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.     

Measuring fractions of beta diversity and their relationships to nestedness: a theoretical and empirical comparison of novel approaches

Beta diversity and nestedness are central concepts of ecology and biogeography and evaluation of their relationships is in the focus of contemporary ecological and conservation research. Beta diversity patterns are originated from two distinct processes: the replacement (or turnover) of species and the loss (or gain) of species leading to richness differences. Nested distributional patterns are generally thought to have a component deriving from beta diversity which is independent of replacement processes. Quantification of these phenomena is often made by calculating a measure of beta diversity, and the resulting value being subsequently partitioned into a contribution by species replacement plus a fraction shared by beta diversity and nestedness. Three methods have been recently proposed for such partitioning, all of them based on pairwise comparisons of sites. In this paper, the performance of these methods was evaluated on theoretical grounds and tested by a simulation study in which different gradients of dissimilarity, with known degrees of species replacement and species loss, were created. Performance was also tested using empirical data addressing land‐use induced changes in endemic arthropod communities of the Terceira Island in the Azores. We found that the partitioning of β_cc (dissimilarity in terms of the Jaccard index) into two additive fractions, β_‐3 (dissimilarity due to species replacement) plus β_rich (dissimilarity due to richness differences) reflects the species replacement and species loss processes across the simulated gradients in an ecologically and mathematically meaningful way, whilst the other two methods lack mathematical consistency and prove conceptually self‐contradictory. Moreover, the first method identified a selective local extinction process for endemic arthropods, triggered by land‐use changes, while the latter two methods overweighted the replacement component and led to false conclusions. Their basic flaw derives from the fact that the proposed replacement and nestedness components (deemed to account for species loss) are not scaled in the same way as the measure that accounts for the total dissimilarity (Sørensen and Jaccard indices). We therefore recommend the use of β_cc=β_‐3+β_rich, since its components are scaled in the same units and their responses are proportional to the replacement and the gain/loss of species.     

A meta‐analysis of nestedness and turnover components of beta diversity across organisms and ecosystems

Aim

The number of studies investigating the nestedness and turnover components of beta diversity has increased substantially, but our general understanding of the drivers of turnover and nestedness remains elusive. Here, we examined the effects of species traits, spatial extent, latitude and ecosystem type on the nestedness and turnover components of beta diversity.

Location

Global.

Time period

1968–2017.

Major taxa studied

From bacteria to mammals.

Methods

From the 99 studies that partition total beta diversity into its turnover and nestedness components, we assembled 269 and 259 data points for the pairwise and multiple site beta‐diversity metrics, respectively. Our data covered a broad variation in species dispersal type, body size and trophic position. The data were from freshwater, marine and terrestrial realms, and encompassed geographical areas from the tropics to near polar regions. We used linear modelling as a meta‐regression tool to analyse the data.

Results

Pairwise turnover, multiple site turnover and total beta diversity all decreased significantly with latitude. In contrast, multiple site nestedness showed a positive relationship with latitude. Beta‐diversity components did not generally differ among the realms. The turnover component and total beta diversity increased with spatial extent, whereas nestedness was scale invariant for pairwise metrics. Multiple site beta‐diversity components did not vary with spatial extent. Surprisingly, passively dispersed organisms had lower turnover and total beta diversity than flying organisms. Body size showed a relatively weak relationship with beta diversity but had important interactions with trophic position, thus also affecting beta diversity via interactive effects. Producers had significantly higher average pairwise turnover and total beta diversity than carnivores.

Main conclusions

The present results provide evidence that species turnover, being consistently the larger component of total beta diversity, and nestedness are related to the latitude of the study area and intrinsic organismal features. We showed that two beta‐diversity components had generally opposing patterns with regard to latitude. We highlight that beta‐diversity partition may give additional insights into the underlying causes of spatial variability in biotic communities compared with total beta diversity alone.     

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.     

Once again on the components of pairwise beta diversity

Presence–absence based beta diversity defined for pairs of sites may be partitioned into components following two different ways of thinking. Within the framework of Baselga (abbreviated hereafter as BAS), nestedness is crucial and dissimilarity is partitioned into replacement (turnover) and nestedness-resultant fractions. The method proposed by Podani and Schmera (POD), however, places emphasis on the mathematical additivity of components and divides dissimilarity into replacement and richness difference components. A recent comparison by Baselga and Leprieur (2015), on the example of the Jaccard family of indices, emphasizes the independence of replacement component from absolute richness difference and concludes that the replacement function of the BAS framework is the only true measure of species replacement. As a response to this study, we show here that 1) the sacrifice one must make for independence is that the components themselves are scaled differently and are not always comparable ecologically, 2) absolute (raw) replacement and richness difference are not independent, so that independence from the latter cannot be a fundamental criterion that a replacement measure should satisfy, 3) relativization applied in the POD framework is ecologically interpretable, leading to a meaningful conceptualization of species replacement, 4) the BAS and POD methods are linked through a generalized replacement function, 5) both the BAS and POD approaches may produce high correlations with environmental variables, whereas 6) the POD approach offers in many respects more illuminating demonstrations of the underlying changes of pattern than the graphs of Baselga and Leprieur for both artificial and actual fish distribution data.     

A multiple-site dissimilarity measure for species presence/absence data and its relationship with nestedness and turnover

Multiple-site dissimilarity may be caused by two opposite processes of meta-community organization, such as species nestedness and turnover. Therefore, discriminating among these contributions is necessary for linking multiple-site dissimilarity to ecosystem functioning. This paper introduces a measure of multiple-site dissimilarity or beta diversity for presence/absence data that is based on information on species absences from the species × sites matrix. It is also shown that the newly proposed dissimilarity index can be additively partitioned into species nestedness and turnover.     

Distinguishing between turnover and nestedness in the quantification of biotic homogenization

Compositional changes through local extinction and colonization are inherent to natural communities, but human activities are increasingly influencing the rate and nature of the species being lost and gained. Biotic homogenization refers to the process by which the compositional similarity of communities increases over time through a non-random reshuffling of species. Despite the extensive conceptual development of the homogenization framework, approaches to quantify patterns of homogenization are scarcely developed. Most studies have used classical dissimilarity indices that actually quantify two components of compositional variation: turnover and nestedness. Here we demonstrate that a method that partitions those two components reveals patterns of homogenization that are otherwise obscured using traditional techniques. The forest understorey vegetation of an unmanaged reserve was recorded in permanent plots in 1979 and 2009. In only thirty years, the local species richness significantly decreased and the variation in the species composition from site to site shifted towards a structure with reduced true species turnover and increased dissimilarity due to nestedness. A classic analysis masked those patterns. In summary, we illustrated the need to move beyond the simple quantification of homogenization using classical indices and advocate integration of the multitude of ways to quantify community similarity into the homogenization framework.     

Multiple site dissimilarity quantifies compositional heterogeneity among several sites,while average pairwise dissimilarity may be misleading

Several measures of multiple site dissimilarity have been proposed to quantify the overall heterogeneity in assemblage composition among any number of sites. It is also a common practice to quantify such overall heterogeneity by averaging pairwise dissimilarities between all pairs of sites in the pool. However, pairwise dissimilarities do not account for patterns of co‐occurrence among more than two sites. In consequence, the average of pairwise dissimilarities may not accurately reflect the overall compositional heterogeneity within a pool of more than two sites. Here I use several idealized examples to illustrate why pairwise dissimilarity measures fail to properly quantify overall heterogeneity. Thereafter, the effect of this potential problem in empirical patterns is exemplified with data of world amphibians. In conclusion, when the attribute of interest is the overall heterogeneity in a pool of sites (i.e. beta diversity) or its turnover or nestedness components, only multiple site dissimilarity measures are recommended.     

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.     

Species and individual replacements contribute more than nestedness to shape vertebrate scavenger metacommunities

Understanding the mechanisms that organize biodiversity is central in ecology and conservation. Beta diversity links local (alfa) and regional (gamma) diversity, giving insight into how communities organize spatially. Metacommunity ecology provides the framework to interpret regional and local processes interacting to shape communities. However, the lack of metacommunity studies for large vertebrates may limit the understanding and compromise the preservation of ecosystem functions and services. We aim to understand the mechanisms underlying differences in species composition among vertebrate scavenger communities ? which provide key ecosystem functions, e.g. carrion consumption ? within a metacommunity context. We obtained species richness and abundances at scavenger communities consuming ungulate carcasses monitored through motion‐triggered remote cameras in seven terrestrial ecosystems in Spain. We partitioned beta diversity to decompose incidence‐based (species presence/absence) and abundance‐based dissimilarities into their components (turnover/balanced variation and nestedness/abundance gradient, respectively). We identified the environmental factors explaining the observed patterns. The vertebrate scavenger metacommunity consisted of 3101 individuals from 30 species. Changes in composition among ecosystems were mostly (> 84%) due to species or individual replacement (i.e. turnover or balanced variation). Species or individual loss/gain (i.e. nestedness or abundance gradient) accounted for 13–16% of these changes. Mean carcass weight, elevation and habitat diversity were the main factors explaining species/individual replacement. Our findings suggest that local processes such as species‐sorting through habitat heterogeneity would dominate scavenger metacommunity dynamics together with stochastic forces (i.e. related to carrion unpredictability and scavenging being a widespread strategy among vertebrates). The presence of structured patterns (i.e. nestedness) in beta diversity could reflect a role of deterministic processes: mass‐effects through dispersal and defaunation. Vultures are long‐distance foragers and functionally dominant species, which would connect local assemblages within the metacommunity, supporting scavenger diversity and functions across space. These results highlight the importance of managing vertebrate scavenger assemblages within a metacommunity context.     

Climatic history and dispersal ability explain the relative importance of turnover and nestedness components of beta diversity

Aim We tested whether the geographic variation in the proportion of beta diversity attributed to nestedness or turnover components was explained by the effect of past glaciation events. Specifically, we tested the hypothesis that most of the beta diversity in regions retaining ice until recent periods was due to nestedness. Additionally, we tested whether the variation was influenced by thermal tolerance and the dispersal ability of species. Location This study analysed data from the New World. Methods We used presence/absence data for amphibians, birds and mammals of the New World. We calculated beta diversity among each 1°× 1° cell and the adjacent cells using the Sorensen dissimilarity index that expresses the total beta diversity. Furthermore, we partitioned it into turnover and nestedness components. The relative importance of the two latter components was expressed as the proportion of total beta diversity explained by nestedness (β_ratio). We calculated the correlation between β_ratio and the time each cell was free of ice since the last glaciation (cell age). To control the effects of spatial autocorrelation, we calculated geographically effective degrees of freedom. Results The proportion of beta diversity attributed to nestedness was negatively correlated with cell age. Moreover, this effect was stronger for amphibians than mammals, and stronger for mammals than birds. Main conclusions Our results are in accordance with the hypothesis that the nestedness component of beta diversity is more important in areas affected by glaciations until recent time. The beta diversity in high latitudes is the result of past extinctions and recent recolonization, which result in higher levels of nestedness. This process is more evident for vertebrates with lower dispersal ability and lower temperature tolerance.     

Turnover and nestedness in subtropical dung beetle assemblages along an elevational gradient

Aim

We investigated changes in dung beetle β‐diversity components along a subtropical elevational gradient, to test whether turnover or nestedness‐related processes drive the dissimilarity of assemblages at spatial and temporal scales.

Location

An elevational gradient (200–1,600 m a.s.l.) of the Atlantic Forest in southern Brazil.

Methods

We investigated the extent to which β‐diversity varied along the elevational gradient (six elevations) at both spatial (among sites at different elevations) and temporal (different months at the same site) scales. We compared both the turnover and nestedness‐related dissimilarity of species and genera using multiple‐site or multiple‐month measures and tested whether these measurements were different from random expectations.

Results

A mid‐elevation peak in species richness along the elevational gradient was observed, and the lowest richness occurred at the highest elevations. We found two different groups of species, lowland and highland species, with a mixing of groups at intermediate elevations. The turnover component of β‐diversity was significantly higher for both spatial (i.e. elevational) and temporal changes in species composition. However, when the data for genera by site were considered, the elevational turnover value decreased in relative importance. Nestedness‐related processes are more important for temporal dissimilarity patterns at higher elevation sites.

Main conclusions

Spatial and temporal turnover of dung beetle species is the most important component of β‐diversity along the elevational gradient. High‐elevation assemblages are not subsets of assemblages that inhabit lower elevations, but this relationship ceases when β‐diversity is measured at the generic level. Environmental changes across elevations may be the cause of the differential establishment of distinctive species, but these species typically belong to the same higher taxonomic rank. Conservation strategies should consider elevational gradients in case‐specific scenarios as they may contain distinct species assemblages in lowlands vs. highlands.

     

Habitat amount drives the functional diversity and nestedness of anuran communities in an Atlantic Forest fragmented landscape

Natural environments disturbed by human activities can suffer from species extinctions, but some can still harbor high taxonomic diversity. However, disturbances may have impacts beyond the species level, if the species lost represent unique functions in the ecosystem. In this study, we evaluated to what extent the amount of habitat can determine the functional diversity and nestedness of amphibian communities in an Atlantic Forest fragmented landscape in Brazil, and if there is a threshold of habitat amount beyond which there is severe loss of functional diversity. As species responses may depend on their habitat type, we performed the analyses for three different sets of species: all species, forest‐dependent species, and generalist species. We also evaluated the relative importance of turnover and nestedness components to total functional dissimilarity among sites. Habitat amount affected functional diversity of frogs, especially for forest‐dependent species where a linear reduction was detected. The functional dissimilarity among sites was mostly explained by the nestedness component. The reduction of functional diversity was mediated by an ordered loss of traits, leading to a functionally nested metacommunity. These sensitive traits were closely related to habits and reproductive modes that depend on rivers and streams. The maintenance of functional diversity of frogs in fragmented landscapes must rely on the conservation of both terrestrial and aquatic environments, as some species and their traits can disappear from remnants of native vegetation lacking some specific habitats (e.g. streams). Abstract in Portuguese is available with online material.     

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.     

A comparative evaluation of pairwise nestedness measures

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

Partitioning multiple-site tree-like beta diversity into turnover and nestedness components without pairwise comparisons

In this letter, I extend a species-level partitioning framework for a multiple-site dissimilarity index established by Ricotta and Pavoine (2015) to account for tree-like information (i.e., evolutionary history, taxonomic classification or functional divergence of species). This novel framework can be applied to evaluate the relative contribution of turnover versus nestedness to total multiple-site tree-like beta diversity in empirical settings. The feature of the framework is to account for expectedly and unexpectedly absence of species in the sites without pairwise comparisons between sites. Simple examples with step-by-step calculation details and corresponding R computing code are provided to better understand and apply the proposed framework.     

Temporal changes in fish diversity in lotic and lentic environments along a reservoir cascade

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Environmental drivers of species composition and functional diversity of dung beetles along the Atlantic Forest–Pampa transition zone

Human activities are causing a rapid loss of biodiversity, which impairs ecosystem functions and services. Therefore, understanding which processes shape how biodiversity is distributed along spatial and environmental gradients is a first step to guide conservation and management efforts. We aimed to determine the relative explanatory importance of biogeographic, environmental, landscape and spatial variables on assemblage dissimilarities and functional diversity of dung beetles along the Atlantic Forest–Pampa (i.e. forest–grassland) transition zone located in Southeast South America. We described each site according to their biogeographic position, environmental conditions, landscape features and spatial patterns. The compositional dissimilarity was partitioned into turnover and nestedness components of β‐diversity. Mantel tests and generalised dissimilarity models were used to relate β‐diversity and its components to biogeographic, environmental, landscape and spatial variables. Variation partitioning analysis was used to estimate the pure and shared variation in species composition and functional diversity explained by the four categories of predictors. Biome domain was the main factor causing dung beetle compositional dissimilarity, with a high species replacement between Atlantic Forest and Pampa. Biogeographic, environmental, landscape and spatial distances also affected the patterns of dung beetle dissimilarity and β‐diversity components. The shared effects of the four sets of predictors explained most of the variation in dung beetle composition. A similar response pattern was found for dung beetle functional diversity, which excluded biogeographic effects. Only the pure effects of environmental and spatial predictors were significant for species composition and functional diversity. Our results indicate that dung beetle species composition and functional diversity are jointly driven by environmental, landscape and spatial predictors with higher pure environmental and spatial effects. The forest–grassland transition zone promotes a strong species and trait replacement highly influenced both by environmental filtering and dispersal limitation.     

A general framework for analyzing beta diversity,nestedness and related community-level phenomena based on abundance data

We describe a procedure for evaluating the relative importance of beta diversity, nestedness, and similarity properties of ecological data matrices containing density, cover or biomass scores of species. Our goals are achieved by extension of the simplex approach – originally proposed for presence–absence data – to abundances. Basically, the method involves decomposition of the Marczewski–Steinhaus coefficient of dissimilarity between pairs of sites into two fractions, one derived from differences between total abundance and the other from differences due to abundance replacement. These are contrasted by the similarity function counterpart, known as the Ruzicka coefficient, and are displayed graphically using ternary (or 2D simplex) plots. Interpretation is aided by calculating percentage contributions from these components to the (dis)similarity structure. Measures of replacement and nestedness are new for abundance data; these are considered complementary phenomena reflecting antithetic ecological processes that are analogous to those operating at the presence–absence level. The method is illustrated by artificial data and a range of actual ecological data sets representing different groups of organisms, different scales and different types of data. While the simplex diagrams and associated coefficients are meaningful by themselves, their comparison with presence–absence based results gives additional insight into data structure and background factors.