Quentin Groom
email: quentin.groom@plantentuinmeise.be

Lauren Weatherdon

Ilse R Geijzendorffer

Is citizen science an open science in the case of biodiversity observations?

Keywords: biodiversity, citizen science, data licensing, data mobilization, data sharing, GBIF, open data, reproducibility, sustainability, volunteers

There is a high demand for biodiversity observation data to inform conservation and envi-ronmental policy, and citizen scientists generate the vast majority of terrestrial biodiversity observations. As this work is voluntary, many people assume that these data are openly avail-able for use in conservation and scientific research.

2.

Here, the openness of biodiversity observation data that are contributed to the Global Biodiversity Information Facility is examined by the data provider. Contrary to what many people assume, data sets from volunteers are among the most restrictive in how they can be used.

3.

Policy implications. The assumption that voluntary data collection leads to data sharing does not recognize the wishes and motivations of those who collect data, nor does it respect the crucial contributions of these data to long-term monitoring of biodiversity trends. To improve data openness, citizen scientists should be recognized in ways that correspond with their motivations. Furthermore, organizations that manage these data should make their data sharing policies open and explicit.

Introduction

Citizen science in biodiversity research covers a wide variety of volunteer activities, from the collection of casual observations through to conducting detailed species monitoring (Wiggins & Crowston 2011). The skills of citizen scientists range from general members of the public with little scientific experience through to expert amateurs and retired professionals. The EuMon project has calculated that volunteers outnumber professionals 18 to 1 in species monitoring in Europe [START_REF] Eumon | /eumon.ckff[END_REF]. The voluntary aspect of the time invested by citizen scientists is generally interpreted as being motivated primarily by its contribution to society and that society should profit from this effort through openly accessible data. For example, in the European Union's Digital Agenda for Science, citizen science is listed as a subcategory of open science (European Commission 2015), implying that citizen science data are open, permissively licensed and available to all.

Materials and methods

The Global Biodiversity Information Facility (GBIF) is a long-standing, influential global resource on biodiversity distribution information with a pan-taxonomic approach. It is funded by governments of participating countries to provide open information exchange on biodiversity. As such, it is a highly suitable data set for this analysis. Observation data from GBIF are only one of a diverse range of data types collected by citizen science projects. However, unlike many other data sets, the data available in GBIF are accessible with comparatively clear licensing (Table 1). Data set metadata were extracted from GBIF using R (version 3.2.0) on 19 January 2016 using the 'RGBIF' package (version 0.9.0) [START_REF] Chamberlain | Package 'rg-bif': Interface to the Global 'Biodiversity' Information Facility 'API[END_REF]. Where the legal right to use the data was explicitly mentioned, it was represented by either a short rights statement in the metadata or a link to a longer licence document. The 'rights' statements or URL to a licence was extracted for all occurrences and survey data sets with one or more observations. A total of 12 458 data sets were extracted, but only 11% of these data sets included an explicit data-usage-rights statement in the data set metadata. The licensing information can be found in three places in the 'RGBIF' output: once in the data set metadata and twice in the occurrence record, wherein the licensing is noted in both the 'rights' and 'accessRights' fields. The 'rights' field is a deprecated term that preceded the 'accessRights' term, originating from the Darwin Core standard. Darwin Core is used in GBIF to define fields in the data base and as a data exchange format (Wieczorek et al. 2012).

When a rights statement was missing from the data set metadata, the occurrence-level rights information was obtained from the first record of each data set. It is assumed that the rights within a data set are uniform and that the first record is representative of all records in that set. Rights statements for a further 0 25% of data sets were obtained this way.

Licensed data sets use standard licences such as a Creative Commons or an Open Data Licence, while the remainder use bespoke licence statements of various sorts. To simplify the interpretation of the different licences, the intention of the licence holder was interpreted and simplified into seven categories. Each of these categories was then given a data openness score from zero to three, from the least to the most open, respectively. Details of these categories are given in Table 2.

The sources of the data sets were classified into thirteen types based on the data set names and provider names (Table 3). These types were chosen by reviewing the word frequency in the data providers' titles. For example, common words in data provider titles included 'University', 'Museum', 'Institute', 'Research' and 'Herbarium'. If the data provider's name could not be used to assign a type or was ambiguous, the data set description, domain name and organization's website were used to guide attribution. The majority of data sets are described in English; for all others, Google Translate was used to interpret the titles and descriptions. Finally, the names of the data sets were reviewed to ensure they had been classified correctly. For example, some citizen science and scientific society data sets are submitted to GBIF by data centres of various types and can be recognized from their data set name. If these could be identified, they were then reclassified. It is acknowledged that many institutions fall within multiple types -for example, some museums will also be research institutions and vice versa -but each organization was assumed to belong to their self-identified type and that the data set's description took precedence over the provider's name. It is also assumed that all data sets consist of one type of data. We used a non-parametric Mann-Whitney U-test to determine the significance of differences between data openness scores, which was considered a rigorous test on these categorical and bounded scores.

Results

Our assessment showed that citizen science data sets com-prise 10% of data sets on GBIF, but account for 60% of all observations. The largest data set by far is from eBird (Cornell Lab of Ornithology 2015), which is a citizen science data set that contains over 200 million observations. When comparing the data openness scores of GBIF data sets with the data source types (Fig. 1), the citizen science projects ranked low on the openness of their data, although the vast majority do not include a licence statement (mean data openness scores 1 67, n = 33), whereas institutions such as museums, educational institutions and research institutes ranked higher (mean data openness scores 2 13, n = 335; 2 04, n = 324 and 2 01, n = 219, respectively). Commercial organizations ranked the most open (mean data openness score 2 82, n = 11). Of course, some data from citizen science projects were entered into GBIF using other organizations as intermediaries and are therefore hidden from our view. This is particularly true of data centres, which also score poorly (1 80, n = 368) and of societies (2 10, n = 39). A comparison of the scores of the three data set types together ('citizen science', 'societies' and 'data centres') demonstrated lower scores for these predominantly volunteer-provided data sets (mean 1 83, n = 440), than for all other data sets together (mean 2 10, n = 1048) (Mann-Whitney U-test, W = 194680, P < 0 01).

Discussion

The results confirm the important contribution of citizen scientists to biodiversity research. However, contrary to expectations, biodiversity data sets on GBIF derived from citizen science projects were often associated with more restrictive licences than other data types, and frequently restricted the data use by commercial organizations. Data centres, which distribute citizen science data as an intermediary, also receive low scores. Even though these data are collected voluntarily, the circumstances under which these data are managed and distributed seem to result in more restrictive data sharing. Scientific societies scored better on their accessibility. As these societies often have a largely voluntary member-ship, this raises questions on why their openness differs from citizen science projects. This category does, how-ever, contribute fewer observations, forming only 2% of those contributed by citizen science and data centres. Surprisingly, commercial organizations scored highest on open access to biodiversity data. However, as the provisioning of biodiversity data is not the core business of these organizations, they form only a small fraction of providers and observations.

Heterogeneous licensing

Within the GBIF data sets, there are a wide variety of licences. For example, 26% of licensed data sets restrict commercial usage, presumably to avoid undermining potential revenue sources for the data provider. However, they may be unaware that this stipulation also prevents not-for-profit research that they may assume is permitted [START_REF] Hagedorn | Creative Commons licenses and the non-commercial condition: Implications for the reuse of biodiversity information[END_REF]). This limitation is also true for the 88% of GBIF data sets that lack licensing information. Although it is perhaps assumed by some users that no licence information implies that the data can be used openly, this is not the case [START_REF] Groom | The importance of open data for invasive alien species research, policy and management[END_REF]. Academic users can probably risk using these data, but the potential risk is much higher for commercial users. Policymakers should be aware that this makes it difficult to outsource the reporting of biodiversity targets that require these data. The heterogeneity of licensing is yet another obstacle that users need to resolve. The GBIF acknowledges these problems of data licensing and is transitioning to a simpler obligatory system that offers only three licensing options (Table 1) [START_REF] Desmet | Interpreting licenses of GBIF registered data[END_REF]GBIF 2015).

Data use barriers

In addition to licensing issues, there are also an unknown number of organizations and individuals who hold data but do not share these openly. For instance, commercial companies may not want to share data that might be used against them (e.g. urban development projects can be delayed or blocked by the presence of protected species). Furthermore, we are aware from personal experience that many publicly available citizen science data sets are obfuscated by reducing their spatial or temporal resolution. For example, volunteers provide observations with a precise grid reference and date, but the data providers only supply summary data to GBIF, combining all observations for a year and grid cell into one record. In personal communications with several European GBIF nodes, they acknowledged that much of their country's data was obfuscated before these were provided to GBIF. An example is the National Biodiversity Network in the UK that provides most of the UK data available in GBIF, most of which comes from volunteer observers. At least 50% of these observations have their coordinates obfuscated at the request of the data providers (NBN Trust 2015).

The fact that some biodiversity observation data are either restricted, obfuscated or inaccessible may have several probable causes. For instance, data holders may use a conservation-based argument, such as protecting locations of species vulnerable to persecution or exploitation. Data holders may also withhold data at the request of a landowner or because they did not receive legal per-mission to access the area where the observations were made. Among professional scientists, funding shortages and institutional support for data openness are important reasons for not sharing data [START_REF] Tenopir | Data sharing by scientists: practices and perceptions[END_REF][START_REF] Fecher | What drives academic data sharing?[END_REF].

The mandate for sharing

These reasons might also inhibit citizen scientists' data sharing, but there are additional reasons. For example, the mandate for decisions on sharing citizen science data is not held by the citizens themselves, but with intermediary organizations such as data distribution centres or citizen science organizations. Multiple reasons can cause these organizations to be unwilling to share data. For instance, data can be used as leverage to fund their activities, or to obtain acknowledgement of their contributions, particularly by being included as authors on publications. With the difficulty of finding sufficient funding, these are understandable reasons for withholding data, even though they considerably reduce the value of the data and can act contrary to the missions of these organizations. Indeed, commodification is a serious area of conflict between amateurs, their managing organizations and data aggregators [START_REF] Ellis | Caught between the cartographic and the ethnographic imagination: the whereabouts of amateurs, professionals, and nature in knowing biodiversity[END_REF]. Funding agencies should recognize that sustainability is fundamental to the reliable provisioning of good quality biological observations to long-term monitoring. For instance, some scientific societies have an enviable record in longevity. The Botanical Society of Britain and Ireland and the Audubon Society were established in 1856 and 1896, respectively, among other examples. The value of these sustainable models should not be underestimated.

Moving forward

There are some inspiring examples of advancements that can be applied. One crucial step forward is for organizations managing citizen science data to implement explicit data management policies with standard licences to pre-vent misconceptions regarding data sharing. A good example is Wikipedia, which has clear policies and no restrictions on commercial usage, but requires acknowledgement and 'share alike'. In the field of biodiversity observations, iNaturalist.org allows users to select from a range of Creative Commons licences, including releasing their data into the public domain.

Volunteers tend to have a particularly local conservation-based focus, whereas professionals may concentrate on international issues [START_REF] Turnhout | Databases, scaling practices, and the globalization of biodiversity[END_REF]. This can lead to a lack of understanding between professional organizations and amateur societies, which have different goals and perspectives [START_REF] Ellis | Caught between the cartographic and the ethnographic imagination: the whereabouts of amateurs, professionals, and nature in knowing biodiversity[END_REF]. For example, volunteers are perhaps less likely to be motivated by citation in academic journals, but welcome acknowledgements that are visible to their local peer group. Some of the most productive volunteer observers collect biodiversity data for their own projects, such as producing regional floras or breeding bird atlases. Sharing their data becomes an interesting option for these citizen scientists if they can be assured that their own projects are not affected. Data users should support the activities of citizen scientists and societies through acknowledgement of their contributions in a way that matters for the citizen scientists.

This study illustrates that although citizen scientists contribute important biodiversity data to GBIF, the open-ness of their data ranks low among the different data providers studied. Several methods to stimulate data sharing are feasible. The assumption that voluntary data collection leads to data sharing does not do justice to those who collect data, nor does it acknowledge the contributions of these data to long-term monitoring of biodiversity trends. To improve data openness, citizen scientists should be encouraged in ways that correspond with their motivations. A first step would be for data distribution centres to delineate clearer licensing approaches and to thereby to enable citizen scientists to select appropriate levels of data accessibility. Wieczorek, J., Bloom, D., Guralnick, R., Blum, S., Doring, M., Giovanni, R., Robertson, T. & Vieglais, D. (2012) Darwin Core: an evolving com-munity-developed biodiversity data standard. PLoS ONE, 7, e29715. Wiggins, A. & Crowston, K. (2011) From conservation to crowdsourcing: a typology of citizen science. System sciences (HICSS), 2011 44th Hawaii international conference, pp. 1-10. IEEE.

Fig. 1 .

 1 Fig. 1. The average data openness score of data sets on GBIF separated by the organization type of the data set provider. Only data sets with an explicit expression of data usage rights have been included. A data set with a score of zero is not usable with-out express permission of the owner; a data set with a score of one does not permit commercial use, requires acknowledgement and may have other restrictions; a score of two only requires acknowledgement; a score of 3 is given to data sets which are completely open. Error bars show the 95% confidence interval using a t distribution.

Table 1 .

 1 An explanation of some widely used data sharing licences from Creative Commons and Open Data Commons BY and CC-BY-NC are the licence options recommended by GBIF. Strictly speaking, Open Data Commons licences are more suitable for data licensing, but Creative Commons are nevertheless widely used.

	CC0 and	Under the Creative Commons zero dedication
	ODC-PDDL	and the Open Data Commons Public Domain
		Dedication and Licence, the copyright holder
		releases the work to the public domain waiving
		their rights under copyright law.
		This does not change the conventions of
		scientific citation
	CC-BY and	Under the Creative Commons Attribution
	ODC-By	Licence and the Open Data Commons
		Attribution Licence users can use the
		copyright material; however, they wish, even
		for commercial purposes, as long as they
		provide attribution
	CC-BY-NC:	Under the Creative Commons Attribution
		Non-commercial licence, users can use the
		copyright material for non-commercial
		purposes, as long as they provide attribution
	CC-BY-SA:	Under the Creative Commons Attribution Share
		Alike licence, users can use the copyright
		material however they wish, even for
		commercial purposes, as long as they provide
		attribution to the originator and the derivatives
		are shared under the same licence
	CC0, CC-

Table 2 .

 2 The interpreted data usage rights from GBIF data sets, their data openness score and the number of data sets in each class

	Interpreted
	intention	Data openness	Number
	of the licence	score	of data sets
	Requires permission to use	0	72
	Non-commercial usage,	1	38
	with attribution and share alike
	With attribution and share alike	1	1
	Non-commercial usage	1	16
	Non-commercial usage,	1	322
	with attribution
	With attribution	2	492
	Public domain	3	546
	Not specified or ambiguous		10 971

Table 3 .

 3 An overview of the different types of data provider defined for this study, with the number of data sets they provided with and without a specific licence statement and the total number of observations and an example of a data set and data provider

	With Without Records

Provider types in bold are considered to contain observations largely from volunteers

Acknowledgements

The authors would like to thanks Graham French, Andre Heughebaert, Donald Hobern, Cees Hof, Rachel Stroud, Dagmar Triebel and Ben Wheeler from the GBIF nodes and the National Biodiversity Network, UK. We acknowledge the support of EU BON (http://www.eubon.eu), funded by the EU Framework Programme under grant agreement No. 308454.

Data accessibility

Data are available from Zenodo (Groom 2016).

to research data.


Shawn J Leroux
email: sleroux@mun.ca

Cécile H Albert

Anne-Sophie Lafuite

Bronwyn Rayfield

Shaopeng Wang

Dominique Gravel

Structural uncertainty in models projecting the consequences of habitat loss and fragmentation on biodiversity

Keywords: Conservation, Generalized Linear Models, Global Change, Metapopulation model, Prediction, Species-Area Relationship, Species Distribution Model

Ecological theory is essential to predict the effects of global changes such as habitat loss and fragmentation on biodiversity. The species-area relationship (SAR), metapopulation models (MEP) and species distribution models (SDM) are commonly used tools incorporating different ecological processes to explain biodiversity distribution and dynamics. Yet few studies have compared the outcomes of these disparate models and investigated their complementarity. Here we show that the processes underlying SAR (patch area), MEP (patch isolation) and SDM (environmental conditions) models can be compared with a common statistical framework. Our approach allows for species and community-level predictions under current and future landscape scenarios, facilitates multi-model comparison and provides the machinery for integrating multiple mechanisms into one model. We apply this framework to the distribution of eight focal vertebrate species in current and future projected landscapes where 10% of the landscape is lost to land-use change in southwestern, Quebec, Canada. Based on a model selection approach, we found that a model including patch area was the top ranked model for four of our focal species and models including patch isolation and environmental conditions were the top ranked models for two focal species each. Community-level predictions of models based on patch area, patch isolation and environmental conditions for both current and future landscapes showed high spatial overlap, however, patch area models always predicted a reduction of species richness per patch whereas both the patch isolation and environmental conditions models predicted an increase or decrease in species richness per patch following habitat loss and fragmentation. Our comparative tool will allow ecologists and conservation practitioners to relate structural uncertainty to key mechanisms underlying each model. Ultimately, this approach is one step in the direction of deriving robust predictions for the change and loss of biodiversity under global change, which is key for informing conservation plans.

INTRODUCTION

Tools for predicting biodiversity change are essential for biodiversity conservation in the face of the global changes [START_REF] Cardinale | Biodiversity loss and its impact on humanity[END_REF], Vellend et al. 2013, Dornelas et al. 2014, Ewers et al. This issue). Ecologists have derived from theory [START_REF] Thuiller | A road map for integrating eco-evolutionary processes into biodiversity models[END_REF]) a suite of models to predict the distribution, abundance, and diversity of species based on environmental conditions and ecological processes (hereafter biodiversity models). Some biodiversity models are commonly used for biodiversity conservation and land-use planning (e.g. species distribution models; [START_REF] Leroux | Accounting for system dynamics in reserve design[END_REF]) while others have seen limited applications (e.g. neutral theory). In most case studies, however, a single biodiversity model is applied to address a particular conservation problem (but see e.g. [START_REF] Moilanen | Metapopulation dynamics: effects of habitat quality and landscape structure[END_REF][START_REF] Keith | Predicting extinction risks under climate change: coupling stochastic population models with dynamic bioclimatic habitat models[END_REF][START_REF] Dullinger | Patch configuration affects alpine plant distribution[END_REF][START_REF] Fordham | Tools for integrating range change, extinction risk and climate change information into conservation management[END_REF], therefore, we lack a good understanding of how the predictions from various models may differ, and the potential for multiple models to provide complementary insights on a given problem (Krosby et al. 2015, Brudvig et al. This issue).

It is not surprising that researchers and conservation practitioners usually apply a single biodiversity model to address a particular conservation problem. The study area, biodiversity element of interest, conservation goals and data availability may dictate the choice of model. For example, a species with very strict habitat requirements, such as the Glanville fritillary butterfly (Melitaea cinxia) in Finland occupies a landscape of habitat patches surrounded by inhospitable matrix and may be most amenable to metapopulation models (e.g. [START_REF] Moilanen | Metapopulation dynamics: effects of habitat quality and landscape structure[END_REF]. Given that the majority of respondents to a recent survey on quantitative training among early career ecologists were not comfortable with their understanding of mathematical models within their field [START_REF] Barraquand | Lack of quantitative training among early-career ecologists: a survey of the problem and potential solutions[END_REF], we surmise that researcher and practitioner experience with quantitative techniques may also explain the paucity of case studies applying multiple biodiversity models. But perhaps the most important reason for the lack of multi-model comparisons is that we do not have a framework for comparing models that are based on different assumptions (e.g. environmental filtering, species-area relationships), parameterized with different types of data (e.g. abundance, presence/absence, co-occurrence), and which provide disparate predictions (e.g. species-level, community-level).

Biodiversity models have a key role to play in exploring the causes and consequences of biodiversity change [START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF][START_REF] Thuiller | A road map for integrating eco-evolutionary processes into biodiversity models[END_REF]. The primary driver of species extinctions and turnover is Accepted Ar ticle 'This article is protected by copyright. All rights reserved.' habitat loss and fragmentation [START_REF] Newbold | Global effects of land use on local terrestrial biodiversity[END_REF]. Habitat loss and fragmentation results in the direct removal of species and their habitat but also the indirect loss of species by providing the pathways for resource extraction (e.g. fishing, forestry) and the arrival of non-native organisms. For example, [START_REF] Kaufman | Impacts of road access on lake trout (Salvelinus namaycush) populations: regional scale effects of overexploitation and the introduction of smallmouth bass (Micropterus dolomieu)[END_REF] report higher exploitation rates of native lake trout (Salvelinus namaycush) and higher prevalence of non-native smallmouth bass (Micropterus dolomieu) in lakes with good road access than lakes with poor road access in northeastern Ontario, Canada. Many biodiversity models have been used to predict the effects of habitat loss and fragmentation on biodiversity. For example, [START_REF] Cord | Inclusion of habitat availability in species distribution models through multitemporal remote-sensing data?[END_REF] incorporate remotely sensed enhanced vegetation index data to improve predictions of anuran species distribution in fragmented habitats in Mexico. Developing a framework for comparing different biodiversity models will allow us to explore and potentially reduce structural uncertainty arising from model specific assumptions and to better manage model complexity.

Here we seek to fill this gap by showing how a common and simple statistical framework can be used for comparing the predictions from different biodiversity models. We begin by reviewing the history, formulation, predictions and applications in biodiversity conservation of three simple but widely applied biodiversity models; species-area relationships (SAR), metapopulation models (MEP), and species distribution models (SDM). Then we map the processes behind these three models to a common statistical framework and apply it to a systematic comparison with a case study of land-use planning in a fragmented landscape in southwestern Quebec, Canada. We end with perspectives for multi-model comparison and integration for real-world biodiversity conservation and land-use planning.

REVIEW OF THREE SIMPLE BIODIVERSITY MODELS

We review species-area relationships, metapopulation models, and species distribution models (Table 1) because they are widely used in ecology and conservation and they are relatively simple with few parameters which makes them easy to parameterize in practice. Classic SAR makes predictions at the community-level whereas classic MEP and SDM models make predictions at the species-level.

Species-area relationships

SARs are among the best-known and most documented observations in ecology [START_REF] Rosenzweig | Species diversity in space and time[END_REF]. SARs describe the dependence of species richness on area at various spatial scales, along environmental gradients and across landscape configurations. A power function S=cA z was the first model proposed to predict the

Accepted Ar ticle

'This article is protected by copyright. All rights reserved.' change of species richness (S) with area (A) across isolated ecosystems [START_REF] Arrhenius | Species and Area[END_REF] where c and z are empirical constants. This formulation of SARs receives good support from ecological data and theory [START_REF] Dengler | Which function describes the species-area relationship best? A review and empirical evaluation[END_REF].

One general pattern revealed by SAR studies is that, all else being equal, larger areas are expected to support more species. Many mechanisms have been proposed to explain this observation, including the null hypothesis of random placement and passive sampling (Connor and McCoy 1979), the area per se hypothesis, i.e. lower extinction probability with larger areas [START_REF] Macarthur | The Theory of Island Biogeography[END_REF], and the habitat diversity hypothesis, i.e. larger areas having greater habitat diversity [START_REF] Rosenzweig | Species diversity in space and time[END_REF].

Recent models have tried to improve the predictive power of SARs through the integration of processes shaping species richness in fragmented landscapes (Whittaker et al. 2005). Specifically, insights from metapopulation theory led to the species-fragmented area-relationship model [START_REF] Hanski | Species-fragmented area relationship[END_REF], while niche theory is at the core of the matrix-calibrated SAR [START_REF] Koh | A matrix-calibrated species-area model for predicting biodiversity losses due to land-use change: Matrix-calibrated species-area model[END_REF]Ghazoul 2010, Tanentzap et al. 2012) and the countryside SAR [START_REF] Mendenhall | Predicting biodiversity change and averting collapse in agricultural landscapes[END_REF]. SARs have been used extensively in ecology and conservation biology to predict species richness from sample-area curves (e.g. [START_REF] Tjørve | The importance of samples and isolates for species-area relationships[END_REF], optimally design nature reserves (e.g. [START_REF] Kukkala | Core concepts of spatial prioritisation in systematic conservation planning: Concepts of systematic conservation planning[END_REF], and predict species extinctions based on habitat loss and fragmentation (e.g. [START_REF] Brooks | Threat from deforestation to montane and lowland birds and mammals in insular South-east Asia[END_REF].

Metapopulation models

Spatially explicit metapopulation models describe the presence and absence of a species across a network of habitat fragments [START_REF] Hanski | Metapopulation ecology[END_REF]. The widely used incidence function model (IFM) for metapopulations represents the occupancy of each habitat patch as a Markov chain with two states, occupied (species is present) and vacant (species is absent) with transition probabilities between the two states determined by local extinction and dispersal-mediated colonization from neighboring patches [START_REF] Hanski | Metapopulation ecology[END_REF].

The original IFM assumed extinction rates decreased with patch area, and colonization rates increased with the connectivity and area of occupied patches [START_REF] Hanski | Metapopulation ecology[END_REF]. While SAR and MEP models both consider the effects of patch area on species, the core of MEP theory is based on dispersal limitations and patch connectivity [START_REF] Levins | Some demographic and genetic consequences of environmental heterogeneity for biological control[END_REF][START_REF] Hanski | Metapopulation ecology[END_REF]. Connectivity between patches can be estimated with simple structural measures, such as straight-line distances between neighboring patches, or more complex

Accepted Ar ticle

'This article is protected by copyright. All rights reserved.' functional measures derived from network theory, circuit theory, or individual-based models [START_REF] Coulon | A stochastic movement simulator improves estimates of landscape connectivity[END_REF].

Both metapopulation (Akçakaya et al. 2006) and habitat connectivity [START_REF] Crooks | Connectivity Conservation[END_REF] models have become increasingly important in conservation. In future conservation applications, it may be important to combine these models because the relationship between habitat connectivity and ecological dynamics has been recently shown to depend not only on the spatial configuration of habitat [START_REF] Holland | Strong effect of dispersal network structure on ecological dynamics[END_REF]Hastings 2008, Thompson et al. 2014) but also on demographic parameters of the species (e.g. extinction and colonization probabilities; [START_REF] Gilarranz | Spatial network structure and metapopulation persistence[END_REF].

Species distribution models

Species distribution models (SDM) correlate species distribution data (e.g. occurrence, abundance) with environmental or spatial covariates to describe the relationship between occupancy and the environment and to predict species distribution within or outside the sampled area [START_REF] Elith | Species distribution models: Ecological explanation and prediction across space and time[END_REF]Leathwick 2009, Araújo and[START_REF] Araújo | Uses and misuses of bioclimatic envelope modeling[END_REF]. Generalized linear models, boosted regression trees, random forest, and general additive models and the combination of several algorithms (i.e., ensemble forecasting procedure; [START_REF] Araújo | Ensemble forecasting of species distributions[END_REF] are the most common statistical approaches for SDMs.

Given most SDMs predict a continuous probability of species occurrence, there are a number of methods for converting continuous model predictions to binary range classifications and these methods make a number of simplifying assumptions (see review in [START_REF] Liu | Selecting thresholds of occurrence in the prediction of species distributions[END_REF].

While the strength of SDMs is the ease with which they can be parameterized for broad sets of species over large spatial extents, SDMs have been widely criticized because they do not account for many ecological processes underlying the observed species distributions (e.g. dispersal, biotic interactions; [START_REF] Elith | Species distribution models: Ecological explanation and prediction across space and time[END_REF]. A new generation of SDMs that integrate process-based approaches have modified classical SDMs in several ways: i) by including physiology (e.g. [START_REF] Kearney | Mechanistic niche modelling: combining physiological and spatial data to predict species' ranges[END_REF], species interactions (e.g.

Trainor & Schmitz 2014), population dynamics (e.g. [START_REF] Leroux | Mechanistic models for the spatial spread of species under climate change[END_REF] and movement (e.g. [START_REF] Vasudev | From dispersal constraints to landscape connectivity: lessons from species distribution modeling[END_REF], ii) by formulating hybrid models that pair correlative models with additional ecological processes (e.g. population viability model; [START_REF] Haby | Scale dependency of metapopulation models used to predict climate change impacts on small mammals[END_REF], and iii) by using co-occurrence data as a covariate in joint SDMs [START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a joint species distribution model (JSDM)[END_REF].

Accepted Ar ticle

'This article is protected by copyright. All rights reserved.' SDMs are commonly used for a variety conservation applications including spatial conservation prioritization and land-use management (e.g. protected areas design; [START_REF] Leroux | Accounting for system dynamics in reserve design[END_REF][START_REF] Meller | Ensemble distribution models in conservation prioritization: from consensus predictions to consensus reserve networks[END_REF] and restoration planning [START_REF] Chetkiewicz | Use of resource selection functions to identify conservation corridors[END_REF]. They are also used to improve the sampling of species distributions [START_REF] Guisan | Using niche-based models to improve the sampling of rare species[END_REF], or to map the potential risk of species invasions (e.g. [START_REF] Gallien | Invasive species distribution models -how violating the equilibrium assumption can create new insights: Beyond the equilibrium assumption of SDMs[END_REF], disease (e.g. [START_REF] Kulkarni | High resolution niche models of malaria vectors in northern Tanzania: A new capacity to predict malaria risk?[END_REF], and species responses to climate change (e.g. [START_REF] Kerr | Climate change impacts on bumblebees converge across continents[END_REF].

A STATISTICAL FRAMEWORK TO MODEL THE CONSEQUENCES OF HABITAT LOSS AND FRAGMENTATION ON BIODIVERSITY

Here we describe a general and common statistical approach to compare predictions from the different biodiversity models described above. We aim to emphasize the differences among biodiversity models and therefore focus on the key process represented by each of them.

A general model for species distribution in fragmented landscapes

Let us consider a general situation of isolated patches of favorable habitat in a matrix of inhospitable areas. It is convenient to express the immigration and extinction dynamics at a location at the species level. The time dynamics of species i being present at location x, p ix , could be described as:

( ) (1)
where I ix is the immigration rate of species i from the 'mainland' to the location x, and E ix is the extinction rate of species i at location x. Thus, both rates are species and location specific. At equilibrium, immigration balances extinction, and we get the probability of finding species i in locality x:

^ (2)
where ^ denotes the equilibrium occurrence probability. We could also express this quantity with a linear model, using a logit transformation:

( ^ ) ( ^ ^ ) ( ) ( ) (3)
It is straightforward to get back to the community level and derive the expected species richness at location x ( ^ ), assuming that species are distributed independently of each other [START_REF] Gravel | Trophic theory of island biogeography[END_REF]) and summing species-specific occurrence probabilities:

^ ∑ ^ (4)

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where V is the total number of species in the regional pool. If species are not distributed independently (e.g.

predator-prey) then approaches such as joint species distribution models [START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a joint species distribution model (JSDM)[END_REF]) may be used for community level predictions.

It is not straightforward to measure I and E directly in the field and even less so for measuring species and location specific values. It is nonetheless possible to derive likely estimates according to species distribution data and some constraints such as patch area, isolation and local environmental conditions.

The distribution of individual species in a locality is usually modeled statistically as a binomial process conditional on local site characteristics:

( ) (5)
where ν mx is the value of covariate m at location x and β im is the species-specific coefficient for this covariate.

This, for instance, is a common approach for SDMs (reviewed in [START_REF] Elith | Species distribution models: Ecological explanation and prediction across space and time[END_REF]. Such a modeling framework may include linear and non-linear (e.g. quadratic) terms for covariates, ν mx , as well as interactions between covariates. It is flexible enough to include a diversity of covariates, such as patch area or isolation, allowing the direct comparison of SDM with SAR or MEP theories. To date several studies have incorporated patch and landscape characteristics into SDMs. For example, [START_REF] Dullinger | Patch configuration affects alpine plant distribution[END_REF], [START_REF] Betts | A species-centered approach for uncovering generalities in organism responses to habitat loss and fragmentation[END_REF], and

McCune (2016) combine patch (e.g. area) and landscape (e.g. connectivity) and climate covariates to predict the distribution of Alpine plants in the Calcareous Alps of Austria, birds in Oregon, USA, and rare plants in southern Ontario, Canada, respectively. [START_REF] Boulangeat | Accounting for dispersal and biotic interactions to disentangle the drivers of species distributions and their abundances[END_REF] added propagule pressure as a covariate in their SDMs of plant species in the French Alps. It is easy to map the above model (Eq. 5) onto Eq. 3 in order to interpret the resulting parameters in terms of immigration and extinction dynamics, thus explicitly bridging the gap with theory through the set of equations introduced above (Eqs 1-2).

Beginning with Eq. 5, we now turn to the interpretation of I ix and E ix from knowledge of patch area, patch isolation and environmental conditions, respectively, in order to link a single statistical approach with the different processes underlying the original SAR, MEP, and SDM models.

Patch area: Application to species area relationship models

It is commonly assumed that species extinction rates should decrease with increasing patch area [START_REF] Hanski | Metapopulation ecology[END_REF]. The underlying rationale is that larger patches sustain larger populations, thus reducing demographic

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'This article is protected by copyright. All rights reserved.' stochasticity [START_REF] Lande | Stochastic population dynamics in ecology and conservation[END_REF] and the chance of random extinction despite favorable environmental conditions. Here, we assume and I ix is a species-specific constant. According to Eq. 5, we could represent patch area dependent occurrence probabilities as:

( ) ( ) (6)
where is a species-specific intercept related to the immigration rate. A SAR then can be computed by summing across all species, as described in Eq. 4.

Patch isolation: Application to metapopulation models

In the theory of island biogeography, [START_REF] Macarthur | The Theory of Island Biogeography[END_REF] hypothesized that I ix scales inversely to the distance to the mainland. Later, [START_REF] Hanski | Metapopulation ecology[END_REF] developed spatially explicit metapopulation theory and generalized the approach to archipelagoes (or networks of patches), thus predicting that immigration should scale with the number of connected patches. More precisely, in a spatially explicit setting, the immigration rate could be described as:

(∑ ( ) ) (7)
where f(.) is some link function, N x denotes the set of neighbor patches of x, and k i (x,y) is a species-specific dispersal kernel describing the probability that a species colonizes patch x coming from patch y. Note that the summation is taken across all neighboring patches, assuming we know their occupancy . Unfortunately this information is often missing, in which case p iy is simply considered as a constant (i.e. all neighboring patches have the same average occupancy) and I ix depends simply on a local, species-specific measure of the connectivity of patch x: ∑ ( ) . Here we assume a power function for and E ix is a species-specific constant. Using the same logic as Eq. 5, we would therefore model presence-absence from the connectivity matrix using the following statistical model:

( ) ( ) (8)
where is a species-specific intercept related to the extinction rate. This formulation of the MEP model focuses on dispersal limitations, which allows for quantitative comparison of predictions from models of patch area (i.e. SAR) and patch isolation (i.e. MEP).

Environmental conditions: Application to species distribution models

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Local patch quality can also influence both species establishment success and extinction from a location.

Establishment of a population is the end result of several processes taking place after first immigrants reach the location, from the initial dispersal event up to the development of a sustained population. Local environmental conditions could influence the germination success of seeds, the decision of an animal to stay at the location, or the growth of a population. Local conditions could also influence population size, and for the same argument as area, they could influence extinction rate. It is thus possible to express both immigration and the extinction rates as functions of local environmental conditions such that

I ix = f i (ν 1x , …, ν mx ) and E ix = g i (ν 1x , …, ν mx ).
The corresponding statistical model of presence-absence could then be described by Eq. 5.

Note that in this case, the absence of information about immigration and extinction dynamics prevents disentangling differential effects of the environment on each process. Such estimates could be obtained using state transition data.

From theory to practice

In practice, a species' occurrence probability does not necessarily follow the log-linear assumption described here. We took this approach as it maps naturally to generalized linear models, but emphasize that more flexible statistical models could be used. To compare the performance of patch area (SAR), patch isolation (MEP), or environmental conditions (SDM)-based models, we could compute model likelihoods and compare them by AIC, as long as we know the exact number of parameters. Goodness of fit for each model could be evaluated using statistics such as the pseudo , or model predictive accuracy could be measured with the TSS (True Statistic Skill) and AUC (Area Under the receiver operating characteristic Curve, [START_REF] Allouche | Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS): Assessing the accuracy of distribution models[END_REF]).

Overall, we show how we can build patch area, isolation and environmental conditions as covariates in a general statistical framework (Eq. 5) to produce models that map the underlying processes of SAR (Eq. 6), MEP (Eq. 8) and SDMs (Eq. 5) to a common currency. Although our SAR, MEP, and SDM formulations may differ from classic representations, we capture the essence of the classic models by incorporating key processes into our formulations. Following our framework, we fit statistical models of the presence/pseudo-absence of a focal species in a patch with a binomial error structure and logit link. We used a 1:1 presence:pseudo-absence sampling scheme with 100 different pseudo-absence data sets for each species. We compared the three model classes (patch area, patch isolation, environmental conditions) in terms of their ability to characterize present and predict future distributions of our 8 focal species. We hypothesized which model class would best fit each focal species' distribution based on dispersal and habitat preference traits. A detailed description of our study area, data, methods and hypotheses is provided in Supplementary material Appendix 1.

COMPARING PREDICTIONS OF BIODIVERSITY MODELS

We used stepAIC to determine the most parsimonious set of covariates for each model class per set of pseudo-absences (n = 100) per species (n = 8). additional covariate in the environmental conditions model for anuran species (ν mx in Eq. 5 Supplementary material Appendix 1).

Species-specific patch connectivity was defined as the sum of the dispersal probabilities between neighboring patches (see Eq. 7). We modeled dispersal probabilities as a negative exponential dispersal kernel with ( )

( ) ⁄
where dist(x,y) is the Euclidean distance between the edges of patches x and y and D50 i is the median dispersal distance for species i (see Table 2). The set of neighboring patches in Eq. 7 (N) was defined as patches with adjacent polygons in a Voronoi tessellation of the landscape. Habitat patches neighboring the more continuous mountain areas were kept as sources, i.e. they were included in the habitat networks and the calculation of species-specific patch connectivity, but we did not predict the probability of occurrence of each focal species in these patches. To differentiate between the patch area and isolation effects processes, we only included isolation effects in our MEP model and patch area in our SAR model. For all three model classes, we tested linear and quadratic terms for each covariate but did not include covariate interaction terms.

Spatial predictions of species occurrences under current and future land-use scenarios

We randomly selected a single pseudo-absence iteration per species (results were similar when randomly taking another pseudo-absence iteration) to predict the probability of occurrence of the focal species across our full landscape based on patch area, patch isolation, and environmental condition models. Following our statistical framework (Eq. 4), we summed the species-specific probability of occurrences for each model to create a predictive "species richness" map and multiplied Eq. 4 by 1000 [START_REF] Distler | Stacked species distribution models and macroecological models provide congruent projections of avian species richness under climate change[END_REF]. We only included species for which the best model reached both a TSS > 0.3 and AUC > 0.7 for each model class [START_REF] Thuiller | Does probability of occurrence relate to population dynamics?[END_REF]. We calculated the spatial coherence of the patch area, patch isolation and environmental condition model predictions on species richness at time t with Spearman correlations (ρ) for the

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entire set of patches. In addition, we calculated Jaccard coefficients of the model predictions on species richness at time t for the top 10% richest forest patches by area.

We used the same set of patch area, patch isolation and environmental condition models parameterized under current conditions to predict the probability of occurrence of our focal species into the future (see Supplementary material Appendix 1 for description of future landscape scenario) and used the same metrics as above to compare future "species richness" maps.

All analyses were conducted with the statistical software R 3.0.2 (R Core Team 2015) and the species distribution modeling library biomod2 [START_REF] Thuiller | BIOMOD -a platform for ensemble forecasting of species distributions[END_REF].

RESULTS

Patch area, patch isolation and environmental condition model selection

The patch area model was the most frequent top ranking model for four species (P. 3). The top models for all species had a mean predictive accuracy that was good to very good (TSS > 0.3 and ROC > 0.7; [START_REF] Thuiller | Does probability of occurrence relate to population dynamics?[END_REF], except for the top models for B. americanus and D. pileatus which had a mean predictive accuracy that was poor (TSS > 0.2 and ROC > 0.6) (Supplementary material Appendix 2). Given the poor fit of

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'This article is protected by copyright. All rights reserved.' models for B. americanus and D. pileatus, we did not include these two species in our calculations of predicted species richness (i.e. Eq. 4). The top-ranked model did not consistently match our hypotheses based on species traits (Table 2, Appendix 1).

Comparisons of spatial predictions for stacked species occurrences in current landscape

All predictions of species richness for the current landscape are positively correlated and show high spatial overlap, but there is nonetheless substantial variability in patch-specific predictions among models (Fig. 3). The patch area and environmental condition model predictions were most similar based on Spearman's ρ, particularly for small patches (ρ = 0.6, Fig 3) whereas the patch isolation and environmental condition model predictions were least similar based on Spearman's ρ (ρ = 0.31, Fig 3). The spatial overlap in the 10% most species rich patches by area based on the Jaccard coefficient show slightly different patterns (Fig. 3). When considering only these richest patches, patch area and patch isolation models showed the highest spatial overlap (Jaccard coefficient = 0.82) and the patch area and environmental condition models showed the lowest spatial overlap (Jaccard coefficient = 0.59).

Comparisons of spatial predictions for stacked species occurrences under future land-use scenario

Our 2050 landscape was composed of less habitat area (-10% of total area), more forest patches (9,585 patches representing a 30 % increase), but patches were smaller on average (median=18,900 m 2 representing a 55 % decrease; Fig. 2). Similar to the current landscape, all model predictions for the future landscape were positively correlated (Fig. 3). The patch area and environmental condition model predictions

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were most similar whereas the patch isolation and environmental condition model predictions were least similar based on Spearman's ρ (ρ = 0.46 and 0.29, respectively, Fig 3). When considering only the 10% richest patches by area, patch area and patch isolation models showed the highest spatial overlap (Jaccard coefficient = 0.82) and both the patch area and environmental condition models and the patch isolation and environmental condition models had lower spatial overlap (both with Jaccard coefficient = 0.62).

There was considerable spatial variability of change in species richness within model class predictions (Supplementary material Appendix 3, Fig. A2). While patch area models, because of their definition, always predicted a reduction in species richness due to habitat loss, patch isolation and environmental condition models gave more contrasted results (Fig. 4). On the one hand, some patches had an apparent increase in species richness according to the patch isolation model, which is an artifact of an increase in the number of close neighboring patches due to fragmentation following habitat loss. On the other hand, the repositioning of patches following habitat loss lead to changes in average patch condition and mostly reduced species richness predictions according to the environmental condition model (Fig. 4).

The greatest change in species richness following habitat loss was predicted by the patch isolation and patch area models (Fig. 4, Supplementary material Appendix 3, Fig. A2).

PERSPECTIVES ON THE USE AND INTEGRATION OF SIMPLE BIODIVERSITY MODELS IN

CONSERVATION

Mathematical models have played a fundamental role in the development of both ecological theory (Caswell 1988, Codling and[START_REF] Codling | Mathematical and theoretical ecology: linking models with ecological processes[END_REF] and a toolbox to predict the impacts of human activities on biodiversity

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'This article is protected by copyright. All rights reserved.' (e.g. [START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF]. While there is an increasing number of studies incorporating environmental conditions and landscape predictors in the same model (e.g. [START_REF] Calabrese | Stacking species distribution models and adjusting bias by linking them to macroecological models[END_REF][START_REF] Betts | A species-centered approach for uncovering generalities in organism responses to habitat loss and fragmentation[END_REF][START_REF] Mccune | Species distribution models predict rare species occurrences despite significant effects of landscape context[END_REF], we are aware of only a few studies that compare the predictions of different theoretical models for a given landscape (see [START_REF] Moilanen | Metapopulation dynamics: effects of habitat quality and landscape structure[END_REF][START_REF] Keith | Predicting extinction risks under climate change: coupling stochastic population models with dynamic bioclimatic habitat models[END_REF][START_REF] Dullinger | Patch configuration affects alpine plant distribution[END_REF], Fordham et al. 2013, Brudvig et al. This issue). Here, we apply a common and flexible statistical framework to compare the predictions of simple biodiversity models and apply it to investigate present and future biodiversity in a real, fragmented landscape. Our framework enabled us to uncover complementarities among model predictions and also limitations of incorporating a single mechanism for predicting the distribution of species richness; patch area (SAR), patch isolation (MEP) and environmental conditions (SDM).

It is common practice in ecology and conservation biology to compare the performance of different formulations within a class of biodiversity models. For example, DeCamargo and Currie (2014) compare the predictions and fit of three types of SAR models for bird communities in Ontario, Canada; the classic power function SAR model, a polynomial SAR model and the endemic-area model. Likewise, [START_REF] Meynard | Predicting species distributions: a critical comparison of the most common statistical models using artificial species: Comparison of species-distribution models[END_REF] compare the performance of four different SDMs on virtual species data; generalized additive models, logistic regression, classification trees, and the genetic algorithm for rule-set production (GARP). While comparing predictions within a model class is valuable, it is also limited because a particular model class assumes specific drivers of biodiversity distribution and inference from within model class comparisons are constrained to the adopted model structure. For example, SAR models assume that species richness is related to area and therefore residual variation that may be explained by other mechanisms (e.g. patch isolation, environmental conditions) will not be uncovered when comparing predictions of different SAR formulations.

Comparisons among model classes are rare because such comparisons require a flexible framework that can be applied to diverse models. We provide one solution to fill this gap with a generalized linear model that can be parameterized with presence/pseudo-absence data, which may allow ecologists and conservation biologists to evaluate predictions from different biodiversity models in order to improve predictions of the effects of global changes on biodiversity. This framework is equivalent to developing an SDM with patch, landscape and environmental covariates. However, the above framework allows ecologists to build on previous studies that integrate multiple classes of covariates into SDMs in a few ways. First, the approach we present here is based on theory and is not purely phenomenological. SAR, MEP and SDM have different

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'This article is protected by copyright. All rights reserved.' histories and different user groups and the framework we outline allows us to relate each theory to a specific statistical model. The roadmap we provide is an explicit attempt to show how these different theories can be integrated into a common and simple statistical framework. As such, it allows us to test and compare hypotheses and reveal structural uncertainty in model selection (i.e. has the modeler selected the right model/process?). Second, our approach allows comparison of these three biodiversity models at species (Eq. 5) and community levels (Eq. 4). This is critical for disentangling how different species respond to different drivers and for comparing predictions from different models. Finally, the long-term trajectories of biodiversity in fragmented landscapes may differ (e.g. Collins et al. This issue, Ewers et al. This issue) and a processbased approach at species and community levels may yield more robust predictions for future scenarios and long-term land-use planning [START_REF] Leroux | Mechanistic models for the spatial spread of species under climate change[END_REF][START_REF] Thuiller | A road map for integrating eco-evolutionary processes into biodiversity models[END_REF].

The application of this framework to the case study revealed that patch area is an important driver of the distribution of many of the 8 focal vertebrate species, but that connectivity and environmental conditions were also important for at least four focal species (Table 3). Clearly, adoption of a single model class for all species would have overlooked key correlates of the distribution of some of the focal species. Haddad et al (This issue) also find evidence that patch area, isolation and configuration are key determinants of species richness in two experimental systems. Taken together, these results provide evidence in contrast to the recently proposed Habitat Amount Hypothesis [START_REF] Fahrig | Rethinking patch size and isolation effects: the habitat amount hypothesis[END_REF]). Determining which model was best for each species a priori, based on traits alone, was not reliable (only matched the top ranked model in Table 3 for 50% of the species, Appendix 1) which underscores the need to consider multiple models. However, given the small number of focal species we consider, the overall low quality of these data (very incomplete set of presence/absence data with, on average 3% of the patches as occupied), the poor sampling of smaller patches, and the fact that the data come from various sampling protocols, we prefer to consider this as an illustration of model comparison and limit our biological interpretation of our results.

Habitat loss and fragmentation alter the distribution of patch area, connectedness and environmental conditions [START_REF] Fahrig | Effects of habitat fragmentation on biodiversity[END_REF]. Consequently, a model that focuses on a single of these components of land-use change may not capture its full effects on biodiversity (Brudvig et al. This issue, Haddad et al. This issue).

Disentangling the relative impacts of patch area and isolation on biodiversity has been a driver of fragmentation research for decades [START_REF] Haddad | Habitat fragmentation and its lasting impact on Earth's ecosystems[END_REF]. By comparing predictions from multiple models that

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'This article is protected by copyright. All rights reserved.' incorporate the effects of different fragmentation processes we can better understand the relative and combined importance of these processes on species distribution and richness under land-use change. In the case study, patch area models, by definition, always predicted a patch-level decrease in species richness, whereas patch isolation and environmental condition models predicted either an increase or a decrease in patch-level species richness following habitat loss and fragmentation (Fig. 4). The predicted magnitude of change in any single patch was greatest for patch isolation and patch area models (Fig. 4). Over all patches, patch area and environmental condition models predicted an 11% decline and the patch isolation model predicted a 7% decline in species richness following habitat loss and fragmentation.

Application of these simple models to predict change in biodiversity is critical for conservation policy and practice (Resasco et al. This issue). For example, the Millennium Ecosystem Assessment (2005) applied SARs to predict species extinction rates following projected habitat loss. The choice of this model class for such predictions, however, presupposes key drivers of species extinction rates under global change.

The framework we outline allows us to better capture how structural uncertainty arises from different underlying processes, which may help to explain why some model predictions are not consistent with empirical observations. Some have argued for the need to integrate biodiversity models for better predictions of the effects of global change on biodiversity [START_REF] Moilanen | Metapopulation dynamics: effects of habitat quality and landscape structure[END_REF][START_REF] Keith | Predicting extinction risks under climate change: coupling stochastic population models with dynamic bioclimatic habitat models[END_REF][START_REF] Dullinger | Patch configuration affects alpine plant distribution[END_REF], Fordham et al. 2013, Brudvig et al. This issue). For example, [START_REF] Fordham | Tools for integrating range change, extinction risk and climate change information into conservation management[END_REF] provide an overview of the key insights gained by integrating metapopulation dynamics into SDMs, [START_REF] Koh | A matrix-calibrated species-area model for predicting biodiversity losses due to land-use change: Matrix-calibrated species-area model[END_REF] incorporate aspects of patch quality in their matrix-calibrated SAR model and [START_REF] Talluto | Cross-scale integration of knowledge for predicting species ranges : a metamodeling framework[END_REF] develop a methodological approach to integrate models across spatial scales in order to reduce error propagation arising from mechanistic SDMs. Based on the statistical framework we adopt, an integrated model may take the form of Eq. 5 where the species occurrence probability is based on covariates describing local site characteristics including patch area, patch isolation and environmental conditions. Such an integration must balance the cost of added model complexity with the benefit of improved model fit and predictions [START_REF] Merow | What do we gain from simplicity versus complexity in species distribution models?[END_REF].

CONCLUSION

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We provide a roadmap based on ecological theory for comparing and potentially integrating different classes of biodiversity models. The common and simple statistical framework we apply allows researchers and conservation practitioners to understand trade-offs between model complexity and model predictive accuracy and therefore make better informed modelling decisions with repercussions on predictions of biodiversity responses to global changes. Future development of this framework could involve applications to other biodiversity models (e.g. neutral model) and evaluation of integrated models. We hope that this approach encourages empiricists to collect and share biodiversity data that would allow more cross-model class comparison and integration. These cross-model class comparisons will facilitate feedbacks between theory and data which is essential for improving predictions for biodiversity change under global change.

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  cinereus (97%), R. sylvatica (66%), S. aurocapilla (78%), and S. varia (81%), the patch isolation model was the most frequent top ranking model for two species (D. pileatus (71%) and S. canadensis (81%)) and the environmental conditions model was the most frequent top ranking model for two species (B. americanus (52%) and S. minor (55%)). Five of the eight species had high model selection uncertainty with at least two model classes ranking as top model in ≥ 20% of pseudo-absence iterations (Table

  SDMs is firmly rooted in ecological studies of biodiversity along environmental gradients, the concept of ecological niche and in classic studies of species' responses to their environment.

FIGURE LEGENDS Figure 1 .Figure 2 .

 LEGENDS12 FIGURE LEGENDSFigure 1. Location of the study area in and around the St. Lawrence River near Montreal, Quebec, Canada. Red lines outline the boundary of the St. Lawrence lowlands ecoregion. Map is presented with North America Datum 1983 and Transverse Mercator projection.Accepted Ar ticle

Figure 3 .

 3 Figure 3. Pairwise correlations between model predictions for the current (top row) and future (bottom row) landscapes. Spearman ρ is reported for all patches and the Jaccard Coefficient for the 10% most species rich patches by area as predicted by each model. Black dots are the patches that make up the top 10% area of richest patches (along the x-axis). The axes are the predicted species richness (i.e. Eq. 4) multiplied by 1000 for each model. The two species (B. americanus, D. pileatus) with poor model fit were excluded from the species richness calculation.Accepted Ar ticle

Figure 4 .

 4 Figure 4. Predictions of current and future species richness (Eq. 4) multiplied by 1000 for the patch area, patch isolation, and environmental condition models. The two species (B. americanus, D. pileatus) with poor model fit were excluded from the species richness calculation. Each point represents the predictions (current and future) for the centroid location of a current patch. Future predictions of species richness = 0 are for patches where the centroid location was lost with habitat loss.

  We apply our statistical framework for comparing SAR, MEP, SDM models for focal species in a conservation case study in the fragmented, peri-urban landscape surrounding Montreal, Canada (centered on 45°400N, 73°150W). The landscape covers approximately 27 500 km 2 , the majority of which occurs in the fertile lowlands of the St. Lawrence River valley where small forest fragments are surrounded by agriculture and urban areas (Fig.1, 2). We selected 8 vertebrate focal species: 5 birds and 3 amphibians, to represent the forest biodiversity in this region (Supplementary material Appendix 1). The focal species span a range of forest habitat preferences (i.e. composition and age ranging from relative generalists across all forest types to specialists preferring old, coniferous forest), patch size requirements (i.e. minimum patch area ranging from 0.5 to 5 ha) and dispersal abilities (i.e. median dispersal ranging from 16 to 40,889 m; Table2, Supplementary material Appendix 1).

IN THE ST. LAWRENCE LOWLANDS SURROUNDING MONTREAL, CANADA

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  The three model classes included different covariates. As outlined in the statistical framework, the model with patch area is our representation of a SAR model (A x in Eq. 6), the model with species-specific patch connectivity (k ix in Eq. 7) is our representation of a MEP model, and the model with environmental conditions of soil drainage, soil deposit, % deciduous forest, % coniferous forest and maximum forest stand age is our representation of a SDM for all species. The presence of wetlands was included as an

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TABLE LEGENDS Table 1 .

 LEGENDS1 Summary of the three biodiversity models we considered in this study; SAR, MEP and SDM. The summary includes information on the goals, history and recent developments, key assumptions and mechanisms, predictions and software for each model class.

Table 2 .

 2 Traits of focal species used in the case study. Traits characterize dispersal ability and habitat preference: minimum habitat patch area (MA); median dispersal distance based on natal dispersal (D 50 ); preference for deciduous (D), mixed (M) or coniferous (C) forest; preferred forest type (Type); sensitivity to soil drainage (SD); and sensitivity to distance to wetlands (DW). Grey shading indicates a preference or sensitivity to feature.

	Recent efforts aim towards mechanistic
	SDMs, which link SDMs with process-
	based approaches, e.g. population
	viability model, physiology, species co-
	occurrences.

'This article is protected by copyright. All rights reserved.' 'This article is protected by copyright. All rights reserved.' 'This article is protected by copyright. All rights reserved.'

Table 3 .

 3 Summary of patch area, patch isolation and environment condition model class comparison for our eight focal species. We report the percentage of iterations for each model class (n = 100 sets of pseudoabsence) where it was ranked as the top model based on ΔAIC. The best supported model for each species is shaded in grey. We report the fit statistics (TSS, AUC) for each model in Supplementary material Appendix 2, TableA1).

	Species Bufo americanus Dryocopus pileatus Plethodon cinereus Rana sylvatica Scolopax minor Seiurus aurocapilla Sitta canadensis Strix varia Accepted Ar ticle	Patch area 47 6 97 66 45 78 18 81	Model classes Patch isolation 1 71 0 0 0 0 81 11	Environmental conditions 52 23 3 34 55 22 1 8

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ACKNOWLEDGEMENTS

SJL and DG were supported by Natural Science and Engineering Research Council of Canada Discovery Grants, CHA was supported by a Marie Curie International Outgoing Fellowship under the 7th European Community Framework Program (DYVERSE project, no. 272284), BR was funded by the OURANOS ÉCOBIOCC project, SW gratefully acknowledges the support of the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig funded by the German Research Foundation (FZT 118). ASL was supported by the TULIP Laboratory of Excellence (ANR-10-LABX-41) and the Midi-Pyrenees Region. This work contributes to the Labex OT-Med (no. ANR-11-LABX-0061) funded by the French government through the A*MIDEX project (no. ANR-11-IDEX-0001-02). We thank A. Gonzalez, M. Dumitru, and B. Holt for their thoughtful help on earlier stages of this work.

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Supplementary material (Appendix EXXXXX at <www.oikosoffice.lu.se/appendix>). Appendix 1-3.

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Keywords: information and media education, info-documentary look, epistemology, discipline, information culture

Information and Media Education across Disciplines:

Where is Coherence of Info-documentary Knowledge?

Yolande Maury Laboratoire GERiiCO (Lille 3), Artois/ESPé LNF, France, yolande.maury@noos.fr

This paper draws on the first results of ongoing research in the context of French secondary education (colleges, high schools) of three academies (Paris, Nancy-Metz, Lille)1 . The objective was to study current changes in the field of Information and Media Education (IME) in today's digital world: the degree to which the info-documentary dimension has been progressively introduced into the curricula of traditional disciplines and whether this resulted in curricular recompositions; the scope and the contents of this education with the aim to understand whether or not it could build an info-documentary look that might provide an interpretative framework for understanding the world.

The French research context

Regarded as a necessity today, information and media education is an unified concept marked by a shift from a singular to a pluralist conception of information culture "in the new age". As a field of practice, information-documentation has not been regarded as a discipline. But recent official documents introduced "interdisciplinary practical teachings", focusing on digital learning and linking information-communication and citizenship. A clear reference is made to information and communication sciences and to the sociology of culture and media.

And the role of teacher-librarian is more prominent: he or she is described as the person in charge of supervising the acquisition by all students of "an information and media culture". However, without dedicated teaching, information-documentation is addressed only on a pragmatic and operative mode and the responsibility of the different actors remained unclear.

Far from opposing 'education' and 'teaching', these areas of uncertainty are studied: in particular, how the actors seize the institutional guidelines, and who does what?

Methodology

To answer these and other questions, a questionnaire survey of 17 open and closed questions was administered to all actors in information and media education (e.g., teachers, teacher-librarians, principal educational advisers, school leaders), via academic mailing lists.

In this first phase, the questionnaires helped to identify trends concerning the integration of IME, including perceived importance, aims and issues, modalities of inclusion, supporting devices, collaborations and partnerships, contents such as knowledge and progression, barriers, and levers to its implementation.

The second phase is a more qualitative one. It aimed at deepening the understanding of the practices declared by the actors through interviews and observations, in a few selected schools.

First findings

Several elements emerged that highlighted a strong disciplinary mark that can be an obstacle to an open and pluralistic approach of EIM. Key among these results is evidence that information-documentation is rarely thought as an epistemological unit in its continuity and its coherence.

« L'éducation à l'information et aux médias (EIM), à l'heure du web

2.0 et des réseaux : Mise en cohérence des savoirs et recompositions curriculaires ». Y. Maury (dir.), Espé Lille Nord de France, 2015-2016.