Phylogenetic diversity measures based on Hill numbers

We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional parametric species-neutral approach (based on 'effective number of species' or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on 'total phylogenetic length') to incorporate species abundances. The proposed measure quantifies 'the mean effective number of species' over any time interval of interest, or the 'effective number of maximally distinct lineages' over that time interval. The product of the measure and the interval length quantifies the 'branch diversity' of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning.     

Neutral Theory Predicts the Relative Abundance and Diversity of Genetic Elements in a Broad Array of Eukaryotic Genomes

It is universally true in ecological communities, terrestrial or aquatic, temperate or tropical, that some species are very abundant, others are moderately common, and the majority are rare. Likewise, eukaryotic genomes also contain classes or “species” of genetic elements that vary greatly in abundance: DNA transposons, retrotransposons, satellite sequences, simple repeats and their less abundant functional sequences such as RNA or genes. Are the patterns of relative species abundance and diversity similar among ecological communities and genomes? Previous dynamical models of genomic diversity have focused on the selective forces shaping the abundance and diversity of transposable elements (TEs). However, ideally, models of genome dynamics should consider not only TEs, but also the diversity of all genetic classes or “species” populating eukaryotic genomes. Here, in an analysis of the diversity and abundance of genetic elements in >500 eukaryotic chromosomes, we show that the patterns are consistent with a neutral hypothesis of genome assembly in virtually all chromosomes tested. The distributions of relative abundance of genetic elements are quite precisely predicted by the dynamics of an ecological model for which the principle of functional equivalence is the main assumption. We hypothesize that at large temporal scales an overarching neutral or nearly neutral process governs the evolution of abundance and diversity of genetic elements in eukaryotic genomes.     

Towards a unifying approach to diversity measures: bridging the gap between the Shannon entropy and Rao's quadratic index

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity (Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.     

The generalized replication principle and the partitioning of functional diversity into independent alpha and beta components

The replication principle was first proposed by Hill (1973, Ecology 54: 247– 432) as an advantageous property of his family of diversity indices. Later Jost (2007, Ecology 88: 2427– 2439) discovered that diversity measures satisfying this principle allow partitioning of gamma diversity into independent alpha and beta components by simple multiplicative partitioning. Despite the emerging agreement on measuring taxonomic beta‐diversity by multiplicative partitioning of Hill diversity, there is no consensus on how to measure functional beta diversity. Two different generalizations of Hill numbers for measuring functional diversity were proposed by Leinster and Cobbold (2011, Ecology 93: 477– 489) and Chiu and Chao (2014, PLoS One 9: e1000014). Both generalizations attempted to satisfy the generalized replication principle, but they formulate it in different ways. The aims of this paper are 1) to review approaches for measuring functional diversity in units of equivalent numbers without explicit reference to replication principle; 2) to compare the two proposed replication principle and to point out some important differences in the behavior of diversity families derived from the two principles; 3) to explore the conditions necessary for partitioning functional diversity of Leinster and Cobbold into meaningful alpha and beta components; 4) and, finally, to explore how transformation of among‐species distances into similarities influences the sensitivity of functional diversity to the scale parameter.     

Diversity of Basidiomycetes in Michigan Agricultural Soils

We analyzed the communities of soil basidiomycetes in agroecosystems that differ in tillage history at the Kellogg Biological Station Long-Term Ecological Research site near Battle Creek, Michigan. The approach combined soil DNA extraction through a bead-beating method modified to increase recovery of fungal DNA, PCR amplification with basidiomycete-specific primers, cloning and restriction fragment length polymorphism screening of mixed PCR products, and sequencing of unique clones. Much greater diversity was detected than was anticipated in this habitat on the basis of culture-based methods or surveys of fruiting bodies. With “species” defined as organisms yielding PCR products with ≥99% identity in the 5′ 650 bases of the nuclear large-subunit ribosomal DNA, 241 “species” were detected among 409 unique basidiomycete sequences recovered. Almost all major clades of basidiomycetes from basidiomycetous yeasts and other heterobasidiomycetes through polypores and euagarics (gilled mushrooms and relatives) were represented, with a majority from the latter clade. Only 24 of 241 “species” had 99% or greater sequence similarity to named reference sequences in GenBank, and several clades with multiple “species” could not be identified at the genus level by phylogenetic comparisons with named sequences. The total estimated “species” richness for this 11.2-ha site was 367 “species” of basidiomycetes. Since >99% of the study area has not been sampled, the accuracy of our diversity estimate is uncertain. Replication in time and space is required to detect additional diversity and the underlying community structure.     

Evolutionary processes,dispersal limitation and climatic history shape current diversity patterns of European dragonflies

We investigated the effects of contemporary and historical factors on the spatial variation of European dragonfly diversity. Specifically, we tested to what extent patterns of endemism and phylogenetic diversity of European dragonfly assemblages are structured by 1) phylogenetic conservatism of thermal adaptations and 2) differences in the ability of post‐glacial recolonization by species adapted to running waters (lotic) and still waters (lentic). We investigated patterns of dragonfly diversity using digital distribution maps and a phylogeny of 122 European dragonfly species, which we constructed by combining taxonomic and molecular data. We calculated total taxonomic distinctiveness and mean pairwise distances across 4192 50 × 50 km equal‐area grid cells as measures of phylogenetic diversity. We compared species richness with corrected weighted endemism and standardized effect sizes of mean pairwise distances or residuals of total taxonomic distinctiveness to identify areas with higher or lower phylogenetic diversity than expected by chance. Broken‐line regression was used to detect breakpoints in diversity–latitude relationships. Dragonfly species richness peaked in central Europe, whereas endemism and phylogenetic diversity decreased from warm areas in the south‐west to cold areas in the north‐east and with an increasing proportion of lentic species. Except for species richness, all measures of diversity were consistently higher in formerly unglaciated areas south of the 0°C isotherm during the Last Glacial Maximum than in formerly glaciated areas. These results indicate that the distributions of dragonfly species in Europe were shaped by both phylogenetic conservatism of thermal adaptations and differences between lentic and lotic species in the ability of post‐glacial recolonization/dispersal in concert with the climatic history of the continent. The complex diversity patterns of European dragonflies provide an example of how integrating climatic and evolutionary history with contemporary ecological data can improve our understanding of the processes driving the geographical variation of biological diversity.     

An index for measuring functional extension and evenness in trait space

Most existing functional diversity indices focus on a single facet of functional diversity. Although these indices are useful for quantifying specific aspects of functional diversity, they often present some conceptual or practical limitations in estimating functional diversity. Here, we present a new functional extension and evenness (FEE) index that encompasses two important aspects of functional diversity. This new index is based on the straightforward notion that a community has high diversity when its species are distant from each other in trait space. The index quantifies functional diversity by evaluating the overall extension of species traits and the interspecific differences of a species assemblage in trait space. The concept of minimum spanning tree (MST) of points was adopted to obtain the essential distribution properties for a species assembly in trait space. We combined the total length of MST branches (extension) and the variation of branch lengths (evenness) into a raw FEE₀ metric and then translated FEE₀ to a species richness‐independent FEE index using a null model approach. We assessed the properties of FEE and used multiple approaches to evaluate its performance. The results show that the FEE index performs well in quantifying functional diversity and presents the following desired properties: (a) It allows a fair comparison of functional diversity across different species richness levels; (b) it preserves the essence of single‐facet indices while overcoming some of their limitations; (c) it standardizes comparisons among communities by taking into consideration the trait space of the shared species pool; and (d) it has the potential to distinguish among different community assembly processes. With these attributes, we suggest that the FEE index is a promising metric to inform biodiversity conservation policy and management, especially in applications at large spatial and/or temporal scales.     

Abundance decline in the avifauna of the European Union reveals cross‐continental similarities in biodiversity change

Although global assessments provide evidence of biodiversity decline, some have questioned the strength of the evidence, with local assemblage studies often showing a more balanced picture of biodiversity change. The multifaceted nature of biodiversity and imperfect monitoring datasets may partially explain these findings. Here, using an extensive dataset, we find significant biodiversity loss in the native avifauna of the European Union (EU). We estimate a decline of 17–19% in the overall breeding bird abundance since 1980: a loss of 560–620 million individual birds. Both total and proportional declines in bird numbers are high among species associated with agricultural land. The distribution of species’ population growth rates (ln) is centered close to zero, with numerical decline driven by substantial losses in abundant species. Our work supports previous assessments indicating substantial recent biodiversity loss and calls to reduce the threat of extinctions and restore species’ abundances, for the sake of nature and people.     

Life in the desert: The impact of geographic and environmental gradients on genetic diversity and population structure of Ivesia webberi

For range‐restricted species with disjunct populations, it is critical to characterize population genetic structure, gene flow, and factors that influence functional connectivity among populations in order to design effective conservation programs. In this study, we genotyped 314 individuals from 16 extant populations of Ivesia webberi, a United States federally threatened Great Basin Desert using six microsatellite loci. We assessed the effects of Euclidean distance, landscape features, and ecological dissimilarity on the pairwise genetic distance of the sampled populations, while also testing for a potential relationship between I. webberi genetic diversity and diversity in the vegetative communities. The results show low levels of genetic diversity overall (H _e = 0.200–0.441; H _o = 0.192–0.605) and high genetic differentiation among populations. Genetic diversity was structured along a geographic gradient, congruent with patterns of isolation by distance. Populations near the species’ range core have relatively high genetic diversity, supporting in part a central‐marginal pattern, while also showing some evidence for a metapopulation dynamic. Peripheral populations have lower genetic diversity, significantly higher genetic distances, and higher relatedness. Genotype cluster admixture results suggest a complex dispersal pattern among populations with dispersal direction and distance varying on the landscape. Pairwise genetic distance strongly correlates with elevation, actual evapotranspiration, and summer seasonal precipitation, indicating a role for isolation by environment, which the observed phenological mismatches among the populations also support. The significant correlation between pairwise genetic distance and floristic dissimilarity in the germinated soil seed bank suggests that annual regeneration in the plant communities contribute to the maintenance of genetic diversity in I. webberi.     

Allometric ecological distributions in a local community of Hymenoptera

The present paper describes basic ecological distributions in a community of beech forest Hymenoptera. It shows that the species diversity–body weight and the density–body weight distributions give rise to a new distribution that relates total community biomass to species diversity. For Hymenoptera this distribution follows a power function with a slope of 1.3. Combining this relation with the species–area and the individuals–area relations resulted in two other distributions that relate community biomass to area and individual numbers. It appeared that population densities decrease when computed over larger areas. The biomass–species diversity relation offers a new and simple way to estimate total community biomass from samples. The possible implications of this distribution to the productivity–diversity debate are discussed.     

Global variation in the relationship between avian phylogenetic diversity and functional distance is driven by environmental context and constraints

Aim

If evolutionary distance is akin to evolutionary chance, then it follows that species assemblages that are distantly related will also be more disparate in terms of their traits, features and the niches they occupy. Yet, studies have found that the total phylogenetic distance of an assemblage, known as phylogenetic diversity, is an unreliable surrogate for functional diversity. We investigate global variation in the relationship between Faith's phylogenetic diversity (PD) and mean pairwise functional distance (MPFD) across latitude and the influence of migratory species on both these aspects of diversity.

Location

Global.

Time period

Present day.

Major taxa studied

Birds.

Methods

We measure PD and MPFD for over 9000 species of bird across more than 17,000 globally distributed assemblages. We obtain standardised effect sizes for both indices by simulating assemblage composition under an ecologically informed null model. We employ path analysis to characterize variation in the relationship between PD's and MPFD across latitude, elevation and with proportion of migratory species.

Results

Globally, assemblages that were phylogenetically diverse tended to be less functionally dispersed than expected; however, this relationship showed considerable variation across latitude decreasing with distance from the equator. The proportion of migratory species in an assemblage was found to be an important predictor of functional diversity, with migrant rich assemblages generally showing less functional diversity than expected. We identify the Andes and Hengduan Mountains as regions of exceptional bird functional diversity.

Main conclusions

The relationship between phylogenetic diversity and function diversity is context specific, varying across environmental gradients such as latitude, and influenced by ecological phenomena such as migration. Thus, care should be taken using phylogenetic diversity as a proxy for functional diversity, particularly in clades with sparse functional data. Instead, we recommend that studies consider how phylogenetic diversity's surrogacy for functional diversity may be impacted by environmental context and evaluate empirical observations against biogeographically constrained and ecologically informed null models.     

Sampled‐based estimation of diversity sensu stricto by transforming Hurlbert diversities into effective number of species

A theoretical framework based on Hill numbers has recently been advocated to measure and partition diversity sensu stricto. Hill numbers can be interpreted intuitively as effective number of species (ENS). They conform to the so‐called replication principle allowing a mathematically coherent multiplicative partitioning of diversity. They form a family of ENS defined by the parameter q which controls the weight attributed to rare species. Despite its advantages, this framework was developed without considering its robustness when treating community samples. In this study, we first show that Hurlbert diversity indices (expected number of species among k individuals) can be transformed into ENS that conform asymptotically to the replication principle while controlling the weight given to rare species through parameter k. We investigate the statistical properties of Hill and Hurlbert ENS using simulated communities with contrasted diversity. The properties of multiplicative beta diversity estimators based on ENS are also characterized by simulating communities with different levels of differentiation. We show that Hurlbert ENS provides a better statistical performance than Hill numbers when dealing with small sample sizes. By contrast, Hill numbers and their estimators suffer from substantial bias except when rare species have a low weight (q= 2). An estimator of ENS estimating both Hill numbers for q= 2 and Hurlbert ENS for k= 2 is shown to give the best performance and is recommended for processing real datasets when rare species receive low weight. In order to better take account of rare species, current estimators of Hill numbers are not recommended when sample size is too low while Hurlbert’s ENS performs reliably. In conclusion, while Hill numbers possess some interesting mathematical properties that are not shared by Hurlbert’s ENS, the latter outperforms Hill numbers in terms of statistical properties and is well suited to processing community samples, as illustrated on a real dataset.     

Chromosome numbers in three species groups of freshwater flatworms increase with increasing latitude

Polyploidy in combination with parthenogenesis offers advantages for plasticity and the evolution of a broad ecological tolerance of species. Therefore, a positive correlation between the level of ploidy and increasing latitude as a surrogate for environmental harshness has been suggested. Such a positive correlation is well documented for plants, but examples for animals are still rare. Species of flatworms (Platyhelminthes) are widely distributed, show a remarkably wide range of chromosome numbers, and offer therefore good model systems to study the geographical distribution of chromosome numbers. We analyzed published data on counts of chromosome numbers and geographical information of three flatworm “species” (Phagocata vitta, Polycelis felina and Crenobia alpina) sampled across Europe (220 populations). We used the mean chromosome number across individuals of a population as a proxy for the level of ploidy within populations, and we tested for relationships of this variable with latitude, mode of reproduction (sexual, asexual or both) and environmental variables (annual mean temperature, mean diurnal temperature range, mean precipitation and net primary production). The mean chromosome numbers of all three species increased with latitude and decreased with mean annual temperature. For two species, chromosome number also decreased with mean precipitation and net primary production. Furthermore, high chromosome numbers within species were accompanied with a loss of sexual reproduction. The variation of chromosome numbers within individuals of two of the three species increased with latitude. Our results support the hypothesis that polyploid lineages are able to cope with harsh climatic conditions at high latitudes. Furthermore, we propose that asexual reproduction in populations with high levels of polyploidization stabilizes hybridization events. Chromosomal irregularities within individuals tend to become more frequent at the extreme environments of high latitudes, presumably because of mitotic errors and downsizing of the genome.     

The ecology of differences: assessing community assembly with trait and evolutionary distances

Species enter and persist in local communities because of their ecological fit to local conditions, and recently, ecologists have moved from measuring diversity as species richness and evenness, to using measures that reflect species ecological differences. There are two principal approaches for quantifying species ecological differences: functional (trait‐based) and phylogenetic pairwise distances between species. Both approaches have produced new ecological insights, yet at the same time methodological issues and assumptions limit them. Traits and phylogeny may provide different, and perhaps complementary, information about species' differences. To adequately test assembly hypotheses, a framework integrating the information provided by traits and phylogenies is required. We propose an intuitive measure for combining functional and phylogenetic pairwise distances, which provides a useful way to assess how functional and phylogenetic distances contribute to understanding patterns of community assembly. Here, we show that both traits and phylogeny inform community assembly patterns in alpine plant communities across an elevation gradient, because they represent complementary information. Differences in historical selection pressures have produced variation in the strength of the trait‐phylogeny correlation, and as such, integrating traits and phylogeny can enhance the ability to detect assembly patterns across habitats or environmental gradients.     

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.     

Rarity facets of biodiversity: Integrating Zeta diversity and Dark diversity to understand the nature of commonness and rarity

Measuring commonness and rarity is pivotal to ecology and conservation. Zeta diversity, the average number of species shared by multiple sets of assemblages, and Dark diversity, the number of species that could occur in an assemblage but are missing, have been recently proposed to capture two aspects of the commonness‐rarity spectrum. Despite a shared focus on commonness and rarity, thus far, Zeta and Dark diversities have been assessed separately. Here, we review these two frameworks and suggest their integration into a unified paradigm of the “rarity facets of biodiversity.” This can be achieved by partitioning Alpha and Beta diversities into five components (the Zeta, Eta, Theta, Iota, and Kappa rarity facets) defined based on the commonness and rarity of species. Each facet is assessed in traditional and multiassemblage fashions to bridge conceptual differences between Dark diversity and Zeta diversity. We discuss applications of the rarity facets including comparing the taxonomic, functional, and phylogenetic diversity of rare and common species, or measuring species'' prevalence in different facets as a metric of species rarity. The rarity facets integrate two emergent paradigms in biodiversity science to better understand the ecology of commonness and rarity, an important endeavor in a time of widespread changes in biodiversity across the Earth.     

Horizontal gradient in fish assemblage structures in and around a seagrass habitat: some implications for seagrass habitat conservation

Horizontal gradients in fish assemblage structures in and around a seagrass habitat were evaluated by visual observations. The assemblage structures clearly differed between open microhabitats lacking seagrass, i.e., nearby sand and the area adjoining the outer margin of the seagrass bed (referred to as “outer gap”), and microhabitats with seagrass within the overall seagrass bed, although not differing among the latter microhabitats, including both edge and core portions. Such open microhabitats were found to be not always inferior, but nearly equal to or even sometimes greatly superior in fish species’ diversity and/or abundance to the microhabitats with seagrass. In particular, the outer gap was always ranked first in total species’ number and had outstanding abundance in spring. Similar open microhabitats adjoining seagrass walls facing the sand patch within the seagrass bed (referred to as “inner gap”) in spring were also characterized by higher fish species and individual numbers. The 11 most abundant fishes showed four discrete distribution patterns (three recognized herein and one implied by precedent studies), such contributing to a horizontal gradient in the fish assemblage structure. While no fishes showed a preference for the edge or core of the seagrass bed, group-forming juveniles of several species favored gap microhabitats, suggesting that, in addition to the traditionally recognized edge and core microhabitats, the concept of gap microhabitats should be included in seagrass conservation ecology.     

Effects of Previous Land-Use on Plant Species Composition and Diversity in Mediterranean Forests

At some point in their history, most forests in the Mediterranean Basin have been subjected to intensive management or converted to agriculture land. Knowing how forest plant communities recovered after the abandonment of forest-management or agricultural practices (including livestock grazing) provides a basis for investigating how previous land management have affected plant species diversity and composition in forest ecosystems. Our study investigated the consequences of historical “land management” practices on present-day Mediterranean forests by comparing species assemblages and the diversity of (i) all plant species and (ii) each ecological group defined by species’ habitat preferences and successional status (i.e., early-, mid-, and late-successional species). We compared forest stands that differed both in land-use history and in successional stage. In addition, we evaluated the value of those stands for biodiversity conservation. The study revealed significant compositional differentiation among stands that was due to among-stand variations in the diversity (namely, species richness and evenness) of early-, intermediate-, and late-successional species. Historical land management has led to an increase in compositional divergences among forest stands and the loss of late-successional forest species.     

The Tenebrionidae of California: A Time Sensitive Snapshot Assessment

Due to a diversity of habitats and its geologic history, the US state of California hosts a spectacular assemblage of darkling beetle species (Coleoptera: Tenebrionidae). In addition to being part of the California Floristic Province, one of 34 global biodiversity hotspots identified by Conservation International, California also has additional areas which are parts of the Great Basin, Mojave, and Sonoran deserts. California is divided into nine floristic regions. Each region is assessed in terms of faunal composition and endemism. A “snapshot” of our present knowledge of the Tenebrionidae indicates that 447 currently recognized species, representing 108 genera, occur in California of which one hundred and ninety are endemic. California is compared to other nearby regions in diversity and endemism. An analysis of currently valid species vs a more realistic species account based on unpublished records of likely synonyms and known species yet to be described in the scientific literature is presented. The California Floristic Region, rather than other more arid parts of California, has the highest number of total and endemic species. Because of their high diversity and endemism, tenebrionids could potentially provide a valuable tool for monitoring the environment for conservation purposes.