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Null model analysis has been a popular tool for detecting pattern in binary presence-absence matrices, and previous tests have identified algorithms and metrics that have good statistical properties. However, the behavior of different metrics is often correlated, making it difficult to distinguish different patterns. We compared the performance of a suite of null models and metrics that have been proposed to measure patterns of segregation, aggregation, nestedness, coherence, and species turnover. We found that any matrix with segregated species pairs can be re-ordered to highlight aggregated pairs. As a consequence, the same null model can identify a single matrix as being simultaneously aggregated, segregated or nested. These results cast doubt on previous conclusions of matrix-wide species segregation based on the C-score and the fixed-fixed algorithm. Similarly, we found that recently proposed classification schemes based on patterns of coherence, nestedness, and segregation and aggregation cannot be uniquely distinguished using proposed metrics and null model algorithms. It may be necessary to use a combination of different metrics and to decompose matrix-wide patterns into those of individual pairs of species or pairs of sites to pinpoint the sources of non-randomness.

This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson-Neyman tests (which require a fully-specified null distribution) and specific process-based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence-absence matrices to incorporate species-level traits (such as abundance) and site-level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years.

A key focus in ecology is to search for community assembly rules. Here we compare two community modelling frameworks that integrate a combination of environmental and spatial data to identify positive and negative species associations from presence–absence matrices, and incorporate an additional comparison using joint species distribution models (JSDM). The frameworks use a dichotomous logic tree that distinguishes dispersal limitation, environmental requirements, and interspecific interactions as causes of segregated or aggregated species pairs. The first framework is based on a classical null model analysis complemented by tests of spatial arrangement and environmental characteristics of the sites occupied by the members of each species pair (Classic framework). The second framework, (SDM framework) implemented here for the first time, builds on the application of environmentally-constrained null models (or JSDMs) to partial out the influence of the environment, and includes an analysis of the geographical configuration of species ranges to account for dispersal effects. We applied these approaches to examine plot-level species co-occurrence in plant communities sampled along a wide elevation gradient in the Swiss Alps. According to the frameworks, the majority of species pairs were randomly associated, and most of the non-random positive and negative species associations could be attributed to environmental filtering and/or dispersal limitation. These patterns were partly detected also with JSDM. Biotic interactions were detected more frequently in the SDM framework, and by JSDM, than in the Classic framework. All approaches detected species aggregation more often than segregation, perhaps reflecting the important role of facilitation in stressful high-elevation environments. Differences between the frameworks may reflect the explicit incorporation of elevational segregation in the SDM framework and the sensitivity of JSDM to the environmental data. Nevertheless, all methods have the potential to reveal general patterns of species co-occurrence for different taxa, spatial scales, and environmental conditions.

Many species are accumulating climatic debt as they fail to keep pace with increasing global temperatures. In theory, concomitant decreases in other stressors (e.g. pollution, fragmentation) could offset some warming effects, paying climatic debt with accrued environmental credit. This process may be occurring in many western European rivers. We fit a Markov chain model to ~20,000 macroinvertebrate samples from England and Wales, and demonstrate that despite large temperature increases 1991–2011, macroinvertebrate communities remained close to their predicted equilibrium with environmental conditions. Using a novel analysis of multiple stressors, an accumulated climatic debt of 0.64 (±0.13 standard error) °C of warming was paid by a water-quality credit equivalent to 0.89 (±0.04)°C of cooling. Although there is finite scope for mitigating additional climate warming in this way, water quality improvements appear to have offset recent temperature increases, and the concept of environmental credit may be a useful tool for communicating climate offsetting. Both climate change and environmental degradation pose harm to freshwaters. Here the authors find that macroinvertebrate communities in England and Wales maintained equilibrium with the environment from 1991 to 2011, and attribute this to water quality improvements offsetting rising temperatures.

The search for traits associated with plant invasiveness has yielded contradictory results, in part because most previous studies have failed to recognize that different traits are important at different stages along the introduction–naturalization–invasion continuum. Here we show that across six different habitat types in temperate Central Europe, naturalized non-invasive species are functionally similar to native species occurring in the same habitat type, but invasive species are different as they occupy the edge of the plant functional trait space represented in each habitat. This pattern was driven mainly by the greater average height of invasive species. These results suggest that the primary determinant of successful establishment of alien species in resident plant communities is environmental filtering, which is expressed in similar trait distributions. However, to become invasive, established alien species need to be different enough to occupy novel niche space, i.e. the edge of trait space. Plant functional traits may help distinguish introduced species that will become invasive from those that do not. Here, Divíšek et al. show that functional profiles of naturalized plant species are similar to natives, while those of invasive plant species exist at the edge of the functional trait space.

The role human activities play in reshaping biodiversity is increasingly apparent in terrestrial ecosystems. However, the responses of entire marine assemblages are not well-understood, in part, because few monitoring programs incorporate both spatial and temporal replication. Here, we analyse an exceptionally comprehensive 29-year time series of North Atlantic groundfish assemblages monitored over 5° latitude to the west of Scotland. These fish assemblages show no systematic change in species richness through time, but steady change in species composition, leading to an increase in spatial homogenization: the species identity of colder northern localities increasingly resembles that of warmer southern localities. This biotic homogenization mirrors the spatial pattern of unevenly rising ocean temperatures over the same time period suggesting that climate change is primarily responsible for the spatial homogenization we observe. In this and other ecosystems, apparent constancy in species richness may mask major changes in species composition driven by anthropogenic change. The response of marine fish assemblages to global change is not fully understood. Analysing a 29-year time-series, Magurran et al. show that despite little change in species richness, high species turnover is leading to North Atlantic groundfish assemblages becoming spatially homogenized, likely as a result of climatic change.

While human activities are known to elicit rapid turnover in species composition through time, the properties of the species that increase or decrease their spatial occupancy underlying this turnover are less clear. Here, we used an extensive dataset of 238 metacommunity time series of multiple taxa spread across the globe to evaluate whether species that are more widespread (large-ranged species) differed in how they changed their site occupancy over the 10–90 years the metacommunities were monitored relative to species that are more narrowly distributed (small-ranged species). We found that on average, large-ranged species tended to increase in occupancy through time, whereas small-ranged species tended to decrease. These relationships were stronger in marine than in terrestrial and freshwater realms. However, in terrestrial regions, the directional changes in occupancy were less extreme in protected areas. Our findings provide evidence for systematic decreases in occupancy of small-ranged species, and that habitat protection could mitigate these losses in the face of environmental change. Whether a species declines under the current biodiversity crisis could partly depend on its range size. Here, the authors use replicated metacommunity data to identify global patterns in the relationship between species’ range size and changes in occupancy through time.

The influence of negative species interactions has dominated much of the literature on community assembly rules. Patterns of negative covariation among species are typically documented through null model analyses of binary presence/absence matrices in which rows designate species, columns designate sites, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site. However, the outcome of species interactions ultimately depends on population-level processes. Therefore, patterns of species segregation and aggregation might be more clearly expressed in abundance matrices, in which the matrix entries indicate the abundance or density of a species in a particular site. We conducted a series of benchmark tests to evaluate the performance of 14 candidate null model algorithms and six covariation metrics that can be used with abundance matrices. We first created a series of random test matrices by sampling a metacommunity from a lognormal species abundance distribution. We also created a series of structured matrices by altering the random matrices to incorporate patterns of pairwise species segregation and aggregation. We next screened each algorithm-index combination with the random and structured matrices to determine which tests had low Type I error rates and good power for detecting segregated and aggregated species distributions. In our benchmark tests, the best-performing null model does not constrain species richness, but assigns individuals to matrix cells proportional to the observed row and column marginal distributions until, for each row and column, total abundances are reached. Using this null model algorithm with a set of four covariance metrics, we tested for patterns of species segregation and aggregation in a collection of 149 empirical abundance matrices and 36 interaction matrices collated from published papers and posted data sets. More than 80% of the matrices were significantly segregated, which reinforces a previous meta-analysis of presence/absence matrices. However, using two of the metrics we detected a significant pattern of aggregation for plants and for the interaction matrices (which include plant-pollinator data sets). These results suggest that abundance matrices, analyzed with an appropriate null model, may be a powerful tool for quantifying patterns of species segregation and aggregation.

Nestedness analysis has become increasingly popular in the study of biogeographic patterns of species occurrence. Nested patterns are those in which the species composition of small assemblages is a nested subset of larger assemblages. For species interaction networks such as plant-pollinator webs, nestedness analysis has also proven a valuable tool for revealing ecological and evolutionary constraints. Despite this popularity, there has been substantial controversy in the literature over the best methods to define and quantify nestedness, and how to test for patterns of nestedness against an appropriate statistical null hypothesis. Here we review this rapidly developing literature and provide suggestions and guidelines for proper analyses. We focus on the logic and the performance of different metrics and the proper choice of null models for statistical inference. We observe that traditional 'gap-counting' metrics are biased towards species loss among columns (occupied sites) and that many metrics are not invariant to basic matrix properties. The study of nestedness should be combined with an appropriate gradient analysis to infer possible causes of the observed presence-absence sequence. In our view, statistical inference should be based on a null model in which row and columns sums are fixed. Under this model, only a relatively small number of published empirical matrices are significantly nested. We call for a critical reassessment of previous studies that have used biased metrics and unconstrained null models for statistical inference.

Two opposing patterns of meta-community organization are nestedness and negative species co-occurrence. Both patterns can be quantified with metrics that are applied to presence-absence matrices and tested with null model analysis. Previous meta-analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co-occurrence (Gotelli and McCabe 2002). We clarified the relationship between nestedness and co-occurrence by creating random matrices, altering them systematically to increase or decrease the degree of nestedness or co-occurrence, and then testing the resulting patterns with null models. Species co-occurrence is related to the degree of nestedness, but the sign of the relationship depends on how the test matrices were created. Low-fill matrices created by simple, uniform sampling generate negative correlations between nestedness and co-occurrence: negative species co-occurrence is associated with disordered matrices. However, high-fill matrices created by passive sampling generate the opposite pattern: negative species co-occurrence is associated with highly nested matrices. The patterns depend on which index of species co-occurrence is used, and they are not symmetric: systematic changes in the co-occurrence structure of a matrix are only weakly associated with changes in the pattern of nestedness. In all analyses, the fixed-fixed null model that preserves matrix row and column totals has lower type I and type II error probabilities than an equiprobable null model that relaxes row and column totals. The latter model is part of the popular nestedness temperature calculator, which detects nestedness too frequently in random matrices (type I statistical error). When compared to a valid null model, a matrix with negative species co-occurrence may be either highly nested or disordered, depending on the biological processes that determine row totals (number of species occurrences) and column totals (number of species per site).