Research frontiers in null model analysis

Null models are pattern‐generating models that deliberately exclude a mechanism of interest, and allow for randomization tests of ecological and biogeographic data. Although they have had a controversial history, null models are widely used as statistical tools by ecologists and biogeographers. Three active research fronts in null model analysis include biodiversity measures, species co‐occurrence patterns, and macroecology. In the analysis of biodiversity, ecologists have used random sampling procedures such as rarefaction to adjust for differences in abundance and sampling effort. In the analysis of species co‐occurrence and assembly rules, null models have been used to detect the signature of species interactions. However, controversy persists over the details of computer algorithms used for randomizing presence–absence matrices. Finally, in the newly emerging discipline of macroecology, null models can be used to identify constraining boundaries in bivariate scatterplots of variables such as body size, range size, and population density. Null models provide specificity and flexibility in data analysis that is often not possible with conventional statistical tests.     

Mid-domain models as predictors of species diversity patterns: bathymetric diversity gradients in the deep sea

Geometric constraints represent a class of null models that describe how species diversity may vary between hard boundaries that limit geographic distributions. Recent studies have suggested that a number of large scale biogeographic patterns of diversity (e.g. latitude, altitude, depth) may reflect boundary constraints. However, few studies have rigorously tested the degree to which mid-domain null predictions match empirical patterns or how sensitive the null models are to various assumptions. We explore how variation in the assumptions of these models alter null depth ranges and consequently bathymetric variation in diversity, and test the extent to which bathymetric patterns of species diversity in deep sea gastropods, bivalves, and polychaetes match null predictions based on geometric constraints.
Range–size distributions and geographic patterns of diversity produced by these null models are sensitive to the relative position of the hard boundaries, the specific algorithms used to generate range sizes, and whether species are continuously or patchily distributed between range end points. How well empirical patterns support null expectations is highly dependent on these assumptions. Bathymetric patterns of species diversity for gastropods, bivalves and polychaetes differ substantially from null expectations suggesting that geometric constraints do not account for diversity–depth patterns in the deep sea benthos.     

A dimmer shade of pale: revealing the faint signature of local assembly processes on the structure of strongly filtered plant communities

Trait‐based ecology suggests that abiotic filtering is the main mechanism structuring the regional species pool in different subsets of habitat‐specific species. At more local spatial scales, other ecological processes may add on giving rise to complex patterns of functional diversity (FD). Understanding how assembly processes operating on the habitat‐specific species pools produce the locally observed plant assemblages is an ongoing challenge. Here, we evaluated the importance of different processes to community assembly in an alpine fellfield, assessing its effects on local plant trait FD. Using classical randomization tests and linear mixed models, we compared the observed FD with expectations from three null models that hierarchically incorporate additional assembly constraints: stochastic null models (random assembly), independence null models (each species responding individual and independently to abiotic environment), and co‐occurrence null models (species responding to environmental variation and to the presence of other species). We sampled species composition in 115 quadrats across 24 locations in the central Pyrenees (Spain) that differed in soil conditions, solar radiation and elevation. Overall, the classical randomization tests were unable to find differences between the observed and expected functional patterns, suggesting that the strong abiotic filters that sort out the flora of extreme regional environments blur any signal of other local processes. However, our approach based on linear mixed models revealed the signature of different ecological processes. In the case of seed mass and leaf thickness, observed FD significantly deviated from the expectations of the stochastic model, suggesting that fine‐scale abiotic filtering and facilitation can be behind these patterns. Our study highlights how the hierarchical incorporation of ecological additional constraints may shed light on the dim signal left by local assembly processes in alpine environments.     

Species richness and altitude: a comparison between null models and interpolated plant species richness along the Himalayan altitudinal gradient, Nepal

We compare different null models for species richness patterns in the Nepalese Himalayas, the largest altitudinal gradient in the world. Species richness is estimated by interpolation of presences between the extreme recorded altitudinal ranges. The number of species in 100-m altitudinal bands increases steeply with altitude until 1,500 m above sea level. Between 1,500 and 2,500 m, little change in the number of species is observed, but above this altitude, a decrease in species richness is evident. We simulate different null models to investigate the effect of hard boundaries and an assumed linear relationship between species richness and altitude. We also stimulate the effect of interpolation when incomplete sampling is assumed. Some modifications on earlier simulations are presented. We demonstrate that all three factors in combination may explain the observed pattern in species richness. Estimating species richness by interpolating species presence between maximum and minimum altitudes creates an artificially steep decrease in species richness toward the ends of the gradient. The addition of hard boundaries and an underlying linear trend in species richness is needed to simulate the observed broad pattern in species richness along altitude in the Nepalese Himalayas.     

An integrated framework to improve the concept of resource specialisation

Resource specialisation, although a fundamental component of ecological theory, is employed in disparate ways. Most definitions derive from simple counts of resource species. We build on recent advances in ecophylogenetics and null model analysis to propose a concept of specialisation that comprises affinities among resources as well as their co‐occurrence with consumers. In the distance‐based specialisation index (DSI), specialisation is measured as relatedness (phylogenetic or otherwise) of resources, scaled by the null expectation of random use of locally available resources. Thus, specialists use significantly clustered sets of resources, whereas generalists use over‐dispersed resources. Intermediate species are classed as indiscriminate consumers. The effectiveness of this approach was assessed with differentially restricted null models, applied to a data set of 168 herbivorous insect species and their hosts. Incorporation of plant relatedness and relative abundance greatly improved specialisation measures compared to taxon counts or simpler null models, which overestimate the fraction of specialists, a problem compounded by insufficient sampling effort. This framework disambiguates the concept of specialisation with an explicit measure applicable to any mode of affinity among resource classes, and is also linked to ecological and evolutionary processes. This will enable a more rigorous deployment of ecological specialisation in empirical and theoretical studies.     

Random placement models predict species–area relationships in duck communities despite species aggregation

Species–area relationships are the product of many ecological processes and their interactions. Explanations for the species–area relationship (SAR) have focused on separating putative niche‐based mechanisms that correlate with area from sampling effects caused by patches with more individuals containing more species than patches with fewer individuals. We tested the hypothesis that SARs in breeding waterfowl communities are caused by sampling effects (i.e. random placement from the regional species pool). First, we described observed SARs and patterns of species associations for fourteen species of ducks on ponds in prairie Canada. Second, we used null models, which randomly allocated ducks to ponds, to test if observed SARs and patterns of species associations differed from those expected by chance. Consistent with the sampling effects hypothesis, observed SARs were accurately predicted by null models in three different years and for diving and dabbling duck guilds. This is the first demonstration that null models can predict SARs in waterbirds or any other aquatic organisms. Observed patterns of species association, however, were not well predicted by null models as in all years there was less observed segregation among species (i.e. more aggregation) than under the random expectation, suggesting that intraspecific competition could play a role in structuring duck communities. Taken together, our results indicate that when emergent properties of ecological communities such as the SAR appear to be caused by random processes, analyses of species associations can be critical in revealing the importance of niche‐based processes (e.g. competition) in structuring ecological communities.     

Estimating species – area relationships by modeling abundance and frequency subject to incomplete sampling

Models and data used to describe species–area relationships confound sampling with ecological process as they fail to acknowledge that estimates of species richness arise due to sampling. This compromises our ability to make ecological inferences from and about species–area relationships. We develop and illustrate hierarchical community models of abundance and frequency to estimate species richness. The models we propose separate sampling from ecological processes by explicitly accounting for the fact that sampled patches are seldom completely covered by sampling plots and that individuals present in the sampling plots are imperfectly detected. We propose a multispecies abundance model in which community assembly is treated as the summation of an ensemble of species‐level Poisson processes and estimate patch‐level species richness as a derived parameter. We use sampling process models appropriate for specific survey methods. We propose a multispecies frequency model that treats the number of plots in which a species occurs as a binomial process. We illustrate these models using data collected in surveys of early‐successional bird species and plants in young forest plantation patches. Results indicate that only mature forest plant species deviated from the constant density hypothesis, but the null model suggested that the deviations were too small to alter the form of species–area relationships. Nevertheless, results from simulations clearly show that the aggregate pattern of individual species density–area relationships and occurrence probability–area relationships can alter the form of species–area relationships. The plant community model estimated that only half of the species present in the regional species pool were encountered during the survey. The modeling framework we propose explicitly accounts for sampling processes so that ecological processes can be examined free of sampling artefacts. Our modeling approach is extensible and could be applied to a variety of study designs and allows the inclusion of additional environmental covariates.     

Phylogeny and co‐occurrence of mammal species on Southeast Asian islands

Aim Islands have often been used as model systems in community ecology. The incorporation of information on phylogenetic relatedness of species in studies of island assemblage structure is still uncommon, but could provide valuable insights into the processes of island community assembly. We propose six models of island community assembly that make different predictions about the associations between co‐occurrences of species pairs on islands, phylogenetic relatedness and ecological similarity. We then test these models using data on mammals of Southeast Asian islands. Location Two hundred and forty islands of the Sundaland region of Southeast Asia. Methods We quantified the co‐occurrence of species pairs on islands, and identified pairs that co‐occur more frequently (positive co‐occurrence) or less frequently (negative co‐occurrence) than expected under null models. We then examined the distributions of these significantly deviating pairs with respect to phylogenetic relatedness and ecological differentiation, and compared these patterns with those predicted by the six community assembly models. We used permutation regression to test whether co‐occurrence patterns are predicted by relatedness, body size difference or difference in diet quality. Separate co‐occurrence matrices were analysed in this way for seven mammal families and four smaller subsets of the islands of Sundaland. Results In many matrices, average numbers of negative co‐occurrences were higher than expected under null models. This is consistent with assemblage structuring by competition, but may also result from low geographic overlap of species pairs, which contributes to negative co‐occurrences at the archipelago‐wide level. Distributions of species pairs within plots of phylogenetic distance × ecological differentiation were consistent with competition, habitat filtering or within‐island speciation models, depending on the taxon. Regressions indicated that co‐occurrence was more likely among closely related species pairs within the Viverridae and Sciuridae, but in most matrices phylogenetic distance was unrelated to co‐occurrence. Main conclusions Simple deterministic models linking co‐occurrence with phylogeny and ecology are a useful framework for interpreting distributions and assemblage structure of island species. However, island assemblages in Sundaland have probably been shaped by a complex idiosyncratic set of interacting ecological and evolutionary processes, limiting the predictive power of such models.     

Null model analysis of communities on gradients

Aim I employed a novel null model and metric to uncover unusual species co‐occurrence patterns in a herpetofaunal assemblage of 49 species collected at discrete elevations along a gradient. Location Mount Kupe, Cameroon. Methods Using a construction algorithm that started from a matrix of 0s, a sample null space of 25,000 unique null matrices was generated by simultaneously conserving (1) the number of occurrences of each species, (2) site richness and (3) species range spans derived from the observed incidence matrix. I then compared the number of times each pair of confamilial species co‐occurred in the null space with the same number derived from the observed incidence matrix. Two cases dealing with embedded absences in species ranges were tested: (1) embedded absences were maintained, and (2) embedded absences were assumed to be sampling omissions and were replaced by presences. Results In the observed absence/presence assemblage there were 147 possible confamilial species pairs. Therefore, 5% or eight were expected by chance alone to have co‐occurrence patterns that differed from chance expectations by chance alone. Of these confamilial species pairs, 38 were congeneric and so 5% or two were expected to differ from chance expectations. For case (1) 16, and for case (2) 17 confamilial species pairs’ co‐occurrence patterns differed significantly from chance expectations. For case (1) nine congeneric species pairs, and for case (2) 10 congeneric pairs differed significantly from chance expectations. For case (1) four, and for case (2) five congeneric species pairs formed checkerboards (patterns of mutual exclusion). Results from case (1) were a proper subset of case (2) indicating that sampling omissions did not alter greatly the results. Main conclusions I have demonstrated that null models are valuable tools to analyse ecological communities provided that proper models are employed. The choice of the appropriate null space to analyse distributions is critical. The null model employed to analyse birds on islands of an archipelago can be adapted to analyse species along gradients provided an additional range constraint is added to the null model. Moreover, added precision to results can be obtained by analysing each species pair separately, particularly those in the same family or genus, as opposed to applying a community‐wide metric to the faunal assemblage. My results support some of the speculations of previous authors who were unable to demonstrate their suspicions analytically.     

Process-based models of species distributions and the mid-domain effect

Null models that place species ranges at random within a bounded geographical domain produce hump-shaped species richness gradients (the "mid-domain effect," or MDE). However, there is debate about the extent to which these models are a suitable null expectation for effects of environmental gradients on species richness. Here, I present a process-based framework for modeling species distributions within a bounded geographical domain. Analysis of null models consistent with the mid-domain hypothesis shows that MDEs are indeed likely to be ubiquitous consequences of geographical domain boundaries. Comparing the probability distributions of range locations for the process-based and randomization-based models reveals that randomization models probably overestimate the contribution of MDEs to empirical patterns of species richness, but it also indicates that other testable predictions from randomization models are likely to be robust. I also show how this process-based framework can be extended beyond null models to incorporate effects of environmental gradients within the domain. This study provides a first step toward an ecological theory of species distributions in geographical space that can incorporate both "geometric constraints" and effects of environmental gradients, and it shows how such a theory can inform our understanding of species richness gradients in nature.     

The river domain: why are there more species halfway up the river?

Biologists have long noted higher levels of species diversity in the longitudinal middle‐courses of river systems and have proposed many explanations. As a new explanation for this widespread pattern, we suggest that many middle‐course peaks in richness may be, at least in part, a consequence of geometric constraints on the location of species’ ranges along river courses, considering river headwaters and mouths as boundaries for the taxa considered. We demonstrate this extension of the mid‐domain effect (MDE) to river systems for riparian plants along two rivers in Sweden, where a previous study found a middle‐course peak in richness of natural (non‐ruderal) species. We compare patterns of empirical richness of these species to null model predictions of species richness along the two river systems and to spatial patterns for six environmental variables (channel width, substrate fineness, substrate heterogeneity, ice scour, bank height, and bank area). In addition, we examine the independent prediction of mid‐domain effects models that species with large ranges, because the location of their ranges is more constrained, are more likely to produce a mid‐domain peak in richness than are species with small ranges. Species richness patterns of riparian plants were best predicted by models including both null model predictions and environmental variables. When species were divided into large‐ranged and small‐ranged groups, the mid‐domain effect was more prominent and the null model predictions were a better fit to the empirical richness patterns of large‐ranged species than those of small‐ranged species. Our results suggest that the peak in riparian plant species richness in the middle courses of the rivers studied can be explained by an underlying mid‐domain effect (driven by geometric constraints on large‐ranged species), together with environmental effects on richness patterns (particularly on small‐ranged species). We suggest that the mid‐domain effect may help to explain similar middle‐course richness peaks along other rivers.     

When are adaptive radiations replicated in areas? Ecological opportunity and unexceptional diversification in West Indian dipsadine snakes (Colubridae: Alsophiini)

Aim We examine diversification in Caribbean alsophiine snakes and hypothesize that, given the ecological opportunity presented by colonization of the West Indies, alsophiines should show the signature of an early burst of diversification and associated low within‐clade ecological and morphological disparification. We also test whether changes in morphology and ecology are associated with changes in diversification rate, as trait‐dependent diversification is hypothesized to affect historical inferences of diversification and disparification. Finally, as replicated radiations are found across the West Indies in the anoles, we test for significant differences in ecological and morphological assemblages and rates among the major island groups. Location The West Indies. Methods A time‐calibrated phylogeny produced from six genes using relaxed clock methods in beast was constructed to estimate ancestral areas using Lagrange . Maximum body size and ecological niche were scored for all species in the phylogeny, and comparative phylogenetic methods in R using geiger , laser , ape and our own code were used to examine diversification through time, disparification and trait‐dependent diversification from this dated phylogeny. Results The pattern of species diversification did not differ significantly from the Yule model of diversification. Morphology and ecology fitted a Brownian and white noise model of diversification, respectively. Although not significantly different, morphological disparification was lower than the Brownian null model, whereas ecological disparification was significantly greater than the null. Trait‐dependent diversification analyses suggested that the constant null models provided the best fit to these data. There was no significant signal of rate variation among the major island groups for size, but moderate evidence for niche. Main conclusions Although ecological opportunity was similarly present for alsophiines as it was for anoles, the snakes fail to show an early burst of speciation. Potential reasons for this include the young age of the group, and staggered diversification due to waiting times between island colonization. In turn, ecological and morphological disparities do not necessarily follow predictable patterns related to species diversification. Thus, the presence of ecological opportunity alone is not necessarily sufficient to trigger replicated adaptive radiations in areas.     

基于零模型的宁夏荒漠草原优势种群点格局分析

植物种群空间分布格局是多种生态过程综合作用的结果。明确植物优势种群个体的空间分布格局与形成机制有助于认识种群生态适应对策与群落多样性维持机制。以宁夏荒漠草原优势种群蒙古冰草、短花针茅、牛枝子和牛心朴子为研究对象,采用完全空间随机零模型分析其种群空间分布格局特征,并通过异质泊松零模型与泊松聚块零模型探讨生境异质性、扩散限制等因子在其空间分布格局形成过程中的作用。结果显示:(1)完全空间随机零模型下,4个物种在4 m尺度范围内表现为聚集分布,随尺度增大,逐渐过渡到随机分布和均匀分布。(2)在排除生境异质性的异质泊松零模型下,蒙古冰草种群在整个研究尺度上表现为随机分布;牛枝子、短花针茅和牛心朴子种群仅分别在0—0.2、0.1—0.4 m与0—0.2 m尺度范围内发生偏离,表现为均匀分布与聚集分布,其他尺度均为随机分布。(3)在排除扩散限制的泊松聚块零模型下,所研究种群均表现为随机分布。综上,荒漠草原优势种群在小尺度范围内主要表现为聚集分布;生境异质性与扩散限制均是驱动其空间分布格局形成的重要因子,相对而言,小尺度空间范围内扩散限制的作用更为显著。     

Patterns of plant species turnover along grazing gradients

Questions: How are plant species distributed along grazing gradients? What is the shape of species richness patterns? How can we test for the existence of potential discontinuities in species turnover pattern? Location: Semi‐deserts in the eastern Caucasus, Azerbaijan, Gobustan district. Methods: We studied the distribution of vascular plant species along transects 900‐m long, perpendicular to five farms, and estimated grazing intensity as current livestock units per distance. We modelled species response curves with Huismann–Olff–Fresco (HOF) models and calculated species turnover by accumulating the first derivatives of all response curves. To test for potential discontinuities in changes of vegetation composition along the grazing gradient, we introduce a new null model based on the individualistic continuum concept that uses permutations of the observed pattern of species responses. Results: Most species show a sigmoidal negative response to grazing intensity, while a few species respond with a unimodal pattern. The monotonic decrease in species richness with increasing grazing intensity marks a process of overgrazing that leads to the complete extirpation of plant species. Although the species turnover pattern shows a clear peak, it does not deviate significantly from the null model of individualistic continuous changes. Conclusions: Our approach offers a method for differentiating between transition zones and continuous shifts in species composition along ecological gradients. It also provides a valuable tool for rangeland management to test state‐and‐transition concepts and gives deeper insights into ecological processes affected by grazing.     

Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.     

Continental and regional ranges of North American mammals: Rapoport's rule in real and null worlds

Aim To assess the relationship between species richness and distribution within regions arranged along a latitudinal gradient we use the North American mammalian fauna as a study case for testing theoretical models. Location North America. Methods We propose a conceptual framework based on a fully stochastic mid‐domain model to explore geographical patterns of range size and species richness that emerge when the size and position of species ranges along a one‐dimensional latitudinal gradient are randomly generated. We also analyse patterns for the mammal fauna of North America by comparing empirical results from a biogeographical data base with predictions based on randomization null models. Results We confirmed the validity of Rapoport's rule for the mammals of North America by documenting gradients in the size of the continental ranges of species. Additionally, we demonstrated gradients of mean regional range size that parallel those of continental range. Our data also demonstrated that mean range size, measured both as a continental or a regional variable, is significantly correlated with the geographical pattern in species richness. All these patterns deviated sharply from null models. Main conclusions Rapoport's statement of an areographic relationship between species distribution and richness is highly relevant in modern discussions about ecological patterns at the geographical scale.     

Reconsidering null models of diversity: Do geometric constraints on species ranges necessarily cause a mid‐domain effect?

Recent null models that place species ranges randomly within a bounded domain have produced controversial results. Many such geometric constraint models predict a peak in species richness in the centre of domains in the absence of underlying environmental gradients or interspecific interactions. We used two-dimensional simulation models to explore different ways that species ranges could interact with the domain boundary. In the rejection model, a randomly generated range that overlaps a domain boundary is removed from the simulation. In the reshaping model, a range that overlaps the domain boundary is reshaped so that the entire range is placed within the domain. The truncation model allows potential ranges to extend across the boundary, but only that portion of the range within the domain is included in the realized range. Both rejection and reshaping models produced a drop in species richness near domain boundaries, though the effect was less pronounced in the reshaping model. Our truncation model did not produce any spatial pattern in species richness. Thus the random placement of species ranges within a bounded domain does not necessarily lead to a mid-domain effect.
  Range truncation is consistent with bioclimate envelope models, which can successfully predict a species range in response to the availability of appropriate climate conditions. We argue that such flexible range sizes are more realistic than the assumption that range size is an unvarying characteristic of a species. Other range characteristics, including size and shape, can change near domain boundaries in the null models, including the truncation model. A broader consideration of range characteristics near domain boundaries could be productive.     

Ecological traits reveal functional nestedness of bird communities in habitat islands: a global survey

The widespread destruction and fragmentation of natural habitats around the world creates a strong incentive to understand how species and communities respond to such pressures. The vast majority of research into habitat fragmentation has focused solely on species presence or absence. However, analyses using innovative functional methodologies offer the prospect of providing new insights into the key questions surrounding community structure in fragmented systems. A key topic in fragmentation research is nestedness (i.e. the ordered composition of species assemblages involving a significant tendency for packing of the presence–absence matrix into a series of proper subsets). To date, nestedness analyses have been concerned solely with nestedness of species membership. Here, we capitalize on the publication of a recent nestedness index (traitNODF) in which the branch lengths of functional dendrograms are incorporated into the standard NODF nestedness index. Using bird community data from 18 forest‐habitat‐island studies, and measurements of eight continuous functional traits from over 1000 bird species, we conduct the first synthetic analysis of nestedness from a functional perspective (i.e. a nestedness analysis which incorporates how similar species are in terms of their ecological traits). We use two null models to test the significance of any observed functional nestedness, and investigate the role of habitat island area in driving functional nestedness. We also determine whether functional nestedness is driven primarily by species composition or by differences in species’ traits. We found that the majority (94%) of datasets were functionally nested by island area when a permutation null model was used, although only 11–22% of datasets were significantly functionally nested when a more conservative fixed‐fixed null model was used. Species composition was always the most important driver of functional nestedness, but the effect of differences in species traits was occasionally quite large. Our results isolate the importance of island area in driving functional nestedness where it does occur and show that habitat loss results in the ordered loss of functional traits. This analysis demonstrates the potential insights that may derive from testing for ordered patterns of functional diversity. Synthesis The widespread fragmentation of natural habitats around the world creates a strong incentive to understand how ecological communities respond to such pressures. A key topic in this research agenda is nestedness; however, to date, nestedness analyses have been concerned solely with species presence or absence. Using data from 18 bird‐habitat‐island studies we conduct the first synthetic analysis of nestedness from a functional perspective (i.e. a nestedness analysis which incorporates how similar species are in terms of their ecological traits). Our findings suggest that many bird‐habitat island communities are significantly functionally nested, although our results were sensitive to the null model used. Our study demonstrates the benefits of testing for ordered patterns of functional diversity.     

Co‐occurrence is not evidence of ecological interactions

There is a rich amount of information in co‐occurrence (presence–absence) data that could be used to understand community assembly. This proposition first envisioned by Forbes (1907) and then Diamond (1975) prompted the development of numerous modelling approaches (e.g. null model analysis, co‐occurrence networks and, more recently, joint species distribution models). Both theory and experimental evidence support the idea that ecological interactions may affect co‐occurrence, but it remains unclear to what extent the signal of interaction can be captured in observational data. It is now time to step back from the statistical developments and critically assess whether co‐occurrence data are really a proxy for ecological interactions. In this paper, we present a series of arguments based on probability, sampling, food web and coexistence theories supporting that significant spatial associations between species (or lack thereof) is a poor proxy for ecological interactions. We discuss appropriate interpretations of co‐occurrence, along with potential avenues to extract as much information as possible from such data.