Katelin D Pearson

MYLA Gil Nelson

Myla Aronson

Pierre Bonnet

Laura Brenskelle

Charles C Davis

Ellen G Denny

Elizabeth R Ellwood

Hervé Goëau

J Mason

F J Aronson

J Mason Heberling

Alexis Joly

Titouan Lorieul

Susan J Mazer

Emily K Meineke

Brian J Stucky

Patrick Sweeney

AND Alexander E White

Pamela S Soltis

Machine Learning Using Digitized Herbarium Specimens to Advance Phenological Research

Keywords: phenology, machine learning, biodiversity, climate change, deep learning

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

S easonal variation in the timing of life cycle (phenological) events (e.g., leaf-out, flowering, and fruiting) critically affects plant ecology and evolution through interactions between plants and climate [START_REF] Cleland | Shifting plant phenology in response to global change[END_REF], herbivores [START_REF] Meineke | Early pest development and loss of biological control are associated with urban warming[END_REF], mutualists [START_REF] Diamond | Unexpected phenological responses of butterflies to the interaction of urbanization and geographic temperature[END_REF], and inter-and intraspecific competitors [START_REF] Heberling | Phenological mismatch with trees reduces wildflower carbon budgets[END_REF]. Changes in the timing of plant phenological events can alter species interactions, such as those between plants and their pollinators [START_REF] Burkle | Plant-pollinator interactions over 120 years: Loss of species, co-occurrence, and function[END_REF]) and even disrupt interactions at higher trophic levels, such as those between bears and salmon [START_REF] Deacy | Phenological synchronization disrupts trophic interactions between Kodiak brown bears and salmon[END_REF]. The significance and complexity of plant phenology on local and global scales lead to many compelling questions for science and society [START_REF] Ellwood | Emerging frontiers in phenological research[END_REF], especially as anthropogenic changes in habitat, biodiversity, and climate alter phenological events [START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF].

Wide-ranging and complex phenological responses to climate change have been discovered in many taxa across the globe (Willis et al. 2017a), but our understanding of the mechanisms driving these complicated phenomena and their subsequent effects are incomplete. Critical questions remain about the effects and interactions of climate, traits, geography, and phylogeny on the phenological sensitivities of plants and how these effects propagate throughout ecosystems (box 1). These factors could play key roles in understanding, predicting, and potentially ameliorating environmental changes that threaten biodiversity and humankind.

The variable and context-dependent nature of plant phenology renders its study particularly challenging because long-term data sets are necessary to detect the patterns, causes, and consequences of phenological change for a given taxon in a given location [START_REF] Wolkovich | Warming experiments underpredict plant phenological responses to climate change[END_REF]. Historical phenological observations [START_REF] Primack | Uncovering, collecting, and analyzing records to investigate the ecological impacts of climate change: A template from Thoreau's Concord[END_REF], agricultural records (e.g., crop harvest records; [START_REF] Ellwood | Cranberry flowering times and climate change in southern Massachusetts[END_REF], long-term field stations [START_REF] Taylor | Comparison of large-scale citizen science data and long-term study data for phenology modeling[END_REF], and, more recently, citizen science networks [START_REF] Bison | Comparison of budburst phenology trends and precision among participants in a citizen science program[END_REF]) have proven vital sources of phenological data. However, none of these resources provides the spatiotemporal coverage available from herbarium specimens. Herbarium specimens have been archived for hundreds of years from across the globe and therefore represent a rich source of phenological data [START_REF] Zalamea | Continental-scale patterns of Cecropia reproductive phenology: Evidence from herbarium specimens[END_REF], especially as specimen data (e.g., date, species, and locality) and specimen images become digitally available through large-scale digitization projects [START_REF] Nelson | The history and impact of digitization and digital data mobilization on biodiversity research[END_REF]. Specimenbased studies have greatly informed our understanding of

Questions about ML methodology

This list consists of questions relating to the methodology and limitations of machine learning for assessing phenology from herbarium specimens.

• Can ML algorithms reliably recognize plant reproductive structures?

• Can ML methods appropriately convey the level of confidence or uncertainty associated with any given classification or count?

• How many training images are necessary to train phenological data sets, and does this number exceed the number of specimens needed to conduct phenological studies?

• How does a computer "decide" how to classify specimens, and is the decision process generalizable?

• What are systematic errors from ML that could propagate and impact studies that use automatically annotated data?

• At which taxonomic scales and physical dimensions can ML contribute to phenological studies?

• How can the robustness of phenological annotations with ML approaches be ensured in data-deficient contexts (e.g., rare species or neglected floras)?

phenological change beyond what was previously possible (Willis et al. 2017a). To date, most phenological studies using herbarium specimens have relied on manual annotation (see table 1 for a glossary of italicized terms) of specimens to record phenological traits (Willis et al. 2017a). Herbarium staff might record the presence or absence of reproductive structures while transcribing specimen data, or, more commonly, researchers classify phenological traits from physical specimens or specimen images for specific projects. Such methods are time and labor intensive, and the accuracy and precision of the resulting phenological annotations depend on the botanical expertise and consistency of the scorer, as well as on how easily the relevant anatomical structures can be identified on dried, pressed plants. To study phenology on a global scale, many thousands-even millions-of specimens must be annotated, but manual annotation at this scale is not feasible. Machine learning (ML) approaches have the potential to overcome this challenge by automating phenological data acquisition. ML approaches have empowered advances in many areas of science and technology, with applications from self-driving cars [START_REF] Wulff | Early fusion of camera and lidar for robust road detection based on U-Net FCN[END_REF]) to biomedical imaging [START_REF] Ronneberger | U-Net: Convolutional networks for biomedical image segmentation[END_REF]. Plant phenology, one of the best-known indicators of climate change, presents a fast-growing frontier for the deployment of these powerful methods. ML algorithms build statistical models from input data (i.e., training data), and these models can then be applied to make predictions on novel data [START_REF] Lecun | Deep learning[END_REF]. For image annotation tasks, for example, ML algorithms create statistical models ("learn") from a training data set of images that have already been annotated. Then, the algorithms use these models to predict annotations for images that have not been annotated. ML has been successfully applied to many biological studies requiring classification of visual information, including the recognition and classification of animals in camera trap images [START_REF] Norouzzadeh | Automatically identifying, counting, and describing wild animals in camera-trap images with deep learning[END_REF] and the automated species identification of herbarium specimens (e.g., [START_REF] Unger | Computer vision applied to herbarium specimens of German trees: Testing the future utility of the millions of herbarium specimen images for automated identification[END_REF][START_REF] Carranza-Rojas | Going deeper in the automated identification of herbarium specimens[END_REF].

Biologist's Toolbox

Successful application of ML techniques to phenological annotation tasks has only recently been demonstrated for herbarium specimen images [START_REF] Lorieul | Toward a large-scale and deep phenological stage annotation of herbarium specimens: Case studies from temperate, tropical, and equatorial floras[END_REF]). In the present article, we describe a generalized ML workflow for phenological annotation of plant specimen images, and we discuss the advantages, limitations, and potential future improvements of this workflow. Furthermore, we explore how technological advances in ML will facilitate the collection of additional phenological and other trait data from images, enhancing ecoevolutionary research and biodiversity education.

Machine learning with digitized herbarium specimens

Figure 1 presents a workflow of five components for phenological annotation of herbarium specimen images (storage, generating training data, machine learning, deployment, and testing and analysis; figure 1), further described below. A detailed discussion of ML methodology can be found in Lorieul and colleagues (2019). In the present article, we use the term annotation to describe the general process of adding ancillary data to a specimen record. Although we focus on phenological annotation-recording of the phenological status of a specimen-many other types of annotation exist, such as georeferencing, taxonomic identification, and scoring of nonphenological traits. Core specimen data, such as collection date, scientific name, collector name, and textual locality information, are often captured and mobilized as part of large-scale digitization initiatives (e.g., more than 120 million specimen records contain this information in iDigBio; www.idigbio.org). Therefore, we do not describe the use of ML for harvesting these data. We focus in the present article on the application of ML to automatically identify and record the phenological status of specimen images, ideally those images for which these core specimen data are already available.

Storage. Input and output data for ML approaches consist of digital images of specimens, associated core specimen data (e.g., specimen identifier, collection date, etc.), and phenological annotations. High-resolution images (e.g., up to tens of millions of pixels per specimen) can represent a very large

Figure 1. Key components of a generalized, modular machine learning (ML) workflow applied to the annotation of herbarium specimen images for phenological traits. Specimen images are retrieved from storage, and a representative subset of the focal images are used to generate a set of training data. The training data, which have been manually annotated according to the desired phenological scoring protocol (e.g., flowers present or absent), are used as input data for ML. The resulting statistical model is then deployed to predict phenological annotations for previously unannotated specimens. The accuracy and precision of the ML model(s) can be tested using a subset of manually annotated data to compare predicted annotations to those recorded by expert observers. Newly annotated specimens, combined with specimen label data, georeferenced localities, and other data sets (e.g., historical climate data), can then be used in an array of phenological research.

https://academic.oup.com/bioscience XXXX XXXX / Vol. XX No. X • BioScience 5

volume of data (4-10 megabytes per image), and their storage therefore requires software and hardware infrastructure designed for large amounts of data.

Generating training data. The images used to "train" ML algorithms must first be manually annotated with phenological information according to the desired protocol. For example, if a researcher is interested only in whether a specimen has flowers, each specimen image would be annotated as flowers "present" or "absent. " A model based on these training data will classify specimens as either of these two classes.

If the researcher wishes to detect individual reproductive structures on a specimen, for example, in order to count them or estimate their relative proportions, these could be delineated by bounding boxes, which indicate the general location of structures, or segmentation masks, which designate all pixels belonging to a reproductive structure. To produce these more complex annotations, specific annotation tools are usually required (e.g., CocoAnnotator, https:// annotator.justinbrooks.ca; LabelMe, http://labelme.csail.mit. edu/Release3.0; ImageTagger, https://github.com/bit-bots/ imagetagger). Regardless of the type of phenological annotation being created, it is important to recognize that ML is a form of statistical inference that finds patterns in the training data, and predictions will therefore reflect any biases in those data. Therefore, the training data set should include a representative sample of taxon (or taxa) and phenological attributes or categories that should appear in the data set on which the trained model will be applied. A lack of visual diversity in the manual annotations will result in the same lack of diversity in the predictions. Similarly, noisy, imprecise, or incomplete annotations may result in noisy, imprecise, or incomplete predictions. A subset of the training data should also be reserved for model validation (see the "Testing and analysis" section).

The number of specimens necessary to train a model depends on the complexity of the classification task, the number and morphological diversity of taxa included in the data set, and whether the model will be trained iteratively. Initial models with a small set of training data (at least 500 specimens) can be used to annotate a much larger set of data, and the ML-generated annotations can be revised and enriched through additional manual annotation, and then used to train the model further (see [START_REF] Affouard | Pl@ntnet app in the era of deep learning[END_REF]. As the annotated training data set grows, models will improve and become more useful for identifying edge cases (e.g., specimens on which phenological attributes are partially obscured, taxa that are represented by only a few specimens) that might be missing in a small training data set, as well as phenological phases that are morphologically highly variable or represented by very small reproductive structures.

Machine learning and deep learning. For image data, the most effective machine learning techniques are deep learning neural networks, or more precisely, convolutional neural networks (CNN), or extensions such as CNNs for object detection (e.g., R-CNN) or instance segmentation (e.g., Mask-R-CNN). Like any neural network, a CNN is a composition of functions that receive an image as input and provide predictions as output (e.g., a phenological score of the entire specimen or a set of bounding boxes around reproductive structures). The term convolutional refers to the fact that for each input pixel, the functions return the result of a local computation (a filter) based on the pixel and its neighboring pixels. The number of neighboring pixels (i.e., filter size) is set as a parameter of the model. Each filter can be interpreted as a detector of a specific, local visual pattern.

CNNs consist of multiple layers of processing. The first layers of a CNN detect low-level patterns (color changes, angles, textures, etc.), whereas the last layers recognize complex visual patterns (such as reproductive structures on a specimen) by combining the patterns found in previous layers. The main objective of the training phase of a CNN model is to estimate the parameters of these filters on the basis of the training data. This is done by iteratively minimizing a loss function measuring the error between the predictions and the expected manual annotations.

As the number of parameters to be estimated can be in the millions, this training phase consumes significant computational resources, because the training process requires efficient storage to handle frequent access to the training set and efficient graphics processing units (GPUs) to reduce the training time. The type of model may differ depending on the task, but the duration of the training phase is strongly related to the GPU number and characteristics. The greater the availability of computational resources, the more training a model can undergo, and the better the final model architecture and parameter selection can be.

Available online tools can enable inexperienced users to train ML models, but these tools are limited to simple image classification tasks and low data volumes. Therefore, at present, developing accurate models is often achieved by involving a data scientist for several days, weeks, or months depending on the difficulty of the task. The software frameworks most commonly used to develop CNNs are Pytorch (https://pytorch.org), TensorFlow (www.tensorflow. org), CAFFE (https://caffe.berkeleyvision.org), and MXNET (https://mxnet.incubator.apache.org). The framework that is best for a given task will depend on a variety of factors, including the availability of preexisting models or code for the targeted task, the hardware used, or simply the data scientist's skills with respect to a particular framework.

Deployment. Once an ML model is trained, it can be deployed to predict phenological annotations for previously unannotated specimens. This process could be implemented in several ways, including via a web service available to other applications that returns the model output for any submitted image, a standalone program, or an end-user graphical user interface (GUI) web application. Inference is usually a less computationally intensive task than training and therefore requires fewer resources. Models can be publicly shared through software repositories hosted on sites such as GitHub (https://github.com), GitLab (https://gitlab.com), or dedicated platforms such as Model Zoo (https://modelzoo.co). Such sharing encourages cross-model improvement based on transfer learning [START_REF] Bengio | Deep learning of representations for unsupervised and transfer learning[END_REF] or domain adaptation techniques [START_REF] Long | Unsupervised domain adaptation with residual transfer networks[END_REF].

Testing and analysis. Once deployed, a model can be evaluated through qualitative judgments or quantitative measurements. Qualitative judgments are typically performed through a GUI, allowing the researcher to visualize and assess the automated predictions of the model on this test data set. For more robust measures of model accuracy, quantitative measurements of the quality of the predictions can be readily calculated and visualized (see [START_REF] Lorieul | Toward a large-scale and deep phenological stage annotation of herbarium specimens: Case studies from temperate, tropical, and equatorial floras[END_REF]). This step cannot be performed on the same data used for training the model; a model can perfectly fit the training data and not fit new data of the same type. Therefore, some of the manually annotated data (e.g., 20%-30%) must be reserved and not used for training purposes [START_REF] Carranza-Rojas | Going deeper in the automated identification of herbarium specimens[END_REF]. As with developing appropriate training data, a deep understanding of the data set and the desired end product is necessary. The goals are to determine whether the model meets the needs of the researcher and to identify the necessary progress points (e.g., new annotations on a particular taxonomic group or phenological stage).

Advantages of machine learning for phenology

The main advantage of using ML for phenological annotation is ML's ability to score very large volumes of data in a short amount of time. Once an algorithm has been trained, it can score tens to thousands of specimens per minute, depending on the task, with a single standard GPU. For example, during summer 2019, more than 490,000 field plant images were analyzed for species identification on the public Pl@ntNet platform in a single day [START_REF] Affouard | Pl@ntnet app in the era of deep learning[END_REF]. Model processing can be further accelerated by using many GPUs in parallel. Another key advantage is that the accuracy of ML annotations can be very high. The deep learning method evaluated in Lorieul and colleagues (2019) correctly detected fertile specimens with an accuracy of 96.3%. Such a success rate is quite high, especially considering that one coauthor of the present article obtained an accuracy of only 87.8% at the same task. Accuracy was slightly decreased for finer-scale phenological annotations (84.3% for the detection of flowers and 80.5% for the detection of fruits) or for determining specific phenophases of specimens, but again, the model's accuracy was slightly better than the accuracy of a human expert.

With the large volumes of phenological data produced from ML methods, it will be possible to create phenoclimatic and other phenological models at unprecedented scales of time, space, and phylogenetic diversity. Leveraging a large number of specimens for phenological models has already helped identify influential climate variables that may have been overlooked in previous studies [START_REF] Park | Overlooked climate parameters best predict flowering onset: Assessing phenological models using the elastic net[END_REF]. Large sample sizes and potentially finer scales of phenological annotation could further elucidate differences in phenological trends among taxa and between regions. Phenological annotation via ML could also be used to address current spatial biases in phenological studies, for example, through applications using herbarium specimens from tropical and subtropical climates, where phenological trends are less well documented (Willis et al. 2017a).

Limitations of machine learning applications

The workflow described above is not without limitations; there are technological, social, and logistical challenges that must be overcome for efficient application of ML in phenological research. Herbarium specimens may themselves limit their utility for phenological scoring, because they differ in quality and quantity (figure 2; for a review, see Willis et al. 2017a). The morphological structures necessary to measure a given phenological trait may be damaged or lost, stored in opaque fragment packets, or obscured by other plant material on the sheet. Some plant taxa have phenological stages that are impossible to determine without dissecting the physical specimen. For example, the fruits of sedges are often indistinguishable from female flowers, and fig flowers are tightly enclosed within vegetative receptacles. Furthermore, herbarium specimens often consist of only a portion of a plant, and therefore the reproductive status of the entire plant may not be readily discernible except via the label or field notes, when they exist. In each of these cases, ML algorithms, no matter how accurate at recognizing reproductive structures on herbarium specimen images, cannot fully determine the phenological status of a plant from a specimen.

Beyond these general issues, there are additional considerations for applying ML to herbarium specimen images. Specimens contain a significant amount of nonplant material such as herbarium stamps or logos, labels, mounting tape, color standard plates, rulers, or evidence of past pest-control measures that may bias certain ML classification tasks (figure 2). Because ML techniques use all visual data available, the algorithms could reflect differences in preparation techniques rather than in the presence or numbers of particular plant structures. Finally, when preparing training data sets, users of herbarium data must be aware of duplicate specimens-the same species collected at the same time in the same place-and of possible misidentified specimens.

Future solutions for developing optimal machine learning workflows Perhaps the greatest limitation of the ML workflow is the requirement for adequate training data sets. Training data sets need not be large, but a visually diverse set of specimen images of focal taxa must be available. Although several million herbarium specimens have been digitized and mobilized online (currently nearly 30 million images in iDigBio), most of the 375 million specimens in herbarium collections As more specimen images become available, they must also be accurately annotated according to the desired phenological classification protocol. Citizen science and crowdsourcing can accelerate the image annotation process, as has been demonstrated by platforms such as Zooniverse (www.zooniverse.org), From the Page (https://fromthepage. com), Pl@ntNet (https://plantnet.org/en), and CrowdCurio (Willis et al. 2017b). Engaging students in this process as a learning experience could be a dual-benefit solution (see the "Extending machine learning" section). Mass annotation by volunteers with heterogeneous skills presents its own challenges, including the need to attract and retain volunteer interest and ensure data quality, but it offers the additional benefits of community engagement and education.

Regardless of how training data sets are created, both input and output data of ML analyses must be accessible, reproducible, and reusable. ML metadata, such as the type of model used to create the prediction, the contact information of the model creator, uncertainty regarding phenological predictions, and reference to the training data set, must be carefully documented so that downstream users can reproduce and assess the utility of the scorings for their specific research purposes. Furthermore, the potentially complex outputs of ML approaches (e.g., coordinates of reproductive structures on an image) must be stored in a way that is interoperable with alternative specimen classification methods (e.g., manual annotation) and intelligible to nonexperts of ML, while at the same time being reproducible by those with ML expertise. The development of standard vocabularies, metadata protocols, and data structures within the scaffold of existing biodiversity data standards (i.e., Darwin Core; see [START_REF] Yost | Digitization protocol for scoring reproductive phenology from herbarium specimens of seed plants[END_REF]) would greatly advance this aim. When designing ML-based phenological studies, researchers should consider how to integrate output data and metadata with existing databases or data sets, ideally using terms and relationships from the Plant Phenology Ontology [START_REF] Stucky | The plant phenology ontology: A new informatics resource for large-scale integration of plant phenology data[END_REF][START_REF] Brenskelle | Integrating herbarium specimen observations into global phenology data systems[END_REF]. A relatively small investment early in the research process can ensure that ML-generated, "extended" data (sensu [START_REF] Lendemer | The extended specimen network: A strategy to enhance US biodiversity collections, promote research and education[END_REF]) can be productively leveraged by other researchers and owners of the original data (i.e., natural history collections), thereby increase the value of the specimens. This process would benefit from further discussion across biological and computer science disciplines, for example, within the framework of the Research Data Alliance (www.rd-alliance.org).

Figure 2. Examples of herbarium specimens displaying visual heterogeneity (e.g., in morphology, labels, and color standards) and challenges related to the morphology and position of reproductive structures. The specimen on the left shows large, isolated reproductive structures that would likely be annotated successfully by ML algorithms. The specimen in the center with small flowers and numerous overlapping fruits would be much more difficult for ML algorithms to parse. The specimen on the right would be very difficult for ML algorithms to delineate or count because of the unclear distinction between flowers and buds. Examples of segmentation masks (see the glossary in box 1) created to delineate reproductive structures are shown by the brightly colored areas in the left and center specimen images.

Another significant advance for ML-based phenological annotation would be a better understanding of the limitations of ML methods for phenological annotation tasks. Current specimen-based studies using ML have yet to diversify beyond simple classification tasks (e.g., whole images classified as "flower present" or "flower absent") to more complex tasks, such as object detection and localization (see [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF] or the use of models that focus on a subset of visual data, rather than the entire image (see [START_REF] Mnih | Recurrent models of visual attention[END_REF]. To move forward with the design and implementation of ML techniques for phenological studies, questions concerning methodology and appropriateness (e.g., table 1) must be addressed with future research.

However, evaluating models with high complexity may not be easy to achieve given presently available, highly localized cyberinfrastructure. ML approaches, especially those using thousands of high-resolution images, require computers with fast GPUs, but high-power computing clusters are generally heavier in central processing units (CPUs) than GPUs. Therefore, having advanced computing resources does not necessarily guarantee the ability to conduct image-based ML experiments. Although publicly accessible GPU resources (e.g., XSEDE; [START_REF] Towns | XSEDE: Accelerating scientific discovery[END_REF]) and sharing of ML methods (e.g., through Model Zoo) are growing, large-scale and collaborative platforms for using and sharing ML techniques for biological applications are lacking. Greater investment in interoperable cyberinfrastructure resources that are available to a broader, collaborative community is needed.

Increased communication, collaboration, and sharing of cyberinfrastructure resources across institutional and disciplinary boundaries (e.g., between computer scientists and biodiversity data managers) are also critical to advancing this field. Fully exploring the potential of ML approaches may require collaboration beyond academia. Several private companies already provide financial or IT resources to advance ML techniques in the fields of biodiversity, agriculture, and the environment, including Microsoft, with the AI for Earth initiative, and Google, which supports workshops on the fine-grained visual categorization of various biological entities. Collaboration with technology companies such as FaceBook, Dell, or Nvidia, which have significant expertise and resources in this field, may be influential in the successful development and deployment of ML applications for large herbarium collections.

Many of the challenges in the phenological workflow outlined above are generalizable, and ML innovations from other disciplines hold promise for applications in herbarium science. Broadly, museum-based applications may benefit from innovations in ML model architectures in which tasks are general (e.g., segmenting images into constituent elements), transfer learning from other domains in which plant images may be used (e.g., agricultural applications), and ML-based applications in associated data-rich domains in which images are associated with rich tabular data (e.g., medical images, which may be linked to multidimensional patient histories) [START_REF] Esteva | Dermatologist-level classification of skin cancer with deep neural networks[END_REF]. Advances in medical imaging in which specific anatomical structures need to be identified, measured, and evaluated for patient diagnosis have already provided the ML community with model architectures [START_REF] Ronneberger | U-Net: Convolutional networks for biomedical image segmentation[END_REF] that are now applied broadly to segmentation tasks in domains as seemingly distant as automated driving [START_REF] Wulff | Early fusion of camera and lidar for robust road detection based on U-Net FCN[END_REF]. Other disciplines that may yield useful innovations include astronomy, single-cell phenotyping, finance, e-commerce, manufacturing, and defense. Potentially useful botanical applications shared with these domains include anomaly detection, segmentation, high-dimensional image-based clustering, and digital transcription. Recent advances in digital agriculture (e.g., [START_REF] Ghosal | An explainable deep machine vision framework for plant stress phenotyping[END_REF]) present a number of promising avenues for extension into phenological research, most importantly because visual models in agriculture are often trained to interpret images of plants and identify important plant structures and attributes [START_REF] Ferentinos | Deep learning models for plant disease detection and diagnosis[END_REF].

Perhaps the most important aspect to improving ML applications for herbarium specimens is open discussion and collaboration between biological and computer science communities. This includes continued development of the community of biologists who are interested in applying these models to ecological and evolutionary questions, as well as finding appropriate avenues through which biologists can communicate pressing goals in biodiversity science to ML experts. Ultimately, these communities must also communicate effectively with end users of automatically scored specimen records, such as ecologists and collection managers, to promote understanding of ML-derived outputs and their limitations.

Diversifying phenological research using machine learning Most herbarium-based phenological research to date has focused on understanding the timing of key flowering events, especially first flowering or peak flowering, using fairly simple phenological annotation protocols (Willis et al. 2017a). However, many specimens contain multiple reproductive structures representing a gradient of phenological stages (e.g., flower buds and open flowers present). ML methods could be leveraged to quantify numbers of reproductive structures on specimens, which provides a more detailed understanding of phenological traits such as flowering duration, the rate of progression between phenophases, and phenophase-specific responses to climate change [START_REF] Love | A new phenological metric for use in pheno-climatic models: A case study using herbarium specimens of Streptanthus tortuosus[END_REF].

The phenology of less well-studied taxonomic and regional groups such as bryophytes, ferns, gymnosperms, and taxa in tropical climates could also be accelerated by ML approaches. Furthermore, herbarium specimens can be used to assess nonreproductive phenological processes such as leaf-out [START_REF] Everill | Determining past leaf-out times of New England's deciduous forests from herbarium specimens[END_REF]. In some taxa, it may even be possible to track phenological patterns of primary growth such as stem elongation. ML-based methods could provide a reliable approach to annotating the vegetative phenology of specimens at a large scale, similar to those for reproductive phenology (table 1).

Extending machine learning analysis of herbarium specimens beyond phenology

The current era of rapid advances in ML coincides with a similarly transformative era for biological collections, especially in global change research. Motivated by widespread museum digitization initiatives, herbarium specimens are increasingly being used in a variety of new ways in research (Meineke et al. 2018a[START_REF] Hedrick | Digitization and the future of natural history collections[END_REF]) and in the effective engagement of the public through citizen science and education (e.g., [START_REF] Lacey | Climate change, collections and the classroom: Using big data to tackle big problems[END_REF]). In the present article, we focused on phenology because phenological inference is an emerging tool with links to adaptation, population success, ecophysiology, carbon and nutrient dynamics, human health and sociocultural applications, and resource management. Many of these efforts could be expanded or transformed by the application of ML tools built to automate tasks because the approaches described above can be applied to a wide array of research questions. In particular, ML shows promise in the study of nonphenological traits, the study of plant interactions with nonplant taxa, and the engagement of the broader community to promote biodiversity literacy.

Nonphenological traits. Herbarium specimens are rich with phenotypic data, and specimen images provide the potential for automated trait measurement. Specimens have long provided morphological characters (e.g., leaf shape, reproductive structures) used to identify plant taxa; however, these measurements were traditionally limited to specieslevel trait means or ranges for identification purposes only. Influenced by developments in functional trait-based ecology (e.g., Reich 2014) and advances in global change biology, specimen phenotypes are being used for studies of evolutionary and ecological change at large taxonomic, temporal, and geographic scales. For example, phenotypic data from specimens have been used to quantify rapid leaf trait evolution in invasive species following introduction [START_REF] Buswell | Is rapid evolution common in introduced plant species?[END_REF]) and to document changes in plant size as a result of human harvesting [START_REF] Law | Human-induced dwarfing of Himalayan snow lotus, Saussurea laniceps (Asteraceae)[END_REF] or climate change [START_REF] Leger | Annual plants change in size over a century of observations[END_REF]). To scale up these studies, ML models could be developed and deployed to efficiently measure functional traits for thousands of herbarium specimens (high-throughput phenotyping; Gehan and Kellogg 2017). These traits could include leaf morphometric traits (size, shape), plant size (height, area), and inflorescence and floral traits (size, number).

Species interactions. Data on species interactions are currently sparse, but hypotheses in this area of global change research are central to ecology and evolutionary biology. Herbarium specimens and other collections provide unique opportunities to quantify interactions across time and over large geographic ranges [START_REF] Lees | Tracking origins of invasive herbivores through herbaria and archival DNA: The case of the horsechestnut leaf miner[END_REF], Meineke et al. 2018b). ML-based approaches have the potential to broaden and deepen the scope of available data and therefore facilitate new discoveries with applications in conservation, ecology, and other fields. For example, ML could automate the recognition of leaf mines, damage from herbivores, or plant diseases [START_REF] Ferentinos | Deep learning models for plant disease detection and diagnosis[END_REF][START_REF] Ingram | Mining herbaria for clues to the historic prevalence of lily leaf spot disease (Pseudocercosporella inconspicua) nn Gray's lily (Lilium grayi) and Canada lily (L. canadense)[END_REF].

Biodiversity literacy. ML methods and ML-generated data can provide educational opportunities beyond what is possible with specimens alone. ML has yet to be widely applied in biodiversity education, but on the basis of work using specimen-based data in undergraduate courses, such data can provide authentic introductions to scientific skill building, biodiversity and data literacy, and workforce training [START_REF] Lacey | Climate change, collections and the classroom: Using big data to tackle big problems[END_REF] and the references within it). Educators can also integrate specimen annotation activities into coursework using online citizen science platforms such as Zooniverse. In addition, students can learn data management skills, investigate research questions of their own design, and gain experience with data analysis and visualization when working with the wealth of data generated from ML. Furthermore, it is possible to involve students in more technical aspects of the ML workflow, such as model creation and validation. The application of ML to digital specimen data provides an engaging, well structured, freely available introduction to data science.

Conclusions

Machine learning offers an efficient approach to collecting large amounts of phenological data from herbarium specimens. When combined with, for example, spatiotemporal data extracted from specimen labels during digitization, these data enable discovery of phenological patterns on unprecedented scales. ML models can annotate thousands to millions of images in relatively short time spans, potentially with greater reproducibility and in finer detail than is feasible with human labor alone. Furthermore, the adaptability of ML models can empower specimen-based research beyond phenological traits, facilitating myriad avenues of biological research. Despite these clear advantages, applying ML to specimen images has limitations and challenges, many of which could be overcome through research and development in several key areas. First, training data sets must be developed through continued digitization of herbarium specimens and annotation of specimen images. Second, research questions such as those in table 1 must be addressed to ensure ML-based methods are being effectively employed. Third, greater attention must be paid to downstream use of automatically generated data. Primary concerns include mapping ML-produced data to existing standards (e.g., Darwin Core, the Plant Phenology Ontology) and linking these data to existing specimen data [START_REF] Lendemer | The extended specimen network: A strategy to enhance US biodiversity collections, promote research and education[END_REF]. Finally, to fully realize the potential of ML approaches to phenology and biodiversity science, there is great need for collaborative cyberinfrastructure to manage large quantities of visual data, including the development of an interdisciplinary

Table 1 . Glossary of machine learning (ML) terms discussed in this article.

 1 Downloaded from https://academic.oup.com/bioscience/advance-article-abstract/doi/10.1093/biosci/biaa044/5825721 by guest on 15 May 2020

	Term	Definition
	Annotation	Data added to a specimen record that is ancillary to the original collection data; annotations include, for
		example, phenological status, taxonomic identification, and georeferenced coordinates of a specimen; or
		the process of adding such ancillary data to a specimen record
	Bounding box	(Often rectangular) area on a two-dimensional image that contains all points belonging to a given object;
		the sides of this area are defined by the extreme edges of the object
	Convolutional neural network (CNN)	Type of neural network especially suited for image analysis that automatically learns relevant filters;
		other approaches use handcrafted filters and handcrafted feature extractors
	Cyberinfrastructure	Computational environment and personnel resources which allow a combination of several tasks,
		including data acquisition, storage, management, mining, visualization, and analysis
	Deep learning	Subset of machine learning techniques consisting of neural network models with a high number of
		successive layers; such models have been especially successful in tackling image, sound, and text tasks
	Domain adaptation	Field of machine learning in which a model trained on a certain set of training data is co-opted for a
		different, but somewhat related, target data set
	Filter	In image analysis, a specific type of local operation, i.e., a convolution, applied on the neighborhood of
		a pixel, designed to remove unwanted features from the image while preserving relevant information to
		perform a task, e.g., edge detectors for classification purposes
	Graphics processing unit (GPU)	Hardware originally designed to accelerate computer graphics operations before being used for other
		kinds of computations; used heavily in deep learning computations
	Instance segmentation	In image analysis, the task of finding the objects present in an image and their segmentation mask
	Machine learning (ML)	Wide class of methods dedicated to the problem of training a computer to automatically learn to make
		predictions about novel data using annotated samples from a training data set
	Metadata	Data used to describe or augment existing data
	Object detection	In image analysis, the task of finding the objects present in an image and their bounding box
	Plant phenology ontology (PPO)	The structured vocabulary for describing plant phenological observations that was developed to
		allow harmonization of data across disparate phenological data sets, including those from herbarium
		specimens (Stucky et al. 2018, Brenskelle et al. 2019)
	Prediction	The output of a learning model, which is used to predict the most likely value or a mask for a new image
	Segmentation mask	Defined path around an object containing exactly all the pixels of an image corresponding to that object,
		and only them
	Training data or data set	Subset of the target data set to be annotated that is used to train ML algorithms according to the
		annotation schema; the training data set must already be annotated and should ideally contain a
		representative sample of the visual variation in the target data set
	Transfer learning	Using knowledge gained from one domain of machine learning to improve another domain

Downloaded from https://academic.oup.com/bioscience/advance-article-abstract/doi/10.1093/biosci/biaa044/5825721 by guest on 15 May 2020

BioScience • XXXX XXXX / Vol. XX No. X https://academic.oup.com/bioscience

BioScience • XXXX XXXX / Vol. XX No. X https://academic.oup.com/bioscience

BioScience • XXXX XXXX / Vol. XX No. X https://academic.oup.com/bioscience

BioScience • XXXX XXXX / Vol. XX No. X https://academic.oup.com/bioscience

Acknowledgments

The authors thank the organizers of the iDigBio Phenology Deep Learning Workshop for bringing us together on this topic. We also thank our collaborators Renato Figueiredo, Nicky Nicolson, Isaac Park, Deb Paul, Katja Seltmann, Annika Smith, and Nadya Williams for their ideas and participation in this workshop. This research was supported by iDigBio, which is funded by a grant from the National Science Foundation's Advancing Digitization of Biodiversity Collections Program (award no. DBI-1547229).

Phenological research questions well suited for ML-based analyses

The following list contains ecoevolutionary questions that require large sample sizes or, potentially, fine-scale data collection, rendering manual collection of phenological data from herbarium specimens infeasible.

• How is morphological variation related to phenology?

• Within or across species, do male and female flowers or individuals have different phenological responses to climate variables?

• Do closely related species differ in their phenological sensitivity to climate? If so, are such differences related to differences between taxa in habitat, climatic tolerance, geographic distribution, mean flowering time, or nonphenological traits?

• Do species with unisexual flowers differ in their phenological responsiveness from species with cosexual (i.e., perfect) flowers?

• How can certain phenophases be quantified in a way that is useful for predicting seasonal allergens, e.g., maturation of male catkins?

• How do global events affect regional phenology?

• What and where are phenological dark data (i.e., taxonomic, geographic, or other groups for which little phenological data are available)?

• How do climate and other factors affect how many flowers in an inflorescence become fruits (i.e., reproductive output)?

• How do climate and other factors affect the sizes and shapes of reproductive structures?

• How does the timing of phenological events and species-specific cues vary with latitude and across the globe? Do these interactions vary with climate change?

• How do nonnative species differ from native species with respect to phenological or distributional responses to climate change?

• How does nonangiosperm phenology (e.g., pollen release dates of gymnosperms) respond to climate and other factors?

• How do changes in plant phenology affect interactions between plants and other communities or trophic levels, including insects, pests, birds, and mammals? community aimed at synergistically advancing ML-based methods for science and society.


Victor Champonnois

Katrin Erdlenbruch
email: katrin.erdlenbruch@inrae.fr

Willingness of households to reduce ood risk in southern France

Keywords: contingent valuation, cost-benet analysis, damage mitigation, dichotomous choice, individual adaptation, ood, France, willingness to pay

This paper looks at the scope for individual adaptation to ood risk in the South of France. From a survey of 418 respondents in two ood-prone areas, we collected data on the adoption of individual adaptation measures and the willingness to pay for individual and collective measures. First, we study the determinants of adoption and of the willingness to pay. We then compare willingness to pay for individual versus collective measures. We end with a cost-benet analysis of individual adaptation. Results show a willingness to pay for adaptation measures, although few have yet been adopted. Perceptions of hazards and damage have dierent inuences: the rst favours the adoption of measures, the second increases the willingness to pay for measures. Finally, the cost-benet analysis suggests that completely dry proong a house up to a certain height may not be economically viable. This calls for the promotion of cheaper and potentially more cost-ecient measures.

Introduction

In France oods are considered the main natural hazard, with 70% of municipalities at risk. Of the risk-reduction tools available, adaptions at the household level have received greater attention in recent decades. Measures, such as erecting ood barriers, raising electrical ttings and protecting valuables (e.g. upstairs) appear to be eective and relatively low-cost options [START_REF] Bubeck | Long-term development and eectiveness of private ood mitigation measures: An analysis for the German part of the river Rhine[END_REF][START_REF] Kreibich | Flood loss reduction of private households due to building precautionary measures -lessons learned from the Elbe ood in August 2002[END_REF][START_REF] Kreibich | Economic motivation of households to undertake private precautionary measures against oods[END_REF][START_REF] Kreibich | A review of damage-reducing measures to manage uvial ood risks in a changing climate[END_REF]. We refer to these as individual adaptation measures [START_REF] Erdlenbruch | Simulating the dynamics of individual adaptation to oods[END_REF][START_REF] Richert | The impact of ood management policies on individual adaptation actions : Insights from a French case study[END_REF] as opposed to collective mitigation measures. 1 This paper investigates willingness to reduce ood risks at the household level. We look at the adoption of measures and assess the willingness to pay for further measures.

A vast literature has focused on the determinants of individual adaptation measures. For example, [START_REF] Osberghaus | The determinants of private ood mitigation measures in Germany -Evidence from a nationwide survey[END_REF] conducted a nation-wide study of 4200 households in Germany and found that adaptations such as adapted building use, structural measures and ood barriers were especially made when individuals had experienced ooding and believed that damage would increase in the future as a result of climate-change. Direct experience was also found to be important in several other, smaller case studies, e.g. [START_REF] Grothmann | People at risk of ooding: Why some residents take precautionary action while others do not[END_REF]; [START_REF] Richert | The determinants of households' ood mitigation decisions in France -on the possibility of feedback eects from past investments[END_REF]. Bubeck, Botzen and Aerts (2012); [START_REF] Bubeck | Detailed insights into the inuence of ood-coping appraisals on mitigation behaviour[END_REF] stressed the importance of coping appraisal as a determinant of adaptation decisions 2 in line with other studies based on the protection motivation theory [START_REF] Grothmann | People at risk of ooding: Why some residents take precautionary action while others do not[END_REF][START_REF] Reynaud | Living with oods: Protective behaviours and risk perception of vietnamese households[END_REF][START_REF] Richert | The determinants of households' ood mitigation decisions in France -on the possibility of feedback eects from past investments[END_REF]. For instance, in a survey of 752 German households exposed to ood risk along the river Rhine, Bubeck, Botzen and Aerts (2012); [START_REF] Bubeck | Detailed insights into the inuence of ood-coping appraisals on mitigation behaviour[END_REF] showed that and those who had not. [START_REF] Owusu | Public attitudes towards ooding and property-level ood protection measures[END_REF] studied WTP for individual adaptation measures in Scotland among households living in ood-prone areas. They reported slightly lower means for those who had previously been ooded (734 pounds) than for those who had never been ooded (834 pounds). The main determinants of a willingness to pay for ood-mitigation policies found in the literature are income, home-ownership, objective measures of ood risks, ood experience and risk perception (see the literature review in [START_REF] Champonnois | How useful are (Censored) Quantile Regressions for Contingent Valuation? Evidence from a ood survey[END_REF]). [START_REF] Botzen | Willingness of homeowners to mitigate climate risk through insurance[END_REF] used a choice experiment to evaluate Dutch households' willingess to pay for individual adaptation measures in exchange for reduced insurance premiums. They found that households would consider adopting low-cost, potentially eective measures: 68% were willing to buy sandbags for a cost of 20 euros in exchange for a 5 euro discount on their annual premium (the mean WTP for ood insurance was 120 euros per year). Similarly, 24% of the sample would move central-heating boilers to a higher oor, for a discount of 10 euros. However, such moves would only protect against relatively small oods. In this study sandbags were expected to prevent water from entering homes in 60% of all cases in one scenario and 30% in another scenario. On the other hand, [START_REF] Botzen | Individual preferences for reducing ood risk to near zero through elevation[END_REF] found that households were willing to make a substantial investment if the ood risk could be eliminated entirely.

In their study of over 400 Dutch households 52% of homeowners were willing to spend up to 10,000 euros to elevate a new house to a safe level. They estimate the 'safety premium' that individuals place on risk elimination at between 35 and 45 euros per month.

This paper assesses the willingness of households in the South of France to reduce ood risk. First we analyse the extent of individual adaptations and their determinants, and whether other measures are planned. We then use stated preferences to test whether people are in favour of further ood mitigation and adaptation measures. In particular, we reveal whether people would be in favour of individual adaptation measures if they were implemented collectively. Finally, we compare the WTP of individually targeted adaptations to that of collective mitigation measures.

The paper is organised as follows: in section 2 we present the survey and the context in which it took place. In section 3 we provide descriptive statistics of the main variables and identify the determinants of individual adaptation and the willingness to pay for individual and collective protective measures. In section 4 we perform a cost-benet analysis based on our survey and some results from the literature. In section 5 we discuss the scope for ood mitigation and adaptation measures in France and conclude.

2 Presentation of the study area and survey

Study area and survey method

We conducted our survey in two departments in the South of France: the Var and Haute-Garonne (see gures 1 and 2). The Var is an area at high risk of ooding. Floods in 2010 (15-16 June) caused extensive damage (around 1 billion euros) and left 25 dead. These were followed by another major ood in 2011 (4-10 November). Bagnères de Luchon, and the surrounding areas in the Haute-Garonne, suered a ash ood in 2013 that also caused signicant damage.

A total of 418 interviews were carried out in spring 2019 across 10 municipalities, of which, 6 were in the Var -Draguignan, Le Muy, Les Arcs, Trans-en-Provence, Taradeau and Vidauban -and 4 were in the Haute-Garonne department -Bagnères de Luchon, Montauban de Luchon, Saint-Mamet and Juzet de Luchon. Face-to-face interviews took place in the respondents' homes. The selection of respondents was made by random walk.

The questionnaire was divided into sections as follows: the sociodemographic features of the household, the type of property, ood experience, attitudes to risk and time, ood-risk perception, individual adaptations and the willingness to pay for individual adaptation and collective protection measures. Our paper focuses on the degree of individual adaptation, its determinants and on the willingness to pay for individual and collective adaptation.

Flood-prevention policy in France

To evaluate the scope for further adaptation and mitigation, it is useful to give a quick overview of some of the existing ood-prevention measures in France.

First, the national disaster compensation scheme (the CatNat system) provides cover to the majority of citizens through a compulsory surcharge of 12% on their home insurance premium. This entitles them to compensation for damage caused by various natural disasters, provided that the event is recognised Second, ood-prone areas are provided with Flood Risk Prevention Plans (FRPPs). These are in two parts: a map of the at risk area (usually determined by to the worst historical ood and the 100year ood) and a regulatory document specifying the extent to which new construction is allowed and whether specic individual adaptation measures are recommended or mandatory in each area [START_REF] Richert | The impact of ood management policies on individual adaptation actions : Insights from a French case study[END_REF]. Each municipality in our study area has an FRPP: the plans for the Var were drawn up in 2010, following a major ood event, and approved in 2014. In the Haute-Garonne they were drawn up in 1997 and approved in 1999. Certain individual adaptations are either recommended or compulsory within the FRPPs and are subsidised by the government. Prior to 2020 40 % of the costs could be recovered. However, these subsidies are rarely requested and there are no incentives from insurers to implement them (see also [START_REF] Thieken | Insurability and mitigation of ood losses in private households in Germany[END_REF]). From 2020 80 % of the costs can be recovered.

Third, most local ood-prevention policies are part of the so-called Flood Prevention Action Programmes, or PAPIs. These are policy packages designed locally and selected for nancial support by the government following competitive bidding (see [START_REF] Erdlenbruch | Risk-sharing policies in the context of the French Flood Prevention Action Programmes[END_REF] for greater detail). The local water manager can choose the strategies they implement such as restoring natural ood plains, erecting dykes, or reducing individual vulnerability. In the study areas of the Var the latest PAPI covers the period 2016-2022. In total 96 million euros were allocated to ood-prevention measures, of which 90.5 million was for investment in ood-mitigation and over 1.3 million to actions that reduce vulnerability. Included in the PAPI were recommendations for individual adaptation measures based on expert assessments of each property, although these had yet to be carried out at the time of our study.

Finally, within a general reform of ood-and water-management policy in France, greater responsibility has been granted to local authorities since 2018. According to a new law local water managers can levy an additional tax of up to 40 euros per year and per resident for ood and water management. At the time of our study this tax was being discussed but had not yet been brought in in our case study areas.

Individual adaptation measures

We asked respondents about specic individual adaptation measures: slot-in ood barriers, sewer nonreturn valves, main rooms and valuables placed upstairs, and electrical ttings set higher up the walls. These are the most common measures, according to previous surveys by [START_REF] Richert | The determinants of households' ood mitigation decisions in France -on the possibility of feedback eects from past investments[END_REF]. We also asked respondents if they had taken any other measures. Eort to improve water ow, pumps and manholes were each mentioned several times.

Willingness to pay for individual and collective measures

We asked respondents about their willingness to pay for individual and collective adaptations. The scenarios are presented in the Appendix. The rst proposes the implementation of collective ood-protection measures and the second proposes expert assessment and implementation of individual protective measures in the at-risk properties. Both scenarios are equally ecient in terms of avoiding damage to the property: they would both prevent damage if the water in the street were to remain below one metre.

The main dierence between the two scenarios is that the individual scenario prevents water from entering the properties while the collective scenario prevents water from ooding the streets at all (including the properties). The payment vehicle is the same, namely a compulsory local tax. Therefore, both WTP amounts should be comparable and informative as to the relative preference for individual and collective adaptation.

Regarding the design of the willingness to pay question we followed the most recent guidelines in stated preference surveys [START_REF] Johnston | Contemporary Guidance for Stated Preference Studies[END_REF]). The elicitation format is a dichotomous choice with bids randomly chosen among the following values: 10, 30, 50, 80, 100 and 130 euros (there is one draw per scenario). This format is recommended because it is incentive compatible. The payment vehicle considered is a local tax, which is binding (non-voluntary), as is also required for incentive compatibility and to prevent free riding. The availability bias was reduced because the scenario was close to the real policy context, in which the introduction of a local tax for ood-mitigation was in process.

The stated preference literature nds that respondents do not always state their true value for the good or service in question. It is therefore usual to check whether respondents stated a protest answer, i.e. that they reject (protest against) some aspect of the proposed scenario. We asked what motivated the answer with an open question in order not to inuence the response with the proposition of answers. Following the literature, we group responses, such as 'I don't trust the institutions', 'it's not me who should pay', 'I don't have enough information', 'I pay too much tax' and classify them as protest responses. There are 45% and 47% of protest respondents for the individual and collective scenarios respectively.

Results

The dataset

The main variables used in our study are summarised in Table 1. Table 2 shows summary statistics of these variables. The average respondent is 60 years old, is an owner of their property, has lived in their property for 17 years and is in a household of 2 or 3 persons. Most of the respondents (74%) have prior experience of ooding, although only a third live in an area with a Flood Risk Prevention Plan (FRPP). As shown in Table 3, only a few individual adaptation measures were present in the households surveyed. Overall, 14% of respondents have individual adaptation measures to reduce their vulnerability at home, of which most common is having placed electrical ttings higher up the walls. Table 4 shows that this was most commonly undertaken by the respondent's household. Overall, 9% of respondents have adopted measures themselves. Almost no respondent has further action planned. This is perhaps due to the fact that the last major oods (2010 for the Var and 2013 for the Haute-Garonne) took place several years ago. Indeed, as shown in our dataset there was a peak in the adoption of new measures in the Var immediately after the 2010 ood, and then a rapid decrease to very low levels.

Mean

Two main factors explain why the respondents do not take protective measures. First, they feel that their accommodation is not at risk and/or they think that oods are rare. However, a third of respondents state that their accommodation was in a ood-prone area (Table 5). Moreover, Table 6 shows that even among those actually living in a ood-prone area (dened here as lying in an FRPP area) reasons such as 'oods are rare' or 'my property is not exposed' are still the most commonly cited. This suggests a discrepancy between ood-risk perception and ocial information about this risk.

We estimated probit models to analyse the determinants of adoption. Results are given in Table 11. The analysis shows that the main determinants of adaptation are having experienced a ood and the perception of risk, both having a positive eect on individual adaptation. Although not displayed here, when we use the discrete specication of the risk-perception variable we nd that only residents with a very acute perception of risk adopt further measures.

The eect of coping appraisal, which is often found to be an important determinant of adaptation in the literature, was not found to be signicant here and so was not included in our results. (We measured coping appraisal by the strenght of rejection of the statement: 'I don't think I will be able to avoid the consequences of ooding in my home. I don't have enough understand of the subject', see [START_REF] Grothmann | People at risk of ooding: Why some residents take precautionary action while others do not[END_REF]

Willingness to pay for individual and collective measures

Tables 7 and8 show the proportion of respondents who accept to pay, given the proposed amount, for the individual and collective scenarios. As expected, the share decreases monotonically as the amount increases.

As shown in Table 9, the mean willingness to pay for the whole sample is 35 euros for the individual scenario and 46 for the collective scenario. When we remove the respondents with a protest attitude, the mean WTP increases to 95 euros for the individual scenario and 91 euros for the collective scenario (Table 9). Recall that the main dierence between the two scenarios is that the individual scenario prevents water from entering the home, while the collective scenario prevents water from ooding the streets at all(including the homes). The impact on the respondent's home is the same in each scenario and the number of protest responses is similar (around 45%). According to Table 10, the willingness to pay increases when we focus only on respondents in the FRPP area, albeit not to a great extent. This increase applies only for non-protest respondents, and even decreases slightly for the whole sample. This is because the share of protest respondents is greater in the FRPP area (e.g. for the individual scenario, there are 60% of protests among the respondents living in the FRPP area but only 46% outside the area). This is a surprising result given that respondents whose homes are at greater risk have more to gain from adaptation. Due to the binary nature of the WTP variable, we estimated probit models to study determinants of the willingness to pay, as shown in Table 11. The regression analysis shows that education, individual income and the perception of the damage to the home that a ood would cause all positively aect the WTP in the collective scenario. 3The perception of damage also positively aects the WTP in the individual scenario. This determinant is a measure of the vulnerability of the property. It is interesting to note that the hazard is a determinant of adaptation behaviour and the vulnerability is a determinant of WTP. It is clear that the respondents have taken into account the amount oered to them, because the proportion of positive responses decreases with the amount. 4 4 Cost-benet analysis Here we compare the willingness to pay results with measures of cost and avoided damage of dry-proong a home as provided in the literature.

Individual scenario

Benets

According to our scenario the average annual WTP for individual adaptation to prevent water from entering the property -if the water remains below one metre -is 35 euros.

With a discount rate δ of 2.5% (as in [START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF] and a time horizon of 30 years the discounted benets in euros are:

30 i=1 W T P/(1 + δ) i = 30 i=1 35/(1 + 0.025) i = 733.
On the other hand, we can use the WTP of non-protesters, which is 100 euros, and with the same discount rate and time period, we nd discounted benets of 2093 euros. Other values of discounted benets for dierent time horizons, discount rates and WTP subsets are given in Table 12.

Discounted benets for a household (Euros) Table 13: Mean benets from dry-proong a property according to the literature [START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF] One can compare our results to average values of avoided damage. Richert, Boisgontier and Grelot (2019) calculated the costs and benets of dry-proong based on expert assessments and numerical models of properties. One of the options they look at is dry-proong techniques that prevent water from entering the building if it is below one metre, which corresponds with our WTP scenarios. They found the mean annual benets of dry-proong to be 1,600, 1,100 and 1,100 euros for a bungalow, two-storey house and a at respectively (see Table 13). This is the order of magnitude of the WTP estimations that exclude protest answers. It is lower than the estimations of the whole sample.

Costs

Richert, Boisgontier and Grelot (2019) nd that the average cost of dry-proong a house up to one metre is 10,400 euros for a bungalow, 7,700 euros for a two storey house and 9,400 euros for a at. The international literature proposed similar average costs for dry-proong: 6,100 euros for an average house in Germany and 8,000 euros for a single-family house in the Netherlands [START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF]

Costs and benets

In a more complete cost-benet analysis, we compare the total cost of dry-proofed homes in the risk area with total benets estimated through willingness to pay in the survey area. To this end, we rst estimate the average number of households at risk using data from ONRN5 , which provides the number of residents in ood-prone areas. 6 We divide the number of residents by the average household size from our survey to estimate the total number of households in the area, as displayed in Table 15. Next, we compute total costs by multiplying individual costs for dry-proong and the total number of households at risk, as indicated in Table 16. We compute the average benets by multiplying individual WTP by the total number of households, as displayed in Table 17.

For the cost-benet analysis we assume an equal distribution of ats, bungalows and two-story dwellings, hence a cost of C=(11,257,400+13,742,800+15,204,800)/3=13,401,667 euros. With a discount rate δ of 2.5% (as in [START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF]) and a time horizon of 30 years, the net present value (NPV) using the whole sample (i.e. a willingness to pay of 35 euros) is : Other results of net present values for dierent time horizons, discount rates and WTP subsets are given in Table 18. It is clear that net present values are nearly always negative, using standard assumptions. Only with high WTP, low discount rates and long time horizons does investment in complete individual dry-proong prove to be ecient. This is the case for example for the sample of non-protesters, a discount rate of 1% and a time horizon of 50 years.

N P V = -C + 30 i=1 W T P/(1 + δ) i = -
Alternatively, the WTP needed to make complete dry-proong ecient could be computed. For example, for the net-present value to be greater than zero when investing in the ood-proong of a two storey house given a discount rate of 2.5% and a time horizon of 30 years one would need a WTP of 186 euros (see Table 19). More generally, for a net-present value greater than zero the WTP would need to be of several hundred euros.

Discussion and conclusion

This study found a relatively low adoption rate of individual adaptation measures, similar to earlier ndings in the literature [START_REF] Kunreuther | Disaster Mitigation and Insurance: Learning from Katrina[END_REF][START_REF] Owusu | Public attitudes towards ooding and property-level ood protection measures[END_REF][START_REF] Kazmierczak | Investigating homeowners' interest in property-level ood protection[END_REF]. One factor underlined in the literature was low coping appraisal (Bubeck, Botzen and Aerts, 2012;[START_REF] Bubeck | Detailed insights into the inuence of ood-coping appraisals on mitigation behaviour[END_REF]. However, our measure of coping appraisal did not have a signicant eect on the adoption variable. Moreover, in our willingness-to-pay scenario the assessment, purchase and installation of adaptation measures are not made by the respondents, so coping appraisal should not play a role in this decision. Thus, low coping does not explain the low willingness to adopt measures in France.

Another reason for low adoption rates is the relative low cost-eciency of individual adaptation in France. Even when respondents have a positive WTP for dry-proong their house, it seems quite low compared to the cost. Indeed, given a time horizon of thirty years and a discount rate of 0.25, our highest WTP estimates (without protesters) is one third of what would be needed to cover the lowest cost estimate. This result suggests that dry-proong might not be economically sound for residents in the surveyed area. This contrasts with many ndings in the literature [START_REF] Bubeck | Long-term development and eectiveness of private ood mitigation measures: An analysis for the German part of the river Rhine[END_REF][START_REF] Kreibich | Flood loss reduction of private households due to building precautionary measures -lessons learned from the Elbe ood in August 2002[END_REF][START_REF] Kreibich | Economic motivation of households to undertake private precautionary measures against oods[END_REF][START_REF] Kreibich | A review of damage-reducing measures to manage uvial ood risks in a changing climate[END_REF][START_REF] Owusu | Public attitudes towards ooding and property-level ood protection measures[END_REF][START_REF] Poussin | Potential of semi-structural and non-structural adaptation strategies to reduce future ood risk: Case study for the Meuse[END_REF][START_REF] Poussin | Eectiveness of ood damage mitigation measures: Empirical evidence from French ood disasters[END_REF][START_REF] Richert | The impact of ood management policies on individual adaptation actions : Insights from a French case study[END_REF][START_REF] Sairam | Quantifying Flood Vulnerability Reduction via Private Precaution[END_REF].7 However, fully dry-proong a property is only one adaptation measure among many options. Some inexpensive adaptations, such as installing sandbag barriers, as in [START_REF] Botzen | Willingness of homeowners to mitigate climate risk through insurance[END_REF], could still be economically viable.

Further, in comparison to the levels found by expert assessment [START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF] the benets revealed by our WTP are low. This might be surprising as expert assessments only value tangible benets whereas WTP includes intangible values. One explanation for low WTP values could lie in the cap that we placed on the proposed bids (a maximum of 130 euros). However, our mean values are close to those found by [START_REF] Champonnois | How useful are (Censored) Quantile Regressions for Contingent Valuation? Evidence from a ood survey[END_REF]. In contrast to previous studies, we measure willingness to pay for both collective and individual measures and nd very similar results. A possible explanation for this is that the scenarios provide the property with the same level of protection. It is also important to note that the individual scenario is somehow 'collective' in the sense that it proposes to set up measures in 'at-risk' households but not necessarily in the respondent's home.

Finally, it is interesting to note that the perceptions of risk and of the consequences of risk are dierent determinants. Risk perception only aects adoption while the perception of damage aects willingness to pay for collective mitigation. This diers from ndings by [START_REF] Bubeck | Do ood risk perceptions provide useful insights for ood risk management? Findings from central Vietnam[END_REF]: the perception of consequence was the determinant of intention to adopt, while the perception of risk had no eect.

To conclude, we can derive some policy implications from our study: if French ood managers wish to continue to promote the adoption of individual adaptation measures, they should target their information, and the subsidies, towards low-cost adaptation measures, such as sandbags or adapted property use, rather than the complete dry proong of buildings with costly devices.

Figure 1 :

 1 Figure 1: Surveyed municipalities in the Var

Figure 2 :

 2 Figure 2: Surveyed municipalities in the Haute-Garonne

  /(1 + 0.025) i = -10, 878, 730.

Table 1 :

 1 Description of the variables

	Variable Risk perception	Description 'Do you live in a ood area?' (Yes/No/Don't know)
	Flood experience	'Have you already experienced a ood?'
	Age	Age of the respondent
	Household size	Number of persons in the household
	Education	Education level of the respondent
	Income	Individual income of the respondent
	Risk perception	'What is the likelihood of a ood below one metre in your street in the next ten year'
	Damage perception	'If your house was ooded, would there be important damage ?'
	Measure installed	At least one individual protection measure was installed by the household
	Within FRPP	Property located in an FRPP area
	Duration since installation Number of years since installation
	Owner	Household is the owner of the property
	Var	Property in the Var department
	Responsibility	Responsibility of ood protection (state authority, individuals, everyone)
	WTP individual	WTP for the individual scenario
	WTP collective	WTP for the collective scenario

Table 2 :

 2 Descriptive statistics 3.2 Individual adaptation measures 40% of the respondents live in elevated accommodation (with raised oor or crawl space) and are therefore better protected against ooding. However, this does not seem to have been an active choice, since respondents rarely took ood risk into account when choosing their property. As shown in our dataset, ood risk had a greater inuence on property choice prior to 1960, but the receded in the period from 1960 to 2000, only reappearing in 2010.

	SD Median Min Max	N

Table 4 :

 4 Who took the decision to install? it would be ineective in the event of a ood 0.97 0.03 because you think it would not do much good in the event of a ood 0.97 0.03

	No Yes

Table 5 :

 5 Reasons for not installing adaptation measures (whole sample)

Table 6 :

 6 .) Reasons for not installing adaptation measures (respondents in FRPP area)

	No Yes

Table 7 :

 7 Proportion of respondents accepting to pay given the proposed amount: individual scenario

	No Yes Did not answer
	10 0.24 0.71	0.05
	30 0.37 0.56	0.07
	50 0.50 0.41	0.09
	80 0.67 0.25	0.08
	100 0.75 0.16	0.10
	130 0.82 0.13	0.05

Table 8 :

 8

Proportion of respondents accepting to pay given the proposed amount: collective scenario

Table 10 :

 10 Mean WTP, respondents in FRPP area

	Collective scenario

Table 11 :

 11 Probit model

Table 12 :

 12 Total discounted benets depending on time horizon, discount rate and WTP sample

	Time horizon (years) Discount rate WTP = 35	WTP = 100
	30	0.010	903	2581
	50	0.010	1372	3920
	30	0.025	733	2093
	50	0.025	993	2836
	30	0.050	538	1537
	50	0.050	639	1826
	Property type		Mean benets for a dwelling (Euros)
	Two storey house in France	1100
	Flat in France		1100
	Bungalow in France	1600

Table 14 :

 14 -see Table14. Costs of dry-proong a property according to the literature[START_REF] Richert | Economic assessment of precautionary measures against oods: Insights from a non-contextual approach[END_REF]

	Property type	Individual costs (Euros)
	House in Germany		6100
	Two storey house in France	7700
	House in Netherlands		8000
	Flat in France		9400
	Bungalow in France		10400
	Municipality	Number of hh. at risk Total number of hh. Ratio
	Bagnères-de-Luchon		925	1049	0.88
	Juzet-de-Luchon		129	165	0.78
	Montauban-de-Luchon		165	215	0.77
	Saint-Mamet		130	246	0.53
	Les Arcs		1532	3093	0.50
	Draguignan		7018	17194	0.41
	Le Muy		1341	4009	0.33
	Taradeau		227	785	0.29
	Trans-en-Provence		834	2557	0.33
	Vidauban		2324	5133	0.45
	Average		1462	3444	0.53
	Table 15: Estimated number of households per municipality
	Property type	Individual costs (Euros) Total costs (Euros)
	House in Germany		6100	8,918,200
	Two storey house in France	7700	11,257,400
	House in the Netherlands	8000	11,696,000
	Flat in France		9400	13,742,800
	Bungalow in France		10400	15,204,800
	Table 16: Individual and total costs
	Individual WTP (Euros) Total WTP (Euros)
			35	120,540
			100	344,400
	Table 17: Individual and total WTP
			Net present value for the study area (Euros)
	Time horizon (years) Discount rate WTP = 35	WTP = 100
	30	0.010	-10,290,806	-4,513,492
	50	0.010	-8,676,967	97,476
	30	0.025	-10,878,730	-6,193,274
	50	0.025	-9,982,874	-3,633,687
	30	0.050	-11,548,672	-8,107,395
	50	0.050	-11,201,098	-7,114,326

Table 18 :

 18 Net present value depending on time horizon, discount rate and WTP sample

	Time horizon (years) Discount rate WTP needed (Euros)
	30	0.010	151
	50	0.010	99
	30	0.025	186
	50	0.025	137
	30	0.050	253
	50	0.050	213

Table 19 :

 19 WTP necessary to reach positive NPV for costs in at risk area of -13.4 million Euros

We also estimated a model with the perception variables treated discretely to capture possible non-linearities, but the results are almost the same.

The variable 'Order of scenarios' is equal to one when the collective scenario is posed rst. It has a negative impact on the WTP for the individual scenario, which means that the WTP for this scenario is weaker when it is posed second.

the 'Observatoire National des Risques Naturels'

The ONRN 'Observatoire National des Risques Naturels' is a nation-wide observatory. Flood-prone areas used here correspond to the EAIP area 'Enveloppe Approchée des Inondations Potentielles', which is larger than the FRPP area.

Note that residents in the FRPP area are subsidised at 40% (80% since 2020) when adopting individual adaptation measures. Yet, even with the subsidy the net cost at the lowest estimate is 3,660 euros, which is still above the total discounted benets calculated for a range of parameters in Table12.

Acknowledgements

The study was funded by the ANR as part of the i-Nondations (e-Flooding) project, ANR-17-CE39-0011.

Data availability statement: The data that support the ndings of this study are available from the corresponding author upon reasonable request.

Appendix A WTP scenario

The description of scenario 1 was: 'Let's imagine that the government created a Flood Management Fund to nance the construction of collective ood protection works (dykes, retention basins, improvement of rainwater drainage networks). The works would protect you from oods that would cause the water to rise up to one metre in your street. The fund would be nanced by an additional local tax compulsory for all households in the communes.' The description of scenario 2 was 'Let's imagine that the government created a Flood Management Fund to nance expert assessments and implement protective measures in high-risk areas. These would prevent water from entering homes provided the level in your street was no more than one metre high. The fund would be nanced by an additional local tax compulsory for all households in the communes.'

CEE-M Working Papers