studies and explore broader issues.

We will commence by identifying review articles interested in AI for ecology and conservation, and a selection of outstanding applications. Next, we will present dataintensive approaches for predicting the IUCN extinction risk status of unassessed species. The third focus will be on the future trajectories of conservation indicators influenced by climate change. Finally, optimising strategies for spatial conservation will be briefly introduced.

AI for ecology and conservation

Review articles

First, we should start this section by mentioning again the two excellent reviews that introduce deep learning for ecology [START_REF] Borowiec | Deep learning as a tool for ecology and evolution[END_REF][START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. They are an excellent starting point for ecologists who want to break into AI concepts. Next, Lamba et al., 2019 produced a short essay on the promises, pitfalls and priorities for deep learning in conservation, with a convincing summary Figure 2.15 reproduced here. While we have only focused on the subfield of "ecological modelling and prediction", we believe that most of the pitfalls and priorities illustrated resonate strongly with our work in this manuscript. Similarly, we believe that the concerns of conservation scientists expressed in [START_REF] Walker | Caution Needed When Predicting Species Threat Status for Conservation Prioritization on a Global Scale[END_REF] are legitimate and important to clearly identify (e.g. the need for better metrics) in order to catalyse mitigation efforts. Furthermore, Tuia et al. ( 2022) provide insightful perspectives on machine learning approaches to wildlife conservation.

They examine examples where ML has successfully impacted the field, as well as the specific resources available, sensors already in use, and those that hold promise. Finally, [START_REF] Mouquet | REVIEW: Predictive ecology in a changing world[END_REF] take a step back to review the history and interpret what ecological predictions mean and Stupariu et al. ( 2022) lead a litterature reivew on ML methods applied to landscape ecology.

While prediction has always been part of ecology (see Fig. 2.16 and Darwin's prediction on the Madagascan comet orchid), they recognise that new challenges have arisen. One of these is to clarify the distinction between explanatory and anticipatory predictions. The latter are not necessarily based on a mechanistic understanding of ecological drivers. They should be seen as guides to current action rather than actual descriptions of the future [START_REF] Harfoot | Integrated assessment models for ecologists: the present and the future[END_REF] -which is already a massive contribution. Moreover, an . Predictive ecology has become increasingly important in recent years (especially in predicting species distributions). However, prediction is not new to ecology. In 1862, Charles Darwin received orchids from Madagascar. One species in particular, the Madagascan comet orchid Angraecum sesquipedale, with a surprisingly long nectar spur (20-35 cm), caught his attention. No insect with a proboscis of this length had ever been described, but Darwin was convinced of its existence because the plant could not reproduce without a suitable pollinator. The pollinator, a hawk moth, was indeed discovered in 1903, 41 years after Darwin's prediction. Illustration Laurence Meslin. Reproduced from [START_REF] Mouquet | REVIEW: Predictive ecology in a changing world[END_REF], with permission from John Wiley and Sons.

under-exploited avenue at the interface between IA, ecology and conservation is transfer learning. Indeed, ecological studies are often highly context-specific, resulting in relatively small (or focused) datasets providing valuable insights. Data science approaches such as transfer learning, use of synthetic data and causal inference increase the value of such specific datasets beyond their original purpose [START_REF] Todman | Small Data'for big insights in ecology[END_REF]. Therefore, not only should their collection continue, but their reusability and collection should be incentivised as well. To conclude this review paragraph and link to the following one, [START_REF] Christin | Applications for deep learning in ecology[END_REF] provides the perfect review article on deep learning applications in ecology. They cover the main applications of deep learning, but also suggest useful guidelines, recommendations and resources.

A selection of outstanding applications • Species identification. Deep learning has become inevitable in the field of species identification, especially for citizen science [START_REF] Affouard | Pl@ntnet app in the era of deep learning[END_REF][START_REF] Unger | iNaturalist as an engaging tool for identifying organisms in outdoor activities[END_REF]. However, difficult problems remain, such as high class imbalance and high ambiguity (both inter-and intra-class), as in the Pl@ntNet-300K dataset [START_REF] Garcin | Pl@ntNet-300K: a plant image dataset with high label ambiguity and a long-tailed distribution[END_REF]. Other forms of automated species identification remain challenging. Herbarium sheets hold unique value for the world's botanical history, evolution and biodiversity, and are increasingly being digitised. However, their identification with DL is hampered by taxonomic mismatches, small datasets from different sampling protocols that are difficult to analyse together [START_REF] Carranza-Rojas | Going deeper in the automated identification of Herbarium specimens[END_REF][START_REF] Lutio | The Herbarium 2021 Half-Earth Challenge Dataset and Machine Learning Competition[END_REF].

• Entomology. While most animals on Earth are insects, and reports suggest they may be in drastic decline, this group remains highly understudied. Deep learning could help the field in a range of applications: automatic identification, but also estimation of abundance, biomass, diversity, quantification of phenotypic traits, behaviour and interactions, population monitoring, etc. [START_REF] Høye | The PREDICTS database: a global database of how local terrestrial biodiversity responds to human impacts[END_REF].

• Wildbooks. Conservation of keystone species requires close monitoring at population and then individual level. Animal images collected on the Internet are rapidly becoming one of the richest sources of wildlife data. Wildbooks have been developed to harness this information and allow automatic identification of individuals of target species [START_REF] Berger | ESA's sentinel missions in support of Earth system science[END_REF]). An example is the whale wildbook called Flukebook, see https://www.wildme.org/.

• Earth science. As a collection of all natural sciences related to the planet, Earth science includes ecology, but also atmospheric science, geology, geography, oceanography, etc. Deep learning is a logical tool to process the amount of data generated by Earth observation. First, Camps-Valls et al. ( 2021) provide a comprehensive book on this topic. [START_REF] Reichstein | Deep learning and process understanding for datadriven Earth system science[END_REF] argues that hybrid models coupling physical processes with ML are the next step in understanding the Earth system (see also physics-informed neural networks, [START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF]. While much attention is focused on optical data, Synthetic Aperture Radar (SAR) also has great potential [START_REF] Zhu | Deep Learning Meets SAR[END_REF]. Finally, Earth observation and DL have the potential to support the UN Sustainable Development Goals [START_REF] Persello | Deep learning and earth observation to support the sustainable development goals: Current approaches, open challenges, and future opportunities[END_REF]. For instance, the work of [START_REF] Metzger | Fine-grained population mapping from coarse census counts and open geodata[END_REF] allows the estimation of 100 m population maps. This information in turn benefits urban planning, environmental monitoring, public health and humanitarian operations.

Predicting the missing conservation status of species

Unlike the index-based methods already introduced in section 2.3.1.5, prediction-based methods bypass the official IUCN extinction risk criteria. Instead, such a method directly learns a mapping between features qualifying species (geographic range, bioclimatic preferences, exposure to anthropogenic pressures, species traits, phylogeny, etc.) and the IUCN extinction risk status. Exploring the covariates of species extinction risk (in particular the biological traits of animals) has been the subject of studies since the emergence of the Red List in the early 2000s (using regression analyses, Purvis et al., 2000). Boosted by machine learning and the increasing availability of data, this line of research is still very active. Novel methods and applications to new taxa are published regularly. Before presenting recommendations and challenges, we present a brief literature review organised by model class. In chapter 5, we propose a prediction-based method that uses deep-SDMs. The species features exploited are flexible enough to project the impact of future climate scenarios on species extinction risk. For a more comprehensive review, we refer to the work of [START_REF] Cazalis | Bridging the research-implementation gap in IUCN Red List assessments[END_REF], which covers 73 prediction-based approaches and 25 index-based methods.

Statistical models and phylogenetic imputation

A classic approach is to 1) exploit the phylogeny of taxa to impute species missing biological or ecological traits, and 2) use this completed information (possibly alongside other spatial and widely available features) as input to a traditional statistical model. For example, [START_REF] Jetz | Towards a general framework for predicting threat status of data-deficient species from phylogenetic, spatial and environmental information[END_REF] assessed the global extinction risk of mammals using GLMs, and González-del-Pliego et al. ( 2019) highlighted that a thousand amphibians are threatened with extinction using a generalised least squares approach.

Random forest and decision trees

As a performing and easy-to-use ML model, the random forest algorithm and all decision trees are perfect candidates for predicting species extinction risk. [START_REF] Leão | Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions[END_REF] tested how vegetation type, growth form and geographic range size relate to species extinction risk for Brazilian angiosperms using decision trees, but also standard and phylogenetic regression. RF has been applied to, among others, terrestrial mammals (Di [START_REF] Marco | Human pressures predict species' geographic range size better than biological traits[END_REF], bulbous monocot species described by coarse distribution data [START_REF] Darrah | Using coarse-scale species distribution data to predict extinction risk in plants[END_REF] and 150,000 plant species using open-source geographic, ecological and morphological trait data [START_REF] Pelletier | Predicting plant conservation priorities on a global scale[END_REF]. More recently, [START_REF] Caetano | Automated assessment reveals that the extinction risk of reptiles is widely underestimated across space and phylogeny[END_REF] used the XGBoost algorithm [START_REF] Chen | Assessing the conservation status of Chinese freshwater fish using deep learning[END_REF] to assess 4,369 reptiles, with impressive performance demonstrated on the validation data.

Neural networks and the IUCNN approach Zizka et al. ( 2020) developed a method based on neural network classification and demonstrated its excellent performance on the orchid family. Species are associated with features representing their geographic, bioclimatic, human footprint and biome preferences. For raster covariates, the rationale is to take the species average across observations. A user-friendly R package called IUCNN has made this method a reference in the field [START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. In addition, further developments have opened up new possibilities for users, including quantifying uncertainty using a Bayesian approach and limit predictions with a confidence threshold. The method has now been applied to many taxa, including 21,000 globally distributed tree species [START_REF] Silva | Global Estimation and Mapping of the Conservation Status of Tree Species Using Artificial Intelligence[END_REF] and 1,162 freshwater fish species in China [START_REF] Chen | Assessing the conservation status of Chinese freshwater fish using deep learning[END_REF].

Ensembling and representation learning

Ensembling is an effective way to improve the generalisation power of already good classifiers. Prediction of species extinction risk is no exception, as shown in (Borgelt et al., 2022a). The authors carried out a convincing work and trained an ensemble model based on 220 ML models (including GLMs, RFs, gradient boosted classification trees and deep NNs). The final model is based on 20 boosted trees and 3 deep neural networks. An impressive number of covariates (more than 400, geographic, bioclimatic, environmental, threats) are included, see their supplementary Table 2. Here, raster covariates are summarised by species with statistics (mean, median, min, max) taken from range maps and occurrence cells or native countries. Finally, [START_REF] Mukadam | Future impacts of climate change and deforestation on endemic trees of Western Ghats, South India[END_REF] published an original study associating species embeddings generated by applying representation learning to Wikipedia text and animal taxonomy data. This work, involving natural language processing techniques for conservation biology, is an example of interdisciplinary research. Online text mining can provide valuable information for describing species.

Model comparison

Few independent studies have attempted to compare the predictive performance of models. Nic [START_REF] Lughadha | The use and misuse of herbarium specimens in evaluating plant extinction risks[END_REF] tested five different approaches (four index-based methods and RF) using herbarium-derived data for trees, shrubs and herbs. Random forest performed best, but the less data-intensive approaches also achieved good results. Besides, [START_REF] Bland | Predicting the conservation status of data-deficient species[END_REF] compared seven ML models on terrestrial mammals. They concluded that classification trees and k-nearest neighbours (simpler and less computationally intensive) achieved lower classification performance than random forests, boosted trees, support vector machines and neural networks. Finally, new comparative studies, including recent developments, are needed to provide clear guidance on which modelling method is best [START_REF] Cazalis | Bridging the research-implementation gap in IUCN Red List assessments[END_REF]. The field is indeed developing rapidly. Methods that have been evaluated on different taxa and with different species covariates cannot be compared, as the difficulty of the classification task can vary greatly.

Recommendations

Given the importance of assessing species extinction risk, [START_REF] Walker | Caution Needed When Predicting Species Threat Status for Conservation Prioritization on a Global Scale[END_REF] recommends caution when using predictive methods. In particular, modellers should ensure that per-formance is clearly reported, that the implications of modelling choices are explored, that threats are analysed and that limitations of biodiversity data (gaps, biases, uncertainties) are addressed. There is also a trade-off between occurrence cleaning and species coverage. Indeed, many species are represented by a very limited number of observations (long-tail distribution), and occurrence cleaning (especially with respect to geolocation errors) results in the removal of all observations of certain species. For a traditional thresholdbased method, rigorous cleaning is necessary to achieve the best performance. However, the performance of ML methods (random forest) has been shown to be robust to minimal data cleaning [START_REF] Walker | Evidence-based guidelines for developing automated conservation assessment methods[END_REF], allowing a large species coverage to be maintained.

Challenges and opportunities

There are several challenges to automated extinction risk assessment. Taken together, they can explain why a research-implementation gap is observed [START_REF] Cazalis | Bridging the research-implementation gap in IUCN Red List assessments[END_REF]. Indeed, while many prediction-based methods have been developed, few have been integrated into assessment practice. In response, the last authors urge academic researchers and Red List practitioners to collaborate (e.g. by involving Red List stakeholders early in the development process) and identify the need to develop and maintain user-friendly platforms. In addition, hybrid methods, which better incorporate Red List criteria and benefit from the generalisation power of ML, have the potential to facilitate uptake.

Comparative work on environmental covariates and drivers of extinction risk is also needed. While threat exposure is highly taxon and context dependent, classic covariates are commonly used and can be summarised from the observation or range level to the species level in different ways. More generally, we believe that a standard protocol for covariate selection and integration for extinction risk prediction would benefit the community. Finally, uncertainty quantification, as proposed by IUCNN, is necessary because the ultimate goal of such an assessment is to aid conservation planning and resource guidance.

Future trajectories of conservation indicators

Climate change can affect species on at least three non-exclusive aspects [START_REF] Bellard | Impacts of climate change on the future of biodiversity[END_REF]: i) physiology [START_REF] Antala | Impact of climate change-induced alterations in peatland vegetation phenology and composition on carbon balance[END_REF], i.e. their biological traits and behaviours, ii) phenology [START_REF] Collins | Experimental warming differentially affects vegetative and reproductive phenology of tundra plants[END_REF], e.g. with shifts in flowering timing (climate change indicator), and iii) geographic distribution [START_REF] Lenoir | Species better track climate warming in the oceans than on land[END_REF]. These three dimensions are sources of potential mismatch in biotic interactions [START_REF] Renner | Climate Change and Phenological Mismatch in Trophic Interactions Among Plants, Insects, and Vertebrates[END_REF], or the required adaptation may be too demanding (e.g. large spatial shifts or rapid evolutionary response) for certain species [START_REF] Corlett | Will plant movements keep up with climate change?[END_REF][START_REF] Parmesan | Ecological and Evolutionary Responses to Recent Climate Change[END_REF]. However, the vulnerability of species to climate change is diverse and the assessment methods are numerous [START_REF] Pacifici | Assessing species vulnerability to climate change[END_REF]. Ultimately, climate change has consistently been shown to be a driver of biodiversity loss [START_REF] Urban | Accelerating extinction risk from climate change[END_REF]. Furthermore, the redistribution of biodiversity under climate change has been shown to have impacts on ecosystem functioning, human well-being (e.g. shifts in the distribution of disease vectors such as mosquitoes) and the dynamics of climate change itself, creating amplifying feedbacks [START_REF] Pecl | Biodiversity redistribution under climate change: Impacts on ecosystems and human well-being[END_REF]. These effects may accumulate in certain highly exposed regions such as the Arctic.

Modelling trajectories of biodiversity requires scenarios to project future environmental conditions [START_REF] Peterson | Scenario planning: a tool for conservation in an uncertain world[END_REF]. Such projections in turn depend heavily on socio-economic scenarios (see [START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF] Figure 1 for a schematic overview of how biodiversity scenarios are constructed). Changes in species distribution are then the most studied effect of climate change. SDMs are used to project future species distribution and range loss rates are compared to IUCN thresholds [START_REF] Thuiller | Climate change threats to plant diversity in Europe[END_REF] or the species-area relationship [START_REF] Thomas | Extinction risk from climate change[END_REF]) is exploited to estimate likely species extinction rates. Biodiversity indicators, e.g. at species and population level, such as the IUCN extinction risk [START_REF] Moat | Least concern to endangered: Applying climate change projections profoundly influences the extinction risk assessment for wild Arabica coffee[END_REF] and the Living Planet Index (see section 2.2.1) can therefore be projected into the future [START_REF] Visconti | Projecting Global Biodiversity Indicators under Future Development Scenarios[END_REF]. This is what we do in the chapter 5 of this thesis. The final objective is to communicate on the projected rates to try to influence policy, bend scenarios and mitigate biodiversity loss through conservation [START_REF] Schwartz | Using niche models with climate projections to inform conservation management decisions[END_REF]. Machine learning can help tackle climate change at many levels [START_REF] Rolnick | Tackling climate change with machine learning[END_REF], including predicting biodiversity indicators through species distribution modelling (see section 2.3.2).

Climate change ecology is a young field full of challenges [START_REF] Bellard | Impacts of climate change on the future of biodiversity[END_REF]. To effectively guide conservation and policy with the projected trajectories of biodiversity indicators, methodological developments are needed in a variety of facets. First, due to uneven data availability, climate impact studies are still highly biased in terms of taxonomic and geographic coverage [START_REF] Feeley | Most 'global' reviews of species' responses to climate change are not truly global[END_REF]. As a result, tropical and marine ecosystems, as well as entire taxa such as plants, are underrepresented. Moreover, species are often the level of study, leaving the impact of climate change on functional, phylogenetic and genetic diversity rarely assessed [START_REF] Thuiller | BIOMOD -a platform for ensemble forecasting of species distributions[END_REF](Thuiller et al., , 2006b)). Second, projecting biodiversity's response to climate change requires working with a variety of scenarios (socio-economic, emissions, climate) that strongly influence the results. Comparative and interdisciplinary studies are needed to identify the most likely directions. Ensembling and uncertainty quantification methods help to increase confidence in predictions. In addition, species response to climate change is highly taxon-specific and can have counterintuitive effects, adding to the complexity. For example, milder temperatures may have local positive effects on certain plants. The dispersal capacity of species also has a strong influence on projected distributions. Without this data, two extreme scenarios are often considered: no dispersal or universal dispersal capacity [START_REF] Thomas | Extinction risk from climate change[END_REF]. Overall, more focused studies of species characteristics and responses to climate change are critically needed [START_REF] Todman | Small Data'for big insights in ecology[END_REF]. SDMs are good candidates for exploring species redistribution under climate change, but temporal and physiological responses are rarely studied. Finally, drivers of extinction risk are often studied independently, although they are likely to be interdependent and create amplifying patterns (e.g. land-use change through deforestation and climate change, see [START_REF] Sala | Global Biodiversity Scenarios for the Year 2100[END_REF] for a review). Given these sources of uncertainty and the specific responses of species, meta-analyses are valuable to provide synthetic messages on climate-induced biodiversity loss [START_REF] Maclean | Recent ecological responses to climate change support predictions of high extinction risk[END_REF][START_REF] Urban | Accelerating extinction risk from climate change[END_REF].

In conclusion, the impact of climate change on biodiversity is an active area of research that depends on critical data both at large scale (e.g. bioclimatic projections) and at small scale (dispersal capacities, species responses and plasticity, etc.). With the evidence of spatial redistribution of biodiversity (both current and future), concerns have arisen about the effectiveness of protected areas [START_REF] Araújo | Climate change threatens European conservation areas[END_REF][START_REF] Araújo | Would climate change drive species out of reserves? An assessment of existing reserve-selection methods[END_REF][START_REF] Dobrowski | Protectedarea targets could be undermined by climate change-driven shifts in ecoregions and biomes[END_REF][START_REF] Hole | SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers[END_REF]. Indeed, there is a possibility that current PA implementation may be insufficient to protect species that are shifting their spatial range. Spatial conservation planning should ultimately anticipate this pitfall by accounting for likely biodiversity redistribution in the process of PA design.

Optimising spatial conservation

Spatial conservation prioritisation is a highly complex problem constrained by multiple trade-offs between implementation costs and benefits in terms of biodiversity, economic and social values. The basic objective is to identify areas that maximise complementary values at minimal or reasonable cost [START_REF] Margules | Systematic conservation planning[END_REF]. Surrogates and biodiversity indicators are used and spatial design constraints (e.g. connectivity) also come into play [START_REF] Ferrier | Mapping Spatial Pattern in Biodiversity for Regional Conservation Planning: Where to from Here?[END_REF]. There are many aspects to consider and assessing the effectiveness of PAs is remarkably challenging (Rodrigues & Cazalis, 2020). Citizen scientists can contribute to the monitoring of PA species thanks to automatic identification [START_REF] Bonnet | How citizen scientists contribute to monitor protected areas thanks to automatic plant identification tools[END_REF]. As already mentioned, purely area-based international targets can lead to inefficient PA implementation [START_REF] Maxwell | Area-based conservation in the twenty-first century[END_REF] and leave areas of high conservation value under serious threat [START_REF] Rodrigues | Global Gap Analysis: Priority Regions for Expanding the Global Protected-Area Network[END_REF]. Success metrics including biodiversity protection and threat mitigation measures are therefore critical.

In our work we have not addressed the issue of spatial prioritisation. However, we believe that some of our findings could ultimately benefit such a task. Therefore, we briefly introduce the field as a final section of our state of the art. For the fundamentals of spatial conservation prioritisation we refer to [START_REF] Wilson | Fundamental concepts of spatial conservation prioritization[END_REF] and for a comprehensive review of the field to [START_REF] Moilanen | Spatial conservation prioritization: quantitative methods and computational tools[END_REF]. Here we will present only a few existing frameworks, with a focus on two IA-based approaches.

Two of the reference frameworks currently in use are Marxan [START_REF] Ball | Marxan and relatives: software for spatial conservation prioritisation[END_REF][START_REF] Watts | Marxan with Zones: Software for optimal conservation based land-and sea-use zoning[END_REF] and Zonation [START_REF] Mod | Prioritizing multiple-use landscapes for conservation: methods for large multi-species planning problems[END_REF][START_REF] Moilanen | Novel methods for spatial prioritization with applications in conservation, land use planning and ecological impact avoidance[END_REF]. Marxan13 is the most widely used reserve planning software in the world. It is based on simulated annealing, a stochastic optimisation technique. It has been used to define many protected areas around the world (both marine and terrestrial), including the Great Barrier Reef, Australia and the Galapagos Islands. Zonation14 is another popular spatial prioritisation software. It is based on an iterative conditional sorting algorithm and has been continuously updated since 2005 to provide flexible and realistic decision support.

Artificial intelligence has embraced the problem of prioritising spatial conservation.

Here we present two promising approaches: Conservation Area Prioritisation Through Artificial INtelligence (CAPTAIN) from [START_REF] Silvestro | Improving biodiversity protection through artificial intelligence[END_REF] and constraint programming.

Based on reinforcement learning (a machine learning paradigm, see [START_REF] Sutton | Reinforcement learning: An introduction[END_REF], CAPTAIN allows the exploration of multiple biodiversity metrics with a limited budget and accounts for dynamic changes in the system (e.g. in biodiversity monitoring). It has been shown to outperform state-of-the-art software, achieving conservation goals more reliably and producing more interpretable prioritisation maps. Constraint programming is a hybrid AI technique that allows users to explicitly specify rules in an optimisation problem [START_REF] Rossi | Handbook of constraint programming[END_REF]. This expressive AI paradigm is promising in a field such as spatial conservation planning, where on-the-ground realities (social, economic, historical, etc.)

Abstract

Species Distribution Models (SDMs) are widely used numerical tools that rely on correlations between geolocated presences (and possibly absences) and environmental predictors to model the ecological preferences of species. Recently, SDMs exploiting deep learning and remote sensing images have emerged and have demonstrated high predictive performance. In particular, it has been shown that one of the key advantages of these models (called deep-SDMs) is their ability to capture the spatial structure of the landscape, unlike prior models. In this paper, we ask whether the temporal dimension of remote sensing images can also be exploited by deep-SDMs. Indeed, satellites such as Sentinel-2 are now providing data with high temporal revisit and it is likely that the resulting time-series of images contain relevant information about the seasonal variations of the environment and vegetation. To confirm this hypothesis, we built a substantial and original dataset (called DeepOrchidSeries) aimed at modelling the distribution of orchids on a global scale based on Sentinel-2 Image Time-series. It includes around 1 million occurrences of orchids worldwide, each being paired with a twelve-month-long time-series of high resolution images (640 x 640 m RGB+IR patches centered on the geolocated observations). Thanks to this ambitious dataset, we trained several deep-SDMs based on Convolutional Neural Networks (CNNs) whose input was extended to include the temporal dimension. To quantify the contribution of the temporal dimension, we designed a novel interpretability methodology based on temporal permutation tests, temporal sampling and temporal averaging. We show that the predictive performance of the model is greatly increased by the seasonality information contained in the temporal series. In particular, occurrence-poor species and diversity-rich regions are the ones that benefit the most from this improvement, revealing the importance of habitats temporal dynamics to characterise species distribution.

Introduction

Context

Understanding and mapping species distributions is a major topic in conservation biology [START_REF] Pecl | Biodiversity redistribution under climate change: Impacts on ecosystems and human well-being[END_REF]. Species Distribution Models (SDMs) have recently become a key instrument: over the last 20 years, 6,000 peer-reviewed studies were found with this keyword according to [START_REF] Araújo | Standards for distribution models in biodiversity assessments[END_REF]. These statistical algorithms learn the correlations between species presence (and possibly absence) records and some environmental predictors provided. Under certain modelling assumptions [START_REF] Zurell | A standard protocol for reporting species distribution models[END_REF], they can estimate species distribution by generalising learned habitat preferences over time and space [START_REF] Phillips | Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation[END_REF][START_REF] Thuiller | BIOMOD -a platform for ensemble forecasting of species distributions[END_REF]. A major issue for the use of SDMs concerns the ecological relevance of the predictive variables used [START_REF] Fourcade | Paintings predict the distribution of species, or the challenge of selecting environmental predictors and evaluation statistics[END_REF], [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. Layer 1 : Sentinel-2 image time-series were collected around each occurrence geolocation, keeping least cloudy data tiles every month between March 2020 and February 2021. Images are made of 640 x 640 m RGB+IR channels with 10 m spatial resolution. The dataset is available on Zenodo and the method to create it on the Gitlab.inria platform. Layer 2 :

We then trained deep Species Distribution Models (deep-SDMs) based on convolutional neural network (Inception v3) to capture the spatio-temporal context and environmental preferences of species. Next, we conducted experiments where the input temporal dimension was modified (randomized, averaged or sampled) so as to measure its contribution on model performance. Layer 3 : the results are finally broken down into three main dimensions of analysis: species frequency in the dataset, bioregion, and species diversity in these bioregions. The analysis reveals that occurrence-poor species and diversity-rich regions are the ones that benefit the most from the improvement provided by the temporal information. see section 2.3.1.4. Furthermore, collecting appropriate data at large scale is usually very challenging. Global bio-climatic variables do not systematically provide enough information to draw conclusions on a species presence. Many other factors like species dispersal capacities [START_REF] Monsimet | Explicit integration of dispersal-related metrics improves predictions of SDM in predatory arthropods[END_REF] or shifts in land use actually come into play.

After having revolutionised computer vision, neural networks -and especially Convolutional Neural Networks (CNNs) -are also increasingly recognised in ecology (Botella et al., 2018a;[START_REF] Brodrick | Uncovering Ecological Patterns with Convolutional Neural Networks[END_REF][START_REF] Heikkinen | Does the interpolation accuracy of species distribution models come at the expense of transferability?[END_REF][START_REF] Williams | Using species distribution models to predict new occurrences for rare plants[END_REF]. They allow to identify environmental patterns on images like tree crowns [START_REF] Csillik | Identification of citrus trees from unmanned aerial vehicle imagery using convolutional neural networks[END_REF] or forest type limitations [START_REF] Wagner | Using the U-net convolutional network to map forest types and disturbance in the Atlantic rainforest with very high resolution images[END_REF]. Local environment spatial structure has already been proven to add relevant information to SDMs involving convolutional layers [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. In addition, remotely sensed data can grasp key features of vegetation functioning and thus convey relevant insights on species habitats [START_REF] Adhikari | Micro-site conditions of epiphytic orchids in a human impact gradient in Kathmandu valley, Nepal[END_REF][START_REF] He | Will remote sensing shape the next generation of species distribution models?[END_REF][START_REF] Remm | Similarity-based large-scale distribution mapping of orchids[END_REF]. Unmanned aerial vehicles allow finer and finer-scale coverage at local, regional or even country scale [START_REF] Kattenborn | Convolutional Neural Networks accurately predict cover fractions of plant species and communities in Unmanned Aerial Vehicle imagery[END_REF]. Thanks to such imagery, the nature and spatial structure of ecosystems can be characterised and learned in SDM training. RGB and IR image patches around species occurrences (or digitized geolocated presence of species) are thus added to the environmental predictors, so as to include information on vegetation and land-use heterogeneity around the occurrences (Deneu et al., 2021a).

Satellite missions like Copernicus Sentinel-2 (S2) [START_REF] Berger | ESA's sentinel missions in support of Earth system science[END_REF] now provide RGB and IR channels with fine spatial resolution and temporal revisit frequency worldwide (see subsection 3.2.1.1), which can feed high-resolution, CNN-based SDM models. However, there is still much potential ahead for bringing together remote sensing and deep learning (Camps-Valls et al., 2021). Remote sensing datasets that are (i) readily available for deep learning applications and (ii) exploiting the spatial, spectral and temporal dimensions of new satellite missions are still very few. For instance, among the twenty-three benchmark datasets implemented in TorchGeo [START_REF] Stewart | TorchGeo: deep learning with geospatial data[END_REF], only two encompass a temporal dimension. There is then an opportunity to build RGB+IR image time-series around occurrences spread worldwide. By sampling S2 data for a whole year, prominence is given to the seasonal evolutions of the plants habitats. These time-series are capturing the signature of ecosystems phenology and productivity. Our hypothesis is that this information can significantly help SDM predictions.

Contributions

This chapter contribution is threefold: First, we built a substantial and original dataset pairing nearly 1 million geolocated occurrences of the Orchidaceae family with satellite image time-series. This dataset and the associated method scripts, released as open data and code, should be useful for conservation biologists and SDM users in general. To our knowledge, no similar ready-to-use dataset is already available. Second, we designed interpretability tests of the deep-SDMs trained on this dataset in order to measure the importance of seasonal landscape variability in characterising species habitat and niche. Figure 3.1 provides the visual abstract of our method. Finally, we test which SDM modality allows our model to better capture species' environmental preferences on a global scale between satellite image time-series, bioclimatic and static variables.

Static should be considered in contrast to the other two modalities, which capture more dynamic information. It includes altitude, position (longitude and latitude, making this SDM spatial-explicit), human footprint and ecoregions. We hypothesise that in a global assessment, it is the bioclimatic variables that would be more valuable for drawing species distributions [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF].

Materials and Methods

DeepOrchidSeries dataset

Raw input data description

Orchid occurrences dataset. The Orchidaceae family is of great interest because of its diversity (about 28 000 species estimated) and its aesthetic attractiveness [START_REF] Chase | An updated classification of Orchidaceae[END_REF]. Orchids are of major concern for ecologists due to the numerous threats they are facing: habitat destruction, climate change, pollution, and illegal harvesting for horticulture and tourism industries [START_REF] Wraith | Quantifying anthropogenic threats to orchids using the IUCN Red List[END_REF]. They are also considered as a relevant proxy of their ecosystem's health [START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. Moreover, orchids are found on all continents in a wide range of habitats and they are blooming at very different altitudes. Such a range or environmental amplitude is difficult to achieve with other families, making the orchid family an excellent candidate for the purpose of our study (i.e., to measure the importance of seasonal variability in characterising species habitat and niche).

Rather than collecting a new set of orchid occurrences to build our image time-series dataset, we decided instead to re-use the one introduced in [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. Their objective was different from ours (i.e. estimating the conservation status of orchids) but the set of occurrences they collected from GBIF meets two main criteria of interest for our study: (i) global scale, and (ii) suitable data quality thanks to several data filtering and cleaning processes (including the use of the R package CoordinateCleaner v. 2.0-9, [START_REF] Zizka | CoordinateCleaner: Standardized cleaning of occurrence records from biological collection databases[END_REF]. The complete process they use is summarised in the supplementary information Table 1 of their paper [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. Another benefit of reusing [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]'s occurrence data is to support the potential reuse of our deep-SDM for the automated assessment of orchid's IUCN status. In the long term, this will improve the reproducibility and comparability of newly developed methods in this regard.

In total, the dataset contains 999,407 occurrences of 14,148 species with: 70 records per species in average, 4 in median and 3,537 species (25%) with more than 13 observations. The (heavily-tailed) distribution of the number of occurrences per species is shown on Figure 3.2A (through a Lorenz curve). Figure 3.2B represents the temporal distribution of the occurrences in the dataset. Half of the observations dated from 1997, one quarter from 2010. 14.6% of the set (145,641 occurrences) came with no timestamp at all. The oldest occurrence was from 1901 as a result of the filtering process that got rid of data records older than 1900. Only observations with a position uncertainty higher than 100 km were discarded. Perspectives and limits related to the use of such large and imbalanced occurrence dataset will be discussed in the final Section 3.4.

Materials and Methods

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Cumulative share of species. Species are sorted by number of occurrences. Sentinel-2 multispectral images. Sentinel-2 multispectral data comes from two identical satellites in the same orbit but diametrically opposite to one another. Sentinel-2A was launched on 23 June 2015 and its counterpart Sentinel-2B on 7 March 2017. This satellite mission is part of the European Earth observation project Copernicus1 [START_REF] Drusch | Sentinel-2: ESA's optical high-resolution mission for GMES operational services[END_REF]. Thirteen channels from the visible to short-wave infrared are monitoring the planet, with 10, 20 or 60 m spatial resolution and a 5-day temporal revisit above any point on Earth. Additional satellites 2C and 2D are planned to ensure the continuity in the coming years and the next generation of Sentinel-2 satellites are being prepared. We only kept four out of the thirteen channels, i.e. the three RGB channels and the Infrared (IR) channel (842 nm). These wavelengths are expected to convey the most relevant information about the environment [START_REF] He | Will remote sensing shape the next generation of species distribution models?[END_REF] and are also the finer in terms of spatial resolution (10 m). The smallest geographic units downloadable via the sentinelsat2 API are 109.8 x 109.8 km square data tiles in WGS84/UTM projection. They were defined following a military grid splitting Earth planisphere. The field square from a given satellite orbit at a given sensing time interval does not always cover a whole tile, so that several products must be merged and cropped to get an image of the whole tile.

Data products are made available to the user at two distinct levels: Top-of-Atmosphere (TOA) or and Bottom-of-Atmosphere (BOA). The important difference is the application of an atmospheric correction algorithm such as Sen2Cor [START_REF] Ientilucci | Atmospheric Compensation of Hyperspectral Data: An Overview and Review of In-Scene and Physics-Based Approaches[END_REF][START_REF] Louis | Sentinel-2 sen2cor: L2a processor for users[END_REF]. Water vapour and other atmospheric components alter the satellite image caption with complex non-linear deformations. When and how atmospheric correction should be performed prior to exploit remote sensing data depends on the desired information and thus the targeted application. About classification and change detection tasks, a recognised work from [START_REF] Song | Classification and Change Detection Using Landsat TM Data: When and How to Correct Atmospheric Effects?[END_REF] advises to perform simple corrections only when multi-temporal data is used. Otherwise, having both training and test sets from the same relative scale proved to be sufficient: no significant performance gain would result from the addition of an atmospheric correction step. A more recent article estimating the relation between sea surface salinity and Sentinel-2 Imagery with a neural network and 2,700 points obtained better results with TOA than BOA imagery (Medina-Lopez, 2020). On their specific application, they found that the atmospheric correction entailed information loss due to alteration of actual multispectral relationships. They also observed that the time and computational resources spared by using the TOA products was an important element to consider. Using TOA products time-series, [START_REF] Rußwurm | Multi-temporal land cover classification with sequential recurrent encoders[END_REF] obtain state-of-the-art land cover classification performances. BOA products are not readily available at the global scale and, when needed, atmospheric corrections have in this case to be applied by users. Considering the conclusions of previous surveys and the large size of the targeted data, we decided to work with TOA products. Moreover, the atmosphere information could be valuable for our application and we believe deep-SDMs are capable of correctly learning without this additional filter.

Dataset construction

Figure 3.3 summarises the workflow followed to obtain image time-series from a set of geolocated occurrences. The first step is to define the set of Sentinel-2 tiles containing all targeted occurrences, for which more details are provided in the Global scale processing paragraph. Second and third steps are to define the patch size and the time sampling strategy. Our choices are presented in the two dedicated paragraphs hereafter. Finally a last paragraph introduces our method to select least cloudy S2 data. We have furthermore considered only the four spectral bands available at 10 m resolution, but our workflow could be applied as well to bands at 20 m and 60 m resolution after a down-sampling step. Sentinel-2 queries and downloads were made with the Scihub Copernicus API3 . We then extracted the patches by parallelizing the processing by UTM zone to gain speed. Code and details are available at https://gitlab.inria.fr/jestopin/sen2patch. Global scale processing. First step consists then in defining the minimal set of Sentinel-2 tiles containing all our orchid observations. The Sentinelsat python API provides the option to query data by various geographical means, mainly: coordinates, polygons, tiles or satellite orbits. However, querying the API on an occurrence-by-occurrence basis for a dataset containing nearly one million occurrences is counterproductive. It is much more efficient to first download the tiles containing occurrences and then extract them locally (see Fig. 3.4A for the histogram of the number of occurrences per tile). To do so, we implemented the following two steps: • First, we created a dictionary linking each tile with its WGS84 geometry thanks to the Sentinel-2 Level-1C tiling grid provided by the ESA Sentinel-2 official portal4 .

• Then an iterative process on all occurrences was implemented, testing each time if the new observation is included in the union of the already retained tiles set. If not, a tile containing the occurrence location is downloaded and added to the set.

The final tiles set map is given on Figure 3.4C. It illustrates the full geographical scope of the dataset with 7,563 targeted tiles. 50% of all land areas (Antarctica excluded) were included in the collected data. The color scale proportional to the number of observations per tile (with a log10-scale) further shows a geographic (or observation) bias in the occurrences set: Europe, south Australia and New Zealand are gathering huge numbers of records.

Patch size. The size of the patches associated with each occurrence is an important hyper-parameter to set. Patches should be large enough to contain the most relevant spatial information, but not too large to avoid introducing patterns that are too distant from the occurrence. They should also be large enough to compensate for the geographic imprecision of the occurrences (see geolocation uncertainty distribution in Supplementary Information (SI) Fig. S1 and [START_REF] Wüest | Macroecology in the age of Big Data -Where to go from here?[END_REF], but not too large to avoid computational issues. Considering all that constraints, our final choice was patches of size 640 x 640 m (only powers of two were considered to optimise memory usage). Figure 3.4B illustrates three different patch sizes around an observation on an island of the South Australian coast. It shows that the 640 x 640 m patch (40.96 ha) captures important landscape patterns around the record as well as potential threats due to surrounding land-use.

Time-series extent and temporal resolution. On of the main contributions of our study is to consider time-series of satellite images rather than a single date image, with the objective of better characterising the habitat of species. Two important parameters in this regard are the temporal extent of the series and its resolution. Here too, there is a compromise to be made. The extent and resolution must be high enough to capture important (spatio-)temporal patterns, but cannot be too high due to computational constraints. We finally chose one-year time-series with a resolution of 1 month (i.e. twelve images, one per month).

Such twelve-month time-series allow to grasp the main seasonal variations of the environmental and ecological context including vegetation phenology, yearly weather variations as well as landscape annual variations linked to human activity (e.g. agriculture). Noticeably, such seasonal variations are often neglected in SDMs devised at global scale. Figures 3.5A and 3.5B show significant seasonal changes that can be meaningful to differentiate species habitats. In Figure 3.5A, the tree cover greatly vary depending on the season and in 3.5B snow covers the field half of the year. What if we only had one month of data? Environmental contexts would be characterised very partially and wrong inferences could be done on species ecological preferences (imagine having only one image covered by snow for Figure 3.5B). These examples illustrate the gain of ecologically relevant information when considering a twelve-month image-series.

Another parameter to be set, is the starting date of the time-series. Ideally, it should be chosen so that the date of the occurrences is included in the one-year period covered for the time-series. There are in practice various reasons impeding a perfect match between the occurrences dates and the associated predictive data. To begin with, Sentinel-2 satellite was launched only in 2015 so that older occurrences cannot be matched. Secondly all occurrences do not come with a precise date, some having no date information at all. Thirdly some S2 tiles from the defined minimal set would have to be downloaded a huge number of times to inform all observations at different dates. Lastly, there is no simple and open access to data older than a rolling year on Copernicus Open Access Hub. Because of all that constraints, we finally chose a fixed period for all twelve-month time-series, with a staring date on the 1st of March 2020 and an ending date on the 29th of February 2021 (the choice of the recent period being linked to the temporal distribution of the number of occurrences, see figure 3

.2B).

Data selection based on cloud cover. Remote sensing data at RGB/IR channels are directly dependent on potential clouds covering the satellite's field of view. For-tunately S2 products are including in their metadata a cloud cover percentage (cc%). Thereby when querying the Sentinelsat API over a given area and time window, one can ask to only keep the less cloudy products. The wider the chosen time window is, the more likely an almost cloud-free product will be available within. Based on this metadata, we selected the least cloudy S2 products within each month in the targeted time window. With this selection process, we expect the large majority of time-series to be cloud-free like Figure 3.5A or 3.5B. Figure 3.6 provides an overview of the cloud coverage distribution in selected products compared to all available products in the queried time window. When, despite our efforts to select least cloudy products, the obtained satellite data around an occurrence present many cloudy frames, it could nonetheless be interpreted as an information contributing to the species ecological niche. Furthermore, in this case the environment structure can still be captured from clear scenes at other dates of the time-series (see for instance April, May and November 2020 on Figure 3.5C).

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All months

Species Distribution Models trained with satellite image time-series

In this section, we describe the architecture and learning procedure of the deep-SDMs that we trained based on the DeepOrchidSeries dataset described above. Given an image time-series as input, the model estimates orchids relative probabilities of presence.

Model definition and training procedure

Model architecture. The model used is an extended version of the Inception v3 [START_REF] Szegedy | Rethinking the Inception Architecture for Computer Vision[END_REF] Convolutional Neural Network (CNN). Inception networks are appreciated because of their capacity to grasp patterns -here environmental patternsat multiple scales. It has been shown in [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF] that this architecture provides better species prediction performance than point neural networks, boosted trees or random forests. We use this work to justify our choice of model. Nevertheless, testing other recent neural architectures specifically designed to deal with spatio-temporal data is an avenue to be exploited in the future, see the second perspective of the discussion.

In particular, the performance gain was shown to be the most significant for rare species.

In our context, the Inception v3 architecture was modified so as to accept not only RGB images but the full RGB+IR image time-series. Our inputs are of size (N f , N x , N y ) with N f the number of features equal to 12 * 4 = 48 (12 months x 4 RGB+IR channels), and N x = N y = 64 (corresponding to 640 x 640 m quadrats at 10 m resolution). To speed up the training and regularize the model, batch normalisation [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF] was applied on the convolutional layer activations, just before the nonlinear ReLu function. Dropout [START_REF] Srivastava | Dropout: a simple way to prevent neural networks from overfitting[END_REF] was finally used to prevent the network from overfitting (with a dropout probability of 0.5).

Model loss. The models were trained using the Label-Distribution-Aware Margin (LDAM) loss Cao et al. ( 2019) designed for strong class-imbalance multi-class classification problems. In our context, it allows pushing upwards rare species performance without deteriorating predictions on common species. The LDAM loss is a label-distribution-aware function that leads the model to an optimized trade-off between per-class margins. When considering two species only, say one rare and one common, the decision boundary drawn by this loss will be slightly shifted towards the common species in order to let the benefit of the doubt to the rare species (see [START_REF] Cao | Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss[END_REF] Figure 1 for a meaningful scheme).

The LDAM loss has been shown to perform very well in many deep learning benchmarks involving both a strong imbalance between classes and a high inter-class ambiguity.

Training procedure. The models were fitted using a stochastic gradient descent on multi-GPU nodes from the IDRIS supercalculator Jean Zay5 . They were trained during 70 epochs with a batch size equal to 64. The training process took around 100h per model (with 8 gpus working in parallel). Convolutional and linear layers weights were initialised from a truncated normal continuous random variable. The Deferred Re-Weighting (DRW) training schedule associated to the LDAM loss was used. DRW is a vanilla empirical risk minimization until a given epoch, here 65. Then, the training ends with a re-weighted loss and SGD steps with a re-normalized learning rate, both by batch species frequency.

The learning rate was initialised to 0.1 and later decayed by a ten factor at epochs 50 and 65. A trained model is approximately 600 MB.

Performance evaluation of the model

Data split. The DeepOrchidSeries dataset was split in three parts: (i) Training set (90%), (ii) Validation set (5%) and (iii), Test set (5%). Following the recommendations of [START_REF] Roberts | Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure[END_REF], the split was done using a spatial blocking strategy that enables a more robust estimation of the model's performance. The spatial blocks were defined in the spherical coordinate system according to a 0.025°grid, i.e. square blocks of 2.775 km at the equator. Splitting by block is important to impede the model from being validated or tested at locations very close to the training occurrences. In addition to the spatial blocking, we also used a stratified sampling strategy to ensure that any region of the world has a minimal number of blocks in the training set. We therefore used the World Geographical Scheme for Recording Plant Distributions (WGSRPD) level 2 regions [START_REF] Brummitt | World geographical scheme for recording plant distributions. International working group on taxonomic databases for plant sciences[END_REF]. Within each region, we randomly sampled 90% of the blocks present and assign them to the training set. The remaining blocks were assigned to either the validation set or the test set (at random). Validation and test occurrences from species not in the training set were removed. Table 3.1 provides the number of occurrences and species in each set. Evaluation metrics. Our model being trained with a multi-class classification loss on presence-only data, its output is a categorical probability distribution of the form η s (x) = P(Y = s|X = x) where x is the input tensor (i.e. an RGB+IR image time-series), Y the observed species and η s (x) is the estimated probability that the observed species is s conditionally to x. Because the output is a categorical probability distribution, we have that the sum of probabilities over all species is equal to one ( m s=1 η s (x) = 1). To evaluate the model, we chose not to use pseudo-absences because of the bias induced by such methods [START_REF] Botella | Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection[END_REF][START_REF] Phillips | Sample selection bias and presence-only distribution models: implications for background and pseudo-absence data[END_REF]. Instead, we used a set-valued metric (Chzhen et al., 2021) to assess the quality of the species assemblage predicted by the model for a given input. Specifically, we chose the commonly used top-k accuracy as suggested in [START_REF] Botella | Overview of GeoLifeCLEF 2019: plant species prediction using environment and animal occurrences[END_REF]. It measures the success rate of the model when it returns the top-k most probable species for any input x. More formally:

A k = n i=1 A k (i) n (3.1)
where n is the number of occurrences in the test set (or validation set) and:

A k (i) = 1 if η y i (x i ) ≥ ηk (x i ) 0 otherwise
with y i the true species label of occurrence x i and ηk (x i ) the outputs of the model re-ordered in decreasing order of probabilities.

Because of the high class imbalance of our dataset, a shortcoming of this metric applied on all test occurrences taken together (or micro-average, Sokolova and Lapalme, 2009) is that it gives far too much importance to the most frequent species over the less frequent ones. To compensate for this imbalance, it is preferable to use the macro-average version of this metric [START_REF] Sokolova | A systematic analysis of performance measures for classification tasks[END_REF] consisting in first calculating the score of each species and then averaging the scores over all species. More formally, the macro-average top-k accuracy (MSA) can be defined as:

MSA k = l s=1 SA k,s l (3.2)
where l is the number of species in the test and SA k,s is the top-k accuracy for species s defined as:

SA k,s = y i =s A k (i) n s (3.3)
with n s the number of occurrences of species s in the test set. During the training phase of the model, the macro-average top-k accuracy is computed on the validation set every two epochs for k = 30. The model selected in the end is the one with the highest value.

To analyse the performance of the model according to the number of occurrences available in the training set, we also measured the macro-average accuracy on subsets of species categorised by range of their number of occurrences. If we denote as N s the number of occurrences of a species s in the training set, we can define as S I = {s | N s ∈ I, n s > 0} the set of species in the test set having a number of training occurrences in a given interval I. The macro-average accuracy for a given interval I is then defined as:

MSA k,I = s∈S I SA k,s |S I | (3.4)
Another batch of experiences will focus on performances per geographic region. Spatial units are taken from the WGSRPD. The level 3 division defines the botanical countries that we exploit. Performance per region r is denoted as RA k,r and is defined as the micro-average top-k accuracy computed only on the occurrences encompassed in r:

RA k,r = x i ∈r A k (i) n r (3.5)
where n r is the number of test occurrences in r. Regions with n r fewer than 50 occurrences were excluded as statistically insignificant. Further, performance per region is compared with regions species diversity. Therefore, we computed the diversity index q D r of each region r according to the definition of [START_REF] Hill | Diversity and evenness: a unifying notation and its consequences[END_REF] and [START_REF] Jost | Assessing the Cost of Global Biodiversity and Conservation Knowledge[END_REF]. It is a quantitative measure of biodiversity combining, in a given region, species richness with species relative prevalence. The term prevalence is used instead of abundance to account for the observation bias in our data. Species richness corresponds to the number of distinct species observed (denoted L r ). Species relative prevalence is the share of species occurrences compared to all region's observations: p s,r equals ns,r nr , with n s,r the number of test occurrences from species s in r. The general expression of region's diversity index is:

q D r =          Lr s=1 p q s,r 1 1-q if q ̸ = 1 exp -Lr s=1 p s,r ln(p s,r ) if q = 1 (3.6)
where q is a parameter weighting the trade-off between the importance granted to species richness (small value) VS relative prevalence (big value). 0 D r results in region species richness and 1 D r is the exponential of the Shannon entropy [START_REF] Shannon | A mathematical theory of communication[END_REF]. Performance per region is then averaged per categories I on the diversity index and written as MRA k,I .

In the literature, the majority of studies involving species diversity use it as response variable. They are focusing on its potential drivers like bio-climatic variables, topographic heterogeneity or forest structure [START_REF] Hakkenberg | Forest structure as a predictor of tree species diversity in the North Carolina Piedmont[END_REF]Thuiller et al., 2006a). Here, we exploit species diversity as an explanatory variable possibly explaining our model performances. In a similar manner, [START_REF] Emerson | Species diversity can drive speciation[END_REF] defended that species diversity is a driver of speciation and [START_REF] Dawud | Is Tree Species Diversity or Species Identity the More Important Driver of Soil Carbon Stocks, C/N Ratio, and pH?[END_REF] examined its influence on soil carbon stocks among others.

Interpretability experiments: quantifying the contribution of temporal information

Temporal averaging

Temporal sampling Random permutation

Original time-series Duplicated times the input data in order to suppress some information and to retrain a new model based on this transformed data. The comparison of the model deprived of information with the original model then allows to quantify the importance of the suppressed information. Figure 3.7 gives a comprehensive overview of the procedure detailed hereafter:

M Original time-series. This is the default original model where the input image time-series are kept unchanged (stacked in chronological order). Here the model can learn from the temporal dynamics present in the series. The filters learned by the Inception v3 model are themselves ordered feature maps time-series of 12 months and are likely to capture spatio-temporal redundancies in the input data (e.g. seasonal variations of the environment or phenological patterns).

M 1 Random permutation. In this model, the 12 images of the original time-series are randomly shuffled so that the model can no longer base its predictions on the actual temporal sequencing [START_REF] Garnot | Time-Space Tradeoff in Deep Learning Models for Crop Classification on Satellite Multi-Spectral Image Time Series[END_REF]. All input variance and spatial information remain nonetheless in the input. The filters learned by the Inception v3 model can no longer be specialised by month. Nor can the model differentiate relations between months input. It actually learns from the block of twelve months considering them all equally. This procedure is comparable to the variable importance technique where a given input variable is randomised across samples to test how the model perform without its contribution. However, here we do not randomise a given feature across samples, but features order independently for each sample.

M 2 Temporal averaging. In this model, the input image series are reduced to the mean over the twelve months replicated twelve times. Only the first moment of the distribution over the time dimension is kept and the model only "sees" a mean landscape averaged along the year. The objective here is to test to what extent a simple temporal averaging is sufficient to sum up most of the temporal variation. Each month contributes equally to the mean and the result is blurry. Variance between months has been totally removed. Ecological gradients of the different patch elements are reduced to their sum divided by twelve.

M 3 Temporal sampling. In this model, the input image series are reduced to only one month picked at random and replicated twelve times. The neural network is being provided with only a twelfth of the predictive data and is deprived of any temporal information.

Please notice that for each of the cases (M 1 , M 2 and M 3 ), the data transformation is applied once on the whole dataset (including training, validation and test set) before the model is trained and evaluated.

Model M 1 being deprived only of the months order information, its comparison with Model M can be interpreted as a statistical test of the hypothesis that the composition of species depends on the existence of months specific features, in particular the ones resulting from yearly seasonality cycles. The comparison between M and M 3 can be interpreted as a test of the hypothesis that the species composition does or does not depend on any temporal variability. Model M 2 can be seen as an intermediate scheme where the temporal variability is summarised only by the mean of the distribution.

Accordingly, the comparison between M 1 and M 2 allows to assess how useful statistical moments of higher order than the mean are for characterising the temporal variability.

To compare the performances of two different models, say M and M i with i ∈ {1, 2, 3}, for a given species s in the test set, we set a metric down called relative performance change of M i compared to M, defined as:

S∆ k,s (M, M i ) = SA k,s (M) -SA k,s (M i ) SA k,s (M) (3.7)
where SA k,s is the top-k accuracy of species s (see Eq. 3.3).

In the same manner that we defined the macro-average accuracy per category I on species training set number of occurrences, we can now consider the mean relative performance change per category between two models:

MS∆ k,I (M, M i ) = s∈S I S∆ k,s (M, M i ) |S I | (3.8)
Relative region performance change R∆ k,r (M, M i ) is also calculated as

RA k,r (M)-RA k,r (M i ) RA k,r (M)
. This measure is averaged per categories I on the diversity index as well and is represented by MR∆ k,I (M, M i ).

When computing S∆ k,s (M, M i ) (resp. R∆ k,r (M, M i )) between M and M i models for a given species s (resp. a given region r), it is beforehand necessary to make sure that the denominator, SA k,s (M) (resp. RA k,r (M)), is not null. It can sometimes be when model M fails to predict the correct label for all s occurrences (resp. all occurrences in r). In this case, no performance change can be calculated since it is already null. Species s (resp. region r) is then removed from the calculation of the mean performance change by categories on species training set number of occurrences (resp. on regions diversity index). This is why there is a drop of support between Figure 3.9 (resp. Fig. 3.10) left and right graphs, i.e. there is fewer species (resp. regions) encompassed in the categories, as indicated on the horizontal axis. This effect is a lot more important on the support of the species mean performance change than on the region's one. To sum up, relative performance change can not be calculated for species or regions having already the lowest possible score with the whole temporal information. They are in that case discarded from the mean performance change calculation.

Modality contribution on a global scale

We train three models separately, one with each of the three modalities tested:

• The model trained with satellite imagery is the M model described above (original time-series).

• The bioclimatic model is trained with the 19 variables from WorldClim 2 [START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF]. These are average monthly climate data based on summary statistics (minimum, mean, maximum) of temperature and precipitation for 1970-2000 at a spatial resolution of 30 arc seconds (1 km²). As we keep the same

Results

input data format as for satellite imagery, bioclimatic values are repeated to fill 640 x 640 m patches of 10 m resolution.

• The third model is trained with: i) Elevation from the ASTER global digital elevation model [START_REF] Tachikawa | Characteristics of ASTER GDEM version 2[END_REF] at 1 arc second (30 m²) ii) Latitude and longitude of observation iii) Human Footprint individual rasters (Venter et al., 2016, built environment, population density, electrical infrastructure, cropland, pastureland, roads, railways and navigable waterways) for the years 1993 and 2009 at 1km² resolution. iv) Olson's ecoregions [START_REF] Olson | Terrestrial Ecoregions of the World: A New Map of Life on EarthA new global map of terrestrial ecoregions provides an innovative tool for conserving biodiversity[END_REF] Again, all variables are upsampled to respect the input format of 640 x 640 m at 10 m resolution. The training procedure is the same as for the satellite image time-series experiments. The top-30 and macro-average top-30 accuracy of the four models (M, M 1 , M 2 and M 3 ) are presented on Figure 3.8 (at each epoch of the training phase for the validation set and on the test set for the final selected model). Due to the long-tail distribution of species occurrences (Fig. 3.2A), the top-30 accuracy A 30 is representative of the performance on the most common species whereas the macro-averaged top-30 accuracy MSA 30 is more representative of the performance on the rare species. The final increase of the MSA 30 score at epoch 65 is due to the DRW optimizer previously described: re-weighting the loss towards training's end enables a boost on rare species performances [START_REF] Cao | Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss[END_REF]. The top-30 accuracy A 30 tends to slightly decrease after the first quarter of the training phase. Our hypothesis is that this is mainly due to the use of the LDAM loss: as the training goes by, the models are reaching a better estimation of rare species ecological niche and tend to predict them more often to the detriment of common species that were chosen by default.

Results

Model validation and performance

The model M trained and tested with the original time-series provides better results than the three other models deprived from temporal information. M is the only one where the temporal dynamics are undamaged and hence fully exploitable to statistically draw predictions. The macro-average top-30 accuracy is 0.286 for the unaltered model M, against 0.216 for M 1 trained on shuffled data, 0.215 for M 2 trained on the yearly mean and 0.149 for M 3 trained on a single random month. The following analyses can be made of these results:

1. The strong performance decrease between M and M 3 shows that the temporal information contained in the time-series is a key factor of the predictive performance.

For most species, it appears to be as important as the spatial information alone (cf. macro-average accuracy plot MSA 30 ).

2. The comparison between M and M 1 shows that the decisive temporal information is largely related to the order of the images in the time-series, i.e. to the months specific features captured by the model (such as the ones resulting from yearly seasonality cycles).

3. The comparison between models M 1 and M 2 shows that their performances is almost identical (cf. MSA 30 plot). This means that the decisive information related to the unordered temporal variability can be synthesised efficiently by the mean of the time-series. In other words, higher order statistical moments of the temporal dynamic independent from the time of the year are likely to be useless for predicting species composition (e.g. the standard deviation of acquisition noise).

4. The comparison between models M 1 and M 3 shows that the decisive temporal information is also largely explained by the unordered temporal variability of the images (typically due to some stochastic processes independent from the time of year). better than that of a random predictor. Species having between 3 and 10 occurrences, for instance, are predicted in the set of the top-30 most probable species in 17% of the cases. A random predictor over the 13,700 species of the training set would have a top-30 accuracy below 0.22 %. Figure 3.9B displays the mean relative performance change between the unaltered model M and the three models M i (i ∈ {1, 2, 3}) as a function of the number of species occurrences (see Equation 3.8). It shows that the relative performance drop is inversely correlated with the species number of occurrences. In other words, the rarer the species (in the data), the higher the performance gain obtained thanks to the temporal information. This can be explained by the fact that this is precisely on rare species predictions that the room for improvement is the bigger, as depicted on graph 3.9A. The use of time-series thus makes it possible to compensate for the lack of occurrence data by an increased knowledge of the temporal dynamics of the environment.

Results by number of species occurrences

Results by region and regional diversity index

Figure 3.10 displays all results related to the regional analysis of our models.

The first sub-graph 3.10A shows that the predictive performance of the four models is negatively correlated with the regional diversity index. Regions with small diversity indexes 1 D r are the ones where the model predictions are the better. On the contrary, regions with high diversity see the models achieve poor performance. With q = 1, the diversity index equals the Shannon entropy exponential. This measure strongly depends on species richness. Hence areas with high diversity are where there is a lot of possible different orchids. This means many possible classes for the models and a high risk of confusion between species with similar environmental preferences. Moreover, these areas

Results

are often including a lot of rare species and/or are still poorly observed. Regions with low 1 D r values are regions with relatively low species richness and tend to encompassed common species that the models are predicting well (see Fig. 3.9A).

The second sub-graph 3.10B displays the relative performance change when comparing model M to M i models, as a function of the regional diversity index. The most obvious trend is the red curve: when totally deprived from the habitat temporal dynamics, predictions on most diverse regions are proportionally more impacted than on low diversity regions. The tendency is more irregular for M 1 and M 2 but is globally valid too. It implies that, similarly than for rare species on Figure 3.9B, the temporal information especially benefits highly diverse areas. An enlightenment of this tendency also is that this is where the room for improvement is the largest. Models especially take advantage of further temporal information to progress on hard tasks. Figure S2 presents the results of the same experience but with categories formed on regions' number of occurrences in the training set N r , the total number of occurrences entailed in region r during training. Unlike Figure 3.10A and 3.10B, no tendency can be drawn. It reaffirms our idea that it is regions diversity that is driving results spatially and not only the observation bias.

The map displayed in 3.10C depicts the top-30 accuracy per region achieved by model M (i.e. the unaltered model with original time-series). A clear difference of performances can be observed between southern and northern hemispheres. Looking at regions' diversity index 1 D r , written in green on the map, allows a better understanding of this gap. Northern regions (especially northern Europe) are presenting less species and are well sampled whereas regions around and below the equator (Australia excepted) are a lot more diverse and still insufficiently observed. Models average performances are actually quite consistent on the Earth parallels. This map is the direct illustration of the 3.10A black curve.

Finally, the map 3.10D shows where the loss of the temporal information impacts the more the performances. It corresponds to Figure 3.10B red curve, when the model trained with only one randomly picked and duplicated data month is compared to the reference model trained with full time-series. Relative performance decreases in very diverse regions like southern China or in Bolivia are really pronounced. On the contrary performances in countries with low orchid diversity and well observed like Norway of Finland are relatively spared by the input reduction.

Statistical tests

A t-test between M and M 1 species micro-average accuracies SA 30,s (M) and SA 30,s (M 1 ) does confirm that results are notably different (p-value of 5e-42). The same conclusion arises from the comparison of the average top-30 accuracy per region: MRA 30 (M) = 0.591 with ordered data against MRA 30 (M 1 ) = 0.509 without, p-value of 3.5e-9. This confirms that the order of the images in the time-series does matter and that providing the data stacked in chronological order leads to significantly better performances than when providing data in random order. Figure 3.11A reveals a marked gradient of performance depending on test occurrence observation year. This analysis discarded 15% of the 50,375 test occurrences presenting no observation date information. Each quartile includes approximately 11,000 points. Both micro and macro top-30 accuracy seem to be linearly correlated to the occurrence observation year quartile. The linear behaviour is confirmed when choosing a division with a thinner percentile. Top-30 performances on the last quartile 2010-2019 are impressive: 0.834/0.484 of micro/macro average accuracy. When cutting the test set data at the median 1997, i.e. considering separately the oldest and the most recent half of test observations, performances are of 0.703/0.281 (oldest half) and 0.811/0.409 (most recent half). Moreover it should be noted that all macro-average performances calculated on test set's subsets are comparatively higher than overall performances because less distinct species are considered (see Fig. 3.11 species number in bold, against 4, 261 in the entire test set).

Model evaluation regarding time and spatial data mismatches

Figure 3.11B focuses on the influence of test occurrence coordinates uncertainty on model performance. Test set is divided by quartiles on the studied variable, likewise Fig. 3.11A. 31% of test observations do not include any information on coordinates uncertainty and are consequently put aside. Each quartile contains approximately 9,000 observations. Micro-average top-30 accuracy is identical on first three quartiles and only drops when uncertainty is higher or equal than 5,000 meters. Macro-average top-30 accuracy is similar when uncertainty is kept under 707 meters, i.e. for the first two quartiles only (it is even slightly higher for the second one). Then the macro-average performance goes a step down starting from the median 707 meters. Both micro and macro average performance are severely diminished when coordinates uncertainty is superior or equal to 5 km. Bioclimatic variables outperform Sentinel-2 image time-series in determining global orchid distribution. Static variables also achieve better test performance than satellite data, with positional information likely to make a large contribution. This is true for both micro and macro average test performance (and therefore for both common and rare species). The training process of the model fed with static variables fluctuates strongly before stabilising after epoch 50.

Discussion

SDMs and satellite data. Remote sensing is an invaluable source of predictive features for SDMs, and more widely for deep learning based earth observation applications [START_REF] Borowiec | Deep learning as a tool for ecology and evolution[END_REF][START_REF] He | Will remote sensing shape the next generation of species distribution models?[END_REF][START_REF] Zhu | Deep Learning in Remote Sensing: A Comprehensive Review and List of Resources[END_REF]. Combined together, they offer a key opportunity in monitoring biodiversity facing climate change [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF].

SDMs coupled with remote sensing data are often exploiting the widespread vegetation indexes EVI or NDVI [START_REF] Balmford | Measuring the changing state of nature[END_REF]. These indices are computed from satellite channels and are intended to reflect vegetation properties. The NDVI is said to assess photosynthetic activity and productivity [START_REF] Pettorelli | The Normalized Difference Vegetation Index (NDVI): unforeseen successes in animal ecology[END_REF]. Texture measures derived from satellite EVI were proven adapted to map habitat heterogeneity and bird species richness patterns [START_REF] Farwell | Habitat heterogeneity captured by 30-m resolution satellite image texture predicts bird richness across the United States[END_REF].

The WorldClim variables (weather station data interpolated with satellite-derived covariates, [START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF][START_REF] Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF] certainly are the most widely used global SDM predictors [START_REF] Nogués-Bravo | Predicting the past distribution of species climatic niches[END_REF][START_REF] Svenning | Applications of species distribution modeling to paleobiology[END_REF]. This bio-climatic data approaches habitats annual trends (e.g. annual precipitation) and seasonality (e.g. temperature annual range and standard deviation). Contrary to our one-year DeepOrchidSeries dataset, here the variables are averaged across several decades.

SDMs and remote sensing data can also help rare species detection by capturing the biophysical conditions driving their distributions [START_REF] Cerrejón | No place to hide: Rare plant detection through remote sensing[END_REF]. Recent studies have successfully leverage the spatial structure of satellite images as input to CNN-based SDMs [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. Trained on fine scale tensors, these models were proven able to learn and cluster species ecological preferences like annual mean temperature (Deneu et al., 2021a).

Regarding the use of the temporal dimension of satellite data in SDMs, few studies actually take advantage of it as underlined in [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF]. We can cite [START_REF] Cord | Inclusion of habitat availability in species distribution models through multi-temporal remote-sensing data?[END_REF] who tried in 2011 to include EVI seasonality information in their SDMs inputs. Their study was however on a totally different range than us since they focused on eight Mexican anurans and used one-dimensional predictors.

Benefits of Deep-SDMs trained on remote sensing image time-series.

The main outcome of our study is that using time-series of satellite images significantly improve Deep-SDM performance, in particular for rare species and in most diverse regions, supporting the interest of the approach for conservation science. Rare species are almost always threatened because of their small numbers and lack of conservation measures. Moreover, the World most diverse regions include nearly all undiscovered species [START_REF] Joppa | Biodiversity hotspots house most undiscovered plant species[END_REF]. Better knowledge of the ecological niche of rare or littleprospected species should foster more appropriate and effective conservation measures to ensure their survival.

We collected time-series of remote-sensing images to grasp the temporal variation in habitat properties. Our results confirm that this information is of high value to capture species ecological niches and potential distributions. Our time-series are also providing SDMs with the spatial structure of species habitats, a key information to enhance predictive performances [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. Recent satellite missions offer both high temporal revisit frequency and high spatial resolution at the global scale, supporting the use of such data for niche modelling. Exploiting even more intensive remote sensing data, e.g. all products without any selection by month or on a wider time window, would probably allow even better ecological niche estimation. That said, the Sentinel-2 data curation we devised here represents a good trade-off to acknowledge the phenology of orchid habitats at a broad spatial scale. Trying to avoid as much as possible clouds on selected images was also a sensitive point in our dataset creation workflow. A thinner temporal resolution would have resulted in richer time-series, but also a higher number of cloud frames. The question of whether the presence of clouds is in itself a relevant information for characterising the environment was not addressed in our study and remains nonetheless an open question.

Discussion

Comparison with other open remote sensing datasets for deep learning. Remote sensing datasets for deep learning applications are currently gaining much interest and are more and more accessible. The very recent launch of TorchGeo [START_REF] Stewart | TorchGeo: deep learning with geospatial data[END_REF], a Python library to easily handle geospatial datasets in the PyTorch environment, illustrates the recent and still ongoing progresses. However, the available datasets remain currently few and the temporal information provided by satellite revisits is almost never used [START_REF] Sumbul | Bigearthnet: A Large-Scale Benchmark Archive for Remote Sensing Image Understanding[END_REF]. The available datasets are mostly used for land-cover classification [START_REF] Helber | EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification[END_REF] or semantic segmentation [START_REF] Schmitt | ssdm: An r package to predict distribution of species richness and composition based on stacked species distribution models[END_REF], as described in the benchmark datasets provided in TorchGeo (see [START_REF] Stewart | TorchGeo: deep learning with geospatial data[END_REF] Table 1). Sen12MS is for instance a global dataset including 180,662 patches of Sentinel-1/2 256 x 256 m images and MODIS-derived land cover maps [START_REF] Schmitt | ssdm: An r package to predict distribution of species richness and composition based on stacked species distribution models[END_REF]. Another dataset, similar to ours in terms of spatial coverage, is named Seasonal Contrast (SeCo) [START_REF] Mañas | Seasonal Contrast: Unsupervised Pre-Training from Uncurated Remote Sensing Data[END_REF] and was released in 2021. It gathers 2.65 x 2.65 km Sentinel-2 image time-series around about 200K locations worldwide. Time-series include 5 images separated by approximately 3 months. The objective was to learn an encoder that can be used for a variety of tasks, from land-cover classification to change detection. SeCo includes images from all over the world to represent a wide variety of landscapes. Among the currently available and open datasets, our dataset is, to the best of our knowledge, the only one providing monthly image data at so many points worldwide. In order to allow its reuse and the reproducibility of our experiments, the entire dataset is made publicly available with the Zenodo DOI 10.5281/zenodo.4972593. We also share the scripts that allowed to create it at https://gitlab.inria.fr/jestopin/sen2patch. In particular, these can be used to collect new image time-series at locations other than those covered by our dataset.

Interpretability: in which cases is the modelling of the temporal dynamics the most beneficial ? One of the major conclusions of our study is that the regions benefiting the most from a performance gain due to the modelling of the temporal dynamics of satellite images are those with the highest species diversity. This conclusion may seem counterintuitive at first. Indeed, the regions with the highest diversity are often located towards the tropics and are not those with the most pronounced seasonal patterns. Consequently, the image time-series in these regions are not expected to be the ones with the strongest temporal signal. However, it is important to understand that the model operates on a global scale with thousands of habitats to discriminate from each other. Whatever the temporal signature of a given habitat, it is a useful information for distinguishing it from other habitats. At the extreme, the temporal signature of a constant habitat throughout the year is a strong marker of that habitat. A study lead in Mediterranean natural habitats analyzed habitat discrimination from a variety of multispectral sensors answers simulated from field measurement, including Sentinel-2 [START_REF] Féret | Detecting the Phenology and Discriminating Mediterranean Natural Habitats With Multispectral Sensors-An Analysis Based on Multiseasonal Field Spectra[END_REF]. They showed that multi-temporal acquisitions outperform single data acquisition to discriminate habitats.

The reason for the higher performance gains in high diversity regions is actually more related to the higher model uncertainty in that regions. Species from these regions are indeed those for which there is the least amount of occurrence data available and our study clearly demonstrates that the performance gain is strongly correlated with this variable. In other words, our study shows that the addition of the temporal information allows to reduce the model uncertainty related to the lack of occurrence data in high diversity region. This result appears particularly interesting since habitats with the highest diversity and the rarest species are also the most threatened ones and modelling them is essential to put in place adapted conservation measures.

Key considerations for building new models with our method or using existing ones. Our method could be readily applied to other taxonomic groups than the orchids family. The ease and cost of implementation will mainly depend on the geographical distribution of the occurrences of the target taxon. With a family as large and widespread as the orchids, our method requires significant computing resources. Downloading Sentinel-2 tiles at a very large extent demands a lot of storage available (about 100Tb). To keep model training time reasonable, GPUs have to be used too. A computing cluster is more than welcome and the technical requirements can be a limitation for some researchers. However, once the dataset is built and the model is trained, predictions can perfectly be run on standard local machines. To this end, the model built for our study is shared publicly in the same Zenodo repository as the dataset (DOI 10.5281/zenodo.4972593). Providing new S2 image time-series as input, it can be used to predict species orchids composition anywhere on earth or to build high-resolution maps of specific orchid species at global scale. It may also be used for other ecological tasks via transfer learning approaches (i.e. keeping unchanged all the weights of the model except those of the last layer dedicated to species classification, [START_REF] Torrey | Handbook of research on machine learning applications and trends: algorithms, methods, and techniques[END_REF].

On temporal and spatial biases.

In the context of species and habitats distribution modelling in general, a recurrent challenge is the possible mismatch, both in time and space, between the occurrences and the environmental variables [START_REF] Phillips | Maximum entropy modeling of species geographic distributions[END_REF]. As shown in Figure 3.2B, in particular, a fraction of the occurrences in our dataset date from several decades ago, while the satellite data is from March 2020 to February 2021. If the environment changed since the observation, e.g. because of a housing project or deforestation, the model may learn incorrect relationships. Figure 3.11A focuses on this particular issue and acknowledges the influence of occurrence observation date on model performances. Top-30 test accuracy is gradually higher on more recent occurrences than older ones. Interestingly, common and rare species predictions seem to respond in the same manner to temporal shifts between predictive habitat data and species observation dates. Spatial mismatch can also happen because of the occurrences position uncertainty (See Fig. S1). However, our model being based on convolutional filters, it is highly robust to such spatial shifts until the true occurrence position does not exceed the extent of the input image (here, 640 x 640 m). Ideally, only occurrences with a position uncertainty of less than 320 m (half of the patch size) should be considered with our method. Figure 3.11B traduces the impact of test occurrence coordinates uncertainty on model performance. As expected, top-30 accuracy drops when uncertainty is substantial and there is actually very little chance that the predictive data is anywhere near the actual observation place (see performances on Q 4 quartile). Besides performance on both common and rare species remains almost constant when uncertainty is inferior to the median equal to 707 meters. Thereby, when the maximum uncertainty is of the order of the patch size, the model performs as well as on very precise occurrences. Finally, the Q 3 marked difference of evolution between micro/macro top-30 accuracy could be explained by the following hypothesis: rare species predictions are more affected by a growing coordinates uncertainty than common species because of more locally specific habitat preferences.

In machine learning, such mismatch between labels and predictive data is called label noise [START_REF] Frenay | Classification in the Presence of Label Noise: A Survey[END_REF] and is actively studied [START_REF] Ghosh | Robust loss functions under label noise for deep neural networks[END_REF]Lee et al., 2018). The strength of our dataset in counteracting this noise is its very large size, as demonstrated in [START_REF] Rolnick | Deep learning is robust to massive label noise[END_REF]. Their work showed that deep learning models can learn correct generalizations even with massively noisy datasets.

At last, the strong spatial bias present in the DeepOrchidSeries dataset influences SDMs predictions [START_REF] Beck | Spatial bias in the GBIF database and its effect on modeling species' geographic distributions[END_REF]. Such bias results from a very uneven sampling effort (See Fig. 3.4C map) and not from orchids distribution. Use of methods to mitigate spatial bias at the cost of occurrence number is a promising direction to exploit DeepOrchidSeries (see abovementioned publication). Nonetheless true understanding of orchids distribution and health will only be reached with significant and uniform observation effort. Having access to constructive and global predictive data is remarkably valuable but not sufficient. Biodiversity hotspots [START_REF] Myers | Biodiversity hotspots for conservation priorities[END_REF] urgently need to be sampled with high standards of care to limit human disturbance. Citizen science initiatives are also contributing to enhance biodiversity monitoring worldwide [START_REF] Affouard | Pl@ntnet app in the era of deep learning[END_REF][START_REF] Kobori | Citizen science: a new approach to advance ecology, education, and conservation[END_REF].

Modality contribution on a global scale

Bioclimatic variables have been consistently identified to be the main driver of plant species distributions at large scales [START_REF] Randin | Monitoring biodiversity in the Anthropocene using remote sensing in species distribution models[END_REF][START_REF] Woodward | The impact of low temperatures in controlling the geographical distribution of plants[END_REF]. At fine scales, satellite imagery provides critical information on the habitat (environmental layout, land cover and patterns, [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF]. Our results confirm what is expected from the literature: bioclimatic conditions are the major determinant of vegetation distribution at large scales, ahead of non-climatic predictors such as habitat information provided by satellite imagery time-series. In turn, we assume that such information is most useful at finer scales, as highlighted by [START_REF] Luoto | The role of land cover in bioclimatic models depends on spatial resolution[END_REF] and [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF]. The static variables provided in the third model result in a global species distribution that is, on average, almost as good as that produced by the bioclimatic model. We hypothesise that the combination of elevation, position and ecoregion can be considered a good proxy for bioclimatic state. Bioclimatic information is needed to map plant species on a global scale. By capturing habitat information, satellite imagery provides complementary rather than alternative information. However, collecting satellite imagery on a global scale is an expensive task, which is affordable when it is tailored to a specific dataset, but becomes extremely challenging when the goal is to cover global terrestrial data at the kilometre scale. Ultimately, we decided to conduct the following global-scale analyses without satellite imagery, as the cost-benefit ratio seemed unfavourable for the tasks at hand.

Perspective 1: enriching the input with other predictors informing orchids habitat.

An exciting future development is to add other relevant predictors to our models. Other image time-series like the frequently used bio-climatic variables from WorldClim6 or ecosystem functional attributes [START_REF] Arenas-Castro | Assessing the multi-scale predictive ability of ecosystem functional attributes for species distribution modelling[END_REF] although not independent since they also are computed from satellite data) would bring complementary information on species ecological niche. Altitude7 , available global human footprint rasters8 , soil properties variables9 [START_REF] Batjes | Standardised soil profile data to support global mapping and modelling (WoSIS snapshot 2019)[END_REF] or ecoregions [START_REF] Olson | Terrestrial Ecoregions of the World: A New Map of Life on EarthA new global map of terrestrial ecoregions provides an innovative tool for conserving biodiversity[END_REF] would help to crystallise species preferences and vulnerabilities as well.

Perspective 2: Using NN architectures designed to extract long-term temporal dependencies An active research avenue concerns adapting neural networks architectures to best analyze satellite image time-series with broad temporal and spatial coverages. Recurrent convolutional neural networks [START_REF] Lai | Recurrent Convolutional Neural Networks for Text Classification[END_REF] achieve significant performance gain in land-cover classification tasks [START_REF] Garnot | Time-Space Tradeoff in Deep Learning Models for Crop Classification on Satellite Multi-Spectral Image Time Series[END_REF][START_REF] Rußwurm | Multi-temporal land cover classification with sequential recurrent encoders[END_REF], and we anticipate it should also be relevant for the analysis of species distributions and spatio-temporal dynamics. In our case, we can suggest an hybrid architecture relying on an Inception v3 model to first extract the spatial features at each week or month and then a Recurrent Neural Network (RNN) to encode the temporal dimension over a long period of time. 3D CNNs are another promising candidate architecture but, as pointed out by [START_REF] Garnot | Time-Space Tradeoff in Deep Learning Models for Crop Classification on Satellite Multi-Spectral Image Time Series[END_REF], convolutions in the temporal dimension are not well adapted to grasp long-term dependencies and assume a regular sampling of occurrences in time, which we do not have. Lastly, spatio-temporal encoders with temporal attention could be worth investigating time when seeing their success on other tasks like satellite time-series segmentation [START_REF] Garnot | Panoptic Segmentation of Satellite Image Time Series with Convolutional Temporal Attention Networks[END_REF]. For now, our CNN architecture is considering the stacked time-series of size twelve as a global temporal context. It was proven suited to grasp the local landscape yearly dynamics and globally improve species relative probability of presence prediction. But with larger time-series, attributing more modelling weight to the temporal dimension will be a must. This seems all the more relevant given that predictions of rare species and in very diverse regions benefit in particular from the temporal information.

Conclusion

In this paper, we studied for the first time a worldwide species distribution model based on high resolution remote sensing image time-series. Therefore, we built and shared a substantial dataset (called DeepOrchidSeries) aimed at modelling the distribution of orchids on a global scale from Sentinel-2 data. The spatial structure and phenology of species habitat are captured over a whole year for 999,258 occurrences. We then

Conclusion

trained deep-SDMs resting on an Inception v3 architecture whose input was modified to deal with twelve months time-series of RGB+IR images. The analysis of the resulting model reveals that the temporal information contained in the time-series enables a strong improvement of the predictive performance compared to a purely spatial model. Thanks to interpretability experiments, we did show that seasonal patterns, in particular, are well captured, resulting in a better discrimination of habitats all over the world. We also demonstrated that occurrence-poor species and diversity-rich regions are the ones that benefit the most from this improvement, revealing the importance of habitat temporal dynamics to characterise biodiversity. We hope that this work will pave the way for even more elaborate spatio-temporal models allowing to predict future trajectories of ecosystems.

Introduction

Abstract

Although increasing threats on biodiversity are now widely recognised, there are no accurate global maps showing whether and where species assemblages are at risk. We hereby assess and map at kilometre resolution the conservation status of the iconic orchid family, and discuss the insights conveyed at multiple scales. We introduce a new deep species distribution model trained on 1M occurrences of 14K orchid species to predict their assemblages at global scale and at kilometre resolution. We propose two main indicators of the conservation status of the assemblages: (i) the proportion of threatened species, and (ii) the status of the most threatened species in the assemblage. We show and analyze the variation of these indicators at World scale and in relation to currently protected areas in Sumatra island. Global and interactive maps available online at https://mapviewer.plantnet.org/ show the indicators of conservation status of orchid assemblages, with sharp spatial variations at all scales. The highest level of threat is found at Madagascar and the neighbouring islands. In Sumatra, we found good correspondence of protected areas with our indicators, but supplementing current IUCN assessments with status predictions results in alarming levels of species threat across the island. Recent advances in deep learning enable reliable mapping of the conservation status of species assemblages on a global scale. As an umbrella taxon, orchid family provides a reference for identifying vulnerable ecosystems worldwide, and prioritising conservation actions both at international and local levels.

Introduction

Nearly a million species will face extinction in the coming decades [START_REF] Díaz | Pervasive human-driven decline of life on Earth points to the need for transformative change[END_REF], many of which having high value for medicine, food, materials, etc [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. The Post-2020 Global Biodiversity Framework requires assessing current biodiversity state and quantifying conservation measures impacts [START_REF] Nicholson | Scientific foundations for an ecosystem goal, milestones and indicators for the post-2020 global biodiversity framework[END_REF]. However, the distribution of many species is little known (Wallacean shortfall), and there is lack of comprehensive enough information on species conservation status [START_REF] Schatz | Plants on the IUCN Red List: setting priorities to inform conservation[END_REF]. Land managers still need accurate indicators of species extinction risk that should be available both at a large scale (to allow comparisons between regions) and at a sufficiently fine spatial resolution. Recent automatic assessment of conservation status (Borgelt et al., 2022a;[START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF] have proved promising to complement the assessment based on informing IUCN criteria, which should help tackle the major objective of intensive prediction at broad taxonomic and spatial coverage.

Species distribution and richness patterns are complex, habitat and scale dependent, which entails that species conservation status must be assessed and acknowledged at multiple spatial scales and depending on habitat variation. According to [START_REF] Whittaker | Conservation Biogeography: assessment and prospect[END_REF], protected areas design based on species distribution and richness may be sensitive to spatial scale, and the conservation challenges must be addressed at both global scale and fine-resolution [START_REF] Puglielli | Macroecology of plant diversity across spatial scales[END_REF]). Here we perform (i) multiscale assessment of conservation status, based on (ii) high-resolution characterization of habitat properties, in the case of the emblematic orchid family.

Deep learning offers an unprecedented opportunity to characterize complex, scaledependent relationships between species and their environment [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. In addition, the ever-increasing volume of data stemming from citizen science observations on one hand, and from remote sensing characterization of environmental heterogeneity on the other hand, requires adapted DL workflows [START_REF] Borowiec | Deep learning as a tool for ecology and evolution[END_REF]. DL models can learn from complex effects and interactions between environmental predictors [START_REF] Puglielli | Macroecology of plant diversity across spatial scales[END_REF], and [START_REF] Cai | Global models and predictions of plant diversity based on advanced machine learning techniques[END_REF] have shown that DL can help to isolate relationships between biodiversity and ecological drivers.

Understanding how threatened species are distributed is a task that ecologists have been working on since the nineteenth century [START_REF] Gaston | The spatial distribution of threatened species: macro-scales and New World birds[END_REF][START_REF] Moret | Humboldt's Tableau Physique revisited[END_REF]. Yet there are few quantitative studies of the distribution of threatened species [START_REF] Orme | Global hotspots of species richness are not congruent with endemism or threat[END_REF]. Successful attempts to design anthropogenic threat index at the regional scale [START_REF] Paukert | Development and assessment of a landscape-scale ecological threat index for the Lower Colorado River Basin[END_REF] or even worldwide with the Human Footprint [START_REF] Venter | Global terrestrial Human Footprint maps for 1993 and 2009[END_REF] have lead the community to adopt this information as model predictor. However, several major questions remain unsatisfactorily answered: how do anthropogenic and bioclimatic pressures relate to species environmental niches, at what scale and to what degree? New studies in that regard consist in combining species IUCN status with known or predicted range of species and produce conservation priority maps [START_REF] Han | Integrated modeling to identify priority areas for the conservation of the endangered plant species in headwater areas of Asia[END_REF][START_REF] Mair | A metric for spatially explicit contributions to science-based species targets[END_REF][START_REF] Verones | Global extinction probabilities of terrestrial, freshwater, and marine species groups for use in Life Cycle Assessment[END_REF]. For an overview of recent successful attempts, see the state of the art section 2.2.3.1. Species included in these indices must have been previously assessed and their extinction risk status officially recognised by the IUCN. However, as of 2022, only 7% of the world's described species have an IUCN status (15% for the world's known plants) (IUCN, 2022). Ultimately, there is a strong case to be made for including unassessed species in the design of spatial threat indicators.

In order to widen the currently narrow IUCN coverage, automatic classification methods have made a breakthrough. A major research avenue has emerged from this urgent task [START_REF] Walker | Caution Needed When Predicting Species Threat Status for Conservation Prioritization on a Global Scale[END_REF]. Two families of methods coexist: approaches that estimate IUCN criteria variables in advance to compare with official thresholds [START_REF] Dauby | ConR: An R package to assist large-scale multispecies preliminary conservation assessments using distribution data[END_REF]Stévart et al., 2019), and models that directly predict IUCN status after being trained with predictors and already assessed species (Borgelt et al., 2022a;Gonzálezdel-Pliego et al., 2019;[START_REF] Lughadha | The use and misuse of herbarium specimens in evaluating plant extinction risks[END_REF][START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. Methods in the first category are easier to interpret by construction. However, newer predictive models achieve impressive performance. Research is also exploring the use of SDMs to inform conservation status thanks to their niche modelling capabilities [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF][START_REF] Syfert | Using species distribution models to inform IUCN Red List assessments[END_REF].

SDMs are correlative models learning from the association of species observations with environmental predictors (Elith & Leathwick, 2009). These statistical tools are now widely used and ongoing methodological work continue to improve their convergence and predictive power [START_REF] Lembrechts | Incorporating microclimate into species distribution models[END_REF][START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM)[END_REF][START_REF] Powell-Romero | Improving the predictability and interpretability of co-occurrence modelling through feature-based joint species distribution ensembles[END_REF]. Applications at all scales contribute to grasp diversity patterns and help to hold invasive 4.2. Materials and Methods species back [START_REF] Botella | Jointly estimating spatial sampling effort and habitat suitability for multiple species from opportunistic presence-only data[END_REF], highlight biodiversity hotspots [START_REF] Hamilton | Increasing taxonomic diversity and spatial resolution clarifies opportunities for protecting US imperiled species[END_REF] or orient Protected Areas (PAs) design [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF]. Deep-SDMs embrace deep learning vision architectures to leverage rare and critical environment spatial patterns [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF][START_REF] Leblanc | Species Distribution Modeling based on aerial images and environmental features with Convolutional Neural Networks[END_REF]. Indeed, spatial and temporal [START_REF] Estopinan | Deep Species Distribution Modeling From Sentinel-2 Image Time-Series: A Global Scale Analysis on the Orchid Family[END_REF] contexts were proven significant to model rare species niches and species-rich regions diversity. These models capture the shared environmental preferences between multiple species and let information flow from the most common to the rarest species without corrupting their specific features (Botella et al., 2018b). Spatially Explicit Models (SEM) integrate the location of observations as a predictor variable. While ecologists discourage its use when modelling species' environmental preferences, it has been shown to significantly improve prediction performance and influence conservation planning [START_REF] Domisch | Spatially explicit species distribution models: A missed opportunity in conservation planning?[END_REF]. SEMs can incorporate local heterogeneities, creating positive feedbacks and allowing patterns to emerge at larger scales (DeAngelis & Yurek, 2017).

Our main contribution is to produce kilometre-scale extinction risk maps of species assemblages on a global scale. A species assemblage is simply defined as members of a community that are phylogenetically related, where a community is a collection of species that occur in the same place at the same time [START_REF] Fauth | Simplifying the jargon of community ecology: a conceptual approach[END_REF]. To do this, we trained a deep-SDM model on 1M observations of 14K species distributed worldwide. We then developed a novel method to estimate species assemblages. Coupled with the species' IUCN status, the assemblages are then characterised by extinction risk indicators. Interactive maps are available online at https://mapviewer.plantnet.org/?config=apps/store/orchidstatus.xml. To our knowledge, this is the first realisation of SDM-derived spatial indicators at such resolution, taxonomic and geographic coverage. Four levels of analysis are also discussed: i) How is the extinction risk of orchid assemblages distributed at different scales? ii) Which zones appear to contain the most threatened assemblages? iii) Is there a correlation between the diversity of orchids in a country and the proportion of threatened species? and finally iv) In Sumatra, how do our indicators relate to current PA implementation?

Materials and Methods

Taxonomic focus: the Orchidaceae family

The Orchidaceae family is a perfect taxon to guide our research, both because of its inherent nature and because of its large data coverage [START_REF] Cribb | Orchid conservation: a global perspective[END_REF]. This uniquely diverse taxon comprises around 31,000 species, making it one of the largest flowering plant families (KEW, 2023). Diversity and aesthetic appeal of orchids have made them the focus of attention for botanists and enthusiasts for decades. This has resulted in both a rich scientific literature [START_REF] Cozzolino | Orchid diversity: an evolutionary consequence of deception?[END_REF][START_REF] Givnish | Orchid historical biogeography, diversification, Antarctica and the paradox of orchid dispersal[END_REF] and a wealth of observations: 8M raw GBIF observations, including 6.8M with coordinates (GBIF, 2023). Orchids are present on all continents and are flowering in a very wide range of altitudes and habitats. This is a crucial aspect as our modelling approach aims to capture and project species preferences worldwide. The threats they face -habitat destruction, climate change, pollution and intensive harvesting -make them singularly vulnerable. Moreover orchids are a relevant indicator of the health of their environ-ment [START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. This well-known and change-sensitive family can be used as a proxy to identify ecosystem conservation priorities [START_REF] Yousefi | Using endemic freshwater fishes as proxies of their ecosystems to identify high priority rivers for conservation under climate change[END_REF]. Understanding threats, monitoring populations and distributions, and raising awareness are other key conservation objectives for the group [START_REF] Wraith | Orchid conservation and research: An analysis of gaps and priorities for globally Red Listed species[END_REF]. Orchids are widely used by international institutions as flagship species to lead and give visibility to the conservation debate [START_REF] Cribb | Orchid conservation: a global perspective[END_REF]. The challenge of orchid conservation cannot be tackled at the species level alone. Large-scale and broad approaches should necessarily complement studies carried out on emblematic species with a high risk of extinction [START_REF] Fay | Orchid conservation: how can we meet the challenges in the twenty-first century?[END_REF].

Species assemblage prediction model 4.2.2.1 Definition

Our model for predicting species assemblages is derived from what is called set-valued prediction (or set-valued classification) in the machine learning community (Chzhen et al., 2021;[START_REF] Mortier | Efficient set-valued prediction in multi-class classification[END_REF]. The model is trained on presence-only (single-label) data, but is then used to predict a set of labels by thresholding the output categorical probabilities. In more details, let us consider the following species assemblage prediction problem with C distinct species. The input set made of the predictive features associated to each occurrence location is denoted X = {x 1 , ..., x n }. The matching species label set is Y = {1, ..., C}. The objective is to learn a species assemblage predictor on a training dataset composed exclusively of presence-only occurrences (x 1 , y 1 ), ..., (x nt , y nt ) ∈ X × Y. The pairs (x i , y i ) are supposed to be independently sampled from a unknown probability measure P X,Y . This joint measure can be decomposed into the marginal distribution measure over X , P X , and the conditional distribution of y given an input x denoted η(x) = (η 1 (x), ..., η C (x)) and equal to

η k (x) = P X,Y (Y = k|X = x)
Then, the assemblage of species likely to be present conditionally to x can be defined as:

S * λ (x) := {k ∈ Y : η k (x) ≥ λ}
where λ is a threshold on the conditional probability of species optimised to return precautionary assemblages (see next section on model validation).

In practice, the true conditional probability η(x) is unknown and we assume we are given an estimator η(x) from which we can derive the following plug-in estimator of the species assemblage:

S λ (x) := {k ∈ Y : ηk (x) > λ} (4.1)
One approach to get a good estimator ηk (x) of the conditional probability is to fit a model using the negative log-likelihood which is known to be a strictly proper loss [START_REF] Gneiting | Strictly proper scoring rules, prediction, and estimation[END_REF], i.e. it is minimized only when the model predicts η. The negative log-likelihood loss is defined as:

l log (k, η) = -log ηk (x) (4.2)
In the context of deep learning, η(x) is typically chosen as a softmax function on top of a deep neural network f θ (x) : X → R C so that:

ηk (x) = exp(f k θ (x)) j exp(f j θ (x))
where θ is the set of parameters of the neural network to be optimized by minimizing the loss function of equation 4.2.

Using this very common deep learning framework, it is possible to show that the species assemblage predictor S λ (x) of Equation 4.1 is consistent [START_REF] Lorieul | Uncertainty in predictions of Deep Learning models for fine-grained classification[END_REF], i.e. it tends towards the optimal set S * λ (x) when the number of training samples increases. In other words, our species assemblage predictor is as simple as training a deep neural network with a cross-entropy loss function on the presence-only samples and thresholding the output softmax probabilities to get the assemblage of predicted species.

Our backbone model is an adaptation of the Inception v3 [START_REF] Szegedy | Rethinking the Inception Architecture for Computer Vision[END_REF]. This convolutional neural network learn spatial patterns from two-dimensional predictors (Botella et al., 2018a;[START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. A spatial block hold-out strategy is used to limit the effect of spatial autocorrelation in the data when evaluating the model [START_REF] Roberts | Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure[END_REF]. Blocks are defined in the spherical coordinate system according to a 0.025°g rid (2.8 km square blocks at the equator). The split of the training/validation/test spatial blocks (90%/5%/5%) is stratified by region to ensure that all regions are represented within each set. We use the regions defined by the WGSRPD level 2 [START_REF] Brummitt | World geographical scheme for recording plant distributions. International working group on taxonomic databases for plant sciences[END_REF]. Training is done on Jean Zay, an IDRIS supercomputer. A full description of the model architecture, dataset spatial split and training procedure can be found in supplementary information (SI) Box A. Finally, the species assemblages are post-processed. i) Predictions outside the continents where species are known to occur (according to our observation dataset) are removed, and ii) conditional probabilities associated with orchids are normalised, see Box B.

Validation

The species assemblage model is calibrated and assessed on the unseen occurrences from the validation spatial blocks (see dataset split in Box A). The objective is to guarantee that the true species is included within the kept species assemblage. This optimises recall rather than model precision. It results in species assemblages that are potentially larger than in reality, and consequently in aggregated indicators at species level that are potentially overestimated but precautionary (see next section). Our dataset is highly unbalanced in terms of the number of occurrences per species (see Box F). It is therefore difficult to calibrate a specific threshold for many species. However, this would have been appropriate if we wanted to guarantee an error per species rather than per observation point. The aim is indeed to reduce the marginal error of classification per observation (i.e. we want assemblages with little error on the species observed). The optimal solution is given by a common threshold per species [START_REF] Fontana | Conformal prediction: A unified review of theory and new challenges[END_REF].

The threshold value λ is then an important hyper-parameter of the method. Theoretically, we could consider that any species with a non-null conditional probability η k (x) is potentially present in the assemblage (i.e. by chosing λ = 0). However, in practice, the estimator ηk (x) is never null even for the most unlikely species. Thus, it is required to adjust the value of λ so that only the relevant species are returned in the assemblage. Therefore, we use a subset of the training dataset that is used only for this calibration step. It allows estimating the average error rate for a given value λ:

E(S λ ) = P X,Y [Y / ∈ S λ (X)]
by computing the percentage of samples x i in the calibration set for which the true observed species y i is not in S λ (x i ).

Finally, we can chose λ so as to minimize the average species assemblage size E[|S λ (X)|] -which is equivalent to maximize λ -while guarantying that the average error rate is lower than an ϵ objective:

arg min λ∈[0,1] E[|S λ (X)|] s.t. E(S λ ) ≤ ϵ ⇔ max λ∈[0,1] (λ) s.t. E(S λ ) ≤ ϵ (4.3)
This is equivalent to what is called conformal prediction in machine learning [START_REF] Fontana | Conformal prediction: A unified review of theory and new challenges[END_REF] and guarantees that the actual species is contained within the set with probability at least 1 -ϵ.

In practice, we choose ϵ = 0.03 as explained in more details in the Box C. We predict assemblages that have been validated to contain the initial species in 97% (at the point level) and 80% (at the species level) of cases. The performance at the species level shows the robustness of our assemblages and the performance at the point level its validity in space.

Conservation indices for species assemblages

Indices definition

We define two indices characterising the extinction risk of a predicted species assemblage, I c and I O . They respectfully render the proportion of threatened species in the assemblage and the most critical IUCN status in the assemblage. Let's break down their construction.

IUCN status notations Our indices partly rely on the extinction risk classification scheme from the IUCN Red List of threatened species, https://www.iucnredlist.org/ [START_REF] Mace | Quantification of Extinction Risk: IUCN's System for Classifying Threatened Species[END_REF]. IUCN categories are limited to Least Concerned (LC), Near Threatened (NT), Vulnerable (VU), Endangered (EN) and Critically Endangered (CR). We set the ensemble E status = {LC, NT, VU, EN, CR} with the relation order LC<NT<VU<EN <CR. Additionally, we introduce a general THREAT category corresponding to the union of VU, EN and CR categories. We denote as φ(y) the function that provides the extinction risk status of a species y.

Indicator I O (S): most critical status of the species in the assemblage For a given species assemblage S, our first indicator consists in taking on the most critical species extinction risk status. This is a concise and precautionary index. It aims at providing an information easy to understand and represent. Here is its formal definition:

I O : P(Y) → E status S → max s j ∈S {φ(s j )} (4.4)
Indicator I c (S): proportion of species in the assemblage with a given status Our second indicator I c (S) measures the proportion of species from a given category c in an assemblage S. Let us consider a species assemblage with its associated probability distribution (S, η). I c is defined as the proportion of species with status c in S, with the species being weighted by their relative probability of presence η (see Equation 4.5). The proportion of critically endangered species is for instance denoted I CR (S). And so on for the four other IUCN status in E status and the overall THREAT category.

I c : P(Y) × R C → R [0,1] (S, η) → j∈φ -1 (c) η j (4.5)
The Shannon index I H (S) The Shannon index is one of the most popular measures of biodiversity. It originates from the famous communication theory [START_REF] Shannon | A mathematical theory of communication[END_REF], but was adopted in ecology as early as 1955 [START_REF] Ricotta | Through the Jungle of Biological Diversity[END_REF]. Denoted I H , this metric evaluates the quantity of information of a set. Both the set richness (number of distinct classes) and evenness (classes ratio) influence the index [START_REF] Marcon | Mesures de la biodiversité[END_REF]. Let (S, η) be a species assemblage, with η its associated conditional probability distribution:

I H (S) = - l∈S η l • log(η l ) (4.6)

Missing status completion

Only 889 of our 14,129 orchid species have an official IUCN status in 2021, i.e. 6.3%. It therefore seems unreasonable to ignore all unassessed species in our indicator calculation. We decide to supplement the status information with an automatic preliminary assessment method from the literature called IUCNN [START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. The distributions of the IUCN-assessed and predicted IUCN status are shown in Figure S6. Both indicators can then be computed considering only IUCN-assessed species or the entire species assemblage. By default, the indicators are on all the orchid species from our assemblage, i.e. considering both known IUCN status and predicted IUCN status. When they are restrained on the IUCN-assessed species only, the indicators are denoted with an IUCN superscript: I IUCN .

High-resolution maps construction 4.2.5.1 Global grid design

The aim now is to create a global grid to support our spatial indicators. This is done in two steps. First, we create a regular grid covering all longitudes and latitudes. We sample the longitude range [-180°,180°] and the latitude range [-90°,90°] at 30-second intervals. One second equals 1/3600 degrees, hence r = 30/3600 degrees. Let M = {-180, -180 + r, ..., 180 -r, 180} and N be its latitudinal counterpart. The grid support is then obtained by crossing the two sampled axes M × N . Secondly, we spatially intersect the grid with the land areas of the world. We are indeed only interested in terrestrial regions. The geometry used is the Esri grid of world country boundaries (Esri, 2023). The intersection contains 221M points. Finally, predictive features are assigned to each land grid position. This results in

G = {x m,n | m, n ∈ M × N }.

Maps definition and construction

Maps are constructed in two steps: First, the species assemblages associated to each G grid point are predicted by batch with our model: Ŝλ (G). Second, the spatial indices defined in section 4.2.4.1 are computed on the predicted assemblages:

I(G) = {I(S) | S ∈ Ŝλ (G)}.
This set of indicators {I(G)} constitute our global and kilometre-scale maps (reminder: by default all orchid species are considered and predicted IUCN status thus employed). Within worldwide predicted species assemblages:

• I O (G) highlights the most critical IUCN status

• I c (G) represents the proportion of species with IUCN status c (five maps)

• I THREAT (G) maps the proportion of threatened species

• I H (G) draws the global patterns of predicted orchid diversity.

Details on predictions batch processing and on the website solution are available in Box D.

Zonal statistics

Spatial analysis can necesit aggregated regional indicators. With a kilometre scale resolution, I O and I c can be dissolved at different organization levels. Municipalities, protected areas, states or biodiversity units: the choice depends on the application. To illustrate this method at the global scale, we aggregate our indicators at the WGSRPD level 3. It corresponds to botanical countries which can ignore political borders [START_REF] Brummitt | World geographical scheme for recording plant distributions. International working group on taxonomic databases for plant sciences[END_REF]. We selected countries of at least 2,000 km² to highlight large area priorities (65 countries out of 369 removed).

Region spatial coverage of the most critical IUCN status

This measure is based on I O , the spatial indicator of the most critical IUCN status in the species assemblage. In a given region r, areas with distinct worst IUCN status coexist. Focusing on a given status c, its spatial coverage proportion in r is denoted Area % [I O ](r, c). By default, this variable is computed on the entire species assemblage. Nonetheless, it can also be expressed considering only IUCN-assessed species.

Region average proportions

Second zonal statistic consists in taking I c average for a given region r and status c. It represents region's average proportion of species with c as IUCN status and is written down µ[I c ](r, c). The entire species assemblage is taken into account. Such statistic allows direct comparison between arbitrary zones. For the sake of simplicity, square brackets precising the spatial indicator can be dropped in both zonal statistics.

Data

Orchid occurrences

The orchid occurrence dataset comes from [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF], whose authors queried GBIF in August 2019. This dataset has the advantage of being both global and already geographically/taxonomically curated. Nearly 1 million occurrences of 14,129 different species were used to build our model (999,258 observations after duplicate checking). The average number of observations per species is 70, while the median is 4. 25% of species have more than 13 species. Date distribution summary statistics are min = 1901, Q1 = 1982, med = 1997, Q3 = 2010 and max = 2019. The cumulative number of occurrences per species, the distribution of observation dates, the distribution of georeferencing uncertainty, the observation map and the species richness maps are all available in Box F and Fig. S1.

Predictive features

A large environmental context around each observation is collected and provided to the model: 64 x 64 2D tensors sampled at the kilometre-scale resolution and centred on the observation. Predictors include WorldClim2 bioclimatic variables, Soilgrids pedological variables, human footprint rasters, terrestrial ecoregions of the world and the observation location, see Box G for details. Examples of input are shown in Figure S9 and the full list of predictors is given in Table S2. and I O . IUCN species range data are still very scarce (only 1.2% of species in our dataset have IUCN ranges) and of variable quality: some species have raw model outputs as official IUCN range maps whereas others will have tailored expert-designed maps. Our species assemblage model combined with known IUCN status results in a consistent and contrasted map Fig. 4.1b.

Predictions in tropical Africa, East and South-East Asia and North America include CR species assessed by the IUCN. The presence of CR species in North America may be surprising at first, but given that i) this continent is comparatively well assessed and ii) this indicator is both sensitive and precautionary (only one species is sufficient to reach the CR category), it is reasonable. No CR species are predicted in South America if only known IUCN status are considered. However, when predicted IUCN status are included on Fig. 4.1c, the value of I O across South America is drastically different. Indeed, EN and CR species predictions lead the indicator to change to higher categories of risk. According to our model taking into account predicted IUCN status, Brazil and the Andes are for instance hosts to CR-estimated species on a large part of the territory. On Figure 4.1c, new global patterns are highlighted. These include India and temperate Asia presenting EN species, the Western Ghats and Southeast Asia hosting CR species, and Portugal, western Spain and the French Landes turning orange due to the prediction of EN species. Overall, the differences are more pronounced in the southern hemisphere than in the northern hemisphere. This illustrates the fact that IUCN assessments are biased towards northern countries and that large assessment gaps remain.

Country-level analysis

Table 4.1 shows the botanical countries with the largest I O coverage as CR or as EN. There are many islands in this ranking. All top fifteen countries are almost completely covered by only one status. See supplementary file T3 for the full table. High on the Area % (CR) ranking are Equatorial Guinea, Réunion, Mauritius, Madagascar, Comoros and Laos. CR species are present throughout these countries. By construction, countries with a high CR coverage status cannot also have a high EN coverage. Therefore, countries with high Area % (EN) are different from the first column. European territories such as Corse or Portugal appear in the ranking and Caribbean islands are well represented. .2a shows the Shannon index calculated on our species assemblage predictions (full resolution on the website). As expected, the tropics appear to contain the richest areas. This map can be read in parallel with the Box F second map: the species richness map of our occurrence dataset stratified by botanical country (WGSRPD level 3). The resolution gain is clear. Moreover, some biases in the initial observations set explain I H patterns. Colombia orchid richness, estimated for instance at 4,327 species according to World Plants [START_REF] Hassler | World Plants. Synonymic Checklist and Distribution of the World Flora[END_REF], is for instance under-represented within our occurrence set with only 1,375 species. Global orchid diversity patterns can also be appreciated in relation to the three following maps, which reflect the extinction risk of the predicted species assemblages.

High proportions of threatened species appear in East Africa, South and Southeast Asia on Figure 4.2b I THREAT . The Sahel also has a particularly high proportion of threatened species. Orchids in central North America also appear to have relatively high rates of threatened species, given the low observed and predicted diversity in this region. The threat levels in the Amazon Basin are high. However, compared to East Africa or tropical Asia, they are not as high as the region's impressive orchid richness would suggest. This result is quantified on the scatter plot Figure 4.3. High diversity does not necessarily imply high threat levels.

On Figure 4.1c map (proportion of CR species), the first striking element is certainly the strong emphasis on Madagascar. The patterns in the Himalayan belt, Indonesia and Southeast Asia are both more contrasted and appear more localised than on the I THREAT (b) map. In northern Mexico and the southwestern United States of America, high levels of CR species are appealing and contrasting with the Shannon index. In South America, our model predicts relatively high levels of CR species along the Andes, in Bolivia, Paraguay and southern Brazil. If we compare I CR with I IUCN CR (see website), we can see that the presence of CR species in South America is almost entirely due to predictions whose IUCN status has been automatically classified.

Finally, I EN levels (Fig. 4.2d) are important throughout sub-Saharan Africa, Central and South America, South and Southeast Asia. The patterns observed here are closer to I THREAT than I CR . With these maps we can better understand how the patterns of I CR , I EN and I V U indicators combine to produce the I THREAT map. In Table 4.2, the top three botanical countries with the highest average proportion of threatened species, species classified as CR and species classified as EN are common: Réunion Island, Madagascar and Mauritius Island. Overall, 60% of the species predicted for Madagascar are threatened with extinction. All µ[I THREAT ] top fifteen countries have an overall predicted proportion of threatened species greater than or equal to 40%. Again, the three columns are dominated by East African and tropical Asian countries. See supplementary file T3 for the full table. The scatterplot Figure 4.3 tests the relation between the average rate of threatened species and the Shannon index at the level of botanical countries. The Spearman ρ value is 0.29 (p = 2.5e-7), indicating a positive but relatively law global correlation. The colour code, indexed by continent, reveals different patterns per continent. North American (brown) and European (pink) countries are clearly clustered on the graph, with a medium diversity index and low threat levels on average. The top fifteen µ[I THREAT ] countries (Table 4.2 first column) are this time marked with red borders. The top fifteen pattern following the Barisan Mountains. By construction, a similar trend is drawn on the (d) map representing I THREAT . Such a difference between I CR and I IUCN CR at the regional scale confirms the need to include automatic IUCN assessments when designing extinction risk indicators. Finally, I VU on Fig. 4.2e map indicates the likely presence of VU species inhabiting the lower elevations of the islands.

Country-level analysis

Protected areas cover 12.7% of the island of Sumatra. Three national parks on the spine of the Barisan Mountains were inscribed on UNESCO's World Heritage List in 2004, forming the Tropical Rainforest Heritage of Sumatra. They are the three largest protected areas on the island. From north to south: Gunung Leuser National Park, Kerinci Seblat National Park and Bukit Barisan Selatan National Park. Since 2011, these parks have been placed on a Danger List to help combat numerous threats, including poaching, illegal logging and agricultural encroachment.

Let's look at the zonal statistics for PAs. We calculate the ratio of two indicators, both averaged across PAs: i) the proportion of all CR species (known IUCN status + predicted status combined) and ii) the proportion of IUCN-assessed CR species:

µ[I CR ] µ[I IUCN CR
] (PAs) = 3.1. This ratio is even greater when all threatened species are considered together:

µ[I THREAT ] µ[I IUCN
THREAT ] (PAs) = 7.1 The level of threat in Sumatra's PAs is then significantly higher than the IUCN information alone would suggest. Now let's compare the average CR proportion inside versus outside PAs: µ[I CR ](PAs) = 0.108 and µ[I CR ](PAs) = 0.036. Thus the average proportion of CR species is 3 times higher in PAs than outside PAs. The current design of PAs therefore seems to well match habitats hosting particularly threatened orchids. However, looking closely at the map reveals that many areas with a specially high proportion of CR species are still outside PAs, so that the ratio could be consistently improved. With IUCN-assessed species only, the average proportion of CR species in PAs is 3.4%. It is similar to the proportion of CR species outside PAs with the completed Red List. Again, enriching the current IUCN information within our method changes the narrative on PA efficiency.

Discussion

Modelling choices

Our species assemblage predictor has theoretical guarantees that we have validated on a previously unseen observation set (see Box C). However, some bias in the input data could prejudice its predictions. Unlike some methods, it has the advantage of not being biased by the heterogeneous sampling effort. Indeed, it depends only on the conditional probability P X,Y (Y = k|X = x) and not on the marginal distribution P X . Nonetheless, it is impacted by species detection bias, i.e. by the fact that some species might be observed more than others conditionally to a given x. Largely under-observed species, in particular, may be excluded from the predicted assemblage. Conversely, some over-observed species could be predicted at locations where they are not present. In future work, it would be interesting to study the impact of this type of bias on the assemblage-level indicators introduced in this paper.

When calibrating the species assemblage model, the choice of average error rate translates into a trade-off between model generalisation and over-prediction. Indeed, imposing a lower error rate results in a lower probability threshold and larger predicted assemblages. But are the newly retained species likely to be present, or are they unreasonably predicted? This is a difficult question of model calibration, which we believe deserves more attention in future studies.

Over the validation set, an error is defined as the absence of the true label within the returned species assemblage. What is effectively measured is the recall of the model, i.e. the proportion of relevant species that are successfully retained. In contrast, precision, i.e. the proportion of retained species that are relevant to the test point, is not directly measured (and could not be without absence data). However, precision is a positive function of the conditional probability threshold. Therefore, by maximising the threshold for a given target error rate, we also maximise precision. Finally, a recent study confirms that as long as models are flexible enough and well fine-tuned to avoid overfitting, they make coherent predictions on spatially separated test data [START_REF] Valavi | Flexible species distribution modelling methods perform well on spatially separated testing data[END_REF].

Considerations on covariates

Nature's myriad of elements are interfaced to produce heterogeneous patterns of diversity, unpredictable at a given point, but statistically structured. Measuring some of these factors and feeding them into our model will hopefully allow us to capture biodiversity shapes. However, it is essential to remember that no single mechanism fully explains a given pattern, that inter-scale dependencies and local historical events strongly influence biodiversity, and that no pattern is exempt from variation and exceptions [START_REF] Gaston | How large is a species' geographic range?[END_REF]. Other ecological variables contain valuable information influencing the distribution of orchids. They have not been included because of the currently limited spatial and taxonomic coverage or for practical reasons. Remote sensing is a natural perspective for improvement [START_REF] Gillespie | An image is worth a thousand species: combining neural networks, citizen science, and remote sensing to map biodiversity[END_REF][START_REF] He | Will remote sensing shape the next generation of species distribution models?[END_REF]. The inclusion of biological and functional traits of orchids is another exciting perspective [START_REF] Bourhis | Explainable neural networks for trait-based multispecies distribution modelling-A case study with butterflies and moths[END_REF][START_REF] Puglielli | Macroecology of plant diversity across spatial scales[END_REF][START_REF] Weigelt | GIFT -A Global Inventory of Floras and Traits for macroecology and biogeography[END_REF], as well as mycorrhizal fungi or pollinator distribution [START_REF] Mccormick | Mycorrhizal fungi affect orchid distribution and population dynamics[END_REF].

We believe that predictors of large spatial patterns may play a significant role in the regional diversity of orchids, and that the computer vision model can learn such information. The model's strength is to rely on the best possible input set and exploit complex interactions in order to be as predictive as possible. The trade-off is interpretability, but the AI community is investing heavily in this area and our understanding is getting finer [START_REF] Linardatos | Explainable AI: A Review of Machine Learning Interpretability Methods[END_REF]. For example, deep-SDMs have been shown to construct a feature space with structured functional traits and bioclimatic preferences, even though only remote sensing data were provided [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF].

Our indicators originality

One of the main strengths and originality of our indicators is their scalability. An analysis can start at the country level with zonal statistics before delving deep into regional patterns thanks to the interactive maps online, see the Figure 4.5 for an overview of available tools. For example, India ranks fourth in terms of its average proportion of CR species (Table 4.2 last column). Looking at the I CR indicator, the Western Ghats and eastern India appear to be the main hosts of CR species. Finally, the interactive map allows you to zoom in on patterns, explore and look for terrain correspondence with the base maps. The case study of Sumatra also shows that mountainous regions can host particularly high proportions of CR species. One of the main shortcomings of our indicators is their lack of transparency. A first direct perspective for improvement is to return, for a given point, the names and IUCN status of the species assemblage. However, this is a technical challenge given the global support size of 221M points. Another drawback is the interpretability of deep-SDMs. Feature importance experiments would provide a sense of which features the model relies on most. Again, this is a very active area of research and future work will complement this point [START_REF] Ryo | Explainable artificial intelligence enhances the ecological interpretability of black-box species distribution models[END_REF].

Orchids have specific characteristics that make them valuable indicators of ecosystem health [START_REF] Newman | Orchids as Indicators of Ecosystem Health in Urban Bushland Fragments[END_REF]. They are sensitive to climate change and environmental disturbances [START_REF] Kull | A comparative analysis of decline in the distribution ranges of orchid species in Estonia and the United Kingdom[END_REF], and their interactions with pollinators and mycorrhizal associations contribute to ecosystem functioning [START_REF] Swarts | Terrestrial orchid conservation in the age of extinction[END_REF]. In addition, orchids are easy to monitor in the sense that once a population has been established, it is easy to find it every year. Therefore, as defined by (Jørgensen et al., 2016), orchids can be considered as suitable ecological indicators of ecosystem health. The family is i) easy to monitor, ii) sensitive to small-scale environmental changes, whose response can be quantified and predicted, and iii) globally dispersed. They also are umbrella species and their local disappearance may be an early warning of environmental disturbance [START_REF] Gale | Orchid conservation: bridging the gap between science and practice[END_REF]. However, they don't encompass all aspects of ecosystem biodiversity. While orchids can be used as surrogate species for biodiversity planning, they can't fully represent overall ecosystem health. Taking these elements into account, orchid-based indicators such as I O and I c can be considered to have a wider scope than just qualifying their family, but also a degree of habitat quality. Nonetheless, we do not pretend to be able to fully capture ecosystem health through a single family of indicators. In practice, achieving this goal would require a large number of indicators and measurements. Comparisons with established indicators are provided in Box E.

Orchids conservation

Spatial indicators can be used to identify priority areas and support the design of PAs [START_REF] Almpanidou | Combining a cumulative risk index and species distribution data to identify priority areas for marine biodiversity conservation in the Black Sea[END_REF]. An intuitive method is to select the k-highest percentiles of the indicator as hotspots. In Sumatra, the creation of corridors extending PAs along the Barisan Mountains seems a natural improvement to conserve CR species. While this approach is easy to understand, there is a risk that some aspects of biodiversity will be missed by the indicator and left unprotected [START_REF] Orme | Global hotspots of species richness are not congruent with endemism or threat[END_REF]. It is fair to ask: if the current PAs preserve key aspects of biodiversity and are representative of the other areas identified as most at risk, where is the next priority? The combination of complementary indicators is the key to designing effective PAs with a limited budget [START_REF] Silvestro | Improving biodiversity protection through artificial intelligence[END_REF].

Manual extinction risk assessments should be carried out extensively in the tropics and on islands. Indeed, it is well known that the tropics are poorly assessed, although they host most of the world's biodiversity [START_REF] Collen | The Tropical Biodiversity Data Gap: Addressing Disparity in Global Monitoring[END_REF]. The orchid family follows the same trend. Automated assessment methods will continue to improve, hand in hand with the quality of IUCN assessments in terms of taxonomic coverage, geographical extent and consistency. Finally, special attention must be paid to the assessment and protection of islands: all our indicators point to them as hosts of particularly threatened species assemblages.

Conclusions

Based on deep-SDMs architectures, we have developed global indicators that qualify the extinction risk of species assemblages at an unprecedented kilometre resolution. This allows multiscale analysis from global patterns down to country statistics or landscape discrepancies. The indicators are available as interactive maps online. Although our results show how our novel indicators can be successfully employed, working closely with decision-makers would ultimately allow for more effective guidance of conservation actions [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF]. To enable efficient technology transfer, interdisciplinary studies between computer science and conservation science need dialogue with conservation practitioners [START_REF] Gale | Orchid conservation: bridging the gap between science and practice[END_REF]. This chapter is under review for the Predictive Biogeography special issue of Ecography.

Introduction

and should be set together to allow parallel progress and avoid contradictions [START_REF] Díaz | Set ambitious goals for biodiversity and sustainability[END_REF]. Quantifying the acceleration of extinction risk due to climate change appears to be a top priority in this context [START_REF] Mace | Aiming higher to bend the curve of biodiversity loss[END_REF].

Extinction risk and climate change. The increase in extinction risk due to climate change is an active area of research [START_REF] Carpenter | One-Third of Reef-Building Corals Face Elevated Extinction Risk from Climate Change and Local Impacts[END_REF][START_REF] Maclean | Recent ecological responses to climate change support predictions of high extinction risk[END_REF][START_REF] Malcolm | Global Warming and Extinctions of Endemic Species from Biodiversity Hotspots[END_REF][START_REF] Thomas | Extinction risk from climate change[END_REF], see the state of the art section 2.4.3. A common practice is to use Species Distribution Models (SDMs) to first learn species' environmental preferences and then project the learned relationship into future climates [START_REF] Guisan | Predicting species distribution: offering more than simple habitat models[END_REF]. Species are then predicted to become extinct if their potential habitat is reduced below minimal thresholds. Habitat loss rates can also be compared to the official extinction risk criteria of the IUCN [START_REF] Mace | Quantification of Extinction Risk: IUCN's System for Classifying Threatened Species[END_REF][START_REF] Moat | Least concern to endangered: Applying climate change projections profoundly influences the extinction risk assessment for wild Arabica coffee[END_REF]. While this approach is largely dominant, other ways of estimating extinction risk include using process-based models of physiology or demography, or relying on species-area relationships and expert opinion, as presented in this meta-study [START_REF] Urban | Accelerating extinction risk from climate change[END_REF]. Their literature review concludes that under Representative Concentration Pathway 8.5 (RCP 8.5), one in six species will be at risk of extinction due to climate change.

The IUCN Red list of Threatened Species. As a reminder, the IUCN Red List of Threatened Species (RL) is the reference classification scheme for the extinction risk of species (see Section 2.2.1.1). The risk assessment is uniform for all living organisms (except micro-organisms, [START_REF] Bland | Guidelines for the application of IUCN Red List of Ecosystems Categories and Criteria, version 1.1[END_REF]. It is a strength in terms of coherence and visibility. The Red List is the basis for biodiversity indicators used in international agreements. It allows monitoring of Parties' commitment to conservation. Starting with least concern (LC) and near threatened (NT), the threat categories are ordered by increasing risk of extinction. Threatened species are either vulnerable (VU), endangered (EN) or critically endangered (CR) before possibly becoming extinct (EXT).

IUCN status classification. Manual assessment of extinction risk cannot keep up with the current levels of threats, so species are disappearing before they have been assessed or even discovered (Pimm & Joppa, 2015). As of 2022, only 15% of the world's known plant species have an IUCN status1 . Research has responded to this massive concern by developing compensatory automated assessment methods (Stévart et al., 2019). Such methods are designed to provide preliminary extinction risk categories and focus manual effort where it is urgently needed [START_REF] Bachman | Rapid Least Concern: towards automating Red List assessments[END_REF]. Methods can either estimate IUCN variables to be compared with the official criteria thresholds (index-based methods, see Section 2.3.1.5 for a review) or directly learn a correspondence between species features and IUCN status (prediction-based methods, see Section 2.4.2), [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. Classifiers such as the Random Forest (RF) algorithm and ensemble methods show high performance in differentiating threatened species within this active research area (Borgelt et al., 2022a;[START_REF] Pelletier | Predicting plant conservation priorities on a global scale[END_REF]. Species distribution modelling can inform IUCN assessments by estimating IUCN range variables (as recommended in the Guidelines, index-based methods). Alternatively, SDMs and habitat modelling can be used to test new predictive methods of IUCN categories [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF][START_REF] Brooks | Measuring Terrestrial Area of Habitat (AOH) and Its Utility for the IUCN Red List[END_REF]. The latter authors concluded that SDM-based niche size estimates provide valuable complementary information to range size in assessing species extinction risk, but are not a good proxy for extent of occurrence (EOO) or area of occupancy (AOO).

Other approaches therefore need to be explored.

Contributions.

Our main contribution is a novel method for extracting species traits predictive of IUCN extinction risk status, which allows modelling and testing the impact of bioclimatic projections. Based on a deep species distribution model, it achieves stateof-the-art classification performance while allowing to explore climate change scenarios and test how status distributions might evolve. Thanks to this approach, we proceed by analysing how threatened species would be distributed across continents, latitudes and altitudes under RCP 8.5 and two extreme dispersal scenarios. While the number of threatened species is projected to increase globally, some areas will be particularly affected: Africa, Asia, South America, latitudes around both Tropics and the Equator, and finally the lowlands and intermediate altitudes between 800 and 1500m.

Background information

CMIP6 SSP5-8.5 scenario and climate models. Scenarios that project socioeconomic behaviours called Shared Socioeconomic Pathways (SSP) and corresponding emissions rates Representative Concentration Pathways (RCP) into the future are necessary to model future climate alternatives. Developed in 2011, RCPs are a set of four main scenarios that are intended to span the range of plausible outcomes until 2100 ( [START_REF] Van Vuuren | The representative concentration pathways: an overview[END_REF]. RCP 8.5 is the scenario with the highest assumed fossil fuel use, but also the best match to our current emissions levels and stated policies [START_REF] Schwalm | RCP8.5 tracks cumulative CO2 emissions[END_REF]. A wide range of climate models coexist within the Coupled Model Intercomparison Project Phase 6 (CMIP6). Fortunately, tools are available to assist modellers in selecting the most appropriate model for their application in terms of region and season [START_REF] Parding | GCMeval -An interactive tool for evaluation and selection of climate model ensembles[END_REF]. Scenario planning provides a framework for developing more resilient biodiversity models, and hence conservation policies, in the face of inherent future uncertainty [START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF][START_REF] Peterson | Scenario planning: a tool for conservation in an uncertain world[END_REF].

Species distribution models. SDMs are statistical tools interlinking terrain observations with predictive variables (Elith & Leathwick, 2009). Observations can include opportunistic and/or field surveys presence and absence data, abundances, herbarium collections. Predictive features can be considered on a panel from those directly involved in species presence to those thought to have a loose influence on species preferences, or in other words from proximal to distal predictors [START_REF] Austin | Spatial prediction of species distribution: an interface between ecological theory and statistical modelling[END_REF]. They are classified according to their function: limiting factors (e.g. elevation), disturbances (e.g. competition) and resources (e.g. solar radiation) [START_REF] Guisan | Predicting species distribution: offering more than simple habitat models[END_REF].

Modelling species distributions involves strong assumptions and limitations. First, species are assumed to be in equilibrium with their environment when learning their potential niche and to remain so in the future [START_REF] Araújo | Equilibrium of species' distributions with climate[END_REF]. However, training data can be misleading if species have been observed outside their natural niche, e.g. due to extreme climatic events or mismatches in the predictive data alignment. In addition, species' resilience to climate change, genetic adaptation, competition or pollinator dependence, among other factors, could cause species to thrive under unexpected conditions or, conversely, to disappear from their current environmental niche. Second, data on dispersal capacity and proximal features are often lacking. Other considerations may militate against the use of SDMs to estimate extinction risk, such as approximations to IUCN criteria, inappropriate spatial modelling scale or variable selection [START_REF] Akçakaya | Use and misuse of the IUCN Red List Criteria in projecting climate change impacts on biodiversity: IUCN RED LIST AND CLIMATE CHANGE IMPACTS[END_REF][START_REF] Fourcade | Paintings predict the distribution of species, or the challenge of selecting environmental predictors and evaluation statistics[END_REF]. Nevertheless, it should not be forgotten that i) the design of SDM is rapidly evolving to mitigate acknowledged biases and limitations [START_REF] Rocchini | A quixotic view of spatial bias in modelling the distribution of species and their diversity[END_REF][START_REF] Valavi | Predictive performance of presence-only species distribution models: a benchmark study with reproducible code[END_REF], ii) the generalisation of biodiversity knowledge through species distribution modelling is already at the origin of notable successes [START_REF] Elith | A statistical explanation of MaxEnt for ecologists: Statistical explanation of MaxEnt[END_REF][START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF], and iii) the urgency of raising general awareness and convincing decision-makers to embrace transformative change let us short of other options than working diligently with imperfect but demonstrative tools inherited from decades of research (IPBES, 2019).

Deep-SDM introduction. Building on its many successes in computer vision over the last decade, deep learning is now being applied to ecology to tackle complex tasks [START_REF] Lamba | Deep learning for environmental conservation[END_REF]. The explosion of biodiversity data, resulting from both new techniques (citizen data science, remote sensing) and efforts to pool freely available data such as the GBIF or the World Checklist of Vascular Plants (WCSP), also requires adapted frameworks that the deep learning (DL) community can provide [START_REF] Borowiec | Deep learning as a tool for ecology and evolution[END_REF]. SDM based on DL techniques, in particular Convolutional Neural Networks (CNNs) for spatial patterns, allow to learn complex relationships between species and their environment (Botella et al., 2018a;[START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. Providing deep-SDMs with access to both spatial and temporal contexts of species observations proved to be particularly valuable for shaping rare species distributions [START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF][START_REF] Estopinan | Deep Species Distribution Modeling From Sentinel-2 Image Time-Series: A Global Scale Analysis on the Orchid Family[END_REF]. Finally, research to extend the predictive power of DL and to overcome challenging problems such as class imbalance, model interpretability, multimodality fusion or label noise directly benefits applications in ecology [START_REF] Benedetti | M^3\textFusion$: A Deep Learning Architecture for Multiscale Multimodal Multitemporal Satellite Data Fusion[END_REF][START_REF] Cao | Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss[END_REF][START_REF] Dosovitskiy | An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale[END_REF][START_REF] Rolnick | Deep learning is robust to massive label noise[END_REF][START_REF] Ryo | Explainable artificial intelligence enhances the ecological interpretability of black-box species distribution models[END_REF].

Materials and methods

Method motivation

Current extinction risk assessments of vascular plants mostly rely on their geographic distribution with IUCN's B criterion and the EOO/AOO measures. As a result, the geolocation of observations takes up a central position in species subsequent IUCN category. This affects automated methods that logically obtain the geographic information to be the best predictor of species extinction risk. However, over-relying on species observation locations prevents exploring future scenarios to project species distribution shifts and forecast likely trends in species extinction risks. Using an alternative IUCN criterion is often impossible because of data scarcity. For instance, the application of criterion A measuring reductions of population size over time is hampered by the lack of repeated assessments and knowledge of species generation length. A sensitive response is then to model future species distribution, retain most likely species presence according to a validated selection strategy and apply EOO/AOO thresholds. Yet, changes in SDM-predicted range size were found to be a poor surrogate for species EOO and AOO [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF]. Further research is therefore needed to determine if and how spatial predictions of SDMs can be used to adequately complement current IUCN assessments.

In response of this limitations, our goal is to extract species classification features with high generalisation capabilities in space and time. To this end, we use a deep-SDM to reduce the dimension and capture critical environmental information that correlates with species observations. The successive convolutional filters and pooling layers greatly reduced the input dimension, with the aim of capturing and preserving characteristic patterns. The resulting N -dimensional space is hereafter called the feature space. A fundamental assumption in our method is that these features are not only informative about the species likely to be present conditionally on an observation, but also informative about the species' environmental and spatial niche.

Data on the Orchidaceae family

Species observations

Orchid observations have been filtered from GBIF in [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF] thanks to the R package CoordinateCleaner. [START_REF] Zizka | CoordinateCleaner: Standardized cleaning of occurrence records from biological collection databases[END_REF]. The global dataset contains 999,258 occurrences of 14,129 species. It is highly unbalanced: a few common species have thousands of observations, while most orchids are represented by a few opportunistic samples. The average number of occurrences per species is 70, while the median is 4. Only a quarter of the species have more than 13 occurrences. The oldest occurrences date back to 1901, but three quarters were observed after 1982 (and half after 1997). Metadata on the orchid observation dataset are provided in the Box F.

IUCN Red List status

In July 2023, there are 1,970 orchid species assessed on the Red List, or 6.3% of the estimated 31,000 species of this uniquely diverse family (KEW, 2023). When we checked our orchid observations against the Red List as of December 2021, we found 889 species that had already been assessed. Figure 5.2A shows the distribution of status. These species will be our reference for training our IUCN extinction risk classifier and evaluating its performance. While the binary status distribution (threatened or not) is balanced, LC and EN species are largely dominant at the status level. Together, they represent more than two-thirds of the species assessed by IUCN.

Predictive features

Our predictive features include only global rasters at kilometre resolution. This makes the method easily transferable to other taxa. Large spatial contexts (64 x 64 km tensors) centred on each observation are provided to the model. The available predictors are 5.2. Materials and methods bioclimatic variables from WorldClim2 variables, Soilgrids pedological variables, human footprint rasters, terrestrial ecoregions of the world and the observation location (see Box G for details, input examples Fig. S9 and full list of predictors Tab. S2). No variable selection step was performed as deep convolutional neural networks do not overfit their predictive features under the right settings [START_REF] Poggio | Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review[END_REF]. Within the CMIP6 SSP5-8.5 future scenario, the 19 WorldClim2 bioclimatic variables (averages from 1970-2000) are replaced by the corresponding projections from the EC-Earth3-Veg climate model [START_REF] Döscher | The EC-Earth3 Earth system model for the Coupled Model Intercomparison Project 6[END_REF]. Four time periods are considered: 2021-2040, 2041-2060, 2061-2080 and 2081-2100. More details can be found in the subsection 5.2.3.5.

Method definition

Deep species distribution modelling

The first step consists in using a trained deep-SDM to encode the high-dimensional predictive data around each species occurrence into a reduced feature space (Figure 5.1

Step 1). The model used is an Inception v3 convolutional neural network [START_REF] Szegedy | Inceptionv4, Inception-ResNet and the Impact of Residual Connections on Learning[END_REF]. The data set was divided into training/validation/test sets with spatial blocks of 0.025 degrees in the spherical coordinate system. The 90/5/5% block allocation was further stratified by region to optimise the diversity of the sets. At the occurrence level this results in a set distribution of 902,174 / 46,290 / 50,794. At the species level this leads to a distribution of 14,129 / 4,037 / 4,166. Training was performed on two V100 GPUs from the Jean Zay supercomputer. The model is trained with the LDAM loss, a modified cross-entropy function that gives more weight to rare species during training [START_REF] Cao | Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss[END_REF]. Training on 70 epochs took 42 hours with a batch size of 128 and an initial learning rate of 0.01. Model performance is evaluated every two epochs. The final test set performance is reported for the best validation epoch. Finally, the deep-SDM is retrained on the entire dataset for the best validation epoch prior to feature extraction. Inception v3's multiple convolution and pooling layers allow the input information to be reduced to 2048 dimensions in the original version of the network. However, 2048 dimensions is still too many to perform classification on a few hundred samples. To reduce the feature dimensionality, the Fully Connected (FC) layer with dimensions (2048, #labels) before the final softmax layer of the model was replaced by two layers F C 1 = (2048, N ), F C 2 = (N, #labels), creating a dimensional bottleneck. ReLU activations are also appended after each FC. Finally, the feature associated with an observation o is the N -dimensional test activation extracted after F C 1 and noted as f(o).

Deep-SDM validation. For a given observation, top-k accuracy assesses whether the model returns the true label among the k most likely species. Success rates can then be calculated for all classes together (micro-average) or first by class and then averaged together (macro-average). This means that the micro-average is more representative of performance on common species, whereas the macro-average is a better representation of performance on rare species. Validation performance has plateaued since epoch 66, i.e. after the LDAM loss reweighting scheme in epoch 65. The micro-average top-30 accuracy stabilises around 0.82 and the macro-average top-30 accuracy stabilises around 0.42, with the same performance on the test set. The final deep-SDM is then retrained on the full dataset for 70 epochs.

Dispersal scenarios

As a reminder, a fundamental assumption when inferring species distributions with an SDM is that species maintain the same environmental niche [START_REF] Bailey | Assessing effects of forecasted climate change on the diversity and distribution of European higher plants for 2050[END_REF]. The assumption that species have unlimited dispersal capacity leads to species niches shifting with climate change. In practice, however, species have specific and limited dispersal capacities that prevent them from following climate change [START_REF] Schloss | Dispersal will limit ability of mammals to track climate change in the Western Hemisphere[END_REF]. As data on plant dispersal capacity is extremely scarce, we worked with two extreme scenarios and assumed that the truth lies in between [START_REF] Thomas | Extinction risk from climate change[END_REF][START_REF] Urban | Accelerating extinction risk from climate change[END_REF]:

• No dispersal. Species can only be re-predicted by the deep-SDM at locations of true observations. By construction, this results in species potential presences (support points) prior to SDM inference that can only be fewer in number than in the present.

• Unlimited dispersal. Species can now be predicted at every location in the dataset (999,258 occurrences). In fact, the dataset is considered large enough to be used as an approximation of every possible location an orchid species could occupy.

In both dispersal scenarios, the relative probabilities of presence P(Y |X) returned by the SDM are thresholded to retain only the most likely species predictions (this is traduced by the indicator function in Equation 5.2). The threshold λ was optimised in section 4.2.3 to return precautionary species assemblages. More specifically, the value was set on a calibration set to allow only a 3% error in assessing whether the true label was retained in the assemblage -while keeping the threshold as high as possible. Then the model recall is optimised, which corresponds to the conformal prediction setting [START_REF] Fontana | Conformal prediction: A unified review of theory and new challenges[END_REF]. As the threshold has been optimised to return likely overestimated but precautionary species assemblages, our estimates can be considered as lower bounds on species extinction risk. Finally, species are classified as extinct if they are not predicted to occur at any point. Only the no dispersal scenario leads to this case. A species that is predicted to become extinct in a given time period cannot return to any other status thereafter.

Species niche features for IUCN classifcation

We need an information at the species level to feed an extinction risk classifier (Figure 5.1

Step 3). However, SDMs successively process environmental data at the level of an observation (Figure 5.1 Step 1) before returning the most likely species in these conditions. This is why we need to aggregate the information initially at observation level to species level. To do so, we use summary statistics on vectors from the model's feature space (Figure 5.1 Step 2) corresponding to a set of support points: known points in the present or future potential presences. In a future scenario, the choice of support points to aggregate features at the species level depends on species assumed dispersal capacities.

We now describe in more details the two first steps of our method for extracting species features. The item numbers are matching the steps of Figure 5.1. Step 1 consists in associating a given set of support points (true observations or dispersal scenario) with environmental covariates using deep-SDM inference. Sites where the species has been observed and is predicted to remain are indicated by 'x', abandoned sites by 'o' and new predicted sites by 'X'. Species niches are indicated by dashed circles. In Step 2, the predicted features are summarised by taking their mean, standard deviation and sum, and the result is concatenated. This operation allows the information that was at the point level to be condensed to the species level. Finally, the Step 3 is the mapping between the species summary feature and its conservation status.

Materials and methods

Deep-SDM

After training and validation in the present with real observations (see Results), the random forest classifier is trained within dispersal scenarios to ensure coherence with future projections. Classification can be either binary, as shown, or at the IUCN status level.

1 Identification of the support points of the species and deep-SDM inference. At present, it is the species known sightings for model evaluation and status inference. In the future, the set of support points depends on the dispersal hypothesis made as detailed in section 5.2.3.2. Assuming no dispersal, the set of support points of a given species only includes the geolocations where the species has already been observed. Assuming conversely unlimited dispersal, the set of support points for a species is approximated by the 1M geolocations encompassed in our orchid observation dataset. Another possibility would have been to exploit a global regular grid as support points. However, we preferred to use the proxy of all the locations covered in our orchid dataset to limit computation resources. The deep-SDM was trained beforehand and evaluated with true occurrences and present covariates as described in section 5.2.3.1.

2 Calculation of summary statistics on the resulting features. Weighted mean, standard deviation and sum are computed over the features, along the N dimensions.

The final species feature is the concatenation of the three statistics above (dimension 3N ). Different summary statistics were evaluated. This concatenation led to the best results and will be further discussed in the final section. In addition, different weighting schemes for support points were considered when using a dispersal scenario. First, only points where the given species is predicted to be present with a minimum relative probability are retained, as explained in section 5.2.3.2. Second, among the retained points, their contribution is weighted according to the prediction rank of the target species. Indeed, a first implementation was to weight the contribution of the retained support points by the relative probability of presence of the target species. However, this strategy was not efficient to differentiate the support point contribution according to the most likely species. This is due to the deep-SDM calibration. The model was trained with presence-only observations and, as a result, the distribution of species relative probabilities has low dynamic. Therefore, for a given species, we preferred to weight the contribution of its support points with the inverse of its rank when ordering the most likely species conditional on the observation (see Equation 5.2).

Let K s,t be the set of support points of a species s for the time period t that depends on the dispersal scenario considered (see Section 5.2.3.2). Based on the outputs of the deep-SDM at all points in K s,t , we construct an aggregated feature vector h s,t to be used as input of the final species status classifier:

h s,t = Stats k∈Ks,t [w k .f(k)] (5.1) with:
• Stats = [avg ∥ std ∥ sum], ∥ being the concatenation operator • f(k) the N -dimensional feature vector associated to the environmental covariates x(k) through the deep-SDM. • w k the weight attributed to support point k. The higher the weight, the more likely the species is present at this support point. w k expression depends on the species support points. We denote rank[k s,t ] the position of species s within the ordered list of the most likely species returned by the deep-SDM at the point k and time period t.

w k = 1 if true observations are used 1 P [Y =s|X=x(ks,t)]≥λ • 1 rank[ks,t]
within a dispersal scenario (5.2)

Classifying extinction risk status from species niche features

The final step of our method is to classify the extinction risk status of species from their aggregated feature vector h s,t :

3 Extinction risk classification. Therefore, a random forest classifier is trained using official IUCN status and the present occurrences of the species as support points. In the present, it is then used in inference to determine the preliminary extinction risk status of unassessed species using their observations as support 5.2. Materials and methods points. To be coherent with the future dispersal scenario and for the calibration of the extinction risk classifier, the reference classifier used to predict future IUCN status is also retrained in the present with the same dispersal scenario (either null or unlimited). Otherwise, a classifier that is i) trained with species features computed using true observations as support points, and ii) used to predict the future IUCN categories associated with species features aggregated from unlimited dispersal support points, will result in iii) severely underestimated extinction risk levels. Finally, two levels of classification are considered: one at the binary level (threatened or not, as shown in the scheme) and another at the IUCN status level.

Other classifiers were also considered before selecting the random forest: a shallow multilayer perceptron, a multinomial log-linear regression and linear classifiers with Stochastic Gradient Descent (SGD) training. Performance was evaluated using a 10-fold crossvalidation strategy on the 889 species assessed by IUCN. The best classifier, the random forest, was then compared with the state-of-the-art IUCNN extinction risk classifier [START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF] at both binary and status levels (see model valiation Section 5.2.4).

Once the relationship between species features and extinction risk status has been learned for the 889 IUCN-assessed species, risk status can be predicted for the remaining 13,240 species in the dataset.

Projections within the CMIP6 SSP5-8.5 scenario

Climate model choice. The choice of climate model was made using the GCMeval tool [START_REF] Parding | GCMeval -An interactive tool for evaluation and selection of climate model ensembles[END_REF]. The focus region was set to global and the skill assessment weights were left at their default values (equal importance given to temperature and precipitation, idem for all seasons and skill scores). Finally, the emission scenario was set to SSP5-8.5 and only climate models whose projections were available for download at i) 30 seconds spatial resolution, ii) for all time periods and iii) for the 19 bioclimatic variables on https://www.worldclim.org/ were considered. This led to the adoption of the EC-Earth3-Veg system model projections [START_REF] Döscher | The EC-Earth3 Earth system model for the Coupled Model Intercomparison Project 6[END_REF].

Levels of analysis over time: Continents, latitude and altitude. In addition to the temporal dimension, the predicted status distributions are crossed with three other variables. One is categorical in the inhabited continents and two are continuous in the species mean latitude and mean altitude. Inhabited continents were obtained by spatially intersecting occurrences with WGSRPD level 3 zones. A given species may span several continents. Mean latitude was calculated directly from the observation coordinates.

Finally, elevation values were obtained from a global raster with 15 arc-second spatial resolution downloaded by tile at http://www.viewfinderpanoramas.org/ and processed using GDAL command lines. The predictions of extinction risk are identical to the three facets of the analysis. The only difference is in the presentation of the results. In practice, it is the variable used to group species that varies from one representation to another. Status (macro-average) Classification performance comparison between the state-of-the-art IUCNN method and ours [START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. The 10-fold cross-validation results in an accuracy distribution represented by boxplots. The first row shows the binary classification and the second row the status classification. Micro-and macro-average accuracies are identical, as the binary status distribution is balanced. The IUCNN method achieves an average accuracy of 0.81 for binary classification and our deep SDM method achieves 0.78. However, for status classification, our method gives a micro-average accuracy of 0.61 and a macro-average accuracy of 0.43 and the IUCNN method 0.60 and 0.41 respectively.

Model validation

Classification performance and comparison with the state-of-the-art IUCNN method are shown in Figure 5.2B [START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. While each method has a slight advantage in either binary or status classification, their performances are close enough to consider the deep SDM-based method as competitive with the state-of-the-art method. In addition, deep-SDM confusion matrices for the two classification levels are provided Fig. S10.

Results

We analyse the global dynamics of orchid IUCN status distribution over time and in function of three aspects: continents, latitude and altitude. In the figures below: i) the results from the two dispersal scenarios are averaged to provide synthetic trends (Figure 5.3 represents their difference with error bars) ii) all species are considered to be aiming at broad conclusions at the family level (i.e.

both those already assessed by the IUCN and those that are not) iii) binary statuses are reported as their prediction is more robust.

Results

The same analysis, restricted to species assessed by the IUCN, is presented in Figures S12-S14. Comparing these gives a sense of the generalising power of our approach. The global trend in Figure 5.3 shows an increasing proportion of threatened species across all continents. Individual patterns also appear:

Continents

• Africa and Asia-Temperate are the only two continents with a current majority of threatened orchid species.

• Five percent of African species are predicted to become extinct between 2041 and 2060 (11% of IUCN assessed species).

• In tropical Asia, threatened species become the majority by mid-century, reaching 60% by the end of the century.

• Several continents -notably Europe and North America -see their proportion of threatened species decline in the first half of the century, before recovering to overtake current levels.

• Although South America may appear relatively spared, its increase in the proportion of threatened species is significant and covers six thousand species.

On a global scale, the number of threatened species is expected to increase by an average of one third by the end of the century (14-40% rise depending on dispersal scenario). All status predictions are provided in the supplementary file ALL_species_status.csv. The .csv file is described in Box H. A smaller increase in threatened species is predicted for IUCN-assessed species, see Fig. S11. Unassessed species could therefore be expected to be at even greater risk of extinction than those already assessed.

We also predict that 234 species will become extinct, of which 42 are IUCN-listed: 111 in Africa, 96 in South America, 26 in tropical Asia and one in temperate Asia. The isolated list is also given as supplementary file EXT_species.csv and is described in Box H. A small number of species have been identified in GBIF as having very few and old occurrences. In Figure 5.4, the number of threatened species clearly peaks around the equator and in the tropics, i.e. at latitudes with high species diversity. Species going extinct are also found around the equator. Both high and low latitudes are dominated by non-threatened species.

Latitude

Altitude

Figure 5.5 crosses the number of classified species over time with their average altitude. The profile of threatened species along the altitudinal gradient appears to be stable over time. It shows a peak at low elevations and a concentration of threatened species in the 800-1500 m range. However, the number of threatened species increases at all altitudes. They outnumber non-threatened species in their peaks and also at very high elevations, about 2500 m.

Discussion

Interpretations

We now propose ecological interpretations that account for the different patterns observed.

The relative decline of threatened species by mid-century -particularly pronounced in Europe and North America -is rooted in the unlimited dispersal scenario. Indeed, in these projections, the support for species training and then potential niches can be largely overestimated, leading to lower rates of threatened species. However, this phenomenon is mitigated in the second half of the century, where we assume that bioclimatic change significantly limits species' potential niches. The large proportion of threatened species currently predicted for Africa and Asia-Temperate could be partly explained by a different accounting of LC species. Further analysis at this level is needed to test this possibility. This seems all the more relevant when considering the proportion of threatened species restricted to IUCN-assessed species in Fig. S12.

On average, considering both dispersal scenarios together, the number of threatened species is expected to increase by a third with our method (14-40% rise interval, see Figure S11). This trend may seem small compared to other studies on the extinction risk due to climate change. For example, [START_REF] Urban | Accelerating extinction risk from climate change[END_REF] concluded that under current emissions trajectories, up to one in six species could be threatened with extinction by climate change. However, the global trends we have expressed are relative, i.e. the increase in threatened species relative to current levels. In absolute terms, we predict an 11% increase in the number of all threatened species worldwide (6% if only IUCN-assessed species are considered). This is closer to the 16% absolute increase from [START_REF] Urban | Accelerating extinction risk from climate change[END_REF]. Furthermore, our method construction leads to lower bounds on extinction risk levels as already formulated. Finally, as observed in the analysis of trends by continent, the impact of climate change on species loss is predicted to be greater in the second half of the century than in the first. Similarly, [START_REF] Vuuren | The future of vascular plant diversity under four global scenarios[END_REF] predicts that the impact of climate change will become increasingly important after 2050.

Species that are already IUCN-assessed are predicted to experience a smaller increase in their threatened share than species that are not. We formulate two hypotheses for this pattern. First, plant assessment targets include a majority of species expected to be threatened [START_REF] Bachman | Progress, challenges and opportunities for Red Listing[END_REF], resulting in an overall proportion of threatened plant species of 48%. In comparison, the global estimate is only 21% (Brummitt et al., 2015). This assessment bias therefore contributes to explaining the more stable proportion of threatened species among IUCN-assessed species. Second, since the classifiers were trained on the IUCN-assessed species with current bioclimatic values, we can expect some overfitting on these species. Even if bioclimatic variables change in the future, the classifiers are also provided with static variables, which could indeed explain a higher tendency to re-predict status quo for these species.

The overall latitudinal species distribution follows, as expected, the latitudinal gradient of biodiversity [START_REF] Willig | Latitudinal Gradients of Biodiversity: Pattern, Process, Scale, and Synthesis[END_REF]. However, we found no satisfactory hypothesis to explain the trident shape of the distribution of threatened species along the latitudinal gradient. This shape is also present when only considering IUCN-assessed species, but with the highest number of threatened species peaking around the -20°parallel.

In the case of lowland species at risk, a direct assumption is that land-use change and high exposure to anthropogenic threats are at play. The hump-shaped pattern of threatened species corresponds to the diversity peak known to occur at intermediate altitudes [START_REF] Whittaker | Vegetation of the Siskiyou Mountains, Oregon and California[END_REF]. Indeed, these altitudes are known to be rich transition zones between different habitats and with specific interactions between temperature and water gradients [START_REF] Zhao | Altitudinal Pattern of Plant Species Diversity in Shennongjia Mountains, Central China[END_REF]. However, this does not explain why only threatened species follow this pattern. There may be several reasons. First, speciation rates and endemicity also peak at intermediate altitudes, thanks to an optimal combination of area and isolation for the persistence and divergence of native species according to [START_REF] Lomolino | Elevation gradients of species-density: historical and prospective views[END_REF]. This would result in species with few individuals and/or restricted geographical ranges that are likely to be threatened. Secondly, there is almost no more primary forest at low elevations, in contrast to intermediate elevations. These forests may have been orchid refuges in the past, but may now be increasingly threatened by extensive land change and climate change.

Preliminary results show that terrestrial Human Footprint appears to correlate with the predicted proportion of threatened species, see Fig. S17. This is consistent with previous work showing a strong correlation between human footprint and species extinction risk [START_REF] Marco | Changes in human footprint drive changes in species extinction risk[END_REF] This study even found anthropogenic pressure to be more predictive of extinction risk than environmental or life-history variables.

Limitations

Our method has biases and limitations, which we will acknowledge below. As mentioned previously, the threshold for species re-prediction may be too permissive. In both dispersal scenarios, this may lead to an overestimation of geographic support for learning species features. A more restrictive choice could have the effect of increasing the number of species predictions at risk -further work is indeed necessary. Similarly, the weighting scheme used to compute species features from activations needs more attention. Classification performance was indeed found to be sensitive to changes at this level and validation would allow the most appropriate scheme to be set. Furthermore, our species features are based on points projected in time and space for the dispersal scenario. In the worst case, future bioclimatic conditions combined with static variables create previously unseen contexts leading to out-of-domain model inference. In a conservative scenario, static variables lead to automatic re-prediction of true labels plus likely species, regardless of bioclimatic conditions. This results in constant or underestimated extinction risk depending on the dispersal scenario. Finally, in the targeted scenario, bioclimatic projections combined with static variables shift species contexts in a large enough and structured representation domain, leading to coherent inferences. Thanks to the size of our dataset and previous interpretability study on the generalisation power of deep-SDMs, we believe that the behaviour of the model does indeed tend towards this third scenario.

At the level of status classification, performance drops for NT and VU statuses, i.e. for transition categories (see confusion matrices Fig. S10). While these statuses have relatively low training support (59 and 124 species respectively), we believe that this is largely due to the rather ambiguous definition of the NT category: "A taxon is Near Threatened when it has been evaluated against the criteria but does not qualify for Critically Endangered, Endangered or Vulnerable now, but is close to qualifying for or is likely to qualify for a threatened category in the near future." [START_REF] Bland | Guidelines for the application of IUCN Red List of Ecosystems Categories and Criteria, version 1.1[END_REF] As the reference delimitation between NT and VU species is potentially confused, their respective learning is assumed to be worse than other classes and performance optimisation leads to their abandonment in favour of LC/EN/CR predictions.

Perspectives

The perspectives opened up by this study are many. The SDM-based species features extracted before the final softmax layer of the model were shown to be predictive of extinction risk status. This feature space close to the SDM output is meant to be linearly separable by the different classes. In contrast, activations closer to the SDM input might be less informative about the classes, but more representative of the predictive features. Extracting species features earlier may be advantageous given that the activations flow on a predictors-class information gradient across the model layers.

One of the strengths of our model is its scalability to thousands of species. However, it is not adapted to follow the IUCN species-specific guidelines when using an SDM to estimate the different criteria [START_REF] Bland | Guidelines for the application of IUCN Red List of Ecosystems Categories and Criteria, version 1.1[END_REF]. A direct exchange with the conservation community on their specific needs would certainly help to guide future development efforts. Another natural area for improvement is to focus on a few well-documented species and subject our method to the IUCN guidelines. Furthermore, it is appealing to test our method on another suitable taxon to evaluate its taxonomic generalisation power.

Finally, including additional information that predicts the likely presence and extinction risk of species are other promising directions: species traits [START_REF] Bourhis | Explainable neural networks for trait-based multispecies distribution modelling-A case study with butterflies and moths[END_REF], ecosystem functional attributes [START_REF] Arenas-Castro | Assessing the multi-scale predictive ability of ecosystem functional attributes for species distribution modelling[END_REF] and other threat/habitat rasters such as urban expansion forecasts, forest cover predictions or protected areas (Borgelt et al., 2022a;[START_REF] Vieilledent | Spatial scenario of tropical deforestation and carbon emissions for the 21st century[END_REF]. Indeed, the inclusion of climate change alone inevitably leads to an underestimation of future threats to biodiversity [START_REF] Brook | Integrating bioclimate with population models to improve forecasts of species extinctions under climate change[END_REF].

Conclusion

The prediction of species extinction risk from SDM-based features achieves state-of-the-art performance while being flexible enough to allow testing climate change scenarios. This means that the valuable information provided by the predictors has been successfully encoded by the SDM. Future projections of orchid extinction risk averaged over two dispersal scenarios provide biodiversity trends to support global conservation targets [START_REF] Nicholson | Scenarios and models to support global conservation targets[END_REF]. Indeed, this classification framework allows to investigate the impact of climate change on the distribution of species extinction risk. While the proportion of threatened species is increasing globally, analysis by continent, latitude or altitude reveals specific and escalating patterns.

Results synthesis

In this doctoral project we explored the application of deep learning based species distribution models to conservation science. While the fields of biodiversity modelling and conservation are still largely independent [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF], we believe that our work contributes to identifying and opening up research directions that could ultimately benefit conservation.

First, in chapter 3 we showed that the potential of satellite imagery for modelling species distributions remains largely untapped. To this end, we collected a novel dataset DeepOrchidSeries linking 1M orchid occurrences with image time-series of their habitat (twelve-month RGB+IR series of Sentinel-2 imagery, 640 x 640 m extent and 10 m resolution). We then demonstrated how the habitat phenology captured by these timeseries helps models to shape species distributions. Interestingly, the performance gain is greatest for hard predictions of rare species and in species-rich regions. Furthermore, we have shown that even when the model is trained on partially noisy data (geolocation and temporal mismatches), it generalises well to unseen data and performs best when mismatches are closed. This highlights the value of the increasing amount of accurate observations collected by experts and citizens. In addition, this first chapter provides a comparison between three SDM covariates: bioclimatic conditions, habitat imagery and static variables (elevation, position, human footprint and ecoregions). On a global scale, bioclimatic covariates are identified as the best driver of orchid distribution. Compared to bioclimatic variables, fine-scale habitat imagery provides complementary, rather than alternative, information at very high spatial resolution. Furthermore, static variables cause the spatial-explicit model to perform close to the bioclimatic reference.

Next, in chapter 4, we investigated how spatial inference from deep-SDMs can fill the knowledge gap on the spatial range of understudied taxa (Wallacean shortfall). Applied to a global dataset of orchid observations, our method first predicts likely species assemblages at the kilometre scale from globally available information: bioclimatic, pedological, human footprint variables, ecoregions and position. On a validation set, the true species is guaranteed to be within the predicted assemblage with 97% confidence (conformal prediction). This in turn allows the construction of global, scalable indicators of extinction risk of species assemblages and of the Shannon diversity index. More specifically, our two indicators span (i) the proportion of threatened species and (ii) the status of the most threatened species in the predicted assemblages. In addition, we have shown how the addition of status predictions to current IUCN assessments leads to substantially increased overall threat levels and reveals strong spatial patterns in understudied regions. Analyses can then be carried out at regional, national or international level, thanks to summary statistics and an interactive website displaying our results at https://mapviewer.plantnet.org/?config=apps/store/orchid-status.xml. Using these tools, we have identified regions and countries with highly threatened species assemblages. Southeast Asian countries accumulate very high levels of orchid diversity and extinction risk, while the islands of Madagascar, Reunion and Mauritius host the most threatened orchid assemblages (60% of them are predicted to be threatened). We have also illustrated how the indicators developed relate to the current implementation of protected areas in Sumatra.

Finally, in chapter 5 we used a trained deep-SDM to predict the IUCN extinction risk status of species and forecast future status dynamics. In this context, the model can be seen as a dimension reduction algorithm. It benefits from the generalisation power of deep-SDMs and results in a rich embedding of the species niche. Our classification scheme aims to mitigate the over-reliance on geographic information in flora assessments, thus allowing prediction of future extinction risk patterns. The critical information found to correlate with species observations is propagated through the model layers and is considered representative of the species' environmental preferences. The resulting model activations are structured in a feature space of reduced dimension. We aggregate the features per species and use the summary statistics in a supervised classification task where the objective is to predict the IUCN status of species. This method leads to a competitive classification performance, illustrating the interest of deep-SDMs for downstream tasks. Furthermore, our framework allows us to project the impact of climate change on IUCN status predictions. Under a business-as-usual scenario of pollution rates, bioclimatic conditions are projected into the future. Species are assumed to have either zero or unlimited dispersal capacity. We examined the consequences of climate change under these conditions, analysing the results by continent, latitude and altitude. More than 80% of African orchids could be threatened with extinction by the end of the century. Tropical Asia and South America -the two most species-rich continents considered here -would see a significant increase in the proportion of threatened species. In addition, the predicted number of threatened species peaks at the Equator and the two Tropics, but also in the lowlands and at middle altitudes (800-1,500m), where species used to be relatively unaffected.

Limits and perspectives

Contribution of our work to conservation

To start with, as pointed out in [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF], modelling plays a crucial but under-appreciated role in conservation planning and practice, particularly in setting global conservation targets. The outputs of single-species SDMs are already being used for conservation [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF]. Modern models such as deep SDMs address the same goal of mapping species distributions, but rely on more advanced techniques to harness large amounts of data and help overcome assessment biases along with knowledge shortfalls about biodiversity [START_REF] Hortal | Seven Shortfalls that Beset Large-Scale Knowledge of Biodiversity[END_REF]. One can therefore ask what is slowing down the adoption of modern SDMs by the conservation community? As already mentioned, the reason certainly lies in the "black box" appearance of the model. However, there are solutions and the next section 6.2.2 will explore some of them.

Again, models are needed to help broaden our limited view of biodiversity. In this respect, [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF] distinguishes two classes of models: imputation models, which aim to fill gaps in our knowledge of biodiversity properties (e.g. biological traits, functions), and spatial biodiversity models, which aim to spatially generalise our knowledge to unsampled sites (often for the benefit of conservation planning). In chapter 3, our work on the contribution of satellite image time-series aims to improve such spatial biodiversity models. The multiplication of remotely sensed views of species habitat targets a better characterisation of species environmental preferences and ultimately a better mapping of species distributions. Our research on species assemblage prediction and indicator design (chapter 4) also aims to widen our knowledge of biodiversity in space. In fact, our method lies at the intersection of the two classes of models outlined above: we first use an imputation model to complete the IUCN Red List coverage of a given taxon, and then generalise the knowledge of extinction risk in space. While such a combined method may seem ambitious, we believe that the effort is worthwhile to further our understanding of biodiversity and to illustrate modern modelling capabilities. Finally, our IUCN status classification scheme developed in chapter 5 belongs to the class of imputation models.

Here we discuss additional benefits of our chapter 4 maps that motivate their uptake in conservation. First, our maps are based on a multi-species approach that combines information at the species and assemblage level. [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF] argue that this is highly relevant for conservation applications, as it allows the simultaneous estimation of species-relevant ecological processes and larger-scale attributes. Second, the habitat-based metrics often used in conservation may overlook important facets of biodiversity, such as trophic-level species traits [START_REF] Decker | Incorporating ecological functions in conservation decision making[END_REF][START_REF] Marshall | What are we measuring? A review of metrics used to describe biodiversity in offsets exchanges[END_REF], hence the need for complementary metrics. Furthermore, when multiple species are considered, this is usually done through species richness. This metric alone cannot represent the spatial heterogeneity in extinction risk patterns. Finally, conservation priorities at local, national or global scales can often differ because they take into account different extents, objectives and data [START_REF] Pollock | Large conservation gains possible for global biodiversity facets[END_REF]. Multi-scale indicators prevent such inconsistencies from hampering the conservation planning process.

Naturally, there is room for improvement to increase the relevance of our work for conservation. Regarding our DeepOrchidSeries dataset, adopting the formalism of Essential Biodiversity Variables (EBV, see section 2.2.2.3) would improve its reuse by the community. Next, comparing the orchid assemblages predicted by our method with other initiatives such as the SESAM framework (Spatially Explicit Species Assemblage Modelling, [START_REF] Guisan | SESAM-a new framework integrating macroecological and species distribution models for predicting spatio-temporal patterns of species assemblages[END_REF] could assist in the adoption of our indicators. In addition, further exploration of the implications of our work with orchid conservationists is a logical direction. Defining hotspots of extinction risk for species assemblages would be an easy first step to start the dialogue. Comparing our findings on orchids with the recently reviewed global conservation priorities of the family [START_REF] Fay | Orchid conservation: how can we meet the challenges in the twenty-first century?[END_REF][START_REF] Gale | Orchid conservation: bridging the gap between science and practice[END_REF][START_REF] Vitt | Global conservation prioritization for the Orchidaceae[END_REF][START_REF] Wraith | Orchid conservation and research: An analysis of gaps and priorities for globally Red Listed species[END_REF] is definitely an area for improvement in our work. Furthermore, an analysis of the discrepancies between the extinction risk predictions of different automated methods would allow a better understanding of the strengths and weaknesses of the classifiers. Finally, improving the interpretability and reliability of models is a general perspective for improvement. As we believe that this is a pivotal point in our work, but also in the field of biodiversity modelling, we dedicate the next section to this topic. In addition, the research directions on models and analysis of results presented in section 6.2.3 would ultimately help to inform conservation as well.

Uncertainty and confidence in predictions for conservation

In order to properly inform conservation, quantifying the uncertainty associated with our model predictions and, when appropriate, increasing confidence in the predictions is a priority perspective for improvement [START_REF] Rapacciuolo | Strengthening the contribution of macroecological models to conservation practice[END_REF]. Few directions can be identified at the level of SDMs, IUCN status classification or, more conceptually, for all biodiversity models.

Applying existing xAI tools to explain our SDM predictions is a promising direction [START_REF] Ryo | Explainable artificial intelligence enhances the ecological interpretability of black-box species distribution models[END_REF]. Options are numerous, be it with the popular shapeley values method (SHAP, [START_REF] Lundberg | A unified approach to interpreting model predictions[END_REF], with local interpretable model-agnostic explanation (LIME, [START_REF] Ribeiro | Why should i trust you?" Explaining the predictions of any classifier[END_REF], or with the recently unified Captum PyTorch library [START_REF] Kokhlikyan | Captum: A unified and generic model interpretability library for pytorch[END_REF] among others. With regard to our species assemblage predictions and the indicators derived from them, it would be of great interest to produce the list of retained species in order to increase transparency. This would be a challenging task when considering the global 221M point, but it is definitely worth exploring for a regional or random under-sample. In addition, using the distance of the relative probability of species presence to the selection threshold would give a sense of model confidence. For example, for our spatial indicator of the most critical IUCN status, model confidence could be represented by the probability/threshold distance of the most likely species of that status. As a result, confidence maps could be produced to aid the use of our indicators. Finally, advances and standards in SDM evaluation would ensure more reliable use of SDM predictions for conservation. Model evaluation affects not only final performance reports, but also model training through successive validation steps, hence the need for ecologically relevant metrics [START_REF] Mouton | Ecological relevance of performance criteria for species distribution models[END_REF]. A first challenge concerns the ground truth to evaluate the models: while presence-absence observation data is the best reference, it is really scarce and therefore surrogates such as presence-only data from citizen science or expert range maps are used [START_REF] Mainali | Matching expert range maps with species distribution model predictions[END_REF]. Other challenges include the influence of species prevalence on model assessment (long-tail distribution in the number of observations per species) and covariate spatial autocorrelation, which can lead to overestimation of performance if not controlled [START_REF] Schratz | Hyperparameter tuning and performance assessment of statistical and machinelearning algorithms using spatial data[END_REF].

With regard to our IUCN extinction risk classification method, the use of xAI tools is complicated by the fact that the inputs are not easily interpretable as they are encoded in a reduced dimensional space. However, this representation space has been shown to be structured by species' environmental preferences and bioclimatic information [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF]. Model ensembling is an option to produce more robust predictions, as shown by Borgelt et al. (2022a). We can imagine ensembling models trained with different climate change scenarios to cover the range of possibilities, or different climate models for a given scenario. The use of a Bayesian approach to quantify uncertainty, as in the IUCNN approach, is also a perspective that holds promise. Furthermore, our IUCN prediction method includes a range generalisation step by relying on SDM predictions. We believe that testing the robustness of our classifiers to a degraded number of occurrences would provide useful insights. Similarly, [START_REF] Breiner | Including environmental niche information to improve IUCN Red List assessments[END_REF] tested the impact of local extinction events on species EOO/AOO. In addition, further analysis of the predicted patterns of extinction risk would help to confirm or disprove the method. This is discussed in more detail in section 6.2.3.2.

To conclude, we present three general perspectives on the uptake of biodiversity modelling results. First, conservation actors need flexible tools and platforms to interact with. Rigid products and frameworks are unlikely to be appropriate for specific case studies. In this respect, we believe that the interactive website presenting our indicators is an asset. This leads to the second point raised by [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. To avoid inefficient method development and to optimise the results of biodiversity modelling, conservation stakeholders should be involved early in the model development process. This would allow appropriate conservation objectives, targets and scenarios to be considered. Such dialogue would ultimately increase confidence and acceptance of models. We fully acknowledge this as a specific shortcoming of our research products, as no conservation actor was involved in the early stages of method design. Third, incorporating causal modelling techniques into biodiversity models could greatly support effective conservation action [START_REF] Gonzalez | A framework for the detection and attribution of biodiversity change[END_REF][START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. Causal inference helps machine learning models become more accurate and interpretable by identifying and explaining cause-effect relationships between variables. Already widely used in medicine, economics and political science, its adoption in biodiversity modelling is both promising and necessary.

Research directions

In this section, we detail a few research directions that we believe could directly improve the performance of our models and clarify our results. In contrast, the next section 6.2.4 is broader and addresses general perspectives on the interplay between AI, ecology and conservation.

Species distribution modelling with deep learning

In terms of deep-SDM architecture and readily available covariates, the field is rapidly evolving and the directions of progress are many. First, environmental covariates are often heterogeneous, with different formats and scales, which can make their interaction complex. One possibility is to train independent first layers for each input scale/format and fuse the intermediate representation later (late fusion). Embedding categorical data before model input has several advantages: it speeds up model training, but more importantly it can help to generalise better with sparse data [START_REF] Guo | Entity embeddings of categorical variables[END_REF]. In response to the class imbalance problem, machine learning has produced different loss functions and strategies that help improve rare species predictions, so exploring alternatives and complements to LDAM loss would provide valuable insights [START_REF] Cao | Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss[END_REF][START_REF] Wang | Long-tailed Recognition by Routing Diverse Distribution-Aware Experts[END_REF]. A natural perspective for improvement is to exploit novel deep learning architectures. There are many candidate models from computer vision, with vision transformers and their adaptive receptive fields and the next generation of CNNs showing great promise [START_REF] Liu | Swin Transformer: Hierarchical Vision Transformer Using Shifted Windows[END_REF][START_REF] Liu | A ConvNet for the 2020s[END_REF]. Models specifically designed to capture spatio-temporal dynamics in satellite image time-series should also be considered to capture habitat dynamics and model species distributions [START_REF] Hole | SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers[END_REF][START_REF] Ji | 3D Convolutional Neural Networks for Crop Classification with Multi-Temporal Remote Sensing Images[END_REF][START_REF] Rußwurm | Multi-temporal land cover classification with sequential recurrent encoders[END_REF]. Furthermore, habitat characterisation through remote sensing to feed multi-species SDMs is still in its infancy. We have shown in this first chapter how the temporal dimension can help to differentiate species habitat on a global scale, but many other aspects could be explored. Combining the spatial, temporal and spectral dimensions of satellite imagery with radar data is an exciting opportunity [START_REF] Zhu | Deep Learning Meets SAR[END_REF]. Analysing the test performance as a function of the cloud cover percentage of the image time-series would be an informative validation experiment. Closing the temporal and spatial mismatches between each species observation and its remotely sensed covariates is challenging when dealing with large amounts of data, but promising given the results in section 3.3.5. Assuming the observations are in the centre of the patch, models could attribute particular importance to the central spatial information and gradually diffuse the weight towards the patch periphery. Finally, providing species traits, phylogeny and life forms as SDM inputs, when available, could help shape species distributions and ultimately benefit the IUCN status classification with SDM-encoded features [START_REF] Bourhis | Explainable neural networks for trait-based multispecies distribution modelling-A case study with butterflies and moths[END_REF].

IUCN status prediction

In addition to the required uncertainty quantification already detailed, our IUCN status classification method would benefit from efforts in species modelling and results analysis. Starting with modelling perspectives, providing current forest cover as SDM input and informing future scenarios with deforestation projections [START_REF] Vieilledent | Spatial scenario of tropical deforestation and carbon emissions for the 21st century[END_REF] could help to capture threats to orchids and ultimately benefit the IUCN classification, especially for epiphyte species. Species traits, life form, phylogeny and any other specieslevel information can also be concatenated with the SDM-based features to aid status classification. In the case of epiphyte orchids (about 70% of species according to [START_REF] Atwood | The size of the Orchidaceae and the systematic distribution of epiphytic orchids[END_REF], taking advantage of observational data on their host trees in addition to providing life form information is likely to benefit models [START_REF] Flores-Tolentino | Distribution and conservation of species is misestimated if biotic interactions are ignored: the case of the orchid Laelia speciosa[END_REF]. As our approach focuses primarily on the quality and extent of species' habitats, it is also worth testing restricting the training support to species that are specifically threatened by habitat conversion. Another direction is to explore SDM's intermediate representation spaces to compute species features. Considering that the input environmental information is progressively encoded to translate species presence, intermediate layers could indeed represent relevant trade-off states. Finally, increasing the number and consistency of manual extinction risk assessments will also improve automatic classification. Indeed, they serve as reference for model training and thus have a large influence on automatic classification.

The understanding of IUCN status predictions can be enhanced by further analysis of our results. First, phylogenetic trees provide a great opportunity to examine whether the status distribution is phylogenetically structured (with or without phylogeny explicitly provided as classifier input, [START_REF] González-Del-Pliego | Phylogenetic and Trait-Based Prediction of Extinction Risk for Data-Deficient Amphibians[END_REF]. The same observation applies to species' life form: does it make a difference to IUCN status predictions? IUCN predictions under climate change also merit further analysis. Investigating which species are predicted to change status and where is a first perspective. Moreover, we can imagine calculating the indicators built in chapter 4 with the predicted species distributions and statuses from chapter 5. Highlighting areas of high indicator change could then be revealing.

IA, Ecology & Conservation

In this final section, we address high-level perspectives on the interdisciplinary field of our studies. They apply to our work as well, but their scope is broader than species distribution modelling based on deep learning. First, we have seen throughout this manuscript how taxonomic, spatial coverage, and extinction risk assessments, for example, are still hampered by knowledge gaps. In other words, reference labels to supervise learning algorithms are lacking. The machine learning community faces this problem in many fields, and compensatory strategies are grouped under the terms weak supervision, i.e. supervision with noisy or coarse-grained labels, and semi-supervision: only a subset of the training data has labels [START_REF] Zhou | A brief introduction to weakly supervised learning[END_REF]. In ecology, where standardised data can be expensive to collect [START_REF] Todman | Small Data'for big insights in ecology[END_REF], and meta-databases such as the GBIF are still noisy and biased towards certain regions, taxa and facets of biodiversity, the application of these techniques seems appropriate and necessary. Self-supervised learning is another learning paradigm where the training goal is to learn, for example, to detect input modifications (e.g. degree of image rotation) or even to reconstruct masked parts of the input (e.g. masked image subset or words in a sentence). It allows learning the structure of huge amounts of unlabelled data in a first step, and then possibly fine-tuning models with few labels in downstream tasks. It has great potential for remote sensing where labels are scarce but data is abundant [START_REF] Scheibenreif | Self-supervised vision transformers for land-cover segmentation and classification[END_REF]. These different learning paradigms are not exclusive and can be combined to make the most of the available data. Finally, unsupervised learning approaches are already used in ecology [START_REF] Derkarabetian | A demonstration of unsupervised machine learning in species delimitation[END_REF][START_REF] Sonnewald | Elucidating ecological complexity: Unsupervised learning determines global marine eco-provinces[END_REF] and still have a lot to offer for data exploration, representation, dimension reduction, clustering and anomaly detection (see Pichler and Hartig, 2023 Box 2).

Another promising avenue in ecological modelling is hybrid AI. Physics-informed neural networks (PINN, [START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF] have recently taken off by constraining model learning with proven physical laws. Similarly, ecology-informed models could benefit from field knowledge [START_REF] Pichler | Machine learning and deep learning-A review for ecologists[END_REF]. This would also increase confidence in model predictions. Furthermore, we believe that the flexibility and transparency of constraint programming has potential for ecology in general and for implementing effective conservation measures in particular [START_REF] Justeau-Allaire | Constrained optimization of landscape indices in conservation planning to support ecological restoration in New Caledonia[END_REF].

As a closing remark, there is a strong case for developing deep learning models directly with ecological data. Although it may seem naive, there is sufficient data volume, complexity and diversity to challenge DL research with ecological data. It would also lead to the development of specific architectures that avoid the need to adapt or retrain models for ecological tasks. For example, computer vision models could be benchmarked against a plant identification dataset such as Pl@ntNet-300K instead of ImageNet [START_REF] Deng | ImageNet: A large-scale hierarchical image database[END_REF][START_REF] Garcin | Pl@ntNet-300K: a plant image dataset with high label ambiguity and a long-tailed distribution[END_REF].

Bringing together data science and conservation science is an ambitious task, not only from a practical point of view, but also on a social plan. The research communities are animated by challenges that are difficult to coordinate and link, and that span a wide spectrum from theory to concrete implementation. Moreover, it implies in fact bringing together not two but three fields: data science, biodiversity modelling and biodiversity conservation, as the latter two are still largely independent [START_REF] Guisan | Predicting species distributions for conservation decisions[END_REF][START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF]. However, many additional benefits would result from such a union. As noted by [START_REF] Pollock | Protecting Biodiversity (in All Its Complexity): New Models and Methods[END_REF], modern modelling techniques would benefit conservation, but precise prediction targets for conservation would also catalyse modelling research. The same observation applies between data science and biodiversity modelling: while AI capabilities are often praised, precise modelling targets, case studies and ecological theory provide a meaningful challenge to the data science community. Finally, I would like to end this general perspective with a quote from [START_REF] Jetz | Integrating biodiversity distribution knowledge: toward a global map of life[END_REF] that resonates with my position. It is taken from a paragraph in which the authors outline the challenges and opportunities of their Map of Life project to integrate knowledge of species distributions:

"Although challenges remain in developing statistically robust models to integrate heterogeneous distribution data types, they are unlikely to represent a permanent obstacle. All computational tools to implement the envisioned cyberinfrastructure already exist. Thus, the greatest challenge for fully realizing our vision might be more sociological than technological." [START_REF] Jetz | Integrating biodiversity distribution knowledge: toward a global map of life[END_REF] Considering how deep learning has taken off since then, with the breakthrough of deep convolutional neural networks in the same year [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], see timeline Figure 2.11), the plurality of technological advances, and today's global concerns, I find it a particularly perceptive thought.

Conclusion

Embracing deep learning and satellite imagery to model species distribution opens up new possibilities for informing conservation. Yet this interdisciplinary journey is still in its infancy. Data science offers the opportunity to extract critical information from massive, heterogeneous data describing the state of nature and provide flexible decision support. However, significant efforts are needed to improve model interpretability and quantify uncertainties if we are to properly guide conservation actions with deep learning results. Nevertheless, we believe that the results generated in this project have value to motivate further research, which is urgently needed. In addition, we believe that challenging and complementing the results presented here with alternative strategies would provide additional benefits.

Before closing this manuscript, I would like to mention a few challenging aspects that I encountered during my research. First, publishing research that straddles the boundaries of data science, biodiversity and conservation is likely to require increased attention. It demands effective communication of the significance of the findings to a diverse audience. Second, despite increasing resources, the processing and analysis of global remote sensing datasets still presents computational and logistical hurdles. Finding open, free solutions to facilitate the efficient handling of such promising and public data is imperative. Finally, the limited time frame of PhD programmes can sometimes limit the scope of research. Balancing the need for comprehensive investigation with the constraints of the doctoral format can be difficult. I also believe this is exacerbated for exciting, exploratory projects at the growing intersection of fields such as data science and biodiversity conservation.

The interdisciplinary nature of our work provides a unique vantage point for contributing to pressing conservation issues. By collaborating across disciplines, the potential of species distribution models and data science can be harnessed to drive positive change in conservation. Unlike with categories formed on regions diversity index (Fig. 10A), MRA 30,I (M) does not clearly diminish when regions are including less occurrences (this is not because there is less occurrences that the classification task is harder, the few occurrences can be from very common species). MR∆ 30,I (M, M i ) is not regularly higher in occurrence-poor regions contrary to diversity-rich regions where the predictive data temporal dimension especially help predictions (Fig. 3.10B). | Ŝλ | , i.e. the relative change in the species assemblage size before/after the filtering step. Regions mentioned in (c) are highlighted again. Saharan regions with empty predictions after geo-filtering do not appear to have lost high species number in (c). However, the clear yellow on map (d) indicates that these regions have lost all of the few species they were predicted to host. (e) Statistics on the absolute and relative size difference of the species assemblage before/after geo-filtering. ∆ species corresponds to map (c) and Relative change [%] corresponds to map (d).

scheme. It gives prominence to the rare species, which is why we observe a decrease in performance for A 30 and an increase for MSA 30 . The training and validation curves show no signs of overfitting. The performances of the test sets with the best calibration model (epoch 69) are A 30 = 0.865 and MSA 30 = 0.48.

Calibration of the species assemblage prediction model As discussed earlier, the optimisation of the hyper-parameter λ is done through an average error control method applied on the validation set. In Equation 3, ϵ is set to 0.03. The resulting estimated value for λ is equal to 8.75e-5 (see Figure S5) and the corresponding average size of the predicted species assemblages is equal to 124 species. Reaching 0.97% micro-average accuracy means that the model almost always returns the correct label within the predicted set when a random unseen observation is being provided. The number of observations per class being strongly unbalanced (see Box F Fig. a), the 97% micro-average accuracy is strongly influenced by the performance on common species. Now, when all unseen species are granted the same weight in the average computation (macro-average accuracy), performance is still of 80%. Given how unbalanced the observation dataset is (median occurrence number is four, 25% species have more than 13 occurrences), it becomes clearer that the model's performances are satisfying. Summary statistics on | Ŝλ | are reported on Table S1. Cumulative share of species. Species are sorted by number of occurrences.

Box G: Predictive features description

In selecting predictive features, the main limiting criterion was to use only globally available potential drivers of orchid preferences.

WorldClim2 bioclimatic variables

The nineteen standard bioclimatic variables from WorldClim version 2 were provided to the model [START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF]. They are historic averages over the 1970-2000 at 30-second resolution. This suits our occurrence date distribution. Variables stem from temperature and precipitation data (https://www.worldclim.org/). They are established indicators of climate annual trends, seasonality and extreme values.

Soilgrids pedological variables Soilgrids is a collection of eleven global soil property and class maps produced by machine learning models [START_REF] Poggio | SoilGrids 2.0: producing soil information for the globe with quantified spatial uncertainty[END_REF]. They include soil pH, nitrogen concentration annd clay particles proportions among others (more information in the official FAQ: https://www.isric.org/). The exploited statistical models are fitted with 230,000 soil profiles spread wordwide and environmental covariates. We use the 1-kilometre resolution products.

Human footprint detailed rasters Eight variables measure direct and indirect global human pressure: built environments, population density, electric infrastructure, crop lands, pasture lands, roads, railways, and navigable waterways [START_REF] Venter | Global terrestrial Human Footprint maps for 1993 and 2009[END_REF]. They are provided at a 1-kilometre resolution (https://datadryad.org/) and for two distinct years: 1993 and 2009. These rasters spring form both remotelysensed data and surveys.

Terrestrial ecoregions of the world This is a biogeographic classification of terrestrial biodiversity. Ecoregions are defined by the authors as "relatively large units of land containing a distinct assemblage of natural communities and species, with boundaries that approximate the original extent of natural communities prior to major land-use change" [START_REF] Olson | Terrestrial Ecoregions of the World: A New Map of Life on EarthA new global map of terrestrial ecoregions provides an innovative tool for conserving biodiversity[END_REF]. 867 ecoregions are gathered into 14 biomes such as boreal forests or deserts. Data (https://www.worldwildlife.org/) was resampled at 30 seconds longitude/latitude resolution.

Location The explicit provision of observation coordinates is a key modelling decision. Both a large regional context and precise location information are provided. The model can make the most of this mixed input. Deep learning models can indeed take advantage of complex combinations of heterogeneous inputs. As longitude and latitude are inputted separately, both indications are processed alongside, can interact, but are also interpreted distinctly. We observe that: i) NT and VU proportions are currently significant according to IUCN, but are predicted to disappear over time. This is due to poor classifier performance on these categories and their rather confused definitions, see status confusion matrices Figure S10 and the Discussion. ii) In both cases, the proportions of threatened species appear to be positively correlated with HFP intervals. iii) HFP bins may cover few species (see Figure S16), so the robustness of these results should be further assessed. iv) As with the altitude study, this result shows a correlation, but no causality can be inferred. Again, a confounding variable may be at the origin of this pattern rather than HFP.

1. 1

 1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Thesis motivation and contributions . . . . . . . . . . . . . . 1.2.1 Central research questions and organisation . . . . . . . . . . . 1.2.2 Modelling species distribution from satellite time-series -Ch. 3 1.2.3 Mapping the extinction risk of species assemblages -Ch. 4 . . . 1.2.4 Extinction risk prediction under climate change -Ch. 5 . . . . 1.3 A suited case study family: Orchidaceae . . . . . . . . . . . .

Figure 1 . 1 :

 11 Figure 1.1: Big data dimensions (four Vs) in ecology: (1) Remote sensors of the earth system, mounted on a variety of platforms, which generate large data volumes. (2) Citizen-science efforts that collect data at volumes far beyond the capacity of scientific experts, by individuals with varying degrees of expertise.(3) Near real-time sensor networks that can deliver on-going data feeds at low latency and high velocity. (4) Field observations and experiments by scientists, across a wide variety of measurements, systems, and scales. This mapping of the four Vs to data types is illustrative; all four dimensions are present in all data types. Reproduced from[START_REF] Farley | Situating Ecology as a Big-Data Science: Current Advances, Challenges, and Solutions[END_REF] with permission from Oxford University Press.

Figure 2 . 1 :

 21 Figure 2.1: Generalised Red List assessment workflow from species list to publication on the Red List. Ovals represent processes, grey and coloured rectangles are outcomes and curved rectangles are people or groups. EOO = Extent of occurrence, AOO = Area of occupancy. Arrows indicate direction of flow through different stages, including feedback. Reproduced from (Bachman et al., 2019), CC-BY license.

Figure 2 . 2 :

 22 Figure 2.2: Two examples of EOO and AOO measures. (A) distribution of records of occurrence. (B) minimum convex hulls around records of occurrence to measure EOO. (C) shows two measures of AOO with the sum of the occupied grid squares. Reproduced from (Commission et al., 2001).

Figure 2 . 3 :

 23 Figure 2.3: Two contrasting views of the Living Planet Index: (top) by region and (bottom) trends by taxonomic group. Reproduced from (Ritchie et al., 2022), CC-BY license.

Figure 2 . 4 :

 24 Figure 2.4: From observations to the production of EBVs and indicators. In this example, integrated data from different primary sources of observations (e.g. in situ, remote sensing) are combined within biodiversity models to produce layers of spatial and temporal variation in ecosystem extent and species distribution EBVs. This information is then integrated and summarised within reporting units to calculate an indicator of biodiversity change, used, for instance, for reporting progress towards an Aichi conservation target. EBVs and models can also be used to project changes in the indicator using scenarios. Reproduced from[START_REF] Navarro | Monitoring biodiversity change through effective global coordination[END_REF], CC-BY license.

Figure 2 . 5 :

 25 Figure 2.5: Protection-weighted range-size rarity of imperiled species by taxonomic group: (a) vascular pants, (b) vertebrates, (c) freshwater invertebrates (mussels, crayfishes), (d) pollinators (butterflies, bumblebees). Reproduced from (Hamilton et al., 2022) with permission from John Wiley and Sons.

Figure 2 . 6 :

 26 Figure 2.6: Patterns of Cactaceae biodiversity. a Proportion of species that are threatened (Vulnerable, Endangered and Critically Endangered). b Total species richness. Reproduced from[START_REF] Goettsch | High proportion of cactus species threatened with extinction[END_REF] with permission from Springer Nature.

Figure 2

 2 Figure2.7: The distribution of the predominant threats to biodiversity across Australia. The "predominant threat" is the threat affecting the greatest number of species in each subcatchment. White indicates areas where no threatened species occur. Reproduced from[START_REF] Evans | The Spatial Distribution of Threats to Species in Australia[END_REF] with permission from Oxford University Press.

Figure 2 . 8 :

 28 Figure 2.8: Illustration of how different maps can be combined in conservation planning, based on a case study on marine protected areas in Fiji[START_REF] Tulloch | Incorporating uncertainty associated with habitat data in marine reserve design[END_REF]. Reproduced from[START_REF] Tulloch | Why do we map threats? Linking threat mapping with actions to make better conservation decisions[END_REF] with permission from John Wiley and Sons.

Figure 2 . 9 :

 29 Figure 2.9: Alexander von Humboldt's Tableau Physique (Humboldt & Bonpland, 1807).In 1802, physical geographer Alexander von Humboldt and botanist Aimé Bonpland climbed Chimborazo, an equatorial volcano that was then thought to be the world's highest mountain. They documented the mountain's flora, from the tropical rainforest at its base to the highest lichens. Humboldt's Tableau Physique organises these observations in an innovative diagram showing Chimborazo in cross-section, with text detailing which species live at which elevation. This impressive study is a testament to man's desire to map the natural world. It also is a unique data source for assessing vegetation shifts in response to climate change, and is the oldest existing dataset on altitudinal ranges of tropical mountain vegetation. Today, interdisciplinary work between historians and ecologists allows the validity of such pioneering work to be adjusted[START_REF] Moret | Humboldt's Tableau Physique revisited[END_REF]. CC0 license, public domain.

Figure 2 .

 2 Figure 2.10: GBIF cumulative number of plant records over time categorized by the basis of record. Reproduced from https://www.gbif.org/.

Figure 2 .

 2 Figure 2.11: The three eras of statistical learning. The classical concept of statistics was developed between the 1920s and the 1940s. Common machine learning algorithms or techniques were then discovered between 1980 and the early 2000s. While the theoretical foundations of deep learning were postulated in the 1960s, it has only gained popularity in recent years. The trend lines above the timeline correspond to the frequency of occurrence of each term in the scientific literature. Reproduced from (Pichler & Hartig, 2023), CC-BY license.

Figure 2 .

 2 Figure 2.12: Typical bias-variance trade-offs in classical machine learning (left) and deep learning (right) models for interpolation and extrapolation tasks. In contrast to the classical bias-variance trade-off in panel (a), the bias-variance trade-off for DL in panel (b) shows that after the interpolation threshold (pink dotted line), the training loss is constant (i.e. bias is not improved by increasing model complexity), but the test loss (and thus variance) can still be reduced by increasing model size. For extrapolation tasks (c & d), the total generalisation error is usually higher and the optimal model complexity lower. Reproduced from (Pichler & Hartig, 2023), CC-BY license.

Figure 2 .

 2 Figure 2.15: The promises, pitfalls and priorities for deep learning in conservation. Reproduced from (Lamba et al., 2019), with permission from Elsevier.

Figure 2 .

 2 Figure 2.16: Number of citations per year for articles with 'prediction' and 'ecology' as keywords (Source: Web of Science, search criteria used: Topic = prediction and ecology; Period = All Years). Predictive ecology has become increasingly important in recent years (especially in predicting species distributions). However, prediction is not new to ecology. In 1862, Charles Darwin received orchids from Madagascar. One species in particular, the Madagascan comet orchid Angraecum sesquipedale, with a surprisingly long nectar spur (20-35 cm), caught his attention. No insect with a proboscis of this length had ever been described, but Darwin was convinced of its existence because the plant could not reproduce without a suitable pollinator. The pollinator, a hawk moth, was indeed discovered in 1903, 41 years after Darwin's prediction. Illustration Laurence Meslin. Reproduced from[START_REF] Mouquet | REVIEW: Predictive ecology in a changing world[END_REF], with permission from John Wiley and Sons.

  can impose specific constraints on the implementation of PA. Incorporating socio-economic issues into the modelling process can also facilitate constructive dialogue with stakeholders (Justeau-Allaire et al., 2021). Reserve design (Justeau-Allaire et al., 2019) and restoration planning (with different underlying issues from conservation planning, Justeau-Allaire et al., 2023) have been successfully undertaken using this flexible technique.

  Figure3.1: Visual abstract of the method. Layer 0 : The dataset introduced in this paper (DeepOrchidSeries) is based on a filtered set of GBIF occurrences coming from the study of[START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF]. Layer 1 : Sentinel-2 image time-series were collected around each occurrence geolocation, keeping least cloudy data tiles every month between March 2020 and February 2021. Images are made of 640 x 640 m RGB+IR channels with 10 m spatial resolution. The dataset is available on Zenodo and the method to create it on the Gitlab.inria platform. Layer 2 :We then trained deep Species Distribution Models (deep-SDMs) based on convolutional neural network (Inception v3) to capture the spatio-temporal context and environmental preferences of species. Next, we conducted experiments where the input temporal dimension was modified (randomized, averaged or sampled) so as to measure its contribution on model performance. Layer 3 : the results are finally broken down into three main dimensions of analysis: species frequency in the dataset, bioregion, and species diversity in these bioregions. The analysis reveals that occurrence-poor species and diversity-rich regions are the ones that benefit the most from the improvement provided by the temporal information.

Figure 3 . 2 :

 32 Figure 3.2: (A) Occurrences' distribution. Species are ordered by frequency. The dotted lines are flagging that 90% of the species are only gathering 9.1% of the occurrences. (B) Occurrences' temporal distribution. The two graphs are based on all dataset's occurrences.

Figure 3 . 3 :

 33 Figure 3.3: Creation workflow of the DeepOrchidSeries dataset. Input is a set of geolocated occurrences, output gathers image time-series informing on species habitat preferences. Code and details available at https://gitlab.inria.fr/jestopin/sen2patch.

Figure 3 . 4 :

 34 Figure 3.4: (A) Histogram of the number of occurrences per tile, (B) different patch sizes comparison around an occurrence located at (-39.883306, 144.050000), decimal degree system, (C) map of the selected tiles coloured by number of records contained (log10 scale). Three occurrences are located by α, β and γ. Figure 3.5 provides the three associated image time-series.

AFigure 3 . 5 :

 35 Figure 3.5: Image time-series associated to the three occurrences located in Figure 3.4C map. RGB images are shown on the first line and IR patches on the second. (A) is almost cloud-free and globally normalised before visualisation (i.e. all months are divided by time-series maximum pixel), (B) is a cloudless time-series with a strong environmental gradient because of snow presence and is normalised by frame (i.e. each month data is divided by month maximum pixel, only for visualisation), (C) is an especially cloudy time-series also normalised by frame.

Figure 3 . 6 :

 36 Figure 3.6: Cloud cover percentages of the 1,067,989 tested products, 180,747 (16.9%) selected against 887,242 (83.1%) dismissed. (A) all months taken together, (B) detailed by month.

Figure 3 . 7 :

 37 Figure 3.7: Scheme illustrating the three transformations applied to the input image time-series towards interpreting the contribution of the temporal information. Only 6 RGB images are depicted but these procedures are applied on the whole twelve-month-long time-series, IR channel included (here N = 6 but would normally equal 12). The central image time-series M in black corresponds to the original data, i.e. to the images stacked in chronological order. The image series M 1 is obtained by randomly permuting the original time-series. The image series M 2 is constructed by averaging the 12 images of the original time-series and replicating the resulting mean image N times. The image series M 3 is made of one month picked at random and replicated N times. Please note that the same legend's colours will be used in the figures of the paper presenting the results of these experiments.

Figure 3 . 8 :

 38 Figure 3.8: Micro (A) and macro (B) average top-30 accuracy for model validation and test sets. Micro-average results tend to represent common species whereas macro-average performances are more representative of rare species.

Figure 3 .Figure 3

 33 Figure 3.9A displays the performance of the four models as a function of the number N s of species occurrences in the training set (cf. equation 3.4). Not surprisingly, we can observe that the accuracy of the model is positively correlated with the number of occurrences. The more occurrences in the training set and the better the top-30 accuracy.It should be noted, however, that the performance on the rarest species remains much

Figure 3 . 10 :

 310 Figure 3.10: Region top-30 accuracy (A) and relative top-30 accuracy change (B) averaged per cat. of 1 D r . Map (C) presents region top-30 accuracy with 1 D r indicated in green. Map (D) illustrates spatial decreases of performance when comparing M 3 to M, i.e. without/with the temporal information.

  92

  Figure 3.12: Global comparison of micro (A) and macro (B) average top-30 accuracy on model validation and test sets (final dots) between three SDM modalities: Satellite imagery, bioclimatic variables and static variables.

Figure 4 . 1 :

 41 Figure 4.1: Global comparison of the most critical IUCN status indicator according to three methods. (a) represents the IUCN information on our dataset: observations and available spatial data (polygons and points from https://www.iucnredlist.org/resources/spatial-data-download) taken together. Spatial data is available for only 167 IUCN-assessed orchids from our dataset, i.e. 1.2% of all species. (b) is the result of our species assemblage prediction model coloured by the most critical known IUCN status whereas (c) includes predicted IUCN status too in the indicator calculation. [Figure maps are under-sampled, see the website for full-resolution]

Figure 4

 4 Figure 4.2a shows the Shannon index calculated on our species assemblage predictions (full resolution on the website). As expected, the tropics appear to contain the richest areas. This map can be read in parallel with the Box F second map: the species richness map of our occurrence dataset stratified by botanical country (WGSRPD level 3). The resolution gain is clear. Moreover, some biases in the initial observations set explain I H patterns. Colombia orchid richness, estimated for instance at 4,327 species according to World Plants[START_REF] Hassler | World Plants. Synonymic Checklist and Distribution of the World Flora[END_REF], is for instance under-represented within our occurrence set with only 1,375 species. Global orchid diversity patterns can also be appreciated in relation to the three following maps, which reflect the extinction risk of the predicted species assemblages.

Figure 4 . 2 :

 42 Figure 4.2: Four indicators based on species assemblage predictions. (a) I H the Shannon index, (b) I THREAT the weighted proportion of threatened species, (c) and (d) the weighted proportions of respectively CR species I CR and EN species I EN . [see website for full-resolution]

Figure 4 . 3 :

 43 Figure 4.3: Average proportion of species predicted as threatened by botanical country (WGSRPD level 3) versus average Shannon index. Countries are coloured in function of their continent (WGSRPD level 1) and top-15 countries of both variables are highlighted. Myanmar, Assam and Laos are the only three regions in the top-15 intersection whereas Pakistan and Cape Verde show especially high threatened species proportions with low diversity indices.

Figure 5 . 1 :

 51 Figure 5.1: Method scheme. The first column represents the current time frame (training and evaluation), while the right column represents a future scenario (projection).Step 1 consists in associating a given set of support points (true observations or dispersal scenario) with environmental covariates using deep-SDM inference. Sites where the species has been observed and is predicted to remain are indicated by 'x', abandoned sites by 'o' and new predicted sites by 'X'. Species niches are indicated by dashed circles. In Step 2, the predicted features are summarised by taking their mean, standard deviation and sum, and the result is concatenated. This operation allows the information that was at the point level to be condensed to the species level. Finally, the Step 3 is the mapping between the species summary feature and its conservation status.After training and validation in the present with real observations (see Results), the random forest classifier is trained within dispersal scenarios to ensure coherence with future projections. Classification can be either binary, as shown, or at the IUCN status level.

Figure 5 . 2 :

 52 Figure 5.2: A. Distribution of the 889 IUCN extinction risk status from our dataset. B.Classification performance comparison between the state-of-the-art IUCNN method and ours[START_REF] Zizka | IUCNN -deep learning approaches to approximate species' extinction risk[END_REF]. The 10-fold cross-validation results in an accuracy distribution represented by boxplots. The first row shows the binary classification and the second row the status classification. Micro-and macro-average accuracies are identical, as the binary status distribution is balanced. The IUCNN method achieves an average accuracy of 0.81 for binary classification and our deep SDM method achieves 0.78. However, for status classification, our method gives a micro-average accuracy of 0.61 and a macro-average accuracy of 0.43 and the IUCNN method 0.60 and 0.41 respectively.

Figure 5 . 3 :

 53 Figure 5.3: Binary status proportions per continent and time period. All species are included and their number per continent is given in the subtitles. Error bars account for differences between the two dispersal scenarios.

Figure 5 . 4 :

 54 Figure 5.4: Species count histograms as a function of average latitude and time period. All species are included and colours indicate the binary extinction risk status. Bins cover four degrees of latitude.

Figure 5 . 5 :

 55 Figure 5.5: Species count histograms as a function of their average altitude and over time. All species are included and colours indicate the binary extinction risk status. Bins cover 150 metre elevation ranges.

Figure S1 :

 S1 FigureS1: Histogram of occurrence geolocation uncertainty (60 bins). 31% of the 999,248 occurrences associated with satellite data had no uncertainty provided at all and are not represented in this figure. Uncertainty was limited to 10,000 m on the Figure.First quartile is 100 m, median is 850 m and third quartile is 5,000 m. Recent and citizen science occurrences are usually integrating quite precise geolocation (explaining left peaks accumulation) whereas old observations will be less precise. The peak at 5,000 m certainly witnesses an arbitrary uncertainty value attributed to part of the orchids.

Figure S2 :

 S2 Figure S2: Region top-30 accuracy (A) and relative top-30 accuracy change (B) averaged per category of number of training occurrences per region N r . Unlike with categories formed on regions diversity index (Fig.10A), MRA 30,I (M) does not clearly diminish when regions are including less occurrences (this is not because there is less occurrences that the classification task is harder, the few occurrences can be from very common species). MR∆ 30,I (M, M i ) is not regularly higher in occurrence-poor regions contrary to diversity-rich regions where the predictive data temporal dimension especially help predictions (Fig.3.10B).

FIGURE S3

 S3 FIGURE S3Maps and statistics illustrating the post-filtering step with the geographic-prior. The support is a global regular grid with 0.5 decimal degree resolution (59,823 points). (a) | Ŝλ |, i.e. the species assemblage size before the filtering step. Northern latitudes -and especially northern Europe-present abnormally large species assemblages. This is a consequence of the generalisation / over-prediction trade-off described in Discussion. The prediction model is over-confident because of the extensive occurrence training data in northern European countries. (b) | Ŝ′ λ |, i.e. the species assemblage size after the filtering step. The over-prediction bias at northern latitudes has been largely compensated. Empty predictions zones (red surrounded) have increased because of the geographic filtering, especially in the Sahara. (c) | Ŝ′ λ | -| Ŝλ |, i.e. the absolute size difference of the species assemblage before/after the filtering step. Regions having lost the highest number of species are northern European countries and the South Arabian Peninsula. (d) | Ŝ′ λ |-| Ŝλ |

FIGURE S5

 S5 FIGURE S5Average error control setting on the validation set. Limiting condition on the micro-average accuracy (green curve) is ϵ ≤ 0.03 ⇔ A ≥ 0.97. Optimal threshold λ is highlighted in red while matching macro-average accuracy (grey function) is also reported with a red dashed line. Average set sizes | Ŝλ | are indicated in dashed boxes (hat and subscript being dropped for readability).

  FIGURE S8 (a) Occurrences' distribution. Species are ordered by frequency. The dotted lines are flagging that 90% of the species are only gathering 9.1% of the occurrences. (b) Occurrences' temporal distribution. The two previous graphs are based on all dataset's occurrences. (c) Observations map coloured by number of records in 110 x 110 km tiles (log10 scale). (d) Species richness map stratified by botanical country (WGSRPD level 3). Colours are in log scale.

Figure S17 :

 S17 Figure S17: Predicted status proportions per 2009 Human Footprint (HFP) bin across time periods, considering (a) IUCN-assessed species only or (b) all species in our dataset. (a) Present sub-figure then represents the HFP distribution of currently red listed orchids.We observe that: i) NT and VU proportions are currently significant according to IUCN, but are predicted to disappear over time. This is due to poor classifier performance on these categories and their rather confused definitions, see status confusion matrices FigureS10and the Discussion. ii) In both cases, the proportions of threatened species appear to be positively correlated with HFP intervals. iii) HFP bins may cover few species (see FigureS16), so the robustness of these results should be further assessed. iv) As with the altitude study, this result shows a correlation, but no causality can be inferred. Again, a confounding variable may be at the origin of this pattern rather than HFP.

Table of contents

 of

  .10 illustrates this data explosion on GBIF for the Plantae kingdom. This trend results from the development of attractive and

		Samp. Obs.
	Collection method	Pro.	type	Example
	CS observations	NS	P	Pl@ntNet	(Affouard et al., 2017)
	Historic records	NS	P	Herbarium sheets	(Lutio et al., 2022)
	CS checklists	S	P-A	eBird	(Sullivan et al., 2009)
	Static sensors	S	P-A	Camera traps	(Trolliet et al., 2014)
	Sample collection	S	P-A	Insect trapping	(Child & Pinniger, 1994)
	Expert field surveys	S	P-A	Line transects	(Buckland et al., 2007)
		S	P-A	Vegetation plot	(Chytrý et al., 2016)
		NS	P	Distance sampling	(Buckland et al., 2005)
		NS	P-A	Site-occupancy	(MacKenzie & Nichols, 2004)

Table 2

 2

	.1: Sources of species observation data. Each of these examples represents a method
	of collecting or accessing observations of different species. Citizen science is denoted CS. Only
	presence-absence (P-A) and presence-only (P) observations observation types are listed in this
	table (no abundance or species count listed here for instance). The sampling protocol are either
	Standardised (S) or Nonstandardised (NS). Adapted from (Beery et al., 2021), CC-BY license.

•

  Phenological research. Katal et al. (2022) provided a systematic overview of the DL methods used in the field, identifying research trends and foreseeing promising directions. Lorieul et al. (2019) and Reeb et al. (2022), for example, trained a CNN to successfully detect pheno-phases in CS images and herbarium specimens. Brun et al. (2023) estimated national flowering phenology in Switzerland from seasonal observation probabilities.

  Interpretability experiments: quantifying the contribution of temporal information . . . . . . . . . . . . . 84 3.2.2.4 Modality contribution on a global scale . . . . . . . . 86 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3.1 Model validation and performance . . . . . . . . . . . . . . . . 87 3.3.2 Results by number of species occurrences . . . . . . . . . . . . 88 3.3.3 Results by region and regional diversity index . . . . . . . . . . 89 3.3.4 Statistical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.3.5 Model evaluation regarding time and spatial data mismatches . 92

	Table of contents

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . 74 3.2.1 DeepOrchidSeries dataset . . . . . . . . . . . . . . . . . . . . . 74 3.2.1.1 Raw input data description . . . . . . . . . . . . . . . 74 3.2.1.2 Dataset construction . . . . . . . . . . . . . . . . . . . 76 3.2.2 Species Distribution Models trained with satellite image timeseries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2.2.1 Model definition and training procedure . . . . . . . . 80 3.2.2.2 Performance evaluation of the model . . . . . . . . . . 81 3.2.2.3 3.3.6 Modality contribution on a global scale . . . . . . . . . . . . . . 93 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.1. Introduction

Table 3 .

 3 1: Summary table of the number of occurrences and species in the training, validation and test sets.

	Set	Training Validation Test
	#occurrences 897,296	51,116	50,375
	#species	13,700	4,290	4,261

  Model performances on the test set divided by quartiles Q i on (A) occurrence observation year and (B) occurrence coordinates uncertainty. Test accuracy is higher on more recent observations and on observations with reasonably low coordinates uncertainty.

	Test set accuracy	0.4 0.6 0.8 1.0	A 0.337 0.731 #Species 0.291 0.674 A 30 MSA 30	0.401 0.787	0.484 0.834	Test set accuracy	0.4 0.6 0.8 1.0	0.588 0.875	0.618 0.874	B 0.873 0.475	0.42 0.716 A 30 MSA 30 #Species
		0.0 0.2	1901-1982 Q 1 Quartiles on occurrence observation year 1982-1997 Q 2 1997-2010 Q 3 2010-2019 Q 4 2,098 1,799 1,463 1,271		0.2 Quartiles on occurrence coordinates uncertainty [m] 0-100 Q 1 100-707 Q 2 707-5,000 Q 3 5,000-95,000 Q 4 0.0 700 600 775 966
	Figure 3.11:

Table 4 .

 4 1: Top-15 countries with the largest share of their area covered by CR (left) or EN (right) as most critical IUCN status.

		CR	EN
		B. country Area % B. country	Area %
	1	Eq. Guinea	100.00 Jamaica	100.00
	2	Réunion	100.00 Dominican R.	100.00
	3	Mauritius	100.00 Haiti	99.95
	4	Madagascar	99.76 Cuba	99.86
	5	Comoros	99.60 Afghanistan	99.74
	6	Laos	99.38 French Guiana	99.65
	7	Connecticut	98.71 Guyana	99.45
	8	Vietnam	98.59 Surinam	99.29
	9	Rhode I.	98.49 Costa Rica	99.15
	10 Cambodia	98.26 Portugal	99.02
	11 Jawa	97.93 Corse	98.98
	12 Massachus.	97.25 Tadzhikistan	98.79
	13 E Himalaya	97.07 Puerto Rico	98.71
	14 Thailand	96.99 Windward Is.	98.64
	15 Sumatra	96.93 Galápagos	98.50
		B. country, botanical country (WGSRPD level 3).

Table 4 . 2 :

 42 Top-15 average status proportions per botanical country. From left to to right: threatened species all taken together (THREAT), Critically endangered species (CR) and Endangered species (EN). In average, 60% of the predicted species in Madagascar are threatened by extinction (63% in Réunion island).

		THREAT	CR	EN
		B. country µ[I c ] B. country	µ[I c ] B. country µ[I c ]
	1	Réunion	0.63 Réunion	0.15 Réunion	0.44
	2	Madagascar	0.60 Madagascar	0.12 Madagascar 0.39
	3	Mauritius	0.55 Mauritius	0.10 Mauritius	0.38
	4	Comoros	0.48 Comoros	0.10 India	0.36
	5	Kenya	0.46 Jawa	0.07 Philippines	0.35
	6	Myanmar	0.45 Sumatra	0.04 Taiwan	0.34
	7	Nepal	0.45 Azores	0.03 Myanmar	0.33
	8	E Himalaya	0.44 Philippines	0.03 Sri Lanka	0.33
	9	Somalia	0.44 Vietnam	0.03 E Himalaya	0.33
	10 India	0.44 Laos	0.03 Nepal	0.33
	11 Laos	0.43 Arizona	0.03 Laos	0.32
	12 Assam	0.43 New Mexico	0.03 Assam	0.32
	13 China SC	0.42 Myanmar	0.03 Comoros	0.30
	14 W Himalaya 0.40 Mozambique	0.03 Thailand	0.30
	15 Taiwan	0.40 Lesser Sunda Is. 0.03 Cambodia	0.29

Table of contents

 of 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . 129 5.2.1 Method motivation . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2.2 Data on the Orchidaceae family . . . . . . . . . . . . . . . . . . 130 5.2.2.1 Species observations . . . . . . . . . . . . . . . . . . . 130 5.2.2.2 IUCN Red List status . . . . . . . . . . . . . . . . . . 130 5.2.2.3 Predictive features . . . . . . . . . . . . . . . . . . . . 130 5.2.3 Method definition . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.3.1 Continents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.3.2 Latitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.3.3 Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4.1 Interpretations . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.4.3 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

	5.2.3.1 Deep species distribution modelling . . . . . . . . . . 131
	5.2.3.2 Dispersal scenarios . . . . . . . . . . . . . . . . . . . . 132
	5.2.3.3 Species niche features for IUCN classifcation . . . . . 132
	5.2.3.4 Classifying extinction risk status from species niche
	features . . . . . . . . . . . . . . . . . . . . . . . . . . 134
	5.2.3.5 Projections within the CMIP6 SSP5-8.5 scenario . . . 135
	5.2.4

TABLE S1

 S1 Validation set statistics on | Ŝλ |, i.e. the size of the species assemblage after thresholding the conditional probabilities of presence with λ (46,290 validation points). The minimum number of species retained in the validation set is four. However, on a global scale there are areas with no species above λ, resulting in empty predictions (e.g. western Algeria). It is also very likely that areas are predicted with more than 401 orchids (the maximum on the validation set).Box D: Maps batch processing and online accessBatch processing Species assemblages are predicted by 50,176 batches for volume reasons. PyTorch model 512-size predictions are accumulated in a buffer until exceeding the 50,000 limit and are then exported. Raw predicted classes and probabilities are appended in binary files whereas spatial indicators are computed on the fly and saved in distinct .geotiff format. Finally, geotiffs are merged and converted to the Cloud Optimized GeoTIFF format (COG): 256 x 256 blocks are tiling the data and six levels of overviews are added.Online and interactive map accessThe web mapping solution used to render the raster data in a web environment is simple. It relies upon a serverless front-end application and a map server able to render OGC (Open Geospatial Consortium) compliant web services : Web Map Service, Web Feature Service, etc. The front-end application is an open-source project called MViewer (https://mviewer.netlify.app/) and is mostly implemented by Brittany region. It parses an .xml configuration file to generate an interactive map. The map server is also an open-source project : GeoServer (https://geoserver.org/). It can read COG data among other geospatial data and serves it as a web service to be displayed by the front-end application.Website is available at https://mapviewer.plantnet.org/?config=apps/store/orchidstatus.xml.

	Chapter 4 & 5
	Box F: Orchid dataset distributions
			(a)			(b)
	0%	20%	40%	60%	80%	100%

https://climate.copernicus.eu/

https://www.nasa.gov/

https://www.birdlife.org/

https://idil.edu.umontpellier.fr/en/

https://www.esa.int/

https://www.iucnredlist.org/, accessed on 09/08/23.

https://www.iucnredlist.org/, accessed on 09/08/23.

registered on the Kew platform Plants of the World Online https://powo.science.kew.org/, accessed on 09/08/23, accepted names only.

https://www.bipindicators.net/

https://www.iucnredlist.org/

https://cites.org/

https://www.theguardian.com/

https://www.eea.europa.eu/

https://www.iucnredlist.org/

https://www.eea.europa.eu/ims

Interactive map available at https://natura2000.eea.europa.eu/

https://geobon.org/

https://www.gbif.org/

e.g. https://observation.org/

https://stac.ecodatacube.eu/

https://marxansolutions.org/

https://zonationteam.github.io/

https://www.copernicus.eu/en

https://sentinelsat.readthedocs.io/en/stable/

https://scihub.copernicus.eu/, queries and downloads require an activated Scihub Copernicus account

https://sentinel.esa.int/web/sentinel/missions/sentinel-2

http://www.idris.fr/annonces/annonce-jean-zay-eng.html

http://www.worldclim.org

https://lpdaac.usgs.gov/products/srtmgl1v003/

https://sedac.ciesin.columbia.edu/data/set/wildareas-v3-2009-human-footprint and 1993 version

https://soilgrids.org/

https://www.iucnredlist.org/about/barometer-of-life

Acknowledgements

Je vais essayer de m'en tenir à une page bien que ça risque d'être compliqué. Ces trois We designed several tests to analyse to what extent the trained model uses the temporal information contained in the image time-series. The general principle is to transform

Acknowledgments

We warmly thank Alexander Zizka for providing us with the filtered set of orchid occurrences. Our dataset contains modified Copernicus Sentinel data and Copernicus Service information (2020, 2021). Sentinel-2 MSI data used were available at no cost from ESA Sentinels Scientific Data Hub. This work was granted access to the HPC resources of IDRIS under the allocation 20XX-AD011011389R1 made by GENCI. Finally, we would like to thank the reviewers for their insightful comments that helped us improve our manuscript.

ACKNOWLEDGEMENTS

The research described in this paper was funded by the European Commission via the GUARDEN and MAMBO projects, which have received funding from the European Union's Horizon Europe research and innovation programme under grant agreements 101060693 and 101060639. The opinions expressed in this work are those of the authors and are not necessarily those of the GUARDEN or MAMBO partners or the European Commission. The INRIA exploratory action CACTUS fund also supported this work. This work was granted access to the HPC resources of IDRIS under the allocation 20XX-AD011013648 made by GENCI. Finally, we warmly thank Alexander Zizka for providing us with the filtered set of orchid occurrences.

ACKNOWLEDGEMENTS

The research described in this paper was funded by the European Commission via the GUARDEN and MAMBO projects, which have received funding from the European Union's Horizon Europe research and innovation programme under grant agreements 101060693 and 101060639. The opinions expressed in this work are those of the authors and are not necessarily those of the GUARDEN or MAMBO partners or the European Commission. The INRIA exploratory action CACTUS fund also supported this work. This work was granted access to the HPC resources of IDRIS under the allocation 20XX-AD011013648 made by GENCI. Finally, we warmly thank Alexander Zizka for providing us with the filtered set of orchid occurrences.

This chapter is an extended version of the article (Estopinan et al., 2022) published in Frontiers in Plant Science. It has been expanded to include a comparison of the performance of the global distribution model using Sentinel-2, WordlClim 2 and static variables.

repository of the DeepOrchidSeries dataset described in section 3.2.1 is available at https://zenodo.org/.

-The sen2patch GitLab repository gathers Python code to collect Sentinel-2 image timeAvailable at https://gitlab.inria.fr/.

Data Availability Statement

• Code is available on the sen2patch gitlab: https://gitlab.inria.fr/jestopin/sen2patch

• Occurrences initial GBIF query is https://doi.org/10.15468/dl.4bijtu (accessed August 2019)

• Dataset and models are available on Zenodo with the DOI: 10.5281/zenodo.4972593.

DATA AVAILABILITY STATEMENT

The data and code that support the findings of this study are openly available in figshare at http://doi.org/10.6084/m9.figshare.22803431 [reserved DOI, active if article published]. Private link in the meantime: https://figshare.com/s/15404886eb3b62363a5f

CHAPTER 4

AI-BASED MAPPING OF THE CONSERVATION STATUS OF ORCHID ASSEMBLAGES AT GLOBAL SCALE

Sumatra case study

On the western side of Sumatra, the Barisan Mountains form a sharp relief (see Figure 4.4a). The elevational diversity gradient theory would suggest that species richness is particularly high along the mountainous area. However, according to the I H indicator on (b), the predicted orchid diversity appears to be fairly constant across the island. Considering only the known IUCN assessments, the presence of CR species (c) is not clearly correlated with the mountain range. In addition, there are areas where no CR species are predicted, for example in the northern and southern regions of the island. When the predicted IUCN status are included in the indicator calculation with I CR on (f) map, high proportions of CR species are predicted across the island. There is a sharp

Abstract

The post-2020 global biodiversity framework needs ambitious, research-informed targets. Estimating the accelerated extinction risk due to climate change is critical. Species distribution modelling based on deep learning (deep-SDMs) offers exciting opportunities to harness species-level information from rich biodiversity data. Field observations, which are massively collected on online platforms, are highly biased. However, by applying compensatory techniques and formulating adapted hypotheses, deep learning models have become robust enough to learn species features representative of their environmental niche. Our curated observation dataset comprises 1M occurrences of 14K orchid species distributed worldwide. Predictive features include bioclimatic and pedological variables, human footprint rasters, ecoregions and location. We evaluate a novel method for classifying the International Union for Conservation of Nature (IUCN) extinction risk status of species benefiting from the generalisation power of deep-SDMs. Cross-validation shows that our method matches state-of-the-art classification performance while relying on flexible SDM-based features that capture species environmental preferences. 889 orchids were assessed by the IUCN. Tenfold cross-validation yields average accuracies of 0.61 for status classification and 0.78 for binary classification (threatened or not). Climate change will reshape future species distributions. Under the species-environment equilibrium hypothesis, SDM projections approximate plausible future outcomes. Two extremes of species dispersal capacity are considered: unlimited or null, with the most likely species trajectories assumed to lie in between. The projected species distributions are translated in the features feeding our IUCN classification method. Finally, trends of threatened species are analysed in time and i) by continent and as a function of average ii) latitude or iii) altitude. The proportion of threatened species is increasing globally, with critical rates in Africa, Asia and South America. Furthermore, the proportion of threatened species is predicted peak around both Tropics, at the Equator, in the lowlands and in the 800-1,500 m altitudinal range. Taking only climate change into account, we predict that the total number of threatened orchid species will increase by a third by 2100, with a marked acceleration in the second half of the century, important geographical disparities and an irregular increase along elevation.

Keywords

deep learning, species distribution modelling, IUCN status, extinction risk, orchids

Introduction

Failure to meet any of the 2020 Aichi Biodiversity Targets is a clear signal that transformative change is urgently needed (IPBES, 2019). The post-2020 global biodiversity framework must set ambitious targets with quantified, measurable objectives underpinned by research [START_REF] Mace | Aiming higher to bend the curve of biodiversity loss[END_REF]. Biodiversity targets based on species extinction rates and measures of ecosystem services, for example, should be included [START_REF] Reyers | Getting the measure of ecosystem services: a social-ecological approach[END_REF][START_REF] Rounsevell | A biodiversity target based on species extinctions[END_REF]. Indeed, this could help to galvanise policy in a similar way to the 2°C maximum climate change target. Finally, such goals are inherently interlinked CHAPTER 6 et al., 2016b). Initially designed to accept three-channel rgb images, it was modified to deal with a higher number of channels. This convolutional neural network learn patterns from spatialized input predictors. Letting models benefit from the spatial information was shown successful in various literature applications (Botella et al., 2018a;[START_REF] Deneu | Convolutional neural networks improve species distribution modelling by capturing the spatial structure of the environment[END_REF]. Successive inception modules are composed of convolutional filters of different sizes. This allows the different patch patterns of all sizes to be captured. Convolutional layers reduce the very high input dimension and a final softmax layer outputs the conditional probability distributions. Inputs are concatenated along the channel dimension. It results in N × 64 × 64 tensors with N the total channel number. Pixel resolution is of 1 km.

CONCLUSION AND PERSPECTIVES

A large 64 × 64 km² environmental context is therefore provided. The model is also spatially explicit: observation longitude and latitude are supplied in two dedicated channels along with the other predictors.

Deep learning models successfully process large numbers of inputs and classes with few samples. In fact, the modelling paradigm is completely different from combined per-species models. The filters learned during training are applied to all samples, all classes combined. The final softmax layer, which outputs class probabilities conditionally on an observation, is based on a reduced representation space common to all classes. This space has been shown to be structured by the ecological preferences of species in [START_REF] Deneu | Interprétabilité des mod'eles de distribution d'esp'eces basés sur des réseaux de neurones convolutifs[END_REF]. More generally, deep learning classification with strong class imbalance is a very active research avenue. DL outperforms classical approaches to model classes with few samples. In conclusion, our deep-SDM is not affected by the curse of dimensionality.

Dataset spatial split A spatial block hold-out validation strategy is employed to limit the effect of the spatial auto-correlation in the data in the evaluation of the model (as suggested in [START_REF] Roberts | Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure[END_REF] Box B: Species assemblage post-processing Species assemblages and their relative probabilities are finally post-processed in two steps. We derive first from the initial occurrence set the inhabited continents of each species (WGSRPD level 1). This allows to filter out species predicted by the model outside their known continents of presence. Filtered assemblages of species are denoted Ŝ′ λ . We computed statistics on this filtering step with a geographic prior on a global regular grid with 0.5 decimal degree resolution. The median number of species removed is 6, or 9.1% of the assemblage. Full statistics and map discrepancies are further discussed in Figure S3. Second, kept species conditional probabilities are normalised. Species with a conditional probability of presence smaller than λ are considered absent from the predicted assemblage, as well as species predicted outside their known continents of presence. In both cases, associated conditional probabilities were forced to zero. Normalisation allows to get back to a probability distribution summing to one. For a given input x, final probabilities are obtained with η′

Box C: Model evaluation and calibration

Evaluation of the deep-SDM The deep-SDM model was evaluated on unseen occurrences from the validation spatial blocks. Validation performances set the best epoch choice -the 69 th -for final test set metrics to be computed. Selected metrics are the top-k accuracy and its per-class counterpart the top-k accuracy per species. These set-valued metrics do not require pseudo absences to avoid potential induced bias [START_REF] Phillips | Sample selection bias and presence-only distribution models: implications for background and pseudo-absence data[END_REF]. Top-k accuracy measures if the model returns the correct label among the k most likely classes:

with (x i , y i ) an input/label pair and η the permutation of η sorted in descending order.

The success rate can be calculated for all test set occurrences, all classes combined (micro-average denoted A k ) or first for each class individually and then averaged together (macro-average denoted MSA k ). The former gives prominence to common species by construction, while the latter depends heavily on rare species performances. Macro-average metrics are suitable for highly imbalanced datasets.

Final test set performances at epoch 69 are A 30 = 0.87 and MSA 30 = 0.48. This means that i) the correct label is returned among the first 30 species for 87% of the test observations (representative of common species), and ii) when each species in the test set is given the same weight, the correct label is within the first 30 classes returned almost half the time. This second metric may seem low, but it actually measures a particularly difficult task, given that the test set contains 4,166 species (30/4166 ≤ 1%). Furthermore, it reflects the performance of the model on rare species, and Figure S5 shows that considering on average 124 species significantly improves performance on the validation set, see next paragraph. Finally, training and validation curves show no sign of overfitting, see Figure S4. (b) Considering the same two variables, the Spearman correlation and the ρ-value for all countries of the same continent. According to the ρ-values, the correlations are statistically significant only in Asia-Temperate, Europe and North America. Furthermore, looking at the scatter plot, we can see that the European and North American diversity ranges are limited. Finally, it is only in Asia-Temperate that we observe a significant and positive correlation between threat levels and a wide diversity range.

Box E: Comparison with established indicators

The µ[I THREAT ] top countries (i.e. countries with the highest average proportion of predicted threatened species) largely overlap with the countries identified in [START_REF] Zizka | Automated conservation assessment of the orchid family with deep learning[END_REF] as having the highest proportion of potentially threatened species.

The Red List of Ecosystems (RLE) is a classification scheme of the risk of ecosystem collapse, with categories and an assessment process that mirror the IUCN Red List of Threatened Species [START_REF] Keith | Scientific Foundations for an IUCN Red List of Ecosystems[END_REF]. This promising indicator currently suffers from poor data coverage, with only 509 assessments registered as of April 2023 (https://assessments.iucnrle.org/, accessed on 26/04/23). This comparison highlights the rare global consistency of our indicators. We could also imagine ecosystem-level indicators that take into account the extinction risk of species assemblages in their construction.

Safeguarding ecosystems within the post-2020 global biodiversity framework requires robust indicators that capture different dimensions: area, integrity and risk of collapse [START_REF] Nicholson | Scientific foundations for an ecosystem goal, milestones and indicators for the post-2020 global biodiversity framework[END_REF]. Among the recommendations for selecting indicators, two are particularly relevant to our work: 4. greater testing and validation of indicators is required to understand their ecosystem relevance, reliability and ease of interpretation and 5. the connection between global indicators and national or local policy and reporting needs strengthening. Our indicators meet recommendation five, but suffer from a lack of ground truthing to be confidently applied on the ground, as the fourth recommendation points out.

Protecting species for their evolutionary distinctiveness, combined with an IUCN threatened status, is the approach taken by EDGE (Evolutionary Distinct Globally Endangered, [START_REF] Isaac | The use of EDGE (Evolutionary Distinct Globally Endangered) and EDGE-like metrics to evaluate taxa for conservation[END_REF]. While EDGE species must be officially listed as threatened by the IUCN in addition to having an above-average ED score (Evolutionary Distinctiveness), Vitt et al., 2023 developed a conservation prioritisation method based on ED and rarity as the number of occupied regions or the area of occupancy. Here, the spatial ranges considered are compiled from the World Checklist of Selected Plant Families (WCSP) and Global Inventory of Floras and Traits (GIFT) databases. Tropical Africa does not emerge as a clear priority hotspot as our indicators suggest. However, they highlight the Neotropics and Southeast Asia as hotspots of richness, as does our Shannon index indicator. They also identify islands as having particularly high numbers of rare and distinct species. Interestingly, they point out that orchid ED is highly correlated with their richness (R² = 0.87).

Finally, the closest indicator to date from our work is the global extinction probability of terrestrial vascular plants [START_REF] Verones | Global extinction probabilities of terrestrial, freshwater, and marine species groups for use in Life Cycle Assessment[END_REF]. In a given place, this indicator is high if many threatened species are known to occur there and/or if they have very small ranges. However, we defend our kilometre-scale resolution and the novel way in which we calculate I c . This allows us to weight the contribution of species by their relative probability of occurrence.

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Although the Shannon index measures not only community richness but also its evenness, global vascular plant richness maps such as [START_REF] Cai | Global models and predictions of plant diversity based on advanced machine learning techniques[END_REF] are the closest available point of comparison. Again, both the resolution and construction of our indicator differ from previous work.

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Table S2: List of predictors. They are either categorical or continuous and can be gathered into five groups: the terrestrial ecoregions of the world, the WorldClim2 bioclimatic variables, the Soilgrids pedological variables, the detailed rasters of the human footprint and the location.

Chapter 5

Box H: Description of the .csv files containing the status predictions Description of the status prediction supplementary file ALL_species_status.csv. This .csv lists the status predicted with our classifier for the 14,129 species of our dataset:

-At two different levels: broad, i.e. the binary classification Threatened or not, and detail, i.e. the five IUCN categories from LC to CR. -For two different dispersal scenario: False meaning that no dispersal is allowed and species can only be re-predicted only where they once occurred, and True meaning that species can potentially be re-predicted on all our dataset points. -For five different time periods matching the Worldclim 2 bioclimatic projections: Present, 2021-2040, 2041-2060, 2061-2080 and 2081-2100.

Here are the meanings of the common fields:

species is the GBIF canonical species name -speciesKey is the GBIF unique key associated to the species lat, lon, HFP09, Elevation are the species average values across the dataset's observations for respectively latitude, longitude, 2009 human footprint index and elevation. continents provides the set of WGSRPD level 3 regions in which the species occurs. -IUCNonly indicates whether the species is currently assessed by the IUCN (886) or not (13,243). -For IUCN-assessed species, the present categories are the current official red list levels and not predictions.

Description of the Extinct species supplementary file EXT_species.csv. This .csv lists the 234 species predicted to be extinct by the model. Fields are identical to the ALL_species_status.csv file described below, with the noticeable differences being:

time period is the field indicating the first period from which the species is predicted to be extinct. -All species predicted to be extinct come from the null dispersal scenario. In addition, one species is predicted to be extinct as of now: Dendrobium rhytidothece. This species is not red listed and is known on the GBIF only from six occurrences, five of which date from 1909 and the last one being fuzzy a . There are 42 species currently assessed by the IUCN that are predicted to become extinct (and 192 P r e s e n t 2 0 2 1 / 2 0 4 0 2 0 4 1 / 2 0 6 0 2 0 6 1 / 2 0 8 0 2 0 8 1 / 2 1 0 0 N. America (n=73) P r e s e n t 2 0 2 1 / 2 0 4 0 2 0 4 1 / 2 0 6 0 2 0 6 1 / 2 0 8 0 2 0 8 1 / 2 1 0 0 Pacific (n=12) P r e s e n t 2 0 2 1 / 2 0 4 0 2 0 4 1 / 2 0 6 0 2 0 6 1 / 2 0 8 0 2 0 8 1 / 2 1 0 0

S. America (n=132) Status

Not Threatened Threatened EXT

Figure S12

: Binary status proportions per continent and time period. Only IUCN-listed species are included, and their number per continent is given in the subtitle. Error bars account for differences between the two dispersal scenarios. With this restriction, some different trends are apparent. In North America, out of 73 species, the proportion of threatened species is actually predicted to decrease steadily (same trend for the 12 Pacific species, but there are too few species to be considered a robust result). In Africa, the proportion of threatened species is projected to increase to more than 80% by the end of the century. In tropical Asia, the number of threatened species is increasing but is significantly lower than when all species are considered. Levels are also lower in Europe if only IUCN-assessed species are considered. Overall, it is interesting to observe that continental trends and levels can be quite different when only IUCN-assessed species are considered. For us, this is an indication of the model's ability to generalise without simply overfitting and replicating patterns between neighbouring species. A trident pattern appears for threatened species, but: i) the highest threatened species peak is at about -20°latitude and ii) high counts of threatened species around the 25°parallel do not increase, unlike the figure for all species. Again, the differences between the two species support confirms that our status classifier relies on specific species-level information and not just spatial information. This figure also confirms that the current IUCN assessment is biased towards the northern hemisphere. Only IUCN-listed species are included. Boxes cover 150 metre altitude ranges. Overall, we found the same patterns in this figure as in its all-species counterpart. However, the hump-shaped concentration of threatened species at 800-1,500m is replaced here by a more irregular peak forest. Therefore, in this case, our approach seems to regularise the number of threatened species along the altitudinal gradient. Nevertheless, causality cannot be inferred from our study. A confounding variable such as threat exposure could indeed be at the origin of this pattern. In addition, species already IUCN-assessed and predicted to become extinct seem to be distributed between the lowlands and around 2000 m. [START_REF] Venter | Global terrestrial Human Footprint maps for 1993 and 2009[END_REF].

The species count axis is log-scale. The HFP score of a species is averaged over its current occurrences. These histograms allow us to assess the number of species per bin used to calculate the proportions shown in Figure S17. The main message is that high HFP bins contain very few species and the following proportions should then be treated with caution.

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