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).     

BIODIVERSITY RESEARCH: Nestedness for different reasons: the distributions of birds,lizards and small mammals on islands of an inundated lake

Aim We examined whether the community compositions of birds, lizards and small mammals were nested in a fragmented landscape in the Thousand Island Lake, China. We also assessed whether the mechanisms influencing nestedness differed among these taxonomic groups. Location Thousand Island Lake, China. Methods Presence/absence matrices were compiled for birds (42 islands) and lizards (42 islands) using line‐transect methods, and for small mammals (14 islands) using live‐trapping methods from 2006 to 2009. Nestedness was analysed using BINMATNEST, and statistical significance was assessed using the conservative null model 3. We used Spearman rank correlations and partial Spearman rank correlations to examine associations of nestedness and habitat variables (area, isolation, habitat diversity and plant richness) as well as life‐history traits (body size, habitat specificity, geographical range size and area requirement) related to species extinction and immigration tendencies. Results The community compositions of birds, lizards and small mammals were all significantly nested, but the causal factors underlying nestedness differed among taxonomic groups. For birds, island area, habitat specificity and area requirement were significantly correlated with nestedness after controlling for other independent variables. For lizards, habitat heterogeneity was the single best correlate of nestedness. For small mammals, island area, habitat heterogeneity and habitat specificity were significantly correlated with nestedness. The nested patterns of birds, lizards and small mammals were not attributable to passive sampling or selective colonization. Main conclusions The processes influencing nested patterns differed among taxonomic groups. Nestedness of bird assemblages was driven by selective extinction, and lizard assemblage was caused by habitat nestedness, while nestedness of small mammals resulted from both selective extinction and habitat nestedness. Therefore, we should take taxonomic differences into account when analysing nestedness to develop conservation guidelines and refrain from using single taxa as surrogates for others.     

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.     

Nestedness and niche‐based species loss in moorland plant communities

Communities in isolated habitat patches surrounded by inhospitable matrices often form a nested subset pattern. However, the underlying causal mechanisms and conservation implications of nestedness in regional communities remain controversial. The nested ranks of species in a nested species‐by‐site matrix may reflect a gradient of species vulnerability to extinction or of colonization ability. However, nestedness analysis has rarely been used to explore determinants of species rank; consequently, little is known of underpinning mechanisms. In this study, we examined nestedness in moorland plant communities widely interspersed within the subalpine zone of northern Japan. Moorland sites differed in area (1000–160 000 m²) and were naturally isolated from one another to various extents within an inhospitable forest matrix. We also determined whether site characteristics (physical and morphometric measures) and species characteristics (niche position and breadth, based on species’ traits) are related to nestedness. Moorland plant communities in the study area were significantly nested. The pH and moorland kernel density (proxy for spatial clustering of moorlands around the focal site) were the most important predictors of moorland site nested rank in a nestedness matrix. Niche breadths of species (measured as variation in leaf mass area and height) predicted species’ nested ranks. Selective environmental tolerances imposed by environmental harshness and selective extinction caused by declines in site carrying capacities probably account for the nested subset pattern in moorland plant communities. The nested rank of species in the nestedness matrix can therefore be translated into the potential order of species loss explainable by species niche breadths (based on variation in functional traits). Complementary understanding of the determinants of site ranking and species ranking in the nestedness matrix provides powerful insight into ecological processes underlying nestedness and into the ways by which communities are assembled or disassembled by such processes.     

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.     

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     

Nested assemblages of Orthoptera species in the Netherlands: the importance of habitat features and life-history traits

Aim Species communities often exhibit nestedness, the species found in species‐poor sites representing subsets of richer ones. In the Netherlands, where intensification of land use has led to severe fragmentation of nature, we examined the degree of nestedness in the distribution of Orthoptera species. An assessment was made of how environmental conditions and species life‐history traits are related to this pattern, and how variation in sampling intensity across sites may influence the observed degree of nestedness. Location The analysis includes a total of 178 semi‐natural sites in the Pleistocene sand region of the Netherlands. Methods A matrix recording the presence or absence of all Orthoptera species in each site was compiled using atlas data. Additionally, separate matrices were constructed for the species of suborders Ensifera and Caelifera. The degree of nestedness was measured using the binmatnest calculator. binmatnest uses an algorithm to sort the matrices to maximal nestedness. We used Spearman’s rank correlations to evaluate whether sites were sorted by area, isolation or habitat heterogeneity, and whether species were sorted by their dispersal ability, rate of development or degree of habitat specificity. Results We found the Orthoptera assemblages to be significantly nested. The rank correlation between site order and sampling intensity was high. The degree of nestedness was lower, but remained significant when under‐ and over‐sampled sites were excluded from the analysis. Site order was strongly correlated with both size of sample site and number of habitat types per site. Rank correlations showed that species were probably ordered by variation in habitat specificity, rather than by variation in dispersal capacity or rate of development of the species. Main conclusions Variation in sampling intensity among sites had a strong impact on the observed degree of nestedness. Nestedness in habitats may underlie the observed nestedness within the Orthoptera assemblages. Habitat heterogeneity is closely related to site area, which suggests that several large sites should be preserved, rather than many small sites. Furthermore, the results corroborate a focus of nature conservation policy on sites where rare species occur, as long as the full spectrum of habitat conditions and underlying ecological processes is secured.     

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.     

From sampling stations to archipelagos: investigating aspects of the assemblage of insular biota

Aim To investigate the formation of nestedness and species co‐occurrence patterns at the local (sampling station), the intermediate (island group), and the archipelago scale. Location The study used data on the distribution of terrestrial isopods on 20 islands of the central Aegean (Greece). These islands are assigned to two distinct subgroups (Kyklades and Eastern islands). Methods The Nestedness Temperature Calculator was used to obtain nestedness values and maximally nested matrices, the EcoSim7 software and a modified version of Sanderson (2000 ) method were used for the analysis of species co‐occurrences. Idiosyncratic temperatures of species and the order of species placement in the maximally nested matrices were used for further comparisons among spatial scales. The relationships of nestedness values with beta‐diversity, habitat diversity and a number of ecological factors recorded for each sampling station were also investigated. Results Significant nestedness was found at all spatial scales. Levels of nestedness were not related to beta‐diversity or habitat diversity. Nestedness values were similar among spatial scales, but they were affected by matrix size. The species that contributed most to the nested patterns within single islands were not the same as those that produce nestedness at the archipelago scale. There was significant variation in the frequency of species occurrence among islands and among spatial scales. There was no direct effect of ecological factors on the shaping of patterns of nestedness within individual islands, but habitat heterogeneity was crucial for the existence of such patterns. Positive associations among species prevailed at all scales when species per station were considered, while negative associations prevailed in the species per island matrices. All associations resulted from the habitat structure of sampling stations and from particularities of geographical distributions. Conclusions There was no clear‐cut distinction between nestedness patterns among spatial scales, even though different species, and partially different factors, contributed to the formation of these patterns in each case. There was a core of species that contributed to the formation of nested patterns at all spatial scales, while the patterns of species associations suggested that biotic interactions are not an important causal factor. The results of this study suggest that locally rare species cannot be widespread at a higher spatial scale, while locally common species can have a restricted distribution.     

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.     

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.     

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.     

Nestedness theory suggests wetland fragments with large areas and macrophyte diversity benefit waterbirds

Many artificial wetland constructions are currently underway worldwide to compensate for the degradation of natural wetland systems. Researchers face the responsibility of proposing wetland management and species protection strategies to ensure that constructed wetlands positively impact waterbird diversity. Nestedness is a commonly occurring pattern for biotas in fragmented habitats with important implications for conservation; however, only a few studies have focused on seasonal waterbird communities in current artificial wetlands. In this study, we used the nestedness theory for analyzing the annual and seasonal community structures of waterbirds in artificial wetlands at Lake Dianchi (China) to suggest artificial wetland management and waterbird conservation strategies. We carried out three waterbird surveys per month for one year to observe the annual, spring, summer, autumn, and winter waterbird assemblages in 27 lakeside artificial wetland fragments. We used the NeD program to quantify nestedness patterns of waterbirds at the annual and seasonal levels. We also determined Spearman partial correlations to examine the associations of nestedness rank and habitat variables to explore the factors underlying nestedness patterns. We found that annual and all four seasonal waterbird compositions were nested, and selective extinction and habitat nestedness were the main factors governing nestedness. Further, selective colonization was the key driver of nestedness in autumn and winter waterbirds. We suggest that the area of wetland fragments should be as large as possible and that habitat heterogeneity should be maximized to fulfill the conservation needs of different seasonal waterbirds. Furthermore, we suggest that future studies should focus on the least area criterion and that vegetation management of artificial wetland construction should be based on the notion of sustainable development for humans and wildlife.     

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.     

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     

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.     

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.     

Endemicity biases nestedness metrics: a demonstration, explanation and solution

Nestedness is frequently investigated to understand complex patterns of species occurrences. Temperature (T) is commonly used for comparisons of nestedness of different-sized datasets. However, the assumptions made for the standardization of this metric have not been fully explored, particularly the effects of endemicity. Here we show that T incorrectly indicates an increase in nestedness with the addition of non-nested endemics to matrices that are not perfectly nested – a consequence of standardizing matrix size by the product of species and sites. This problem is common both to test matrices and to real matrices that are typically subjected to nestedness analyses. The latter are often characterized by substantial numbers of endemics and by variation in the numbers of endemics in different taxa. Standardizing by occupancy resolves this problem, which is demonstrated using a derivative of discrepancy, d1. A small modification to T, such that it standardizes matrices by occupancy, would resolve the current problems with this nestedness metric.     

Nested species subsets of amphibians and reptiles on Neotropical forest islands

Nested species subsets are a common pattern of community assembly characteristic of many types of fragmented landscapes and insular systems. Here we describe nested subset patterns of amphibian and reptile occupancy on 23 forest islands in north-eastern Bolivia. We used observed occupancy patterns to differentiate five distributional guilds: widespread species, rare species, poor colonizers, area-sensitive species and supertramps. Amphibian occurrences were nested along a forest island isolation gradient, and when species from each of the distribution classes were removed from subsequent analyses of nestedness, we found that dispersal-limited poor colonizers were responsible for the association between nestedness and isolation. Amphibians associated with the grassland matrix at the study site showed a nested pattern linked with area, although this pattern did not scale up to all amphibians and could not be unequivocally attributed to any of the distributional guilds we recognized. There were no strong associations between two biological characteristics, body size and relative abundance in the matrix, and the likelihood of occupancy along either forest island area or isolation gradients. The relative importance of isolation in shaping nested patterns of amphibians on these forest islands may be a result of either (1) the greater range in isolation values included in this study compared with many others; (2) the long time since isolation in this landscape, manifesting a footprint of isolation not apparent in more recently fragmented patches; (3) the relatively homogeneous grassland matrix surrounding forest islands that likely provides little refuge for animals moving among forest islands.     

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.