An information-theoretical measure of taxonomic diversity

Traditional diversity indices are computed from the abundances of species present and are insensitive to taxonomic differences between species. However, a community in which most species belong to the same genus is intuitively less diverse than another community with a similar number of species distributed more evenly between genera. In this paper, we propose an information-theoretical measure of taxonomic diversity that reflects both the abundances and taxonomic distinctness of the species. Unlike previous measures of taxonomic diversity, such as Rao's quadratic entropy, in this new measure the analyzed taxonomic properties are associated with the single species instead of species pairs.     

A parametric diversity measure combining the relative abundances and taxonomic distinctiveness of species

Most ecological diversity indices summarize the information about the relative abundances of species without reflecting taxonomic differences between species. Nevertheless, in environmental conservation practice, data on species abundances are mostly irrelevant and generally unknown. In such cases, to summarize the conservation value of a given site, so‐called ‘taxonomic diversity’ measures can be used. Such measures are based on taxonomic relations among species and ignore species relative abundances. In this paper, bridging the gap between traditional biodiversity measures and taxonomic diversity measures, I introduce a parametric diversity index that combines species relative abundances with their taxonomic distinctiveness. Due to the parametric nature of the proposed index, the contribution of rare and abundant species to each diversity measure is explicit.     

Functional diversity (FD), species richness and community composition

Functional diversity is an important component of biodiversity, yet in comparison to taxonomic diversity, methods of quantifying functional diversity are less well developed. Here, we propose a means for quantifying functional diversity that may be particularly useful for determining how functional diversity is related to ecosystem functioning. This measure of functional diversity “FD” is defined as the total branch length of a functional dendrogram. Various characteristics of FD make it preferable to other measures of functional diversity, such as the number of functional groups in a community. Simulating species' trait values illustrates how the relative importance of richness and composition for FD depends on the effective dimensionality of the trait space in which species separate. Fewer dimensions increase the importance of community composition and functional redundancy. More dimensions increase the importance of species richness and decreases functional redundancy. Clumping of species in trait space increases the relative importance of community composition. Five natural communities show remarkably similar relationships between FD and species richness.     

Does taxonomic homogenization imply functional homogenization in temperate forest herb layer communities?

Biotic homogenization, the decrease in beta diversity among formerly distinct species assemblages, has been recognized as an important form of biotic impoverishment for more than a decade. Although researchers have stressed the importance of the functional dimension to understand its potential ecological consequences, biotic homogenization has mostly been studied at a taxonomic level. Here, we explore the relationship between taxonomic and functional homogenization using data on temperate forest herb layer communities in NW Germany, for which taxonomic homogenization has recently been demonstrated. We quantified beta diversity by partitioning Rao’s quadratic entropy. We found a general positive relationship between changes in taxonomic and functional beta diversity. This relationship was stronger if multiple functional traits were taken into account. Averaged across sites, however, taxonomic homogenization was not consistently accompanied by functional homogenization. Depending on the traits considered, taxonomic homogenization occurred also together with functional differentiation or no change in functional beta diversity. The species shifts responsible for changes in beta diversity differed substantially between taxonomic and functional beta diversity measures and also among functional beta diversity measures based on different traits. We discuss likely environmental drivers for species shifts. Our study demonstrates that functional homogenization must be explicitly studied as an independent phenomenon that cannot be inferred from taxonomic homogenization.     

The Evolution of Taxonomic Diversity in Helminth Assemblages of Mammalian Hosts

Several studies have searched for the key forces behind the diversification of parasite assemblages over evolutionary time. All of these studies have used parasite species richness as their measure of diversity, thus ignoring the relatedness among parasite species and the taxonomic structure of the assemblages. This information is essential, however, if we want to elucidate which processes have caused an assemblage of parasites to acquire new species. Here, we performed a comparative analysis across 110 species of mammalian hosts in which we evaluated the effects of four host traits (body mass, population density, geographic range, and basal metabolic rate) on the diversity of their assemblages of helminth endoparasites. As measures of diversity, we used parasite species richness, as well as the average taxonomic distinctness of the assemblage and its variance; the latter measures are based on the taxonomic distance between two parasite species, computed across all possible species pairs in an assemblage. Unlike parasite species richness, both the average taxonomic distinctness and its variance were unaffected by the number of hosts examined. These two measures of parasite diversity also proved highly repeatable among host populations of the same mammalian species; in contrast, parasite species richness was unreliable as a species character, as it varied as much within a host species than among different host species. Using phylogenetically independent contrasts, and correcting for potential confounding variables, we found that host population density correlated positively with parasite species richness. There were, however, no other relationships between any of the four host traits investigated and either of our measures of parasite diversity. The processes facilitating the taxonomic diversification of parasite assemblages thus remain unclear, but their elucidation will be necessary if we are to fully understand parasite evolution.     

Parametric scaling from species relative abundances to absolute abundances in the computation of biological diversity: a first proposal using Shannon's entropy

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total information content as special cases of this more general function.     

Responses of taxonomic distinctness and species diversity indices to anthropogenic impacts and natural environmental gradients in stream macroinvertebrates

1. Many studies have shown traditional species diversity indices to perform poorly in discriminating anthropogenic influences on biodiversity. By contrast, in marine systems, taxonomic distinctness indices that take into account the taxonomic relatedness of species have been shown to discriminate anthropogenic effects. However, few studies have examined the performance of taxonomic distinctness indices in freshwater systems. 2. We studied the performance of four species diversity indices and four taxonomic distinctness indices for detecting anthropogenic effects on stream macroinvertebrate assemblages. Further, we examined the effects of catchment type and area, as well as two variables (pH and total phosphorus) potentially describing anthropogenic perturbation on biodiversity. 3. We found no indications of degraded biodiversity at the putatively disturbed sites. However, species density, rarefied species richness, Shannon's diversity and taxonomic diversity showed higher index values in streams draining mineral as opposed to peatland catchments. 4. Of the major environmental gradients analysed, biodiversity indices showed the strongest relationships with catchment area, lending further support to the importance of stream size for macroinvertebrate biodiversity. Some of the indices also showed weak linear and quadratic relationships to pH and total phosphorus, and residuals from the biodiversity index‐catchment area regressions (i.e. area effect standardized) were more weakly related to pH and total phosphorus than the original index values. 5. There are a number of reasons why the biodiversity indices did not respond to anthropogenic perturbation. First, some natural environmental gradients may mask the effects of perturbation on biodiversity. Secondly, perturbations of riverine ecosystems in our study area may not be strong enough to cause drastic changes in biodiversity. Thirdly, multiple anthropogenic stressors may either increase or decrease biodiversity, and thus the coarse division of sites into reference and altered streams may be an oversimplification. 6. Although neither species diversity nor taxonomic distinctness indices revealed anthropogenic degradation of macroinvertebrate assemblages in this study, the traditional species diversity and taxonomic distinctness indices were very weakly correlated. Therefore, we urge that biodiversity assessment and conservation planning should utilize a number of different indices, as they may provide complementary information about biotic assemblages.     

Partitioning diversity for conservation analyses

Aim  Differentiation of sites or communities is often measured by partitioning regional or gamma diversity into additive or multiplicative alpha and beta components. The beta component and the ratio of within-group to total diversity (alpha/gamma) are then used to infer the compositional differentiation or similarity of the sites. There is debate about the appropriate measures and partitioning formulas for this purpose. We test the main partitioning methods, using empirical and simulated data, to see if some of these methods lead to false conclusions, and we show how to resolve the problems that we uncover.
Location  South America, Ecuador, Orellana province, Rio Shiripuno.
Methods  We construct sets of real and simulated tropical butterfly communities that can be unambiguously ranked according to their degree of differentiation. We then test whether beta and similarity measures from the different partitioning approaches rank these datasets correctly.
Results  The ratio of within-group diversity to total diversity does not reflect compositional similarity, when the Gini–Simpson index or Shannon entropy are used to measure diversity. Additive beta diversity based on the Gini–Simpson index does not reflect the degree of differentiation between N sites or communities.
Main conclusions  The ratio of within-group to total diversity (alpha/gamma) should not be used to measure the compositional similarity of groups, if diversity is equated with Shannon entropy or the Gini–Simpson index. Conversion of these measures to effective number of species solves these problems. Additive Gini–Simpson beta diversity does not directly reflect the differentiation of N samples or communities. However, when properly transformed onto the unit interval so as to remove the dependence on alpha and N , additive and multiplicative beta measures yield identical normalized measures of relative similarity and differentiation.     

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.     

Parametric scaling from species to growth-form diversity: an interesting analogy with multifractal functions

We propose a measure of divergence from species to life-form diversity aimed at summarizing the ecological similarity among different plant communities without losing information on traditional taxonomic diversity. First, species and life-form relative abundances within a given plant community are determined. Next, using Rényi's generalized entropy, the diversity profiles of the analyzed community are computed both from species and life-form relative abundances. Finally, the speed of decrease from species to life-form diversity is obtained by combining the outcome of both profiles. Interestingly, the proposed measure shows some formal analogies with multifractal functions developed in statistical physics for the analysis of spatial patterns. As an application for demonstration, a small data set from a plant community sampled in the archaeological site of Paestum (southern Italy) is used.     

Measuring beta‐diversity from taxonomic similarity

Question: The utility of beta (β‐) diversity measures that incorporate information about the degree of taxonomic (dis)similarity between species plots is becoming increasingly recognized. In this framework, the question for this study is: can we define an ecologically meaningful index of β‐diversity that, besides indicating simple species turnover, is able to account for taxonomic similarity amongst species in plots? Methods: First, the properties of existing measures of taxonomic similarity measures are briefly reviewed. Next, a new measure of plot‐to‐plot taxonomic similarity is presented that is based on the maximal common subgraph of two taxonomic trees. The proposed measure is computed from species presences and absences and include information about the degree of higher‐level taxonomic similarity between species plots. The performance of the proposed measure with respect to existing coefficients of taxonomic similarity and the coefficient of Jaccard is discussed using a small data set of heath plant communities. Finally, a method to quantify β‐diversity from taxonomic dissimilarities is discussed. Results: The proposed measure of taxonomic β‐diversity incorporates not only species richness, but also information about the degree of higher‐order taxonomic structure between species plots. In this view, it comes closer to a modern notion of biological diversity than more traditional measures of β‐di‐versity. From regression analysis between the new coefficient and existing measures of taxonomic similarity it is shown that there is an evident nonlinearity between the coefficients. This nonlinearity demonstrates that the new coefficient measures similarity in a conceptually different way from previous indices. Also, in good agreement with the findings of previous authors, the regression between the new index and the Jaccard coefficient of similarity shows that more than 80% of the variance of the former is explained by the community structure at the species level, while only the residual variance is explained by differences in the higher‐order taxonomic structure of the species plots. This means that a genuine taxonomic approach to the quantification of plot‐to‐plot similarity is only needed if we are interested in the residual system's variation that is related to the higher‐order taxonomic structure of a pair of species plots.     

Diversity partitioning of Rao’s quadratic entropy

Many applications of diversity indices are only valid if they are first transformed into their equivalent number of species. These equivalent numbers of species can be multiplicatively partitioned into independent alpha, beta and gamma components, and can be formed into mathematically consistent similarity measures. The utility of beta diversity and similarity measures that incorporate information about the degree of ecological dissimilarity between species is becoming increasingly recognized. The concept of equivalent number of species is here extended to Rao’s quadratic entropy, opening the way to methods of diversity partitioning that take into account taxonomic or ecological differences between species.     

A ‘fast-food approach’ to the standardization of quadratic diversity

Abstract

Intuitively, a community composed of ecologically dissimilar taxa is more diverse than a community composed of more similar taxa. However, since traditional diversity indices such as Shannon's entropy or Simpson's diversity are computed solely from the relative abundances of a given species assemblage, they cannot account for ecological differences between species. There have been recent developments regarding the use of quadratic entropy, a diversity index that incorporates both species relative abundances and a measure of the pairwise ecological differences between species. In this paper we firstly show that under some specific circumstances quadratic entropy can be additively decomposed into α- β- and γ-diversities, a property that renders it a desirable measure of diversity in the ecological practice. Next, we suggest a quick and simple method for obtaining a standardized version of quadratic entropy that may allow an easier interpretation of the resulting diversity values.     

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.     

Combining richness and abundance into a single diversity index using matrix analogues of Shannon's and Simpson's indices

Shannon's and Simpson's indices have been the most widely accepted measures of ecological diversity for the past fifty years, even though neither statistic accounts for species abundances across geographic locales ("patches"). An abundant species that is endemic to a single patch can be as much of a conservation concern as a rare cosmopolitan species. I extend Shannon's and Simpson's indices to simultaneously account for species richness and relative abundances – i.e. extend them to multispecies metacommunities – by making the inputs to each index a matrix, rather than a vector. The Shannon's index analogue of diversity is mutual entropy of species and patches divided by marginal entropy of the individual geographic patches. The Simpson's index analogue of diversity is a modification of mutual entropy, with the logarithm moved to the outside of the summation, divided by Simpson's index of the patches. Both indices are normalized for number of patches, with the result being inversely proportional to biodiversity. These methods can be extended to account for time-series of such matrices and average age-classes of each species within each patch, as well as provide a measure of spatial coherence of communities.     

A comparative test of phylogenetic diversity indices

Traditional measures of biodiversity, such as species richness, usually treat species as being equal. As this is obviously not the case, measuring diversity in terms of features accumulated over evolutionary history provides additional value to theoretical and applied ecology. Several phylogenetic diversity indices exist, but their behaviour has not yet been tested in a comparative framework. We provide a test of ten commonly used phylogenetic diversity indices based on 40 simulated phylogenies of varying topology. We restrict our analysis to a topological fully resolved tree without information on branch lengths and species lists with presence-absence data. A total of 38,000 artificial communities varying in species richness covering 5-95% of the phylogenies were created by random resampling. The indices were evaluated based on their ability to meet a priori defined requirements. No index meets all requirements, but three indices turned out to be more suitable than others under particular conditions. Average taxonomic distinctness (AvTD) and intensive quadratic entropy (J) are calculated by averaging and are, therefore, unbiased by species richness while reflecting phylogeny per se well. However, averaging leads to the violation of set monotonicity, which requires that species extinction cannot increase the index. Total taxonomic distinctness (TTD) sums up distinctiveness values for particular species across the community. It is therefore strongly linked to species richness and reflects phylogeny per se weakly but satisfies set monotonicity. We suggest that AvTD and J are best applied to studies that compare spatially or temporally rather independent communities that potentially vary strongly in their phylogenetic composition-i.e. where set monotonicity is a more negligible issue, but independence of species richness is desired. In contrast, we suggest that TTD be used in studies that compare rather interdependent communities where changes occur more gradually by species extinction or introduction. Calculating AvTD or TTD, depending on the research question, in addition to species richness is strongly recommended.     

Functional dominance rather than taxonomic diversity and functional diversity mainly affects community aboveground biomass in the Inner Mongolia grassland

The relationship between biodiversity and productivity has been a hot topic in ecology. However, the relative importance of taxonomic diversity and functional characteristics (including functional dominance and functional diversity) in maintaining community productivity and the underlying mechanisms (including selection and complementarity effects) of the relationship between diversity and community productivity have been widely controversial. In this study, 194 sites were surveyed in five grassland types along a precipitation gradient in the Inner Mongolia grassland of China. The relationships between taxonomic diversity (species richness and the Shannon–Weaver index), functional dominance (the community‐weighted mean of four plant traits), functional diversity (Rao's quadratic entropy), and community aboveground biomass were analyzed. The results showed that (1) taxonomic diversity, functional dominance, functional diversity, and community aboveground biomass all increased from low to high precipitation grassland types; (2) there were significant positive linear relationships between taxonomic diversity, functional dominance, functional diversity, and community aboveground biomass; (3) the effect of functional characteristics on community aboveground biomass is greater than that of taxonomic diversity; and (4) community aboveground biomass depends on the community‐weighted mean plant height, which explained 57.1% of the variation in the community aboveground biomass. Our results suggested that functional dominance rather than taxonomic diversity and functional diversity mainly determines community productivity and that the selection effect plays a dominant role in maintaining the relationship between biodiversity and community productivity in the Inner Mongolia grassland.     

Can taxonomic distinctness assess anthropogenic impacts in inland waters? A case study from a Mediterranean river basin

1. It is increasingly recognised that adequate measures of biodiversity should include information on the ‘relatedness’ of species within ecological assemblages, or the phylogenetic levels at which diversity is expressed. Taxonomic distinctness measures provide a series of indices to achieve this, which are independent of sample size. Taxonomic distinctness has been employed widely in marine systems, where it has been suggested that this index can provide a reliable measure of anthropogenic impact. 2. We tested the behaviour of three related taxonomic distinctiveness indices (Average Taxonomic Distinctness, Δ⁺; Variation in Taxonomic Distinctness, Λ⁺; and Total Taxonomic Distinctness, sΔ⁺) in relation to putative levels of anthropogenic impact in inland waters and their potential utility in environmental monitoring, using an extensive data set for aquatic beetles from the south‐east of the Iberian Peninsula. 3. Taxonomic distinctness measures were not able to identify human disturbance effects and there were no clear relationships between these new biodiversity measures and the disturbance level recorded at individual localities. Furthermore, the taxonomic distinctness measures used were apparently less sensitive to the effects of anthropogenic impact than other diversity metrics, such as species richness and rarity. 4. We conclude that taxonomic distinctness indices may not always perform as well as other metrics in the assessment of environmental quality. In addition, taxonomic distinctness measure should be interpreted with caution, as their performance and ability to detect anthropogenic disturbance may depend on the phylogenetic structure of sampled taxa within a region, and their evolutionary and ecological history.     

Additive partition of parametric information and its associated beta-diversity measure

A desirable property of a diversity index is strict concavity. This implies that the pooled diversity of a given community sample is greater than or equal to but not less than the weighted mean of the diversity values of the constituting plots. For a strict concave diversity index, such as species richness S, Shannon's entropy H or Simpson's index 1-D, the pooled diversity of a given community sample can be partitioned into two non-negative, additive components: average within-plot diversity and between-plot diversity. As a result, species diversity can be summarized at various scales measuring all diversity components in the same units. Conversely, violation of strict concavity would imply the non-interpretable result of a negative diversity among community plots. In this paper, I apply this additive partition model generally adopted for traditional diversity measures to Aczél and Daróczy's generalized entropy of type . In this way, a parametric measure of -diversity is derived as the ratio between the pooled sample diversity and the average within-plot diversity that represents the parametric analogue of Whittaker's -diversity for data on species relative abundances.     

Analysis of the wild potato germplasm of the series Acaulia with AFLPs: implications for ex situ conservation

The wild potato germplasm of the series Acaulia maintained at the Centre for Genetic Resources, The Netherlands, currently consists of 314 accessions. This collection comprises seed samples of the species Solanum acaule (ssp. acaule, ssp. aemulans, ssp. palmirense and ssp. punae) and Solanum albicans collected from South America. In order to validate taxonomic classification, to investigate the extent of redundancy and to study the distribution of genetic diversity across the collection area, the entire collection was analysed with two AFLP primer pairs on two plants per accession. Within the entire sample a total number of 130 polymorphic bands were scored for the two primer pairs. An UPGMA cluster analysis grouped the majority of plants according to the species and subspecies. A total number of 16 misclassifications were identified, including four cases that did not seem to belong to the series Acaulia. Two accessions were found to consist of plants of different AFLP clusters. AFLP data also allowed the taxonomic classification of the subspecies of 97 accessions that previously were described as S. acaule only. For 126 accessions the two individuals studied displayed identical AFLP profiles. Forty six of these 126 accessions shared their profiles with both or single plants of other accessions. These were all tested for identical profiles for a third primer pair, resulting in 15 duplication groups consisting of a total number of 22 accessions and 14 single plants. Analyses of molecular variance (AMOVA) were performed to examine the distribution of genetic variation. Comparison of geographic distances between the collection site of plants and the number of AFLP polymorphisms revealed no consistent relationship between geographic distance and genetic diversity. AFLP analysis appeared to be an efficient method to verify taxonomic classification and to identify redundancies in the wild germplasm of the series Acaulia. Implications of the results for the ex situ conservation of wild potato germplasm are discussed. Received: 6 November 2000 / Accepted: 20 April 2001