Dr Tamara Münkemüller
email: tamara.muenkemueller@univ-grenoble-alpes.fr

Laure Gallien
email: laure.gallien@univ-grenoble-alpes.fr

Laura J Pollock
email: laura.pollock@univ-grenoble-alpes.fr

Ceres Barros
email: cbarros@mail.ubc.ca

Marta Carboni
email: marta.carboni@gmx.net

Loïc Chalmandrier
email: loic.chalmandrier@usys.ethz.ch

Florent Mazel
email: flo.mazel@gmail.com

Karel Mokany
email: karel.mokany@csiro.au

Cristina Roquet
email: cristina.roquet@gmail.com

Jan Smyčka
email: smyckaj@gmail.com

Matthew V Talluto
email: talluto@igb-berlin.de

Wilfried Thuiller
email: wilfried.thuiller@univ-grenoble-alpes.fr

Do's and don'ts when inferring assembly rules from diversity patterns

Keywords: Community processes, overdispersion, clustering, convergence, divergence, trait diversity, phylogenetic diversity, simulation model

Tamara Münkemüller studies the ecological processes that drive community assembly, the resilience of communities to environmental change and feedbacks between the plant and soil compartment. Her work builds on different types of models (from mechanistic simulation models to statistical models integrating multiple species) and on different types of data (from observational data to experimental data).

Introduction

The diversity of ecological communities is increasingly compromised by ongoing global changes [START_REF] Pereira | Global Biodiversity Change: The Bad, the Good, and the Unknown[END_REF]. Mitigating these threats requires to understand the distribution of diversity along geographic, abiotic and biotic gradients and the underlying assembly processes [START_REF] Lavergne | Biodiversity and Climate Change: Integrating Evolutionary and Ecological Responses of Species and Communities[END_REF][START_REF] Hillerislambers | Rethinking Community Assembly through the Lens of Coexistence Theory[END_REF] Harpole, [START_REF] Hillerislambers | Rethinking Community Assembly through the Lens of Coexistence Theory[END_REF]. A focal question is whether abiotic constraints or rather biotic interactions drive the taxonomic and trait structure of communities. In community ecology, this question has historically been addressed by experiments, with the limitation that these methods are typically constrained to small scales and few species. Thus, to study community assembly at large spatial scales, ecologists have assembled increasingly large community datasets spanning broad spatial extents with both trait and phylogenetic information [START_REF] Diaz | The global spectrum of plant form and function[END_REF]Kunstler, Falster, Coomes, Hui, Kooyman et al., 2016, see Fig. 1a, b ). Trait diversity describes the within-community variation of species' characteristics relevant for their performance, while phylogenetic diversity describes the evolutionary history. Combining data on distribution, traits and phylogeny in a meaningful way holds promise for a revolution in community ecology by opening the door to large-scale analyses of assembly processes [START_REF] Webb | Phylogenies and community ecology[END_REF][START_REF] Mc Gill | Rebuilding community ecology from functional traits[END_REF]. The idea is to harness the information on species niches contained in phylogenetic and trait data. For example, under the assumption that a set of traits represents species' niches well, we could move from a simple species-based description of communities towards a functional characterization, using community weighted mean traits as an estimate of the community niche optimum, and trait diversity as an estimate of species niche overlap (see below for more detail, [START_REF] Violle | Let the concept of trait be functional![END_REF][START_REF] Kraft | Functional traits and niche-based tree community assembly in an amazonian forest[END_REF].

In practice, this idea has mostly been implemented through the filtering framework [START_REF] Diamond | Assembly of species communities. Ecology and evolution of communities[END_REF][START_REF] Keddy | Assembly and response rules: two goals for predictive community ecology[END_REF] that builds on the assumption that both abiotic (e.g. climate or land use) and biotic factors (e.g. competition) define species' carrying capacities and/or growth rates and thus influence their occurrences and abundances (Fig. 1d). The abiotic conditions define the environmental filters selecting species from a regional species pool, originally shaped by biogeographical history [START_REF] Carstensen | Introducing the biogeographic species pool[END_REF], into the local species pool containing all species adapted to the local conditions. Then, biotic interactions influence which species from the local pool can eventually coexist in the community [START_REF] Schneider | Towards an Ecological Trait-data Standard. bioRxiv[END_REF][START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF]. This deterministic view assumes that different ecological filters should lead to distinct and predictable patterns in diversity and composition. Comparing these expected patterns with observed diversity across abiotic and biotic gradients should then allow for deducing underlying community assembly processes, thus moving large-scale community ecology from a purely descriptive discipline to a more process-based understanding [START_REF] Leibold | The metacommunity concept: a framework for multi-scale community ecology[END_REF][START_REF] Vellend | Conceptual synthesis in community ecology[END_REF][START_REF] Morin | Tree species richness promotes productivity in temperate forests through strong complementarity between species[END_REF].

Relatively early on, studies that began to apply the framework used trait diversity patterns (e.g. including behavioural, life-history, morphological and physiological traits, [START_REF] Violle | Let the concept of trait be functional![END_REF] and phylogenetic relatedness [START_REF] Webb | Phylogenies and community ecology[END_REF] to account for species' niche similarities. Doing so assumes that measured traits are relevant for assembly processes [START_REF] Mayfield | Traits, Habitats, and Clades: Identifying Traits of Potential Importance to Environmental Filtering[END_REF] and that closely related species in the phylogeny are ecologically more similar than distantly related ones [START_REF] Burns | More closely related species are more ecologically similar in an experimental test[END_REF]. Trait-phylogeny relationships different from these assumptions would lead to different relationships between niche similarity and phylogenetic relatedness patterns [START_REF] Webb | Phylogenies and community ecology[END_REF]. To infer assembly processes, observed patterns of trait and phylogenetic diversity within a community (i.e. αdiversity) are commonly compared to null expectations (i.e. patterns under random assembly, Fig. 1c). Low trait or phylogenetic α-diversity is assumed to indicate ecological processes that foster the co-occurrence of species with similar niches, such as environmental filtering (Fig. 1b, community A, see also Appendix S1 in Supporting Information). Conversely, high trait or phylogenetic α-diversity can reveal ecological processes that result in limiting similarity, such as competition due to niche overlap (Fig. 1b, community B, see also Appendix S1, [START_REF] Arthur | Limiting similarity convergence and divergence of coexisting species[END_REF]).

An increasingly large number of studies apply the filtering framework (see Appendix S2).

However, first reviews and meta-analyses of empirical (Emerson and Gillespie 2008[START_REF] Vamosi | Emerging patterns in the comparative analysis of phylogenetic community structure[END_REF], Götzenberger et al. 2012[START_REF] Hillerislambers | Rethinking Community Assembly through the Lens of Coexistence Theory[END_REF] and simulation experiments [START_REF] Münkemüller | From diversity indices to community assembly processes: a test with simulated data[END_REF][START_REF] Gallien | Identifying the signal of environmental filtering and competition in invasion patterns -a contest of approaches from community ecology[END_REF][START_REF] Miller | Phylogenetic community structure metrics and null models: a review with new methods and software[END_REF] have strongly dampened the enthusiasm, as they demonstrate that no simple general conclusion can be drawn from the sole observation of trait and phylogenetic diversity patterns. One prominent example is the ongoing debate on the role of competition: While the filtering framework often fails to pinpoint signals of competition, theoretical and empirical research underscores its importance even at broad scales (see Appendix S3 for a detailed discussion). Seemingly, we are not much further than 20 years ago when Lawton concluded that community ecology is a 'mess' [START_REF] Lawton | Community ecology in a changing world[END_REF]. The lingering question is why the filtering framework does not provide general results even though it is built on strong ecological theories [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF][START_REF] Leibold | The metacommunity concept: a framework for multi-scale community ecology[END_REF].

Here, we address this question by pinpointing the major pitfalls linked to the different steps of the standard filtering approach (Fig. 1). While many of the limitations of this framework have already been pointed out in previous reviews with various foci and levels of detail, and sometimes also in combination with possible solutions (e.g. [START_REF] Gerhold | Phylogenetic patterns are not proxies of community assembly mechanisms (they are far better)[END_REF][START_REF] Lopez | A new framework for inferring community assembly processes using phylogenetic information, relevant traits and environmental gradients[END_REF][START_REF] Pontarp | Inferring community assembly processes from macroscopic patterns using dynamic eco-evolutionary models and Approximate Bayesian Computation (ABC)[END_REF], an overarching synthesis and a set of general guidelines for correctly applying the filtering framework is still lacking. Building on existing work, we provide a novel comprehensive and structured overview of the different pitfalls and the solutions that have been developed (Tab. 1). We use the ongoing debate on the ecological importance of biotic interactions at large scales as an exemplary showcase (Appendix S3). Based on the integration of reviewed work we then suggest step-by-step guidelines for correctly applying the filtering framework that should result in better interpretable results in community ecology.

Common Pitfalls

Applying the filtering framework requires ( 1) choosing the study design with focal spatial, environmental and organism-level scales, (2) collecting information and (3) choosing methodological approaches relevant to the research question. Finally, (4) conclusions are drawn from the results while accounting for study limitations. In the following, we review 10 different pitfalls lying in wait along these steps.

Study design

The key aim of studies applying the filtering framework is to identify non-random processes in observed diversity patterns. One of the most discussed cases of non-random diversity patterns that exist despite the evident absence of directional environmental or biotic filters are neutral dynamics. Neutral theory suggests that many of the diversity patterns observed in nature may result from purely stochastic demographic processes that emerge from strong competition and dispersal limitation of functionally equivalent species and thus without any directional filter [START_REF] Hubbell | The unified neutral theory of biodiversity and biogeography[END_REF][START_REF] Münkemüller | From diversity indices to community assembly processes: a test with simulated data[END_REF][START_REF] Boucher | Neutral biogeography and the evolution of climatic niches[END_REF]. However, whether neutral dynamics lead to non-random diversity patterns depends on the focal scale of a study, and this is true for directional assembly processes as well. It is thus a pitfall to assume that: (P1) spatial, environmental and organism-level scale choices have no influence on study results (Fig. 1).

(P1) Certain processes may never be detected if we chose an inappropriate scale. First, ignoring large-scale factors, such as climate gradients, dispersal barriers, historical contingencies and evolutionary history can mask outcomes of smaller-scale processes such as local abiotic filters and competition [START_REF] Cavender-Bares | Phylogenetic structure of floridian plant communities depends on taxonomic and spatial scale[END_REF][START_REF] Swenson | The problem and promise of scale dependency in community phylogenetics[END_REF][START_REF] Vamosi | Emerging patterns in the comparative analysis of phylogenetic community structure[END_REF][START_REF] Cardinale | Biodiversity simultaneously enhances the production and stability of community biomass, but the effects are independent[END_REF]. Second, ignoring small-scale factors, such as intraspecific variation in trait values [START_REF] Albert | On the importance of intraspecific variability for the quantification of functional diversity[END_REF][START_REF] Siefert | A global meta-analysis of the relative extent of intraspecific trait variation in plant communities[END_REF] and the fine scale spatial arrangement of individuals [START_REF] Diekmann | The geometry of ecological interactions: simplifying spatial complexity[END_REF], can lead to overlooking the underlying processes as their effects may not scale up to large-scale diversity patterns [START_REF] Thuiller | Resolving Darwin's naturalization conundrum: a quest for evidence[END_REF][START_REF] Araujo | The geographic scaling of biotic interactions[END_REF][START_REF] Turcotte | Phenotypic Plasticity and Species Coexistence[END_REF]. For example, it has been shown that trait plasticity increases niche differences in communities and thereby stabilize coexistence and promote diversity (Pérez-Ramos, Matías, [START_REF] Pérez-Ramos | Functional traits and phenotypic plasticity modulate species coexistence across contrasting climatic conditions[END_REF]. This biotic filtering mechanism would remain unnoticed when relying solely on species' mean traits. Third, ignoring small-scale environmental variation within the community and study site may lead to high diversity in low-resolution studies and can then be easily misinterpreted as a signal of limiting similarity [START_REF] Price | Withincommunity environmental variability drives trait variability in species-rich grasslands[END_REF].

Collecting information

Trait and phylogenetic diversity are often used as proxies for niche overlap, yet this common practice is often challenged [START_REF] Cadotte | The ecology of differences: assessing community assembly with trait and evolutionary distances[END_REF][START_REF] Gerhold | Phylogenetic patterns are not proxies of community assembly mechanisms (they are far better)[END_REF][START_REF] Li | Can functional traits account for phylogenetic signal in community composition?[END_REF]. It is thus a pitfall to assume that: (P2) trait and phylogenetic diversity are always good proxies for species niche overlap (Fig. 1).

(P2) A first set of questions with regard to trait diversity is whether we are able to identify and measure the traits of ecological relevance for each [START_REF] Mc Gill | Rebuilding community ecology from functional traits[END_REF][START_REF] Funk | Revisiting the Holy Grail: using plant functional traits to understand ecological processes[END_REF], whether traits are closely enough linked to species niches (D'Andrea, Ostling & O'Dwyer James, 2018) and whether we can avoid irrelevant traits that might confound the patterns and lead us to spurious conclusions [START_REF] Kraft | Plant functional traits and the multidimensional nature of species coexistence[END_REF]. This task is facilitated by former work (e.g. [START_REF] Leps | Quantifying and interpreting functional diversity of natural communities: practical considerations matter[END_REF] and some more recent advancements: For some clades and ecological processes, guidelines for the identification of relevant traits and database standards are now available [START_REF] Luck | Improving the application of vertebrate trait-based frameworks to the study of ecosystem services[END_REF][START_REF] Diaz | The global spectrum of plant form and function[END_REF][START_REF] Gravel | The meaning of functional trait composition of food webs for ecosystem functioning[END_REF][START_REF] Schneider | Towards an Ecological Trait-data Standard. bioRxiv[END_REF], open-access databases are improving [START_REF] Kattge | TRY -a global database of plant traits[END_REF][START_REF] Wilman | EltonTraits 1.0: Species-level foraging attributes of the world's birds and mammals[END_REF], and trait syndromes (i.e. observed covariations in traits) can help to reduce trait space to a few relevant dimensions [START_REF] Wright | The worldwide leaf economics spectrum[END_REF][START_REF] Diaz | The global spectrum of plant form and function[END_REF]. However, in many aspects, trait science still remains incomplete [START_REF] Yang | Why Functional Traits Do Not Predict Tree Demographic Rates[END_REF]: (i) frameworks to link traits and niche dimensions are still under development for most clades (e.g. for fungi, [START_REF] Crowther | Untangling the fungal niche: the trait-based approach[END_REF], (ii) even in well-studied clades, some traits are better studied than others (e.g. plant leaf traits over root traits, [START_REF] Funk | Revisiting the Holy Grail: using plant functional traits to understand ecological processes[END_REF], (iii) it is not obvious at what level traits need to be measured (individual or population, [START_REF] Albert | On the importance of intraspecific variability for the quantification of functional diversity[END_REF], and (iv) the relative importance of traits can change over the life cycle [START_REF] Kunstler | Plant functional traits have globally consistent effects on competition[END_REF].

Another question is whether it is more informative to analyse each trait separately or in combination. The main argument for the former is that different traits may drive different processes, and that analyses should thus be process and trait specific [START_REF] Bernard-Verdier | Community assembly along a soil depth gradient: contrasting patterns of plant trait convergence and divergence in a Mediterranean rangeland[END_REF][START_REF] Gross | Uncovering multiscale effects of aridity and biotic interactions on the functional structure of Mediterranean shrublands[END_REF][START_REF] Spasojevic | Using functional diversity patterns to explore metacommunity dynamics: a framework for understanding local and regional influences on community structure[END_REF]. On the other hand, ecological niches are multidimensional and, consequently, multi-trait diversity is more likely to capture niche overlap between species across multiple niche dimensions [START_REF] Kraft | Plant functional traits and the multidimensional nature of species coexistence[END_REF]. Moreover, traits are correlated as a result of physiological trade-offs. Ignoring these trade-offs may lead to spurious conclusions [START_REF] Wüest | Integrating correlation between traits improves spatial predictions of plant functional composition[END_REF]. However, recent work shows that at least some community patterns are robust to the negligence of a relevant niche axis [START_REF] D'andrea | Translucent windows: how uncertainty in competitive interactions impacts detection of community pattern[END_REF].

Using phylogenetic diversity in the filtering approach assumes that phylogenetic relatedness is a good proxy for overlap in the multidimensional niche space [START_REF] Burns | More closely related species are more ecologically similar in an experimental test[END_REF][START_REF] Anacker | Ecological similarity is related to phylogenetic distance between species in a cross-niche field transplant experiment[END_REF]. However, phylogeny does not always represent relationships of traits that are relevant for species' niches [START_REF] Blomberg | Testing for phylogenetic signal in comparative data: Behavioral traits are more labile[END_REF][START_REF] Saito | Phylogenies and traits provide distinct insights about the historical and contemporary assembly of aquatic insect communities[END_REF], and phylogenetic signal of relevant traits should be tested, rather than assumed. Yet, this poses severe methodological problems (as discussed in detail in [START_REF] Gerhold | Phylogenetic patterns are not proxies of community assembly mechanisms (they are far better)[END_REF]. Moreover, relevant traits for this test are often not available and if they are available it is not evident how they should be combined to represent species 'niches' and how strong the signal should be (Mason & Pavoine 2013). Most importantly, if all niche-relevant traits were known and available, phylogenetic proxies would not be needed.

Methodological approach

It has been demonstrated that different methodological choices can give different answers [START_REF] Münkemüller | Scale decisions can reverse conclusions on community assembly processes[END_REF][START_REF] Perronne | How to design trait-based analyses of community assembly mechanisms: Insights and guidelines from a literature review[END_REF]. Thus, pitfalls three, four and five are to assume that (P3) all supposedly similar diversity indices give the same results and that the construction of (P4) adequate species pools and (P5) randomization algorithms for testing deviations from expectations is obvious and straightforward (Fig. 1). (P3) A common pitfall is to assume that different diversity indices can be used interchangeably. While some diversity indices are indeed highly redundant, others quantify different aspects of diversity [START_REF] Mouchet | Functional diversity measures: an overview of their redundancy and their ability to discriminate community assembly rules[END_REF][START_REF] Tucker | A guide to phylogenetic metrics for conservation, community ecology and macroecology[END_REF]. Changing the diversity index can thus change or even invert the observed pattern of diversity [START_REF] Chalmandrier | Effects of species' similarity and dominance on the functional and phylogenetic structure of a plant metacommunity[END_REF][START_REF] Mazel | Influence of tree shape and evolutionary time-scale on phylogenetic diversity metrics[END_REF][START_REF] Perronne | How to design trait-based analyses of community assembly mechanisms: Insights and guidelines from a literature review[END_REF].

Indices can differ in whether they account for (i) species abundances or not [START_REF] Hill | Diversity and evenness: a unifying notation and its consequences[END_REF][START_REF] Chao | Phylogenetic diversity measures based on Hill numbers[END_REF][START_REF] Leinster | Measuring diversity: the importance of species similarity[END_REF], (ii) intraspecific variability or not [START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF][START_REF] Pavoine | New biodiversity measure that includes consistent interspecific and intraspecific components[END_REF] (iii) different phylogenetic (e.g. species, family vs. order level) or functional scales (e.g. species vs. functional groups), and (iv) different dimensions of the structure of assemblages, such as richness, divergence and regularity [START_REF] Villeger | Additive partitioning of diversity including species differences: a comment on Hardy & Senterre (2007)[END_REF][START_REF] Tucker | A guide to phylogenetic metrics for conservation, community ecology and macroecology[END_REF]. While classification schemes for available diversity metrics can help choose an appropriate index [START_REF] Pausas | The Jungle of Methods for Evaluating Phenotypic and Phylogenetic Structure of Communities[END_REF][START_REF] Pavoine | Linking patterns in phylogeny, traits, abiotic variables and space: a novel approach to linking environmental filtering and plant community assembly[END_REF][START_REF] Tucker | A guide to phylogenetic metrics for conservation, community ecology and macroecology[END_REF], it is not always evident which index is the most appropriate for a specific research question.

(P4) The species pool is generally defined as the set of all species existing in a given region that could colonize a focal community [START_REF] Srivastava | Using local-regional richness plots to test for species saturation: pitfalls and potentials[END_REF], but other definitions exist [START_REF] Cornell | What Are Species Pools and When Are They Important? Annual Review of Ecology[END_REF]. In practice, the species pool often is the list of species in the studied dataset, often the result of practical constraints rather than ecological hypotheses. However, ideally, it should be defined based on the focal filtering process that the study sets out to test. Thus, it should include all species that would be selected in the community both with the focal process (filtering) and without it (randomly), but should not include any additional species resulting from another process not of interest. The choice of the species pool affects the null hypothesis associated with the null model and consequently can change the results of the analyses [START_REF] Lessard | Inferring local ecological processes amid species pool influences[END_REF]Pigot & Etienne, 2015). For example, competition can be overlooked when it resulted in the complete exclusion of species from the pool ("dark diversity", [START_REF] Pärtel | Dark diversity: shedding light on absent species[END_REF]. In addition, the spatial extent at which the species pool is defined changes the detectability of certain assembly rules. Typically, signals of competition are prone to be overwritten by strong environmental filtering when the study area includes steep environmental gradients [START_REF] Willis | Phylogenetic community structure in Minnesota oak savanna is influenced by spatial extent and environmental variation[END_REF].

Importantly, not only species richness but also trait diversity in the species pool influences patterns of diversity in local communities [START_REF] Patrick | Species Pool Functional Diversity Plays a Hidden Role in Generating β-Diversity[END_REF].

(P5) The randomization scheme used to create a null distribution of diversity values also has a critical impact on the outcome of the analysis [START_REF] Gotelli | Null model analysis of species co-occurrence patterns[END_REF][START_REF] Miller | Phylogenetic community structure metrics and null models: a review with new methods and software[END_REF].

Randomization breaks down patterns in the data that are caused by ecological processes.

Ideally, a chosen randomization algorithm would only break down the patterns that are supposed to be generated by the process(es) of interest. However, algorithms often randomize several patterns at the same time, including those that are not of interest, and thus test several null hypotheses simultaneously. A significant result indicates only that at least one of the null hypotheses can be rejected, but we do not know which one. For example, a high signal of phylogenetic α-diversity obtained from a null model randomizing the sites can indicate competition but also that the abundance distribution in the phylogenetic tree is non-random (testing implicitly another null hypothesis, Hardy, 2008). Thus, the interpretation of a nonrandom pattern is not always straightforward. This problem of non-specific randomization algorithms has launched the development of more constraining algorithms (Hardy, 2008;[START_REF] Miller | Phylogenetic community structure metrics and null models: a review with new methods and software[END_REF], often at the expense of statistical power.

Drawing conclusions

The most basic shortcoming of the filtering approach is inherent to most observational studies in ecology-it is impossible to deduce a process from an observed pattern in the strict sense. However, given the complexity of nature, ecological research often uses pattern observations to formulate hypotheses or to conclude that a pattern is in (dis)agreement with hypothesized processes. The three major related pitfalls are to assume: (P6) that one pattern can only emerge from one single process, (P7) that one major process dominates the observed pattern and (P8) that biotic interactions are simple (Fig. 1).

(P6) Traditionally, clustered diversity patterns (i.e. coexisting species being in phylogenetic and trait space more similar than expected by chance) have been attributed to an environmental filter (Fig. 1). However, competitive hierarchies can produce a similar pattern [START_REF] Ågren | Limiting Dissimilarity in Plants: Randomness Prevents Exclusion of Species with Similar Competitive Abilities[END_REF][START_REF] Mayfield | Opposing effects of competitive exclusion on the phylogenetic structure of communities[END_REF]Kunstler et al., 2016, Appendix S1). Conversely, symmetric niche competition is assumed to produce overdispersed diversity (i.e. co-existing species being in phylogenetic and trait space more distant than expected by chance), but facilitation can also produce overdispersed diversity patterns [START_REF] Valiente-Banuet | Facilitation can increase the phylogenetic diversity of plant communities[END_REF] McIntire & Fajardo, 2014, Appendix S1).

(P7) When multiple processes interplay, interpreting biodiversity patterns can be misleading [START_REF] Spasojevic | Inferring community assembly mechanisms from functional diversity patterns: the importance of multiple assembly processes[END_REF]. This problem occurs not only when multiple processes act jointly on the same species but also if different processes drive different groups of species in the community (e.g. rare vs. common species, [START_REF] Maire | Habitat filtering and niche differentiation jointly explain species relative abundance within grassland communities along fertility and disturbance gradients[END_REF].

For example, signals of environmental filtering are often stronger than those of competition and thus competition can be easily overlooked as an important driver of assembly (e.g. the overall diversity pattern is clustered while environmentally binned sub-tests would reveal overdispersed diversity patterns, Chalmandrier, Münkemüller, Gallien, de Bello, [START_REF] Chalmandrier | A family of null models to distinguish between habitat filtering and biotic interactions in functional diversity patterns[END_REF][START_REF] Gallien | Identifying the signal of environmental filtering and competition in invasion patterns -a contest of approaches from community ecology[END_REF]. (P8) Ignoring the complex nature of biotic interactions and assuming that the only relevant biotic filter is symmetric competition is another common pitfall. After [START_REF] Mayfield | Opposing effects of competitive exclusion on the phylogenetic structure of communities[END_REF] highlighted that large parts of coexistence theory were commonly ignored, more and more contributions have developed expectations for diversity patterns structured by biotic interactions other than symmetric niche competition [START_REF] Hillerislambers | Rethinking Community Assembly through the Lens of Coexistence Theory[END_REF]Adler, Fajardo, Kleinhesselink & Kraft, 2013, Appendix S1). For example, for hierarchical competition, clustering of species in trait or phylogenetic space could emerge from competition for one limiting resource because only species with adapted traits for this resource will survive (e.g. when species compete for light only tall species will survive, [START_REF] Mayfield | Opposing effects of competitive exclusion on the phylogenetic structure of communities[END_REF].

In contrast, overdispersion is expected to emerge from competition for multiple resources when the respective adaptive traits are different for the different resources [START_REF] Scheffer | Self-organized similarity, the evolutionary emergence of groups of similar species[END_REF]. Contrasting diversity patterns are also expected to depend on the type of facilitative interactions that take place in a community (Appendix S1). For example, if species facilitate each other symmetrically via the same mechanism (e.g. flowers of similar colour attract common pollinators; mutualism), species with similar traits should coexist, leading to trait clustering. However, if one "benefactor" species facilitates others with different life strategies (e.g. commensalism), species with different traits could coexist, resulting in overdispersion or random patterns [START_REF] Valiente-Banuet | Facilitation can increase the phylogenetic diversity of plant communities[END_REF][START_REF] Gallien | Frequency and intensity of facilitation reveal opposing patterns along a stress gradient[END_REF]. Furthermore, complex indirect interactions, such as multi-species indirect facilitation and intransitive competition (competition as in the rock-paper-scissors game, without competitive hierarchies; [START_REF] Gilpin | Limit cycles in competition communities[END_REF][START_REF] May | Non-linear aspects of competition between 3 species[END_REF], may also be important drivers of community structure [START_REF] Allesina | A competitive network theory of species diversity[END_REF][START_REF] Vandermeer | Intransitive loops in ecosystem models: From stable foci to heteroclinic cycles[END_REF]. For these interactions it may be impossible to generate clear expectations for emerging diversity patterns, especially when multispecies coexistence processes are not the mere sum of their pairwise interaction outcomes [START_REF] Barabas | The effect of intra-and interspecific competition on coexistence in multispecies communities[END_REF][START_REF] Gallien | Intransitive competition and its effects on community functional diversity[END_REF]; but see [START_REF] Maynard | Diversity begets diversity in competition for space[END_REF]. Moreover, multi-trophic biotic interactions are so far largely ignored [START_REF] Grilli | Higher-order interactions stabilize dynamics in competitive network models[END_REF]. There are a few first example studies investigating bipartite interaction networks (Van der Plas, [START_REF] Van Der Plas | Trait similarity patterns within grass and grasshopper communities: multitrophic community assembly at work[END_REF][START_REF] Ibanez | How phylogeny shapes the taxonomic and functional structure of plant-insect networks[END_REF]. However, the great challenge lies in extrapolating concepts of niche matching, associated trait and phylogenetic diversity patterns and cascading feedbacks from bipartite to multi-trophic communities [START_REF] Levine | Beyond pairwise mechanisms of species coexistence in complex communities[END_REF].

Beyond these pitfalls inherent to the investigated processes, there are further pitfalls associated to unrelated processes but influential to the studied patterns and thus to the final conclusions. A common misconception of the filtering framework is that we can test for a selection of ecological assembly processes while ignoring background factors. In reality, biogeography, evolution and ecological processes jointly influence species' distributions [START_REF] Warren | Mistaking geography for biology: inferring processes from species distributions[END_REF]. Common pitfalls are to assume that (P9) dispersal and historical contingencies can be ignored and that (P10) communities are at equilibrium (Fig. 1).

(P9) While they can shape the richness and functional-trait diversity of regional species pools (see also P4), diversification and historical contingencies are commonly ignored in community ecology studies [START_REF] Warren | Mistaking geography for biology: inferring processes from species distributions[END_REF]. These processes are often thought to act at regional rather than local scales (i.e. driving the evolution of regional species pools), but longstanding evidence shows that this simplistic dichotomy of different processes acting exclusively at particular scales is fraught with exceptions in the real world [START_REF] Johnson | An emerging synthesis between community ecology and evolutionary biology[END_REF].

Regional species pools and the processes that led to their establishment can sometimes be more important for local community composition than assembly processes [START_REF] Ricklefs | Community diversity : relative roles of local and regional processes[END_REF][START_REF] Chalmandrier | Species pool distributions along functional trade-offs shape plant productivity-diversity relationships[END_REF][START_REF] Lawing | Community functional trait composition at the continental scale: the effects of non-ecological processes[END_REF]. In some cases, both evolutionary and ecological processes occur at the same local community scale [START_REF] Pollock | The Roles of Ecological and Evolutionary Processes in Plant Community Assembly: The Environment, Hybridization, and Introgression Influence Co-occurrence of Eucalyptus[END_REF]. This problem is even more complicated by the fact that some ecological and biogeographical processes can create the same taxonomic or phylogenetic patterns. For example, from a community ecology standpoint, 'phylogenetic dispersion' in a clade can be interpreted as a sign of competitive exclusion, while from a biogeographic perspective, this same pattern can be interpreted as allopatric speciation [START_REF] Warren | Mistaking geography for biology: inferring processes from species distributions[END_REF].

(P10) The fundamental assumption that communities are at equilibrium underlies most efforts to understand community assembly [START_REF] Gerhold | Phylogenetic patterns are not proxies of community assembly mechanisms (they are far better)[END_REF]. However, in the era of the Anthropocene, many observed communities are already exposed to changing environmental conditions and/or the invasion of alien species and thus represent a transient phase. In a transient phase, rapid changes in abiotic and biotic conditions can lead species to not completely fill their potential range, or to occur in unsuitable habitats [START_REF] Ackerly | Community assembly, niche conservatism, and adaptive evolution in changing environments[END_REF]. Thus, in these transient communities current diversity patterns may not well reflect ongoing assembly processes but rather responses to past conditions [START_REF] Mittelbach | Ecological and evolutionary perspectives on community assembly[END_REF][START_REF] Chang | Integrating succession and community assembly perspectives[END_REF]. For example, a recent study shows that climatic legacies can explain a relevant part of the variation in current community assembly [START_REF] Delgado-Baquerizo | Effects of climate legacies on above-and belowground community assembly[END_REF].

Solutions

By now it is well acknowledged that the filtering approach alone will not bring the hoped-for revolution in large-scale community ecology [START_REF] Ricklefs | Disintegration of the Ecological Community[END_REF], see also discussion in Appendix S3 on the importance of competition at large spatial scales as a showcase). Here, we first review proposed solutions organized along the different steps commonly used in the filtering framework (comparable to the pitfall section) and point out how each of these solutions can solve (or partly solve) the different pitfalls (Tab. 1). Next, we highlight novel methods, theoretical advances and newly available data that could prove their utility for community assembly questions.

Study design

We have seen that the filtering approach requires a number of choices and that each of these choices can affect (or even invert) the results [START_REF] Münkemüller | Scale decisions can reverse conclusions on community assembly processes[END_REF]. It is therefore especially important that, at the beginning of a study, the general research question is translated into specific hypotheses and testable predictions (Fig. 2). Based on these, the study design can be developed.

The scale dependence of assembly processes was recognized early on, with most studies focusing on the effects of spatial scales [START_REF] Kraft | Functional trait and phylogenetic tests of community assembly across spatial scales in an Amazonian forest[END_REF][START_REF] Carboni | Darwin's naturalization hypothesis: scale matters in coastal plant communities[END_REF], less on the level of description of organisms (e.g. functional group vs. species vs. individual level) or different life-stages [START_REF] Conti | Biotic resistance to the next generation of ornamental plant invaders: the roles of functional similarity and trait plasticity[END_REF], and very few on temporal scales [START_REF] Chang | Integrating succession and community assembly perspectives[END_REF]. To deal with scale dependence, studies have compared diversity patterns across different scales to separately test for signals of small-vs. large-scale processes (solution S1, Tab. 1). A straightforward approach is a sampling design across different spatial grains and extents, levels of description of organisms and temporal scales (Cavender-Bares et al., 2006;[START_REF] Weithoff | Comparing seasonal dynamics of functional and taxonomic diversity reveals the driving forces underlying phytoplankton community structure[END_REF], including space-for-time substitutions [START_REF] Bhaskar | Community assembly and functional diversity along succession post-management[END_REF]. Sampling and studying diversity patterns across several scales (either using a multi-scale sampling design or a posteriori data aggregation approaches) is an obvious solution when scale choices are important but not easy to make (pitfall P1), for example when influential background factors are scale-dependent as well (e.g. dispersal, P9). This approach can also help to disentangle processes that create similar patterns at one scale but contrasting patterns at others (P6, P8), and to identify the interplay of processes that act at different scales (P7). For example, for trait diversity of plant communities there is some evidence for the dominance of competitive interactions at fine spatial scales and prevalent environmental filtering at coarser scales [START_REF] Cavender-Bares | Phylogenetic structure of floridian plant communities depends on taxonomic and spatial scale[END_REF][START_REF] Carboni | Darwin's naturalization hypothesis: scale matters in coastal plant communities[END_REF].

Applying the filtering approach to dynamic response variables (S2, Tab. 1), such as demographic rates, is a well-known solution for several pitfalls but mostly hampered by data availability. Instead of asking 'do species occur more often with similar or different species?' we ask 'do species perform better with similar or different species in the neighbourhood?', thereby relating the measured performance of focal individuals to their trait and phylogenetic (dis)similarity with their neighbours. At larger spatial scales this has been tested in systems where time-series of species performance are available, like in long-term forest plots [START_REF] Kunstler | Competitive interactions between forest trees are driven by species' trait hierarchy, not phylogenetic or functional similarity: implications for forest community assembly[END_REF], or in systems that provide natural experiments, such as invaded communities [START_REF] Carboni | What it takes to invade grassland ecosystems: traits, introduction history and filtering processes[END_REF]. More recently, researchers set up experiments to test for the link between community assembly and trait or phylogenetic diversity patterns [START_REF] Fayle | Experimentally testing and assessing the predictive power of species assembly rules for tropical canopy ants[END_REF][START_REF] Conti | Biotic resistance to the next generation of ornamental plant invaders: the roles of functional similarity and trait plasticity[END_REF]. Experimentally manipulating the environmental and biotic factors that drive assembly filters allows controlling a number of influential background factors (P9-10) and scale dependencies (P1). In such experiments, individual success is not approximated by a single presence or abundance measure, but is captured via demographic rates at different stages [START_REF] Li | Contrasting effects of phylogenetic relatedness on plant invader success in experimental grassland communities[END_REF][START_REF] Conti | Biotic resistance to the next generation of ornamental plant invaders: the roles of functional similarity and trait plasticity[END_REF]. Performance is often more responsive to ecological drivers than survival and may thus be more suited to measure responses in non-equilibrium situations. Moreover, long time-series can reveal insights into community assembly and provide solutions for non-equilibrium situations (P9-10). For example, time series can be used to estimate the relative importance of environmental filtering, historical legacies and new biotic interactions in the species composition of a community in the face of past, current, and future climates [START_REF] Blonder | Linking environmental filtering and disequilibrium to biogeography with a community climate framework[END_REF]. They can also be used to better understand the turnover of processes during succession [START_REF] Letten | Phylogenetic and functional dissimilarity does not increase during temporal heathland succession[END_REF].

Collecting information

Because numerous pitfalls can bias results when focusing solely on one partial aspect of biodiversity (e.g. P2-3), community ecologists started early on to consider complementary facets of diversity (S3, Tab. 1), by comparing diversity indices between phylogenetic scales and at different levels of trait similarity, e.g. close to the root vs. tips in a trait-based tree [START_REF] Swenson | Phylogenetic and functional alpha and beta diversity in temperate and tropical tree communities[END_REF][START_REF] Graham | Phylogenetic scale in ecology and evolution[END_REF], between richness, regularity and divergence components [START_REF] Raevel | Mechanisms of ecological succession: insights from plant functional strategies[END_REF], as well as by varying the importance of species abundances [START_REF] Chalmandrier | Effects of species' similarity and dominance on the functional and phylogenetic structure of a plant metacommunity[END_REF][START_REF] Götzenberger | Which randomizations detect convergence and divergence in trait-based community assembly? A test of commonly used null models[END_REF] and intraspecific variability [START_REF] Pavoine | New biodiversity measure that includes consistent interspecific and intraspecific components[END_REF][START_REF] Chalmandrier | Spatial scale and intraspecific trait variability mediate assembly rules in alpine grasslands[END_REF]. Guidelines for choosing the right trait and phylogenetic information come from studies from related fields. For example, studies applying the concept of trait syndromes and accounting for several traits simultaneously can aid the choice of trait combinations [START_REF] Diaz | The global spectrum of plant form and function[END_REF]. However, because different traits drive different processes, there is now reasonable consensus that analysing multiple traits separately can uncover important signals in the data that would have remained undetected if all traits had been analysed together [START_REF] Saito | Phylogenies and traits provide distinct insights about the historical and contemporary assembly of aquatic insect communities[END_REF]. Moreover, complementing trait diversity indices with community-weighted mean (CWM) traits can inform about differences in functional strategies between communities and thus can allow teasing apart drivers that leave the same signal in trait diversity. For example, while both environmental filtering for infertile soils and hierarchical competition for light should result in clustering (Appendix S1), the former should select for slow-growing, small species while the latter should select for fast-growing, taller species [START_REF] Kunstler | Competitive interactions between forest trees are driven by species' trait hierarchy, not phylogenetic or functional similarity: implications for forest community assembly[END_REF].

For phylogeny-based analyses, approaches that account for the uncertainty of the phylogeny [START_REF] Rangel | Phylogenetic uncertainty revisited: Implications for ecological analyses[END_REF] and the uncertainty concerning the underlying trait evolution process [START_REF] Gerhold | Phylogenetic patterns are not proxies of community assembly mechanisms (they are far better)[END_REF] can aid in more correctly interpreting phylogenetic pattern analyses. Ultimately, because trait and phylogenetic information might not give equivalent information on species niches (P2), considering them jointly probably represents the most sensible course of action. For example, one may complement phylogenetic measures with trait information (Pavoine & Bonsall, 2011;[START_REF] Lopez | A new framework for inferring community assembly processes using phylogenetic information, relevant traits and environmental gradients[END_REF][START_REF] De Bello | Decoupling phylogenetic and functional diversity to reveal hidden signals in community assembly[END_REF][START_REF] Gianuca | Integrating trait and phylogenetic distances to assess scale-dependent community assembly processes[END_REF], or integrate trait and phylogenetic information in a single measure in order to converge as close as possible to the multidimensional niche [START_REF] Cadotte | The ecology of differences: assessing community assembly with trait and evolutionary distances[END_REF]. In sum, moving forward from traditional single-metric analyses, a combination of different trait and phylogenetic metrics can help to disentangle processes and to detect multiple interacting processes, including different modes of competition (P6-8) and ecological vs. evolutionary processes (P9, [START_REF] Weinstein | Taxonomic, Phylogenetic, and Trait Beta Diversity in South American Hummingbirds[END_REF].

Methodological approach

In our description of pitfalls P4 and P5, we highlighted that the choice of species pools and randomization schemes can decisively influence the outcomes of an analysis [START_REF] Ulrich | Pattern detection in null model analysis[END_REF]. Often different choices are (more or less) implicitly linked to different ecological hypotheses [START_REF] Gotelli | Statistical challenges in null model analysis[END_REF]. Thus, by explicitly linking each ecological hypothesis with the correct combination of species pool and randomization we can develop a set of tests for disentangling different ecological scenarios (S4, Tab. 1). This approach offers a direct solution to the methodological pitfalls (P3-5) and can help circumvent the challenge of disentangling patterns and processes by providing multiple-pattern comparisons (P6-7). For example, depending on the ecological hypothesis to be tested, it can be important to account explicitly for the dynamic nature of the species pool, recognizing that it is shaped by metacommunity dynamics as well as speciation, extinction, and dispersal [START_REF] Mittelbach | Ecological and evolutionary perspectives on community assembly[END_REF]. Indeed, [START_REF] Lessard | Process-Based Species Pools Reveal the Hidden Signature of Biotic Interactions Amid the Influence of Temperature[END_REF] have demonstrated that the implementation of several process-based species pools, i.e. species pools that already account for selected processes and thus can be used to test for the remaining candidates, allows the identification of otherwise hidden filters of biotic interactions. Manipulations of the species pools can also be used to simulate cross-scale sampling instead of investing the time and money to actually sample across different scales [START_REF] Chalmandrier | A family of null models to distinguish between habitat filtering and biotic interactions in functional diversity patterns[END_REF]. For example, aggregating communities or cutting out smaller study areas can create ranges of spatial scales, whereas aggregating species or transforming phylogenies can create ranges of different levels of description of organisms [START_REF] Münkemüller | Scale decisions can reverse conclusions on community assembly processes[END_REF]. Following a similar logic, it is also possible to build reduced functional species pools already accounting for environmental and dispersal limitation filters at broader scales that can then be used to test simultaneously acting processes at community-scale (de Bello, [START_REF] De Bello | Functional species pool framework to test for biotic effects on community assembly[END_REF]. In addition, manipulations of the randomization algorithm can be used to account for dispersal limitations by down-weighting species that do not occur in the larger surroundings (P9), and improve the detection of biotic interactions by down-weighting species for which the local environment is not suitable [START_REF] Peres-Neto | Environmentally constrained null models: site suitability as occupancy criterion[END_REF][START_REF] Chalmandrier | A family of null models to distinguish between habitat filtering and biotic interactions in functional diversity patterns[END_REF].

More recently, community ecologists started to validate their methods and models with the "virtual ecologist" approach, where simulated data are used to mimic real species and how they are "virtually" observed and analysed [START_REF] Zurell | The virtual ecologist approach: simulating data and observers[END_REF]. This validation allows testing the reliability and power of metrics, species pool and randomization choices [START_REF] Münkemüller | From diversity indices to community assembly processes: a test with simulated data[END_REF][START_REF] Botta-Dukat | Testing the ability of functional diversity indices to detect trait convergence and divergence using individual-based simulation[END_REF][START_REF] Miller | Phylogenetic community structure metrics and null models: a review with new methods and software[END_REF]. Additionally, it allows investigating how interacting processes and constraints (including biotic interactions, scale-dependency, trait choices and confounding background factors) influence results of the filtering framework [START_REF] Trisos | Unraveling the Interplay of Community Assembly Processes Acting on Multiple Niche Axes across Spatial Scales[END_REF]. Thus, this approach does not provide direct solutions for any pitfall, but -when using appropriate simulation models -is a powerful tool to further develop or test the filtering approach and to carefully interpret observed signals in diversity data (S5, Tab. 1). The limitation of this approach inherently depends on the quality of the simulated data, and its conclusions are restricted to cases that are comparable to these virtual data (see [START_REF] Zurell | The virtual ecologist approach: simulating data and observers[END_REF] for more detail).

To avoid P7 (assuming that one process dominates the patterns), more and more approaches are being developed to jointly model multiple processes instead of testing for a single, dominant process (S6, Tab. 1). The range of approaches is large. Some are simple extensions of the original filtering framework. For instance, it is possible to account simultaneously for environmental filtering and symmetric competition by relying on the (strong) assumption that this should lead to a pattern where species are not too similar (i.e. due to competitive exclusion) and not too dissimilar (due to environmental filtering) to each other at the same time and by testing for this pattern (e.g. with a quadratic term in a regression model, [START_REF] Gallien | Identifying the signal of environmental filtering and competition in invasion patterns -a contest of approaches from community ecology[END_REF].

Another possibility is to build elaborate null models that allow the inclusion of multiple ecological and evolutionary processes (see also S3). Van der Plas et al. (2015) introduced static, stepwise algorithms of community assembly that simulate processes such as dispersal, environmental filtering or competition and allow estimating their relative importance. [START_REF] Pigot | A new dynamic null model for phylogenetic community structure[END_REF] developed a dynamic null model of assembly that allows estimating the effect of allopatric speciation, colonization and local extinction. Ultimately, the idea is to build more mechanistic, dynamic models of community assembly [START_REF] Connolly | Process, Mechanism, and Modeling in Macroecology[END_REF]Pontarp, Brännström, et al., 2019) that are general enough to include and contrast different ecological theories and processes and can be parameterized inversely with a selection of complementary diversity patterns [START_REF] Cabral | Mechanistic simulation models in macroecology and biogeography: state-of-art and prospects[END_REF]. The logic of this inverse parameterization, in simple terms, is to run the model across the relevant parameter space, to compare simulated patterns with observed patterns using appropriate summary statistics, and to choose the parameter combinations that lead to the best match between simulated and observed patterns [START_REF] Grimm | Pattern-oriented modeling of agent-based complex systems: Lessons from ecology[END_REF][START_REF] Hartig | Statistical inference for stochastic simulation models -theory and application[END_REF]. A coherent and efficient statistical method for this inverse parameterization of complex ecological and evolutionary models is approximate Bayesian computation [START_REF] Csilléry | Approximate Bayesian Computation (ABC) in practice[END_REF]. Interpretation of the identified best parameter values allows quantifying the relative influence of the different ecological, biogeographic and evolutionary processes [START_REF] Pontarp | The Latitudinal Diversity Gradient: Novel Understanding through Mechanistic Eco-evolutionary Models[END_REF]. Very importantly, the parameterized model could also be used to account for transient dynamics (P10) and to make predictions, so far largely unattained aims in large-scale community ecology. Examples of such mechanistic models exist already [START_REF] Kalyuzhny | A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities[END_REF][START_REF] Cazelles | On the integration of biotic interaction and environmental constraints at the biogeographical scale[END_REF][START_REF] Lohier | Predicting stochastic community dynamics in grasslands under the assumption of competitive symmetry[END_REF] but many processes and process combinations are still understudied in this young research field [START_REF] Cabral | Mechanistic simulation models in macroecology and biogeography: state-of-art and prospects[END_REF]. Interestingly, developing and applying such mechanistic models in community ecology will strongly benefit from the solutions outlined here (S1-4) as these provide a range of partly independent diversity patterns (e.g. trait vs. phylogenetic patterns, abundance weighted patterns, small vs. large-scale patterns), an indispensable requisite for inverse parameterization [START_REF] Grimm | Patternoriented modelling in population ecology[END_REF]. Even though this approach of jointly modelling different processes of assembly is very promising, substantial challenges remain [START_REF] Cabral | Mechanistic simulation models in macroecology and biogeography: state-of-art and prospects[END_REF]. For example, calibration and validation are data hungry, computationally demanding, and requires strong expert knowledge.

Drawing conclusions

Observational approaches, including the filtering framework, were never meant to provide final answers to questions about ecological mechanisms and processes, but to feed an ongoing scientific process of generating knowledge and general theories [START_REF] Garland | The scientific method as an ongoing process[END_REF]. Observational studies are supposed to help refine, alter, expand and test hypotheses and to inform further observations, experiments and mechanistic models (see Fig. 2). In a single observational study, it is typically not possible to sample all the necessary data or to apply all the above outlined solutions. For very complex filters (e.g. complex biotic interactions that differ for different species pairs) there may not exist solutions at all. This is not a problem per se as long as these limitations are considered in the conclusions drawn from results. Ultimately, a combination of studies using observations, experiments and mechanistic models with different strengths and limitations will advance our understanding of ecological processes and their importance in realistic vs. laboratory environments.

Future developments and challenges

Novel methods, theoretical advances and newly available data offer opportunities, but also pose challenges to the study of community assembly. Their application for inferring assembly rules from diversity patterns has just started. While broad-scale testing remains to be undertaken, we highlight here general ideas and the potential benefits to community assembly research in each of these areas:

(1) One strong, and certainly in most cases wrong, assumption of the filtering approach is that all species interact with each other (and based on the same underlying processes). Species distribution modelling techniques that allow estimating the covariation of species while modelling their response to abiotic variables may help to relax this assumption (e.g. joint species distribution models, [START_REF] Clark | More than the sum of the parts: forest climate response from joint species distribution models[END_REF][START_REF] Pollock | Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM)[END_REF]. The estimated residual covariance matrices in JSDMs can result from model misspecification, influential but hidden abiotic variables, but could potentially also result from biotic interactions and thus be a signal of assembly rules [START_REF] Ovaskainen | How to make more out of community data? A conceptual framework and its implementation as models and software[END_REF]Tikhonov, Abrego, Dunson & Ovaskainen, 2017;[START_REF] Zurell | Do joint species distribution models reliably detect interspecific interactions from co-occurrence data in homogenous environments[END_REF]. To better understand the ecological meaning of these residual covariance matrices, one could test them using simulated data [START_REF] Zurell | Do joint species distribution models reliably detect interspecific interactions from co-occurrence data in homogenous environments[END_REF], or one could link empirically estimated covariance matrices to trait and/or phylogenetic diversity patterns assuming that a strong correlation would indicate ecological meaning. However, since they rely on correlation matrices, these approaches can only focus on testing for symmetric interactions, which strongly limit their application for inferring interactions.

(2) Recent advances in multi-trophic network theory have highlighted the links of trait [START_REF] Albouy | Predicting trophic guild and diet overlap from functional traits: statistics, opportunities and limitations for marine ecology[END_REF][START_REF] Crea | A new model for ecological networks using specieslevel traits[END_REF] and phylogenetic relationships [START_REF] Aizen | The phylogenetic structure of plant-pollinator networks increases with habitat size and isolation[END_REF][START_REF] Peralta | Merging evolutionary history into species interaction networks[END_REF] with biotic interactions in the networks. Specific interactions are linked to specific trait combinations and thus to trait and phylogenetic diversity patterns. For example, it has been shown for plant-insect interaction networks that certain traits define sets of potentially interacting species and define clear patterns of clustering on the phylogenies of plants and insects [START_REF] Ibanez | How phylogeny shapes the taxonomic and functional structure of plant-insect networks[END_REF]. For food webs, [START_REF] Morlon | Effects of trophic similarity on community composition[END_REF] have suggested and applied a novel framework to estimate the strength of filters of "trophic environment" vs. food-mediated interspecific competition in community assembly. The framework uses trophic similarities, measured via shared predators or prey, and null models. In a similar approach, for multi-trophic tropical fish communities, it was recently highlighted that traits linked to feeding strategies or trophic level (measured based on stable isotope ratios) played an important role in community assembly and accordingly left significant signals in trait diversity [START_REF] Fitzgerald | Using trophic structure to reveal patterns of trait-based community assembly across niche dimensions[END_REF]. Advances in this direction open the door for moving from single-trophic to multi-trophic community assembly [START_REF] Gravel | The meaning of functional trait composition of food webs for ecosystem functioning[END_REF]. Ultimately, integrating complementary information on species differences from traits, phylogenies and interaction networks promises a better understanding of community assembly in space and time [START_REF] Morlon | Effects of trophic similarity on community composition[END_REF].

(3) Finally, new types of data are becoming rapidly available. One example is ampliconbased DNA analysis of environmental samples (i.e. metabarcoding data, eDNA, [START_REF] Taberlet | Soil sampling and isolation of extracellular DNA from large amount of starting material suitable for metabarcoding studies[END_REF][START_REF] Creer | The ecologist's field guide to sequence-based identification of biodiversity[END_REF]. These data provide new information on the potential presence of organisms for calculating diversity patterns (Martinez-Almoyna, [START_REF] Martinez-Almoyna | Multi-trophic β-diversity mediates the effect of environmental gradients on the turnover of multiple ecosystem functions[END_REF][START_REF] Calderón-Sanou | From environmental DNA sequences to ecological conclusions: How strong is the influence of methodological choices?[END_REF]. Combined with databases or expert knowledge on functional traits, phylogenies or trophic meta-webs (containing information on all predator-prey interactions in a regional pool of present taxa) these diversity patterns allow to better approximate niche overlap in communities. The great advantage is the coverage of almost all prokaryote and eukaryote species present in a sample (or taxonomic units with lower resolution, depending on the reference libraries) and the integration over time (for example species are not missed only because they were not visible at the sampling time). While promising, eDNA data also bring new uncertainty with respect to traditional surveys, such as amplification errors, DNA degradation and contamination and barcode assignation [START_REF] Taberlet | Soil sampling and isolation of extracellular DNA from large amount of starting material suitable for metabarcoding studies[END_REF], because reference databanks of DNA sequences that can be used to identify taxonomic units are still incomplete and impede the traditional use of diversity indices based on species concepts [START_REF] Coissac | Towards an universal genome-based DNA barcode-The PhyloAlps project[END_REF]. However, methodological advances in this area will help address earlier limitations (e.g. data limitation for pollination networks, [START_REF] Pornon | DNA metabarcoding data unveils invisible pollination networks[END_REF][START_REF] Calderón-Sanou | From environmental DNA sequences to ecological conclusions: How strong is the influence of methodological choices?[END_REF], and allow studying entirely new types of ecosystems (e.g. by combining soil metabarcoding with information from trait databases one can study the interplay of fungi and bacteria with nematodes and plants, Anslan, Bahram & Tedersoo, 2016;[START_REF] Tedersoo | Tree diversity and species identity effects on soil fungi, protists and animals are context dependent[END_REF]. Another promising new type of data comes from transcriptomic and meta-transcriptomic approaches [START_REF] Gotelli | Environmental proteomics, biodiversity statistics and food-web structure[END_REF][START_REF] Wang | Environmental Microbial Community Proteomics: Status, Challenges and Perspectives[END_REF]. These high-throughput methods allow identifying the proteins or genes being produced by individuals or entire communities at the time of sampling (e.g. environmental proteomics). The patterns of differential protein production and expression provide a direct assessment of physiological responses to abiotic and biotic stimuli and thus to the niche use of individuals or communities. The diversity of expressed functions could help give insights into assembly processes that are much more tightly linked to the actual physiological responses than the standard trait diversity measures that are often based on "soft" traits (i.e. few easily measurable features). For example, a recent community-wide transcriptomic analysis has supported the Janzen-Connell hypothesis by demonstrating that growth rates and survival of individual trees were higher when the neighbourhood consisted of trees with dissimilar (rather than similar) defense genes [START_REF] Zambrano | Neighbourhood defence gene similarity effects on tree performance: a community transcriptomic approach[END_REF]. However, even more than with metabarcoding, this approach adds uncertainty with respect to traditional surveys that are linked to sampling, laboratory work and interpretation of results [START_REF] Wang | Environmental Microbial Community Proteomics: Status, Challenges and Perspectives[END_REF].

Guidelines

Based on our critical synthesis of pitfalls and available solutions (Tab. 1), we suggest considering the following steps when applying the filtering framework:

(1) Translate research question(s) into specific hypotheses and testable predictions. The expected patterns in support of each hypothesis must be identified a priori, and each hypothesis should be tested against each of these predetermined patterns (Fig. 2 and solution S4).

(2) Assemble all data necessary to answer the research question (across scales and diversity facets) but not more (S1, S3). Importantly, use existing naturalist knowledge to decide on ecologically relevant traits. Including extraneous species or irrelevant traits, or conducting the analysis at an inappropriate scale can obscure or distort any signal in the diversity patterns.

(3) Measure dynamic response variables in a spatially explicit context and consider complementing with targeted experiments if the research question and setting allow for it (S2).

This seems especially important when focusing on biotic interactions or studying communities that are far from equilibrium.

(4) Select the diversity metrics most appropriate to the question of interest based on the conceptual framework and existing naturalist knowledge (S3).

(5) Choose species pools and randomization techniques such that null models only break the pattern to be tested and not additional patterns (S4). If this is not possible, use a combination of tests that together allow an unbiased answer to the research question. Test the sensibility of this methodological choice and interpret in consequence (S5). ( 6) If possible, test for the reliability and power of the chosen approach with simulated data (S5). (7) Test whether signals identified as significant are congruent across the a priori identified relevant patterns for each research hypothesis and always interpret them together (Fig. 2,S6). ( 8) If your research question is complex (e.g. implies a multitude of processes or is linked to evolutionary history) it may be necessary to build and parameterize a mechanistic simulation model that embraces the underlying complexity and allows disentangling the different drivers (S6). ( 9) Remember that studying causal processes in the strict sense always requires an experiment and accordingly report results of pattern analyses with the necessary care (Fig. 2).

Conclusion

If we are to fully exploit the filtering framework for a better understanding of community assembly, we need to: (i) ensure we rely on the solutions provided for most of the known pitfalls (Tab. 1) and follow the guidelines suggested here for good scientific practice, (ii) improve current solutions that begin to accommodate multiple confounding processes, more complex biotic interaction types, and different spatial scales, and (iii) integrate the rapidly accumulating types of new data (e.g. environmental metabarcoding) that represent more diverse and so far largely unknown communities (e.g. soil microbes) across an ever-increasing spatial scope.

Adapting the filtering approach to circumvent traditional pitfalls, account for uncertainty, and accommodate new data -all while retaining core fundamental ideas-holds promise to significantly improve our understanding of the ever-widening definition of the ecological community. theories with the ecological filtering framework. The process often starts by an experience or undirected observation (e.g. "plants in alpine meadows are often smaller than in sub-alpine meadows") that leads to further reflection about ecologically interesting questions (e.g. "why are plants smaller?"), related hypotheses (e.g. "plants may be smaller due to environmental constraints") and testable predictions (e.g. "plant height of alpine species is a non-random selection from the mountain plant species pool"). To test these hypotheses, we suggest an interplay of studies using observations, experiments, virtual ecologist approaches (to test the logic of process-patternpredictions and methodological approaches) and/or parameterized mechanistic models to refine, alter, expand and reject the hypotheses on ecological assembly processes. Each of the cycles can repeat many times until a hypothesis becomes so well supported that it can advances community ecology as a corner stone of a more general theory (inspired by the figure "The scientific method as an ongoing process" developed by Theodore Garland, University of California, 2015).

FigureFigure 1 :

 1 Figure

Figure 2 :

 2 Figure 2: Conceptual representation of the ongoing scientific process of generating knowledge and general

Figure 1

 1 Figure 1

Acknowledgements

The first outline of the manuscript was developed during a workshop financed by the European Research Council under the European Community's Seven Framework Program FP7/2007-2013 Grant Agreement no. 281422 (TEEMBIO). TM and WT acknowledge funding from the French Agence Nationale de la Recherche (ANR) through the GlobNets project (ANR-16-CE02-0009) and the GAMBAS project (ANR-18-CE02-0025). F.M. was supported by a Banting postdoctoral fellowship.

The LECA is part of LabexOSUG@2020 (ANR10 LABX56).

Data Accessibility Statement

No data were used.

• sample at different spatial and taxonomic scales [1] • account for temporal (e.g. seasonal) dynamics in sampling design [2] • • simulate a variation of spatial and taxonomic scales with adapted null models [3] • across environmental gradients and variation [4] (S2) Measure more dynamic responses ✔

• demographic rates as response variable [2] • set up experiments [2] • invasive species as "natural experiments" [5] • sample time-series [6] (S3) Consider different biodiversity aspects and indices ✔✔

• traits need to be adequately chosen and grouped [7] • integrate trait and phylogenetic diversity [8] • weight species by their abundances [9] • incorporate intra-specific variability [9] • compare richness, regularity and divergence • partition diversity across evolutionary periods [13] • choose appropriate randomization algorithms [14] (S5) Validate and test the approaches applied ✔

• undertake robustness analyses to identify mismatches between tests [15] • apply virtual ecologist approach, with tests of analyses using simulated data [16] • account for uncertainty in phylogenies [17] (S6) Model multiple processes jointly ✔

• indirectly with regressions by accounting for non-linear responses [18] • estimating relative importance of env. filtering, competition and dispersal [19] • explicitly account for allopatric speciation, colonization and local extinction [20] • mechanistic models with inverse parameterization based on diversity patterns [21]


Salma Loudiyi

The food sovereignty project: Advancing theory and practices

n The Politics of Food Sovereignty: Concept, Practice and Social Movements, editors Annie Shattuck, Christina Schiavoni, and Zoe VanGelder bring together some of the seminal contributions of the Yale McMillan Center Agrarian Studies Program's 2013 conference focused on food sovereignty ("Food Sovereignty: A Critical Dialogue"). These proceedings were originally published in a special issue of the journal Globalizations (volume 12, issue 4, 2015). This book is valuable in general as it discusses the upcoming challenges and contradictions of food sovereignty, a rising concept and political movement in the Global South and North. Contrasting with the food sovereignty literature to date, which has mainly focused on the Global South (from which food sovereignty movements have emerged), this book shows how the original idea has expanded to encompass the Global North and urban communities. This book includes cases I * Salma Loudiyi is a geographer and an associate professor at VetAgro Sup, an institute of higher education under the supervision of the French ministry of agriculture and food. She is currently working on place-based food policies in France and the emerging public policies for food sovereignty in Europe. She can be contacted at salma.loudiyi@vetagrosup.fr studies from the U.S., Canada, Russia, Peru, and Venezuela, demonstrating that many types of sovereignties may exist and coexist at different scales, which is a big challenge.

The book is structured as follows. In the first chapter, the editors set the stage for the rest of the book by bringing up the real challenges of the food sovereignty movements, namely, the contradictions surrounding scale (local vs. national; communal vs. individual), power relations (sovereignty for whom), gender issues, the disconnect between ideas from the rural south and those from the urban north. Then, the authors highlight the research gaps and issues faced by practitioners when operationalizing food sovereignty.

Chapter 2 and 3 present complementary views on food sovereignty from a human rights perspective. In chapter 2, Philip McMichael, who has published widely on the "agrarian question," 1 presents the multiple issues faced by the food sovereignty movements from the land user's point of view. In chapter 3, Priscilla Claeys presents the work over the last 20 years of La Via Campesina to institutionalize both "rights to food sovereignty" and "peasant's rights" as human rights. She shows how the human-rights perspective has the benefit of bringing together activists from different realities, although the human rights perspective's focus on the individual can have limited effects against capitalism and neoliberalism. La Via Campesina emphasizes an alternative conception of human rights that stresses the collective dimension of the peasants' demands and focuses on the different scales of decision-making.

In chapter 4, Christina Schiavoni draws on Raj Patel's concept of multiple and competing sovereignties to develop a conceptual framework and apply it to an example in Venezuela to examine the competing sovereignties practices through the lenses of scales, geography, and institutions. The different conceptions of scales enable her to emphasize the importance of looking at food sovereignty from a relational perspective as developed in the next chapter. Indeed, some of the most interesting 1 Rooted in Marxist political economy, the agrarian question seeks to answer why family farms have persisted despite increased capitalistic pressures and conflicts over land access.

insights of the book are surely those of Alastair Iles and Maywa Montenegro de Wit in chapter 5. They use the concept of relational scale, "the spatial and temporal relationship among processes at different levels, as well as the processes connecting elements between levels" (p. 66), to suggest practical strategies to achieve food sovereignty. What is particularly important with the relational scale approach is that strategies to achieve food sovereignty occur across scales and not solely at the local level. Using the example of the Potato Park in the Peruvian Andes, they show how multiple sovereignties are reached by negotiating and forging partnerships through different scales effectively enabling the Potato Park to gain legitimacy and be recognized as sovereign. This makes food sovereignty a practice of creating connectivity as well as autonomy (p. 74).

Moving from issues of scales in relation to food sovereignty to everyday practices across local contexts, Meleiza Figueroa proposes in chapter 6 to shift from a food-focused analysis to a peoplecentered approach using the example of an urban initiative in the Global North. In other words, she argues that the daily practices of individuals are informed by their resources, histories, knowledges, and personal goals, all of which can be harnessed to advance alternative solutions, gain autonomy, and foster resilience. The people-centered approach then helps us envision political trajectories of food sovereignty considering specific geographical and historical contexts.

Building from chapter 6, the next four chapters (7 through 10) provide examples of how food sovereignty is necessarily place-based, rooted in unique histories and geographies that produce the very circumstances of contestation and activism: in Russia, food sovereignty is somewhat "quiet" since contestation is weak or seen as such (chapter 7); in Hawaii, anti-GMO struggles are also a place-based food sovereignty movement (chapter 8); in California, "occupy the farm" is a way to promote new norms for land access and food sovereignty in the Global North (chapter 9); and in Manitoba, a community-based food program is seen as way to reinforce food sovereignty in an indigenous context (chapter 10). What is valuable about these four chapters is that they provide examples of The main contributions of this book are the conceptual developments, such as multiscale food sovereignties, relational scales, and everyday life practices, as well as the examples that move beyond the global focus of food sovereignty (which nevertheless remains important) to subnational and/or regional levels and from the peasant and rural focus to consider urban experiments. Together, the conceptual development and examples enhance our understanding of the powerful potential of food sovereignty as a project and as a movement. For those who posit that food sovereignty is mostly an ideology or a utopia, this book provides concrete scientific evidence toward sustainable and just ways to transition. A major drawback of the book is that despite the complementarity of the chapters, the editors of the book did not provide a conclusion. Such a conclusion would not only provide an answer to the key interrogations of the book, but would also highlight a research agenda calling for a broadening of food sovereignty research beyond the current focus on the Americas. Indeed, from a European viewpoint, an open call for more comparative research across geographies is urgent to provide more consistency in the exploration of food sovereignty to lead to a greater understanding and stronger theories and conceptualizations across contexts. Thinking about the audience for this edited book, it seems most suitable for graduate students and researchers who already have a grounding in the concept of food sovereignty.

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