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.     

Abundance and nestedness in interaction networks

Nestedness is a useful metric that characterizes the generalist–specialist balance in ecological communities. Although several nestedness indices have been proposed, few have explored how species abundance per se affects their performance and the ability to detect true interaction networks. We here develop a mathematical framework that takes into account abundance in estimates of nestedness. We use an analytical approach to relate abundance and nestedness. In our null model the probability of interaction among species is determined solely as function of their abundances. Assuming a power-law abundance model we analytically find the nestedness index and its coefficient of variability. We find that the sloping abundance distribution of our null model generates more nested structures. On the other hand steeper abundances lead to higher coefficients of variability. Both results suggest that nestedness analysis should be evaluated and explanations sought carefully.     

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.     

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).     

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.     

Habitat amount hypothesis and passive sampling explain mammal species composition in Amazonian river islands

Nested structures of species assemblages have been frequently associated with patch size and isolation, leading to the conclusion that colonization–extinction dynamics drives nestedness. The ‘passive sampling’ model states that the regional abundance of species randomly determines their occurrence in patches. The ‘habitat amount hypothesis’ also challenges patch size and isolation effects, arguing that they occur because of a ‘sample area effect’. Here, we (a) ask whether the structure of the mammal assemblages of fluvial islands shows a nested pattern, (b) test whether species’ regional abundance predicts species’ occurrence on islands, and (c) ask whether habitat amount in the landscape and matrix resistance to biological flow predict the islands’ species composition. We quantified nestedness and tested its significance using null models. We used a regression model to analyze whether a species’ relative regional abundance predicts its incidence on islands. We accessed islands’ species composition by an NMDS ordination and used multiple regression to evaluate how species composition responds to habitat amount and matrix resistance. The degree of nestedness did not differ from that expected by the passive sampling hypothesis. Likewise, species’ regional abundance predicted its occurrence on islands. Habitat amount successfully predicted the species composition on islands, whereas matrix resistance did not. We suggest the application of habitat amount hypothesis for predicting species composition in other patchy systems. Although the island biogeography perspective has dominated the literature, we suggest that the passive sampling perspective is more appropriate for explaining the assemblages’ structure in this and other non‐equilibrium patch systems. Abstract in Portuguese is available with online material.     

Nested subset structure of larval mycophagous fly assemblages: nestedness in a non-island system

Nested subset structure has been studied in archipelagoes and fragmented habitats, and has been attributed to differential colonization and extinction rates among species and nested environmental tolerances. In this experiment, we tested for nestedness in assemblages of mycophagous fly larvae. Twenty mushrooms in each of three size classes (4.8–6.0 g, 10–15 g, 21–32 g) were placed on moist potting soil in experimental cups. The cups were placed in oak and pine forests in Greenville, S.C., USA for 5 days, where they were available to ovipositing flies. Upon collection, the mushrooms were incubated in the laboratory for 3 weeks and all emerging flies were sorted by species, counted, and weighed. A random placement analysis was conducted to determine whether the species richness pattern was a sampling artifact of the species abundance distributions. The actual species richness pattern did not conform to the random placement model; most mushrooms contained significantly fewer species than predicted by random sampling. The communities were strongly nested as measured by two different indices, and the nestedness pattern was related to mushroom size. Small mushrooms usually produced no flies or a single species, Dohrniphora sp. (Phoridae). Medium and large mushrooms typically produced more species-rich communities that usually contained the phorid and Drosophila putrida, D. tripunctata, and Leucophenga varia. This core guild was nested within a more diverse assemblage that included D. falleni, Mycodrosophila dimidiata, a muscid, and two Leptocera sp. (sphaeroceridae). These patterns are tentatively explained in the context of nested desiccation tolerances, mediated by differences in mushroom size.     

Testing multiple assembly rule models in avian communities on islands of an inundated lake,Zhejiang Province,China

Aim A fundamental question in community ecology is whether general assembly rules determine the structure of natural communities. Although many types of assembly rules have been described, including Diamond’s assembly rules, constant body‐size ratios, favoured states, and nestedness, few studies have tested multiple assembly rule models simultaneously. Therefore, little is known about the relative importance of potential underlying factors such as interspecific competition, inter‐guild competition, selective extinction and habitat nestedness in structuring community composition. Here, we test the above four assembly rule models and examine the causal basis for the observed patterns using bird data collected on islands of an inundated lake. Location Thousand Island Lake, China. Methods  We collected data on presence–absence matrices, body size and functional groups for bird assemblages on 42 islands from 2007 to 2009. To test the above four assembly rule models, we used null model analyses to compare observed species co‐occurrence patterns, body‐size distributions and functional group distributions with randomly generated assemblages. To ensure that the results were not biased by the inclusion of species with extremely different ecologies, we conducted separate analyses for the entire assemblage and for various subset matrices classified according to foraging guilds. Results The bird assemblages did not support predictions by several competitively structured assembly rule models, including Diamond’s assembly rules, constant body‐size ratios, and favoured states. In contrast, bird assemblages were highly significantly nested and were apparently shaped by extinction processes mediated through area effects and habitat nestedness. The nestedness of bird assemblages was not a result of passive sampling or selective colonization. These results were very consistent, regardless of whether the entire assemblage or the subset matrices were analysed. Main conclusions Our results suggest that bird assemblages were shaped by extinction processes mediated through area effects and habitat nestedness, rather than by interspecific or inter‐guild competition. From a conservation point of view, our results indicate that we should protect both the largest islands with the most species‐rich communities and habitat‐rich islands in order to maximize the number of species preserved.     

Terrestrial bird community patterns on the coralline islands of the Dahlak Archipelago, Red Sea, Eritrea

Aim This study aims to explain the patterns of species richness and nestedness of a terrestrial bird community in a poorly studied region. Location Twenty‐six islands in the Dahlak Archipelago, Southern Red Sea, Eritrea. Methods The islands and five mainland areas were censused in summer 1999 and winter 2001. To study the importance of island size, isolation from the mainland and inter‐island distance, I used constrained null models for the nestedness temperature calculator and a cluster analysis. Results Species richness depended on island area and isolation from the mainland. Nestedness was detected, even when passive sampling was accounted for. The nested rank of islands was correlated with area and species richness, but not with isolation. Idiosyncrasies appeared among species‐poor and species‐rich islands, and among common and rare species. Cluster analysis showed differences among species‐rich islands, close similarity among species‐poor and idiosyncratic islands, and that the compositional similarity among islands decreased with increasing inter‐island distance. Thus, faunas of species‐poor, smaller islands were more likely to be subsets of faunas of species‐rich, larger islands if the distance between the islands was short. Main conclusions Species richness and nestedness were related to island area, and nestedness also to inter‐island distances but not to isolation from the mainland. Thus, nestedness and species richness are not affected in the same way by area and distance. Moreover, idiosyncrasies may have been the outcome of species distributions among islands being influenced also by non‐nested distributions of habitats, inter–specific interactions, and differences in species distributions across the mainland. Idiosyncrasies in nested patterns may be as important as the nested pattern itself for conservation – and conservation strategies based on nestedness and strong area effects (e.g. protection of only larger islands) may fail to preserve idiosyncratic species/habitats.     

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.     

Using intraspecific variation of functional traits and environmental factors to understand the formation of nestedness patterns of a local forest community

从功能性状的种内变异和环境因子的角度理解局域森林群落嵌套格局的成因     

Determinants of the steep species–area relationship of coral reef fishes

The increase in species richness with area is known as the species–area relationship (SPAR). Although several mutually non-exclusive processes may produce the SPAR, the null, often ignored, hypothesis states that a SPAR can be generated by random placement alone. The log–log-transformed SPAR of coral reef fishes on small patch-reefs revealed a steep slope of 0.55. However, this slope was dependent on the cumulative area of the reef examined and was therefore affected by random placement. After statistically removing the contribution of random placement from the SPAR, the slope was estimated to be 0.21. This is consistent with estimates from other, mostly terrestrial, systems. Furthermore, a randomization procedure, where the probability of fishes to reach a patch was proportional to reef area, showed that the field measured SPAR did not differ from random placement. In addition, fish assemblages on species poor reefs did not form subsets of species rich reefs (i.e., no nestedness) beyond that expected from random placement. Steep log–log-transformed SPARs can be formed by random placement alone, indicating that caution should be used when assigning an ecological meaning to SPARs generated from small spatial scales.     

Interspecific aggregation of ectoparasites on bats: importance of hosts as habitats supersedes interspecific interactions

Patterns of aggregation of species or individuals may result from combinations of interspecific interactions such as competition, facilitation, or apparent facilitation, as well as from equivalent responses to environmental factors. Host–parasite systems are ideal for the investigation of mechanisms that structure assemblages. Interspecific aggregation is documented for multiple groups that are ectoparasitic on mammals and host‐mediated apparent facilitation has been suggested to explain these aggregation patterns. To investigate the generality of this pattern and to determine likely structuring mechanisms, I analyzed species co‐occurrence, correlations of abundances, and nestedness for ectoparasite assemblages from each of 11 species of Neotropical bat. Ectoparasite assemblages on four of 11 host species exhibited significant positive co‐occurrence for the entire assemblage or for at least one pair of species in the assemblage; ectoparasites on two host species exhibited positive co‐occurrence that approached significance. There was no evidence of negative co‐occurrence. Nine species‐pairs exhibited positive abundance correlations, including seven of the eight species‐pairs that exhibited positive co‐occurrence. No species‐pair exhibited a negative correlation of abundances (i.e. density compensation). Ectoparasite assemblages from five of 11 host species exhibited nestedness, including all three assemblages that exhibited assemblage‐wide positive co‐occurrence. Multiple mechanisms associated with host characteristics may contribute to host aggregation in ectoparasite assemblages, including host body size, vagility, home range size, burrow or roost size and complexity, immunocompetence and social structure. In general, data in this study and elsewhere are not consistent with interspecific interactions among ectoparasites, including apparent facilitation, being primary structuring mechanisms of ectoparasite assemblages on mammalian hosts. Rather, host behavior and ecology are likely to affect the frequency of host–ectoparasite encounters and of conspecific host interactions that facilitate transfer of ectoparasites, thereby, molding patterns of ectoparasite co‐occurrence, abundance and species composition on mammalian hosts. Combinations of characteristics that are primarily responsible for molding ectoparasite assemblage composition likely are host‐taxon specific.     

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.     

The quest for a null model for macroecological patterns: geometry of species distributions at multiple spatial scales

There have been several attempts to build a unified framework for macroecological patterns. However, these have mostly been based either on questionable assumptions or have had to be parameterized to obtain realistic predictions. Here, we propose a new model explicitly considering patterns of aggregated species distributions on multiple spatial scales, the property which lies behind all spatial macroecological patterns, using the idea we term 'generalized fractals'. Species' spatial distributions were modelled by a random hierarchical process in which the original 'habitat' patches were randomly replaced by sets of smaller patches nested within them, and the statistical properties of modelled species assemblages were compared with macroecological patterns in observed bird data. Without parameterization based on observed patterns, this simple model predicts realistic patterns of species abundance, distribution and diversity, including fractal-like spatial distributions, the frequency distribution of species occupancies/abundances and the species–area relationship. Although observed macroecological patterns may differ in some quantitative properties, our concept of random hierarchical aggregation can be considered as an appropriate null model of fundamental macroecological patterns which can potentially be modified to accommodate ecologically important variables.     

Species richness, endemism, and abundance patterns: tests of two fractal models in a serpentine grassland

Although scaling relationships that characterize fractal species distributions offer an exciting potential for unification in biogeography, empirical support for fractal theory remains the subject of debate. We synthesize and test multiple predictions of two interrelated fractal models and a null model of random placement using Californian serpentine grassland data describing the spatial location of over 37 000 individually identified plants. The endemics–area relationship and species‐abundance distribution recently derived from a community‐level fractal property performed poorly because of an inaccurate assumption of homogeneity among species. In contrast, a species‐level fractal model that incorporates species‐level differences predicted abundances well, but systematically overestimated endemism and predicted a species–area relationship that violated the observed power law. These findings indicate that in order to make predictions based on the existence of a power‐law species–area relationship, ecologists need a unifying theory of how the community‐level fractal property arises in the presence of species‐level distributional differences.     

Scaling coexistence and assemblage patterns of desert small mammals

Scaling biodiversity patterns has been recognized lately as a very important issue in the search of global processes; however coexistence and assemblage patterns are typically approached at a single spatial scale. Here, we examined coexistence and co-occurrence patterns of desert small mammal communities across different spatial scales in the search of general community patterns. We sampled small mammals in Monte desert (Argentina, South America) for small spatial scales and reviewed published papers from other worldwide deserts for large spatial scale analyses. We used classic community estimators (Shannon, Richness), rank abundance curves and fitting distributions to analyze species coexistence and co-occurrence patterns. Assemblage patterns were analyzed evaluating nestedness across spatial scales and among deserts. Worldwide desert small mammal assemblages are characterized mainly by low species richness and high variation in species composition. The central Monte desert of Argentina showed a consistent assemblage pattern across spatial scales, with a generalist species being the most abundant and widely distributed, accompanied by other subordinate and more narrowly distributed species. All Monte desert communities were significantly nested, with nestedness increasing with scale from patch to regional. Assemblage and coexistence patterns were similar when comparing worldwide deserts despite differences in total richness and faunal singularity. The degree of nestedness varied among worldwide deserts; however all of them showed a consistent nested pattern. Differences in the degree of nestedness could be a result of different regulating factors depending on the desert and scale. These results highlight the importance of including multiscale approaches when dealing with processes that structure desert communities.     

Abundance, diversity and body size: patterns from a grassland arthropod community

1. The empirical relationships among body size, species richness and number of individuals may give insight into the factors controlling species diversity and the relative abundances of species. To determine these relationships, we sampled the arthropods of grasslands and savannahs at Cedar Creek, MN using sweep nets (90 525 individuals of 1225 species) and pitfall traps (12 721 individuals of 92 species). Specimens were identified, enumerated and measured to determine body size.
2. Both overall and within abundant taxonomic orders, species richness and numbers of individuals peaked at body sizes intermediate for each group. Evolution could create unimodal diversity patterns by random diversification around an ancestral body size or from size-dependent fitness differences. Local processes such as competition or predation could also create unimodal diversity distributions.
3. The average body size of a species depended significantly on its taxonomic order, but on contemporary trophic role only within the context of taxonomic order.
4. Species richness ( S _i) within size classes was related to the number of individuals ( I _i) as S _i =  I i^0·5. This relationship held across a 100 000-fold range of body sizes. Within size classes, abundance distributions of size classes were all similar power functions. A general rule of resource division, together with similar minimum population sizes, is sufficient to generate the relationship between species richness and number of individuals.
5. Smaller bodied species had slightly shallower abundance distributions and may, in general, persist at lower densities than larger species.
6. Our results suggest there may be fewer undescribed small arthropod species than previously thought and that most undescribed species will be smaller than arthropods.     

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     

The Rapoport effect is detected in a river system and is based on nested organization

Aim To test two hypotheses: (i) the Rapoport effect is valid for a river continuum, particularly regarding the altitudinal distribution of mayflies over the large‐scale continuum from alpine stream to medium‐sized lowland river, and (ii) the observed Rapoport effect is based on high nestedness of the meta‐assemblage, implying the presence of a common species pool and species‐thinned nested subsets. Location Geometric centre of Eurasia, south‐western Siberia, Russia. Methods Regression analysis of breadth and midpoints of species altitudinal ranges, species richness and altitude. Comparison of the observed patterns with the null model predicted by the mid‐domain effect and conventional null hypothesis. Nestedness analysis. Results The Rapoport effect was explicitly demonstrated: species altitudinal ranges expanded with increase in the ranges’ midpoints and average per‐altitude ranges increased with increase in altitude and concurrent decrease in species richness. The significance of each trend was confirmed with respect to both the null models applied. Nestedness analysis has revealed that the observed Rapoport effect is based on nested organization of the meta‐assemblage over the river altitudinal/longitudinal gradient: a common species pool at low (but not the lowest) altitudes and nested subsets of this pool at higher altitudes. Main conclusions This study for the first time credibly shows the altitudinal Rapoport effect in freshwaters. This finding demonstrates cross‐habitat‐type consistency of the Rapoport effect, but does not suggest that the Rapoport effect is an obligatory attribute of river systems or lotic organisms. High nestedness underlying the observed Rapoport effect together with some previous studies indicate that the Rapoport effect in altitudinal and bathymetric gradients in general may be based on nested organization. The study highlights a deficiency of cross‐habitat‐type analyses of macroecological patterns (i.e. over terrestrial, freshwater and marine habitats).