Disentangling community patterns of nestedness and species co-occurrence

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).     

An evaluation of randomization models for nested species subsets analysis

Randomization models, often termed “null” models, have been widely used since the 1970s in studies of species community and biogeographic patterns. More recently they have been used to test for nested species subset patterns (or nestedness) among assemblages of species occupying spatially subdivided habitats, such as island archipelagoes and terrestrial habitat patches. Nestedness occurs when the species occupying small or species-poor sites have a strong tendency to form proper subsets of richer species assemblages. In this paper, we examine the ability of several published simulation models to detect, in an unbiased way, nested subset patterns from a simple matrix of site-by-species presence-absence data. Each approach attempts to build in biological realism by following the assumption that the ecological processes that generated the patterns observed in nature would, if they could be repeated many times over using the same species and landscape configuration, produce islands with the same number of species and species present on the same number of islands as observed. In mathematical terms, the mean marginal totals (column and row sums) of many simulated matrices would match those of the observed matrix. Results of model simulations suggest that the true probability of a species occupying any given site cannot be estimated unambiguously. Nearly all of the models tested were shown to bias simulation matrices toward low levels of nestedness, increasing the probability of a Type I statistical error. Further, desired marginal totals could be obtained only through ad-hoc manipulation of the calculated probabilities. Paradoxically, when such results are achieved, the model is shown to have little statistical power to detect nestedness. This is because nestedness is determined largely by the marginal totals of the matrix themselves, as suggested earlier by Wright and Reeves. We conclude that at the present time, the best null model for nested subset patterns may be one based on equal probabilities of occurrence for all species. Examples of such models are readily available in the literature. Received: 3 February 1997 / Accepted: 21 September 1997     

Null model analyses of presence–absence matrices need a definition of independence

Tests for species interactions that involve the comparison of a statistic calculated from observed matrix of species presences and absences with the distribution of the same statistic generated from a null model have been used by ecologists for about 30 years. We argue that the validity of these tests requires a specific definition of independence. In particular, we note that an assumption that is often made is that all presence–absence matrices with the same row and column totals are equally likely if there is no interaction. However, we show using a simple model for species presences and absences without any species interactions that, in general, this assumption should be made with caution. Our model incorporates a definition of independence, allowing the computation of probabilities of different patterns in the null matrices. Other definitions of independence are possible; one of them is outlined using a new generalized linear model approach for carrying out tests applicable to different null models with or without the assumption of keeping row and column totals fixed. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A consumer's guide to nestedness analysis

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.     

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.     

Null matrices and the analysis of species co-occurrences

Patterns in species occurrences on islands have been analyzed by several authors. At issue is the number of non-occurring pairs of species (also known as checkerboards). Previous authors have suggested that if the number of checkerboards differs from what is expected by chance, then island communities might have been structured by competition. Investigators have pursued this problem by first generating random (or null) matrices and then testing a metric derived from the collection of null matrices against the metric calculated from the actual species co-occurrence matrix. The random matrices were constrained by requiring the number of species on each island, and the number of islands on which each species occurred to be equal to their observed values. We show that results from previous studies are generally flawed. We present a fast, efficient algorithm to generate null matrices for any set of fixed row and column sums, and propose a modification of a previously proposed metric as a test statistic. We evaluated the efficacy of our construction method for null creation and our metric using incidence matrices from the avifauna of Vanuatu (formerly New Hebrides). Received: 31 March 1997 / Accepted: 8 April 1998     

A new algorithm to calculate the nestedness temperature of presence–absence matrices

Aim The nestedness temperature of presence–absence matrices is currently calculated with the nestedness temperature calculator (NTC). In the algorithm implemented by the NTC: (1) the line of perfect order is not uniquely defined, (2) rows and columns are reordered in such a way that the packed matrix is not the one with the lowest temperature, and (3) the null model used to determine the probabilities of finding random matrices with the same or lower temperature is not adequate for most applications. We develop a new algorithm, BINMATNEST (binary matrix nestedness temperature calculator), that overcomes these difficulties. Methods BINMATNEST implements a line of perfect order that is uniquely defined, uses genetic algorithms to determine the reordering of rows and columns that leads to minimum matrix temperature, and provides three alternative null models to calculate the statistical significance of matrix temperature. Results The NTC performs poorly when the input matrix has checkerboard patterns. The more efficient packing of BINMATNEST translates into matrix temperatures that are lower than those computed with the NTC. The null model implemented in the NTC is associated with a large frequency of type I error, while the other null models implemented in BINMATNEST (null models 2 and 3) are conservative. Overall, null model 3 provides the best performance. The nestedness temperature of a matrix is affected by its size and fill, but the probability that such a temperature is obtained by chance is not. BINMATNEST reorders the input matrix in such a way that, if fragment size/isolation plays a role in determining community structure, there will be a significant rank correlation between the size/isolation of the fragments and the way that they are ordered in the packed matrix. Main conclusions The nestedness temperature of presence–absence matrices should not be calculated with the NTC. The algorithm implemented by BINMATNEST is more robust, allowing for across‐study comparisons of the extent to which the nestedness of communities departs from randomness. The sequence in which BINMATNEST reorders habitat fragments provides information about the causal role of immigration and extinction in shaping the community under study.     

A protocol to compare nestedness among submatrices

Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null-models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined.     

A comparative evaluation of pairwise nestedness measures

This paper deals with nestedness measures that are based on pairwise comparisons of sites, evaluates their performance and suggests improvements and generalizations. There are several conceptual and technical criteria to judge their ecological applicability. It is of primary concern whether the measures 1) have a clear mathematical definition, 2) are influenced by the ordering of the data matrix, 3) incorporate similarity alone or similarity together with a dissimilarity component, 4) consider site pairs with identical species number negatively or positively, 5) show sensitivity to small changes in the data, and 6) are not vulnerable to type I and type II error rates. We performed a detailed comparison of the nestedness metric based on overlap and decreasing fill (NODF), the percentage relativized nestedness and the percentage relativized strict nestedness functions (PRN and PRSN, respectively), based on analytical results as well as on artificial and actual examples. We show that NODF is in fact the average Simpson similarity of sites with different species totals, and that its value depends on how the matrix is actually ordered. NODF is modified to always produce the maximum possible result (NODF_max), independently of the order of columns and rows. Being based on similarities, NODF and NODF_max overemphasize the overlap component of nestedness and underrate richness difference which is also an important constituent of nested pattern in meta‐community data. This latter feature is reflected adequately by PRN and PRSN. However, PRSN is similar to NODF and NODF_max in sharing the disadvantages that 1) complete agreement and segregation in species composition are not distinguished, 2) a random matrix can have a higher value than truly nested patterns, and 3) they are ill‐conditioned statistically. These problems are rooted mostly in that site pairs with tied totals affect the result negatively. We emphasize that PRN is free from these difficulties. PRN, PRSN, and NODF_max, together with mean Simpson similarity exhibit highly similar statistical performance: they are resistant to type I and type II errors for the less constrained null models, although there are subtle differences depending on matrix fill and algorithm of randomization. The most constrained null model, with all marginal totals fixed, makes all statistics more sensitive to type I errors, although vulnerability depends greatly on matrix fill.     

The role of stochastic processes in producing nested patterns of species distributions

Nestedness has received considerable attention in community ecology and conservation biology from both theoretical and empirical perspectives. This has lead to the creation of various metrics and null models to analyze nested subsets, all of which rely on the random placement of species to assess significance. However, if immigration and extinction are the processes that underlie species distributions on island systems, then null models might be better determined on the basis of randomly placed individuals. Consequently, we examined the effects of species–abundance distributions (uniform, dominance–decay, random–assortment, and dominance–preemption), island–size distributions (uniform and linear decrease), and total abundances (128, 256, 512, 1024, 2048, 4096 and 8192) on the degree of nestedness and its significance. Generally, matrices of species presence and absence created from the random placement of individuals were nested significantly according to null models based on the random placement of species. Island size and abundance had less of an effect on nestedness in systems dominated by only a few species than in systems in which abundances were distributed more evenly. Stochastic processes, such as the random placement of individuals, predispose systems to evince patterns of nestedness at the species level, which may account, in part, for the ubiquity of nestedness in nature.     

Nestedness of desert bat assemblages: species composition patterns in insular and terrestrial landscapes

Nested patterns of community composition exist when species at depauperate sites are subsets of those occurring at sites with more species. Nested subset analysis provides a framework for analyzing species occurrences to determine non-random patterns in community composition and potentially identify mechanisms that may shape faunal assemblages. We examined nested subset structure of desert bat assemblages on 20 islands in the southern Gulf of California and at 27 sites along the Baja California peninsula coast, the presumable source pool for the insular faunas. Nested structure was analyzed using a conservative null model that accounts for expected variation in species richness and species incidence across sites (fixed row and column totals). Associations of nestedness and island traits, such as size and isolation, as well as species traits related to mobility, were assessed to determine the potential role of differential extinction and immigration abilities as mechanisms of nestedness. Bat faunas were significantly nested in both the insular and terrestrial landscape and island size was significantly correlated with nested structure, such that species on smaller islands tended to be subsets of species on larger islands, suggesting that differential extinction vulnerabilities may be important in shaping insular bat faunas. The role of species mobility and immigration abilities is less clearly associated with nestedness in this system. Nestedness in the terrestrial landscape is likely due to stochastic processes related to random placement of individuals and this may also influence nested patterns on islands, but additional data on abundances will be necessary to distinguish among these potential mechanisms.     

The empirical Bayes approach as a tool to identify non-random species associations

A statistical challenge in community ecology is to identify segregated and aggregated pairs of species from a binary presence–absence matrix, which often contains hundreds or thousands of such potential pairs. A similar challenge is found in genomics and proteomics, where the expression of thousands of genes in microarrays must be statistically analyzed. Here we adapt the empirical Bayes method to identify statistically significant species pairs in a binary presence–absence matrix. We evaluated the performance of a simple confidence interval, a sequential Bonferroni test, and two tests based on the mean and the confidence interval of an empirical Bayes method. Observed patterns were compared to patterns generated from null model randomizations that preserved matrix row and column totals. We evaluated these four methods with random matrices and also with random matrices that had been seeded with an additional segregated or aggregated species pair. The Bayes methods and Bonferroni corrections reduced the frequency of false-positive tests (type I error) in random matrices, but did not always correctly identify the non-random pair in a seeded matrix (type II error). All of the methods were vulnerable to identifying spurious secondary associations in the seeded matrices. When applied to a set of 272 published presence–absence matrices, even the most conservative tests indicated a fourfold increase in the frequency of perfectly segregated “checkerboard” species pairs compared to the null expectation, and a greater predominance of segregated versus aggregated species pairs. The tests did not reveal a large number of significant species pairs in the Vanuatu bird matrix, but in the much smaller Galapagos bird matrix they correctly identified a concentration of segregated species pairs in the genus Geospiza. The Bayesian methods provide for increased selectivity in identifying non-random species pairs, but the analyses will be most powerful if investigators can use a priori biological criteria to identify potential sets of interacting species.     

Rethinking the relationship between nestedness and beta diversity: a comment on Baselga (2010)

Baselga [Partitioning the turnover and nestedness components of beta diversity. Global Ecology and Biogeography, 19 , 134–143, 2010] proposed pairwise (β_nes) and multiple‐site (β_NES) beta‐diversity measures to account for the nestedness component of beta diversity. We used empirical, randomly created and idealized matrices to show that both measures are only partially related to nestedness and do not fit certain fundamental requirements for consideration as true nestedness‐resultant dissimilarity measures. Both β_nes and β_NES are influenced by matrix size and fill, and increase or decrease even when nestedness remains constant. Additionally, we demonstrate that β_NES can yield high values even for matrices with no nestedness. We conclude that β_nes and β_NES are not true measures of the nestedness‐resultant dissimilarity between sites. Actually, they quantify how differences in species richness that are not due to species replacement contribute to patterns of beta diversity. Finally, because nestedness is a special case of dissimilarity in species composition due to ordered species loss (or gain), the extent to which differences in species composition is due to nestedness can be measured through an index of nestedness.     

Temporal variability of nestedness and idiosyncratic species in stream insect assemblages

Aims The nested subset pattern has been widely studied in the last 20 years, and recent syntheses have challenged the prevalence of this pattern in nature. We examined the degree of nestedness, its temporal variability and its environmental correlates in stream insects of a boreal drainage system. We also examined differences between nested and idiosyncratic species in site occupancy, niche position and niche breadth. Location Koutajoki drainage basin in northern Finland. Methods We used (i) nestedness analyses with three null models for testing the significance of nestedness; (ii) Spearman rank correlation to examine the correlates of nestedness; (iii) outlying mean index analysis to analyse the niche characteristics of species; (iv) and t‐test to examine differences in niche breadth, niche position and site occupancy of idiosyncratic and other nested species. Results Stream insect assemblages were significantly nested in each of the three study years. The maximally packed matrices were significantly nested according to the nestedness calculator based on null models I (species frequencies and site richness equiprobable) and II (species frequencies fixed and site richness equiprobable), but non‐significant based on a conservative null model III (species frequencies and site richness fixed to those of the observed matrix). The most important correlate of nestedness was stream size, whereas isolation, productivity (total phosphorus) and habitat heterogeneity exhibited non‐significant relationship with nestedness. Idiosyncratic species occurred, on average, at more sites than nested species, mirroring the restricted distributions of several nested species that were inclined towards species‐rich sites. Idiosyncratic and nested species also differed in niche position and niche breadth, with idiosyncratic species having, on average, less marginal niche positions and wider niches than nested species. Main conclusions Stream size correlated with nestedness, possibly because small streams were inhabited only by species able to persist under, or colonize shortly after, disturbances, while most species could occur at larger sites where disturbances are less severe. From the conservation perspective, our findings suggest that stream size really matters, given that sites with high species richness and many rare species are more likely to occur in larger streams. However, also the requirements of idiosyncratic species should be accommodated in conservation planning.     

菌根共生网络嵌套性判定的零模型选择

零模型是判定网络嵌套性的重要依据, 菌根共生关系网络经常出现高度非对称性, 该文通过探究矩阵非对称变化对基于不同零模型构建方法的网络嵌套性的影响, 试图为非对称网络零模型的选择提供依据。结果表明: 不同零模型保守性不同, 增加限定条件减少零模型构建过程中的自由空间, 高度限定条件易导致第II类错误。高度非对称网络会增加基于完全随机(r00)零模型的矩阵温度(NT)偏离、降低配对重叠度(NODF)偏离, 标准化指数z-score值显示网络非对称增加后有助于NT和NODF显著性判定。行或列限定对非对称网络嵌套性判定的影响存在差异, 列限定(c0)的网络嵌套性判定对网络非对称性变化的响应规律与r00零模型的响应趋势基本一致, 具有更低的嵌套性偏离和标准差值。行限定(r0, 包括行列限定(backtrack))零模型NT值和NT偏移随矩阵非对称性的变化保持稳定, 较之c0零模型在高度非对称网络中呈现更低的NODF偏离值。选用完全随机和限定零模型相结合的方法, 有助于更加准确判断非对称网络是否具有嵌套结构。高度非对称网络嵌套性判定中对行属性特征比较敏感, 不同非对称性网络间嵌套性水平相比较时选用r0零模型要优于r00和c0零模型。     

Pattern detection in null model analysis

Synthesis The identification of distinctive patterns in species x site presence‐absence matrices is important for understanding meta‐community organisation. 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, indicating that these seemingly opposite patterns are closely related. Recently proposed classification schemes failed to correctly classify realistic matrices that included multiple co‐occurrence structures. We propose using a combination of metrics and decomposing matrix‐wide patterns into those of individual pairs of species and sites to pinpoint sources of non‐randomness. 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.     

Influence of taxonomic resolution on mutualistic network properties

1. Ecologists are increasingly interested in plant–pollinator networks that synthesize in a single object the species and the interactions linking them within their ecological context. Numerous indices have been developed to describe the structural properties and resilience of these networks, but currently, these indices are calculated for a network resolved to the species level, thus preventing the full exploitation of numerous datasets with a lower taxonomic resolution. Here, we used datasets from the literature to study whether taxonomic resolution has an impact on the properties of plant–pollinator networks.
2. For a set of 41 plant–pollinator networks from the literature, we calculated nine network index values at three different taxonomic resolutions: species, genus, and family. We used nine common indices assessing the structural properties or resilience of networks: nestedness (estimated using the nestedness index based on overlap and decreasing fill [NODF], weighted NODF, discrepancy [BR], and spectral radius [SR]), connectance, modularity, robustness to species loss, motifs frequencies, and normalized degree.
3. We observed that modifying the taxonomic resolution of these networks significantly changes the absolute values of the indices that describe their properties, except for the spectral radius and robustness. After the standardization of indices measuring nestedness with the Z‐score, three indices—NODF, BR, and SR for binary matrices—are not significantly different at different taxonomic resolutions. Finally, the relative values of all indices are strongly conserved at different taxonomic resolutions.
4. We conclude that it is possible to meaningfully estimate the properties of plant–pollinator interaction networks with a taxonomic resolution lower than the species level. We would advise using either the SR or robustness on untransformed data, or the NODF, discrepancy, or SR (for weighted networks only) on Z‐scores. Additionally, connectance and modularity can be compared between low taxonomic resolution networks using the rank instead of the absolute values.

     

The Exact Evaluation of 2-way Cross-classifications: An Algorithmic Solution

An algorithm is presented which permits the exact evaluation of sparse cross-classifications and contingency tables. It may be used to compute the exact point and cumulative probabilities of observed values of the X²-like test statistic, or even of the observed tables themselves. For sparser cases, it may also be used to generate part or all of the exact distributions. As a corollary, an operational solution is presented to the enumeration problem of rectangular integer matrices with arbitrarily fixed row and column sums. Exact results obtained with the algorithm accompany this presentation, giving, further support to the recommendation that the Gamma distribution be preferred to the Chi-square in sparse cases.     

A comparative analysis of nested subset patterns of species composition

We present a broad comparative assessment of nested subsets in species composition among ecological communities. We assembled presence-absence data from a broad range of taxa, geographic regions, and spatial scales; and subjected this collection of datasets to common analyses, including a variety of metrics for measuring nestedness and null hypotheses against which to evaluate them. Here we identify ecological patterns in the prevalence and strength of nested subset structure, and assess differences and biases among the available methodologies. In all, we compiled 279 presence-absence matrices, of which 163 do not overlap in their coverage of species and sites. The survey includes studies on vertebrates, arthropods, mollusks, plants, and other taxa; from north temperate, tropical, and south temperate latitudes. Our results were as follows. Statistically significant nestedness was common. Assemblages from landbridge archipelagos were strongly nested, and immigration experiments were least nested. This adds further empirical support to the hypothesis that extinction plays a major role in producing nested structure. Nestedness was positively correlated with the ratio of the areas of the largest and smallest sites, suggesting that the range in area of sites affects nestedness. Taxonomic differences in nestedness were weak. Higher taxonomic levels showed stronger nesting than their constituent lower taxa. We observed no effect of distance of isolation on nestedness; nor any effects of latitude. With regard to methodology, the metrics Nc and Ut yielded similar results, although Nc proved slightly more flexible in use, and deals differently with tied sites. Similarities also exist in the behavior of N0 (“N”) and Up, and between N1 and Ua. Standardized nestedness metrics were mostly insensitive to matrix size, and were useful in comparative analyses among presence-absence matrices. Most metrics were affected by the proportion of presences in the matrix. All analyses of nestedness, therefore, should test for bias due to matrix fill. We suggest that the factors controlling nested subset structure can be thought of as four filters that species pass to occur at a site: a sampling filter, a distance filter, a habitat filter, and an area filter – and three constraints on community homogeneity: evolutionary history, recent history, and spatial variation in the environment. The scale of examination can also have important effects on the degree of nestedness observed. Received: 13 September 1996 / Accepted: 16 September 1997