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.     

Network Dynamics Contribute to Structure: Nestedness in Mutualistic Networks

Both ecological and evolutionary timescales are of importance when considering an ecological system; population dynamics affect the evolution of species traits, and vice versa. Recently, these two timescales have been used to explain structural patterns in host-parasite networks, where the evolution of the manner in which species balance the use of their resources in interactions with each other was examined. One of these patterns was nestedness, in which the set of parasite species within a particular host forms a subset of those within a more species-rich host. Patterns of both nestedness and anti-nestedness have been observed significantly more often than expected due to chance in host-parasite networks. In contrast, mutualistic networks tend to display a significant degree of nestedness, but are rarely anti-nested. Within networks with different interaction types, therefore, there appears to be a feature promoting non-random structural patterns, such as nestedness and anti-nestedness, depending on the interaction types involved. Here, we invoke the co-evolution of species trait-values when allocating resources to interactions to explain the structural pattern of nestedness in a mutualistic community. We look at a bipartite, multi-species system, in which the strength of an interaction between two species is determined by the resources that each species invests in that relationship. We then analyze the evolution of these interactions using adaptive dynamics. We found that the evolution of these interactions, reflecting the trade-off of resources, could be used to accurately predict that nestedness occurs significantly more often than expect due to chance alone in a mutualistic network. This complements previous results applying the same concept to an antagonistic network. We conclude that population dynamics and resource trade-offs could be important promoters of structural patterns in ecological networks of different types.     

Climate drives temporal replacement and nested‐resultant richness patterns of Scottish coastal vegetation

Beta diversity quantifies spatial and/or temporal variation in species composition. It is comprised of two distinct components, species replacement and nestedness, which derive from opposing ecological processes. Using Scotland as a case study and a β‐diversity partitioning framework, we investigate temporal replacement and nestedness patterns of coastal grassland species over a 34‐yr time period. We aim to 1) understand the influence of two potentially pivotal processes (climate and land‐use changes) on landscape‐scale (5 × 5 km) temporal replacement and nestedness patterns, and 2) investigate whether patterns from one β‐diversity component can mask observable patterns in the other. We summarised key aspects of climate driven macro‐ecological variation as measures of variance, long‐term trends, between‐year similarity and extremes, for three important climatic predictors (minimum temperature, water‐balance and growing degree‐days). Shifts in landscape‐scale heterogeneity, a proxy of land‐use change, was summarised as a spatial multiple‐site dissimilarity measure. Together, these climatic and spatial predictors were used in a multi‐model inference framework to gauge the relative contribution of each on temporal replacement and nestedness patterns. Temporal β‐diversity patterns were reasonably well explained by climate change but weakly explained by changes in landscape‐scale heterogeneity. Climate was shown to have a greater influence on temporal nestedness than replacement patterns over our study period, linking nestedness patterns, as a result of imbalanced gains and losses, to climatic warming and extremes respectively. Important climatic predictors (i.e. growing degree‐days) of temporal β‐diversity were also identified, and contrasting patterns between the two β‐diversity components revealed. Results suggest climate influences plant species recruitment and establishment processes of Scotland's coastal grasslands, and while species extinctions take time, they are likely to be facilitated by climatic perturbations. Our findings also highlight the importance of distinguishing between different components of β‐diversity, disentangling contrasting patterns than can mask one another.     

An inverse latitudinal gradient of diversity of peracarid crustaceans along the Pacific Coast of South America: out of the deep south

Aim To understand the ecological and historical/evolutionary processes underlying an inverse latitudinal gradient of richness (LGR) using crustacean peracarid species as a model group. Location The Pacific coast of South America, along the Chilean coast between 18° S and 56° S. Methods The LGR was evaluated using a dataset including 320 marine peracarid species reported for the coasts of Chile. Five ecological hypotheses invoking a relationship between species richness and present‐day conditions were tested: species–energy, species–area, Rapoport rescue effect, mid‐domain geometric constraint and niche breadth. Historical/evolutionary hypotheses (i.e. biogeographic conservatism, and diversification rates) were indirectly tested by analysing the latitudinal variation in the taxonomic distinctness, the taxonomic conservatism of the midpoint of the latitudinal range and the degree of nestedness at different taxonomic levels. Results Richness increased poleward, varying approximately eightfold, following an inverse LGR coupled with an increase in bathymetric distribution. Overall this inverse LGR seems robust to uncertainties in the completeness of the species inventory. We found support for only two of the five ecological hypotheses tested: species–area and Rapoport rescue effect. Historical/evolutionary hypotheses seemed important in structuring the richness pattern, as indicated by the higher taxonomic distinctness in the southern region, the strong taxonomic inertia in the mean range size and the high degree of nestedness of assemblages at different taxonomic levels. Conclusions When combined, these results underscore the importance of long‐term processes and historical/evolutionary explanations for the inverse LGR, conceptualized in what we term the ‘out of the deep south’ hypothesis that involves the effects of both biogeographic niche conservatism and evolutionary rates. We propose that the southern region may be a source of evolutionary novelties and/or exhibit higher diversification rates (i.e. higher speciation/lower extinction rates). Furthermore, phylogenetic conservatism of latitudinal range may limit the geographic expansion of these new taxa towards the depauperated northern region.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

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.     

A new conceptual and methodological framework for exploring and explaining pattern in presence – absence data

A conceptual framework is proposed to evaluate the relative importance of beta diversity, nestedness and agreement in species richness in presence – absence data matrices via partitioning pairwise gamma diversity into additive components. This is achieved by calculating three complementary indices that measure similarity, relative species replacement, and relative richness difference for all pairs of sites, and by displaying the results in a two‐dimensional simplex diagram, or ternary plot. By summing two terms at a time, three one‐dimensional simplices are derived correspondig to different contrasts: beta diversity versus similarity, species replacement versus nestedness and, finally, richness difference versus richness agreement. The simplex diagrams can be used to interpret underlying data structures by showing departure from randomness towards well‐interpretable directions, as demonstrated by artificial and actual examples. In particular, one may appreciate how far data structure deviates from three extreme model situations: perfect nestedness, anti‐nestedness and perfect gradient. Throughout the paper, we pay special attention to the measurement and interpetation of beta diversity and nestedness for pairs of sites, because these concepts have been in focus of ecological reseach for decades. The novel method can be used in community ecology, conservation biology, and biogeography, whenever the objective is to recover explanatory ecological processes behind patterns conveyed by presence–absence data.     

Livestock disturbance in Brazilian grasslands influences avian species diversity via turnover

Managing ecological disturbances at different spatial scales is paramount for maintaining or restoring faunal diversity in grasslands. Whereas some studies have reported varying net effects of livestock disturbance intensity upon species richness in grasslands, most analysis reveal strong effects on beta-diversity. However, beta-diversity can be further partitioned into a nestedness and turnover components, which allows complementary insights on the effects of disturbance on biodiversity across spatial scales. Here we tested for differences in avian species richness and beta-diversity across three intensity levels of livestock disturbance in southern Brazilian grasslands under commercial livestock production. We also tested how disturbance influences the nestedness and turnover components of beta-diversity separately. We found no difference in rarified-extrapolated species richness between disturbance levels. In contrast, we found a significant difference in species composition between disturbance levels, which was attributable to the turnover, but not to the nestedness component. Specifically, livestock disturbance had a predictable effect upon beta-diversity, with turnover of species composition occurring along the gradient of vegetation height in pastures. Our study illustrates the importance of differentiating the turnover and nestedness components of beta-diversity to detect effects of disturbance gradients on biodiversity patterns. We argue that conservation strategies should focus on preserving the mosaic of short- and tall-grass physiognomies associated with the disturbance gradient imposed by livestock production.     

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     

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.     

Nestedness and migratory status of avian assemblages in North America and Europe

We examine patterns of nestedness and species incidence for the resident and migrant components of avifaunas in North America and Europe. While all assemblages were significantly nested, there were no significant differences between North American and European avifaunas overall in nestedness or incidence. Residents did not differ from migrants in their adherence to a nested distribution, but did exhibit significantly higher incidences when continental affiliation was ignored.¶We develop a new nestedness index that examines each species' relative contribution to an assemblage's overall pattern of nestedness. The relative nestedness index exhibits a quadratic relationship with incidence such that species with low incidences and species with high incidences generally increase the overall level of nestedness, while species with intermediate incidence tend to decrease nestedness.     

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.     

Combining projected changes in species richness and composition reveals climate change impacts on coastal Mediterranean fish assemblages

Species Temporal Turnover (STT) is one of the most familiar metrics to assess changes in assemblage composition as a consequence of climate change. However, STT mixes two components in one metric, changes in assemblage composition caused by a process of species loss or gain (i.e. the nestedness component) and changes in assemblage composition caused by a process of species replacement (i.e. the species replacement component). Drawing on previous studies investigating spatial patterns of beta diversity, we propose measures of STT that allow analysing each component (species replacement vs. nestedness), separately. We also present a mapping strategy to simultaneously visualize changes in species richness and assemblage composition. To illustrate our approach, we used the Mediterranean coastal fish fauna as a case study. Using Bioclimatic Envelope Models (BEMs) we first projected the potential future climatic niches of 288 coastal Mediterranean fish species based on a global warming scenario. We then aggregated geographically the species‐level projections to analyse the projected changes in species richness and composition. Our results show that projected changes in assemblage composition are caused by different processes (species replacement vs. nestedness) in several areas of the Mediterranean Sea. In addition, our mapping strategy highlights that the coastal fish fauna in several regions of the Mediterranean Sea could experience a ‘cul‐de‐sac’ effect if exposed to climate warming. Overall, the joint exploration of changes in species richness and composition coupled with the distinction between species replacement and nestedness bears important information for understanding the nature of climate change impacts on biodiversity. These methodological advances should help decision‐makers in prioritizing action in the areas facing the greatest vulnerability to climate.     

Historical climate‐change influences modularity and nestedness of pollination networks

The structure of species interaction networks is important for species coexistence, community stability and exposure of species to extinctions. Two widespread structures in ecological networks are modularity, i.e. weakly connected subgroups of species that are internally highly interlinked, and nestedness, i.e. specialist species that interact with a subset of those species with which generalist species also interact. Modularity and nestedness are often interpreted as evolutionary ecological structures that may have relevance for community persistence and resilience against perturbations, such as climate‐change. Therefore, historical climatic fluctuations could influence modularity and nestedness, but this possibility remains untested. This lack of research is in sharp contrast to the considerable efforts to disentangle the role of historical climate‐change and contemporary climate on species distributions, richness and community composition patterns. Here, we use a global database of pollination networks to show that historical climate‐change is at least as important as contemporary climate in shaping modularity and nestedness of pollination networks. Specifically, on the mainland we found a relatively strong negative association between Quaternary climate‐change and modularity, whereas nestedness was most prominent in areas having experienced high Quaternary climate‐change. On islands, Quaternary climate‐change had weak effects on modularity and no effects on nestedness. Hence, for both modularity and nestedness, historical climate‐change has left imprints on the network structure of mainland communities, but had comparably little effect on island communities. Our findings highlight a need to integrate historical climate fluctuations into eco‐evolutionary hypotheses of network structures, such as modularity and nestedness, and then test these against empirical data. We propose that historical climate‐change may have left imprints in the structural organisation of species interactions in an array of systems important for maintaining biological diversity.     

Partitioning the turnover and nestedness components of beta diversity

Aim  Beta diversity (variation of the species composition of assemblages) may reflect two different phenomena, spatial species turnover and nestedness of assemblages, which result from two antithetic processes, namely species replacement and species loss, respectively. The aim of this paper is to provide a unified framework for the assessment of beta diversity, disentangling the contribution of spatial turnover and nestedness to beta-diversity patterns.
Innovation  I derive an additive partitioning of beta diversity that provides the two separate components of spatial turnover and nestedness underlying the total amount of beta diversity. I propose two families of measures of beta diversity for pairwise and multiple-site situations. Each family comprises one measure accounting for all aspects of beta diversity, which is additively decomposed into two measures accounting for the pure spatial turnover and nestedness components, respectively. Finally, I provide a case study using European longhorn beetles to exemplify the relevance of disentangling spatial turnover and nestedness patterns.
Main conclusion  Assigning the different beta-diversity patterns to their respective biological phenomena is essential for analysing the causality of the processes underlying biodiversity. Thus, the differentiation of the spatial turnover and nestedness components of beta diversity is crucial for our understanding of central biogeographic, ecological and conservation issues.     

Commentary: Do we have a consistent terminology for species diversity? The fallacy of true diversity

There is no single best index that can be used to answer all questions about species diversity. Entropy-based diversity indices, including Hill’s indices, cannot account for geographical and phylogenetic structure. While a single diversity index arises if we impose several constraints—most notably that gamma diversity be completely decomposed into alpha and beta diversity—there are many ecological questions regarding species diversity for which it is counterproductive, requiring decomposability. Non-decomposable components of gamma diversity may quantify important intrinsic ecological properties, such as resilience or nestedness.     

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.     

Inferences about nested subsets structure when not all species are detected

Comparisons of species composition among isolated ecological communities of different size have often provided evidence that the species in communities with lower species richness form nested subsets of the species in larger communities. In the vast majority of studies, the question of nested subsets has been addressed using information on presence‐absence, where a “0” is interpreted as the absence of a given species from a given location. Most of the methodological discussion in earlier studies investigating nestedness concerns the approach to generation of model‐based matrices corresponding to the null hypothesis of a nonnested pattern. However, it is most likely that in many situations investigators cannot detect all the species present in the location sampled. The possibility that zeros in incidence matrices reflect nondetection rather than absence of species has not been considered in studies addressing nested subsets, even though the position of zeros in these matrices forms the basis of earlier inference methods. These sampling artifacts are likely to lead to erroneous conclusions about both variation over space in species richness, and the degree of similarity of the various locations. Here we propose an approach to investigation of nestedness, based on statistical inference methods explicitly incorporating species detection probability, that take into account the probabilistic nature of the sampling process. We use presence‐absence data collected under Pollock's robust capture‐recapture design, and resort to an estimator of species richness originally developed for closed populations to assess the proportion of species shared by different locations. We develop testable predictions corresponding to the null hypothesis of a nonnested pattern, and an alternative hypothesis of perfect nestedness. We also present an index for assessing the degree of nestedness of a system of ecological communities. We illustrate our approach using avian data from the North American Breeding Bird Survey collected in Florida Keys.