Measuring beta-diversity with abundance data (original) (raw)
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Measuring β-diversity with species abundance data
The Journal of animal ecology, 2015
In 2003, 24 presence-absence β-diversity metrics were reviewed and a number of trade-offs and redundancies identified. We present a parallel investigation into the performance of abundance-based metrics of β-diversity. β-diversity is a multi-faceted concept, central to spatial ecology. There are multiple metrics available to quantify it: the choice of metric is an important decision. We test 16 conceptual properties and two sampling properties of a β-diversity metric: metrics should be 1) independent of α-diversity and 2) cumulative along a gradient of species turnover. Similarity should be 3) probabilistic when assemblages are independently and identically distributed. Metrics should have 4) a minimum of zero and increase monotonically with the degree of 5) species turnover, 6) decoupling of species ranks and 7) evenness differences. However, complete species turnover should always generate greater values of β than extreme 8) rank shifts or 9) evenness differences. Metrics should 1...
A conceptual guide to measuring species diversity
Three metrics of species diversity -species richness, the Shannon index and the Simpson index -are still widely used in ecology, despite decades of valid critiques leveled against them. Developing a robust diversity metric has been challenging because, unlike many variables ecologists measure, the diversity of a community often cannot be estimated in an unbiased way based on a random sample from that community. Over the past decade, ecologists have begun to incorporate two important tools for estimating diversity: coverage and Hill diversity. Coverage is a method for equalizing samples that is, on theoretical grounds, preferable to other commonly used methods such as equal-effort sampling, or rarefying datasets to equal sample size. Hill diversity comprises a spectrum of diversity metrics and is based on three key insights. First, species richness and variants of the Shannon and Simpson indices are all special cases of one general equation. Second, richness, Shannon and Simpson can be expressed on the same scale and in units of species. Third, there is no way to eliminate the effect of relative abundance from estimates of any of these diversity metrics, including species richness. Rather, a researcher must choose the relative sensitivity of the metric towards rare and common species, a concept which we describe as 'leverage.' In this paper we explain coverage and Hill diversity, provide guidelines for how to use them together to measure species diversity, and demonstrate their use with examples from our own data. We show why researchers will obtain more robust results when they estimate the Hill diversity of equal-coverage samples, rather than using other methods such as equaleffort sampling or traditional sample rarefaction.
Oecologia, 2009
Almost half a century after Whittaker (Ecol Monogr 30:279–338, 1960) proposed his influential diversity concept, it is time for a critical reappraisal. Although the terms alpha, beta and gamma diversity introduced by Whittaker have become general textbook knowledge, the concept suffers from several drawbacks. First, alpha and gamma diversity share the same characteristics and are differentiated only by the scale at which they are applied. However, as scale is relative––depending on the organism(s) or ecosystems investigated––this is not a meaningful ecological criterion. Alpha and gamma diversity can instead be grouped together under the term “inventory diversity.” Out of the three levels proposed by Whittaker, beta diversity is the one which receives the most contradictory comments regarding its usefulness (“key concept” vs. “abstruse concept”). Obviously beta diversity means different things to different people. Apart from the large variety of methods used to investigate it, the main reason for this may be different underlying data characteristics. A literature review reveals that the multitude of measures used to assess beta diversity can be sorted into two conceptually different groups. The first group directly takes species distinction into account and compares the similarity of sites (similarity indices, slope of the distance decay relationship, length of the ordination axis, and sum of squares of a species matrix). The second group relates species richness (or other summary diversity measures) of two (or more) different scales to each other (additive and multiplicative partitioning). Due to that important distinction, we suggest that beta diversity should be split into two levels, “differentiation diversity” (first group) and “proportional diversity” (second group). Thus, we propose to use the terms “inventory diversity” for within-sample diversity, “differentiation diversity” for compositional similarity between samples, and “proportional diversity” for the comparison of inventory diversity across spatial and temporal scales.
Measures of species diversity in ecology: an evaluation
Twenty-four measures of species diversity, richness and equitability were compared using both real species abundance data (bird censuses on a standard study plot) and simple simulation tests. Based on 20 criteria, the most ecommendable measures for the estimation of alpha diversity of species have been Fager’s “number of moves per specimen”, exponential Shannon’s information (or H’), reciprocal Simpson’s lambda, and species richness (number of species). However, the last index is only appropriate when sample sizes are approximately equal otherwise it can be misleading and Hurlbert’s rarefaction method should be applied. The other measures tested, especially all equitability indices, have been shown to be problematic and should not be used regularly for the measurement of species diversity.
A unified index to measure ecological diversity and species rarity. Ecography 31
2008
Several indices have been created to measure diversity, and the most frequently used are the Shannon-Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S q ; where q is the Tsallis index) and evenness (E q ), based on Tsallis entropy that incorporates the most used indices. It approaches S when q 00, H when q 01 and gives D when q 0 2. In general, varying the value of the Tsallis index (q), S q varies from emphasis on species richness (qB1) to emphasis on dominance (q 1). Similarly, E q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E q
A unified index to measure ecological diversity and species rarity
Ecography, 2008
Several indices have been created to measure diversity, and the most frequently used are the Shannon-Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S q ; where q is the Tsallis index) and evenness (E q ), based on Tsallis entropy that incorporates the most used indices. It approaches S when q 00, H when q 01 and gives D when q 0 2. In general, varying the value of the Tsallis index (q), S q varies from emphasis on species richness (qB1) to emphasis on dominance (q 1). Similarly, E q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E q
Conceptual and statistical problems associated with the use of diversity indices in ecology
Revista de Biología Tropical, 2008
Diversity indices, particularly the Shannon-Wiener index, have extensively been used in analyzing patterns of diversity at different geographic and ecological scales. These indices have serious conceptual and statistical problems which make comparisons of species richness or species abundances across communities nearly impossible. There is often no a single statistical method that retains all information needed to answer even a simple question. However, multivariate analyses could be used instead of diversity indices, such as cluster analyses or multiple regressions. More complex multivariate analyses, such as Canonical Correspondence Analysis, provide very valuable information on environmental variables associated to the presence and abundance of the species in a community. in addition, particular hypotheses associated to changes in species richness across localities, or change in abundance of one, or a group of species can be tested using univariate, bivariate, and/or rarefaction statistical tests. The rarefaction method has proved to be robust to standardize all samples to a common size. Even the simplest method as reporting the number of species per taxonomic category possibly provides more information than a diversity index value. Rev. Biol. Trop. 57 : 451-460. Epub 2009 September 30.
An operational, additive framework for species diversity partitioning and beta-diversity analysis
Journal of Ecology, 2007
1 An important goal of community ecology is the assessment of factors that are likely to influence the spatio-temporal distribution of species assemblages and diversity. Surprisingly, most statistical methods devoted to this have remained poorly interconnected, as well as poorly connected with the popular metrics of diversity estimation. In the present paper we show that important questions related to determinants of species diversity can be specified through a simple multivariate linear model and explored, in common diversity metrics, using standard methods and routines of variance/covariance decomposition. 2 Thanks to an unusual form of presentation of taxonomic data into a table of species occurrences , which considers the individuals as data units, Shannon and Simpson indices as well as species richness can all be expressed as a (weighted) sum of squares. Subsequent apportionments into explained and residual sum of squares provide direct estimates of the beta-and alpha-diversity components with respect to either categorical habitat types or continuous gradient variables. Appropriate statistics and non-parametric tests are available to assess the significance of these components. 3 Explicit analytical relationships exist between the linear approximation of the table of species occurrences by sampling sites, and the more classical table of species abundances by sites. Therefore, direct links with methods of ordination in reduced space, such as correspondence analysis and canonical correspondence analysis, provide opportunities for partitions that preserve consistency with usual diversity indices. The sum of squares of the approximated occurrence table provides measures of intersites beta-diversity, from which measures of dissimilarity with explicit references to diversity indices can be derived. Such measures are amenable to distance-based apportionments through multivariate variograms and multiscale ordination. 4 What are the relative effects of the biological, environmental and anthropogenic factors and of their potential interactions on species diversity? Are these effects stable across scales, from landscape to region, between regions and across ecosystems? The methodological integration proposed in our analytical framework enables one to address these questions using standard statistical tools, and opens new prospects for quantitative biodiversity studies. This also paves the way towards refined models for predicting species diversity at unsampled locations.
Comparing Measures of Species Diversity From Incomplete Inventories: An Update
Methods in Ecology and Evolution, 2010
1. Measuring biodiversity quantitatively is a key component to its investigation, but many methods are known to be biased by undersampling (i.e. incomplete inventories), a common situation in ecological field studies. 2. Following a long tradition of comparing measures of alpha diversity to judge their usefulness, we used simulated data to assess bias of nine diversity measures – some of them proposed fairly recently, such as estimating true species richness depending on the completeness of inventories (Brose, U. & Martinez, N.D. Oikos (2004) 105, 292), bias-corrected Shannon diversity (Chao, A. & Shen, T.-J. Environmental and Ecological Statistics (23) 10, 429), while others are commonly applied (e.g. Shannon's entropy, Fisher's α) or long known but rarely used (estimating Shannon's entropy from Fisher's α). 3. We conclude that the 'effective number of species' based on bias-corrected Shannon's entropy is an unbiased estimator of diversity at sample completeness c. >0·5, while below that it is still less biased than, e.g., estimated species richness (Brose, U. & Martinez, N.D. Oikos (2004) 105, 292). 4. Fisher's α cannot be tested with the same rigour because it cannot measure the diversity of completely inventoried communities, and we present simulations illustrating this effect when sample completeness approaches high values. However, we can show that Fisher's α produces relatively stable values at low sample completeness (an effect previously shown only in empirical data), and we tentatively conclude that it may still be considered a good (possibly superior) measure of diversity if completeness is very low.