Independence of total species richness and richness difference are not the same thing

Leprieur and Oikonomou (2014) criticized that a replacement index β_− 3, a partitioned component of Jaccard index β_jac, was not richness independent and should not be used in biogeographic and ecological studies. However, Leprieur and Oikonomou failed to recognize the difference between richness and richness difference. Independence of total species richness is not equal to independence of richness difference. Theoretically and ideally, it is true that β_− 3 (and β_jac as well) is not independent of richness difference while Simpson index (β_sim) is fully independent of richness difference. However, all these indices actually are independent of total species richness. At last, it is worth mentioning that the ideal independence studied here is easily violated in computational simulation and real-world settings.     

The relationship between species replacement,dissimilarity derived from nestedness,and nestedness

Aim Beta diversity can be partitioned into two components: dissimilarity due to species replacement and dissimilarity due to nestedness ( Baselga, 2010 , Global Ecology and Biogeography, 19 , 134–143). Several contributions have challenged this approach or proposed alternative frameworks. Here, I review the concepts and methods used in these recent contributions, with the aim of clarifying: (1) the rationale behind the partitioning of beta diversity into species replacement and nestedness‐resultant dissimilarity, (2) how, based on this rationale, numerators and denominators of indices have to match, and (3) how nestedness and nestedness‐resultant dissimilarity are related but different concepts. Innovation The rationale behind measures of species replacement (turnover) dictates that the number of species that are replaced between sites (numerator of the index) has to be relativized with respect to the total number of species that could potentially be replaced (denominator). However, a recently proposed partition of Jaccard dissimilarity fails to do this. In consequence, this partition underestimates the contribution of species replacement and overestimates the contribution of richness differences to total dissimilarity. I show how Jaccard dissimilarity can be partitioned into meaningful turnover and nestedness components, and extend these new indices to multiple‐site situations. Finally the concepts of nestedness and nestedness‐resultant dissimilarity are discussed. Main conclusions Nestedness should be assessed using consistent measures that depend both on paired overlap and matrix filling, e.g. NODF, whereas beta‐diversity patterns should be examined using measures that allow the total dissimilarity to be separated into the components of dissimilarity due to species replacement and dissimilarity due to nestedness. In the case of multiple‐site dissimilarity patterns, averaged pairwise indices should never be used because the mean of the pairwise values is unable to accurately reflect the multiple‐site attributes of dissimilarity.     

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.     

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.     

Contrasting responses of beta diversity components to environmental and host-associated factors in insect ectoparasites

1. The present study investigated whether different components (species replacement and species gains/losses) of compositional and phylogenetic beta diversity of insect ectoparasites responded similarly to environmental and host-associated gradients using a large dataset on distribution of fleas and their rodent hosts in Mongolia. 2. Generalised dissimilarity modelling was applied to investigate whether environmental variables or host dissimilarity was the best predictor of species/lineage replacement and species/lineage gains/losses (= richness difference) components of compositional and phylogenetic flea beta diversity. 3. The total compositional beta diversity of fleas was influenced mainly by the gradient in air temperature and, to a lesser degree, by total host beta diversity, with the former effect being associated with the richness difference component and the latter effect being associated with species replacement component. The total phylogenetic beta diversity of fleas was best explained by the total phylogenetic beta diversity of hosts, with this effect being mainly associated with the lineage replacement component, whereas the lineage richness difference component responded mainly to the temperature gradient. 4. The results of the present indicate that not only multiple beta diversity facets are driven by different factors, but also different components of the same beta diversity facet respond to different environmental (for parasites, including host-associated) gradients. These patterns were masked when only total beta diversity was analysed. 5. This emphasizes the importance of considering the components of insect beta diversity separately. Ignoring the separate components of beta diversity can lead to potentially erroneous inferences about the relative contribution of abiotic and biotic effects on beta diversity.     

Vertebrate Dissimilarity Due to Turnover and Richness Differences in a Highly Beta-Diverse Region: The Role of Spatial Grain Size,Dispersal Ability and Distance

We explore the influence of spatial grain size, dispersal ability, and geographic distance on the patterns of species dissimilarity of terrestrial vertebrates, separating the dissimilarity explained by species replacement (turnover) from that resulting from richness differences. With data for 905 species of terrestrial vertebrates distributed in the Isthmus of Tehuantepec, classified into five groups according to their taxonomy and dispersal ability, we calculated total dissimilarity and its additive partitioning as two components: dissimilarity derived from turnover and dissimilarity derived from richness differences. These indices were compared using fine (10 x 10 km), intermediate (20 x 20 km) and coarse (40 x 40 km) grain grids, and were tested for any correlations with geographic distance. The results showed that total dissimilarity is high for the terrestrial vertebrates in this region. Total dissimilarity, and dissimilarity due to turnover are correlated with geographic distance, and the patterns are clearer when the grain is fine, which is consistent with the distance-decay pattern of similarity. For all terrestrial vertebrates tested on the Isthmus of Tehuantepec both the dissimilarity derived from turnover and the dissimilarity resulting from richness differences make important contributions to total dissimilarity, and dispersal ability does not seem to influence the dissimilarity patterns. These findings support the idea that conservation efforts in this region require a system of interconnected protected areas that embrace the environmental, climatic and biogeographic heterogeneity of the area.     

Spatio-temporal drivers of different oomycete beta diversity components in Brazilian rivers

Disentangling the role of mechanisms driving metacommunity structure is fundamental for conservation strategies. Several studies have been done in aquatic communities; however, little is known about the factors driving oomycete communities. This research aimed to investigate beta diversity patterns and assess the role of environmental (chemical, physical, and hydrologic), spatial, and temporal (sampling months) factors in driving oomycete beta diversity in a spatial extent of 33 km from two Brazilian rivers. We took water samples in 10 sites quarterly, from August 2017 to May 2018. The partition of beta diversity into its components – species replacement and richness difference – was performed using the Jaccard dissimilarity index. Distance-based redundancy analysis and variation partitioning were used to assess the relationship between explanatory variables and beta diversity. We found that beta diversity was spatially and temporally high, and the replacement component was the main driver of the oomycete metacommunity’s beta diversity. Replacement and total beta diversity were explained mainly by spatial location and the month of sampling, while the richness difference was more associated with the environmental variables chlorophyll a and ammonia. Our findings suggest that dispersal limitation (spatial) and temporal factors are the main drivers of the total beta diversity and replacement in the oomycete metacommunity, while species sorting (environmental factor) influences the richness difference. Accordingly, that taking temporal factors into account in metacommunity studies is important to explain beta diversity patterns, especially in rivers with remarkable variability in hydrological regime and under eutrophic conditions.

     

Investigating uncertainties in zooplankton composition shifts under climate change scenarios in the Mediterranean Sea

Ensemble niche modelling has become a common framework to predict changes in assemblages composition under climate change scenarios. The amount of uncertainty generated by the different components of this framework has rarely been assessed. In the marine realm forecasts have usually focused on taxa representing the top of the marine food‐web, thus overlooking their basal component: the plankton. Calibrating environmental niche models at the global scale, we modelled the habitat suitability of 106 copepod species and estimated the dissimilarity between present and future zooplanktonic assemblages in the surface Mediterranean Sea. We identified the patterns (species replacement versus nestedness) driving the predicted dissimilarity, and quantified the relative contributions of different uncertainty sources: environmental niche models, greenhouse gas emission scenarios, circulation model configurations and species prevalence. Our results confirm that the choice of the niche modelling method is the greatest source of uncertainty in habitat suitability projections. Presence‐only and presence–absence methods provided different visions of the niches, which subsequently lead to different future scenarios of biodiversity changes. Nestedness with decline in species richness is the pattern driving dissimilarity between present and future copepod assemblages. Our projections contrast with those reported for higher trophic levels, suggesting that different components of the pelagic food‐web may respond discordantly to future climatic changes.     

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.     

Geographical patterns of turnover and nestedness-resultant components of allelic diversity among populations

The analysis of geographical patterns in population divergence has always been a powerful way to infer microevolutionary processes involved in population differentiation, and several approaches have been used to investigate such patterns. Most frequently, multivariate spatial patterns of population differentiation are analyzed by computing pairwise genetic distances or F_ST (or related statistics, such as ?_ST from AMOVA), which are then correlated with geographical distances or landscape features. However, when calculating distances, especially based on presence-absence of alleles in local populations, there would be a confounding effect of allelic richness differences in the population differentiation. Moreover, the relative magnitude of these components and their spatial patterns can help identifying microevolutionary processes driving population differentiation. Here we show how recent methodological advances in ecological community analyses that allows partitioning dissimilarity into turnover (turnover) and richness differences, or nestedness-resultant dissimilarity, can be applied to allelic variation data, using an endemic Cerrado tree (Dipteryx alata) as a case study. Individuals from 15 local populations were genotyped for eight microsatellite loci, and pairwise dissimilarities were computed based on presence-absence of alleles. The turnover of alleles among populations represented 69?% of variation in dissimilarity, but only the richness difference component shows a clear spatial structure, appearing as a westward decrease of allelic richness. We show that decoupling richness difference and turnover components of allelic variation reveals more clearly how similarity among populations reflects geographical patterns in allelic diversity that can be interpreted in respect to historical range expansion in the species.     

A family of functional dissimilarity measures for presence and absence data

Plot‐to‐plot dissimilarity measures are considered a valuable tool for understanding the complex ecological mechanisms that drive community composition. Traditional presence/absence coefficients are usually based on different combinations of the matching/mismatching components of the 2 × 2 contingency table. However, more recently, dissimilarity measures that incorporate information about the degree of functional differences between the species in both plots have received increasing attention. This is because such “functional dissimilarity measures” capture information on the species' functional traits, which is ignored by traditional coefficients. Therefore, functional dissimilarity measures tend to correlate more strongly with ecosystem‐level processes, as species influence these processes via their traits. In this study, we introduce a new family of dissimilarity measures for presence and absence data, which consider functional dissimilarities among species in the calculation of the matching/mismatching components of the 2 × 2 contingency table. Within this family, the behavior of the Jaccard coefficient, together with its additive components, species replacement, and richness difference, is examined by graphical comparisons and ordinations based on simulated data.     

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.     

Nestedness-resultant community disassembly process of extinction debt in a highly fragmented semi-natural grassland

There are two major processes of species disassembly after landscape changes: non-random loss of species resulting in nested assemblages and species replacement resulting in spatial species turnover. Although time-lagged responses of species to landscape change have been widely recognized, few studies have empirically evaluated which of these two processes is more closely related to extinction debt (i.e., postponed species extinction following habitat loss). This study aimed to understand the underlying processes of extinction debt by partitioning β-diversity into components of species nestedness and species turnover. We measured grassland species richness at three spatial extents in a highly fragmented semi-natural grassland landscape in Japan. Dissimilarity-based β-diversity was partitioned into two components (i.e., nestedness-resultant dissimilarity [β_sne] and turnover-resultant dissimilarity [β_sim]), which were further analyzed using principal coordinates analyses (PCoA). The relationships between the variability of PCoA axis 1 scores and the current and past habitat proportions were evaluated. A significant positive relationship between current grassland species richness and past (i.e., the 1910s) grassland proportion was found at the largest spatial extent. The first axis of PCoA based on β_sne showed significant correlation with past habitat proportions, whereas the PCoA axis based on β_sim showed no significant correlation with either the current or past habitat proportions. A non-random loss of grassland species represented by nestedness underlay the extinction debt found at the landscape level. There is a chance of predicting the loss of species from the nested ranks of species which likely reflects the gradient of species vulnerability to historical landscape changes.     

A metric of biodiversity that integrates abundance,phylogeny, and function

A metric of biodiversity is proposed that combines three of its key components: abundance, phylogeny, and ecological function. This metric is an expansion of the current abundance‐based metric that uses Hill numbers, the effective number of types in a sample if all types had the same mean proportional abundance. I define analogous proportional measures of phylogenetic divergence and functional distinctiveness. Phylogenetic divergence is measured as the sum of the proportional share of each species of a given branch of a phylogeny. Functional distinctiveness can be measured in two ways, as the proportional share of each species of a specified ecological function, or as the relative distance of each species based on functional trait values. Because all three aspects of biodiversity are measured in the same fashion (relative proportions) in similar units (effective numbers of species), an integrated metric can be defined. The combined metric provides understanding of covariation among the components and how management for one component may trade off against others. The metric can be partitioned into components of richness and evenness, and into subsets and variation among subsets, all of which can be related through a simple multiplicative framework. This metric is a complement to, rather than a replacement of, current metrics of phylogenetic and functional diversity. More work is needed to link this new metric to ecological theory, determine its error structure, and devise methods for its effective assessment.     

Amphibian Beta Diversity in the Brazilian Atlantic Forest: Contrasting the Roles of Historical Events and Contemporary Conditions at Different Spatial Scales

Current patterns of biodiversity distribution result from a combination of historical and contemporary processes. Here, we compiled checklists of amphibian species to assess the roles of long-term climate stability (Quaternary oscillations), contemporary environmental gradients and geographical distance as determinants of change in amphibian taxonomic and phylogenetic composition in the Brazilian Atlantic Forest. We calculated beta diversity as both variation in species composition (CBD) and phylogenetic differentiation (PBD) among the assemblages. In both cases, overall beta diversity was partitioned into two basic components: species replacement and difference in species richness. Our results suggest that the CBD and PBD of amphibians are determined by spatial turnover. Geographical distance, current environmental gradients and long-term climatic conditions were complementary predictors of the variation in CBD and PBD of amphibian species. Furthermore, the turnover components between sites from different regions and between sites within the stable region were greater than between sites within the unstable region. On the other hand, the proportion of beta-diversity due to species richness difference for both CBD and PBD was higher between sites in the unstable region than between sites in the stable region. The high turnover components from CBD and PBD between sites in unstable vs stable regions suggest that these distinct regions have different biogeographic histories. Sites in the stable region shared distinct clades that might have led to greater diversity, whereas sites in the unstable region shared close relatives. Taken together, these results indicate that speciation, environmental filtering and limited dispersal are complementary drivers of beta-diversity of amphibian assemblages in the Brazilian Atlantic Forest.     

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.     

Partitioning the effects of algal species identity and richness on benthic marine primary production

Influential research in terrestrial habitats indicates that several ecosystem processes are related to plant biodiversity, yet these links remain poorly studied in marine ecosystems. We conducted one field and one mesocosm experiment to quantify the relative effects of macroalgal species identity and richness on primary production in coral reef macroalgal communities off the north coast of Jamaica. We measured production as the net accumulation of algal biomass in the absence of consumers and as photosynthetic rate using oxygen probes in sealed aquaria. We used two recently developed techniques to attribute deviations in expected relative yield to components associated with species identity or diversity and then to further partition diversity effects into mechanistic components based on dominance, trait-dependent complementarity, and trait-independent complementarity. Our results indicate that algal identity had far greater effects on absolute net growth and photosynthesis than richness. The most diverse mixture of macroalgae did not outperform the most productive monoculture or the average monoculture in either measure of primary production (i.e. we did not find evidence of either transgressive or non-transgressive overyielding). Trait-independent complementarity effects were positive but dominance and trait-dependent complementarity were both negative and became stronger when richness was increased. Thus the potentially positive influence of species interactions and niche partitioning on production were negated by dominance and other negative selection effects. These results demonstrate that the counteracting influence of component effects can diminish the net richness effects on production. This could explain frequently observed weak net richness effects in other aquatic and terrestrial systems and suggests that life history tradeoffs greatly reduce the potential for ecologically relevant plant biodiversity effects on ecosystem properties.     

Incorporating functional dissimilarities into sample‐based rarefaction curves: from taxon resampling to functional resampling

Question: Indices of functional diversity have been seen as the key for integrating information on species richness with measures that focus on those components of community composition related to ecosystem functioning. For comparing species richness among habitats on an equal‐effort basis, so‐called sample‐based rarefaction curves may be used. Given a study area that is sampled for species presence and absence in N plots, sample‐based rarefaction generates the expected number of accumulated species as the number of sampled plots increases from 1 to N. Accordingly, the question for this study is: can we construct a ‘functional rarefaction curve’ that summarizes the expected functional dissimilarity between species when n plots are drawn at random from a larger pool of N plots? Methods: In this paper, we propose a parametric measure of functional diversity that is obtained by combining sample‐based rarefaction techniques that are usually applied to species richness with Rao's quadratic diversity. For a given set of N presence/absence plots, the resulting measure summarizes the expected functional dissimilarity at an increasingly larger cumulative number of plots n (n≤N). Results and Conclusions: Due to its parametric nature, the proposed measure is progressively more sensitive to rare species with increasing plot number, thus rendering this measure adequate for comparing the functional diversity of species assemblages that have been sampled with variable effort.     

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

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Computing additive beta-diversity from presence and absence scores: a critique and alternative parameters

Whittaker first proposed to measure the variation in species composition among plots or beta-diversity as the ratio between regional diversity (gamma-diversity) and average local diversity (alpha-diversity). More recently, an alternative way of partitioning diversity for which beta-diversity is obtained as the difference between gamma-diversity and average alpha-diversity has become very popular for linking the structure of species assemblages to ecosystem functioning in a spatially explicit manner. Unfortunately, additive beta-diversity computed from species presences and absences suffers from the major drawback of being dependent on regional species richness. For instance, if the separation between beta-diversity and gamma-diversity is incomplete, so that variation in species composition is affected by species richness, then differences in beta-diversity values among different sets of plots could reflect differences in the species count rather than any fundamental difference in species composition among the plots. Based on the above observation, in this paper I will first propose a basic requirement for beta-diversity measures that adequately captures our intuitive notion of independence of species richness. Next, I will show that additive beta-diversity computed from species presence and absence scores can be interpreted within the framework of fuzzy set theory. Finally, based on this unusual "fuzzy" interpretation of additive beta-diversity, I will introduce two families of parametric beta-diversity measures whose members have varying sensitivities to the presence of rare and frequent species.