Diversity as a Concept and its Measurement

Patil, G. P.; Taillie, C.

doi:10.2307/2287709

Cited by 239 publications

(274 citation statements)

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“…Hurlbert 1971;Routledge 1979;Patil and Taillie 1982;Purvis and Hector 2000;Jost 2006Jost , 2007Jost et al 2010). There have also been intense debates on the choice of diversity partitioning schemes; see Ellison (2010) and the Forum that follows it.…”

Section: Introductionmentioning

confidence: 99%

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Chao

Chiu

Jost³

2016

Biodiversity Conservation and Phylogenetic Systematics

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Conservation biologists need robust, intuitive mathematical tools to quantify and assess patterns and changes in biodiversity. Here we review some commonly used abundance-based species diversity measures and their phylogenetic generalizations. Most of the previous abundance-sensitive measures and their phylogenetic generalizations lack an essential property, the replication principle or doubling property. This often leads to inconsistent or counter-intuitive interpretations, especially in conservation applications. Hill numbers or the "effective number of species" obey the replication principle and thus resolve many of the interpretational problems. Hill numbers were recently extended to incorporate phylogeny; the resulting measures take into account phylogenetic differences between species while still satisfying the replication principle. We review the framework of phylogenetic diversity measures based on Hill numbers and their decomposition into independent alpha and beta components. Both additive and multiplicative decompositions lead to the same classes of normalized phylogenetic similarity or differentiation measures. These classes include multiple-assemblage phylogenetic generalizations of the Jaccard, Sørensen, Horn and Morisita-Horn measures. For two assemblages, these classes also include the commonly used UniFrac and PhyloSør indices as special cases. Our approach provides a mathematically rigorous, self-consistent, ecologically meaningful set of tools for conservationists who must assess the phylogenetic diversity and complementarity of potential protected areas. Our framework is applied to a real dataset to illustrate (i) how to use phylogenetic diversity profiles to completely convey species abundances and phylogenetic information among species in an assemblage; and (ii) how to use phylogenetic similarity (or differentiation) profiles to assess phylogenetic resemblance or difference among multiple assemblages.

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Section: Introductionmentioning

confidence: 99%

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Chao

Chiu

Jost³

2016

Biodiversity Conservation and Phylogenetic Systematics

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“…A further development of these ideas is the exploration of the concept of β−diversity. To accomplish this task, we use the generalized Kullback-Leibler distance, as given by Patil and Taillie [16] and Borland et al [17]. In some sense, this follows the program started by Gorelick to extend Shannon's and Simpson's indices to simultaneously account for species richness and relative abundance, but now we consider a continuous family of q values [18].…”

Section: Introductionmentioning

confidence: 99%

Generalized entropy indices to measure α- and β-diversities of macrophytes

Evangelista¹,

Thomaz²,

Mendes³

et al. 2009

Braz. J. Phys.

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A family of entropy indices constructed in the framework of Tsallis entropy formalism is used to investigate ecological diversity. It represents a new perspective in ecology because a simple equation can incorporate all aspects of α−diversity, from richness to dominance and can be also related to a measure of species rarity. In addition, a generalized Kullback-Leibler distance, constructed in the framework of a nonextensive formalism, is recalled and used as a measure of β−diversity between two systems. These tools are applied to data relative to the macrophytes collected from two not far apart arms of Itaipu Reservoir, in Paraná River basin.

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“…Pielou [1] gave two characteristics an index of diversity should possess: * for given s, the index should be a maximum when the p k are equal; * if the p k are equal, the index should be an increasing function of s. Patil and Taillie [2] proposed a general class of diversity index allowing all diversity measures to be encompassed into a single diversity spectrum. They started by defining diversity as the "average rarity of species within a community".…”

Section: Introductionmentioning

confidence: 99%

“…picture of the structure of the community under study [2] . Monitoring biodiversity is a growing concern of environmental agencies.…”

Section: Introductionmentioning

confidence: 99%

VAR-models for Predicting Biodiversity

Battista¹,

Gattone²,

Granturco³

2005

Journal of Mathematics and Statistics

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Abstract:The aim of this work is to introduce a methodology for monitoring diversity of a biological population by using the tool of diversity profiles. In particular, we develop a theory for studying the diversity profile along the temporal axis. We propose forecasting techniques for diversity profile by using the VAR model on multivariate time series of abundance vector and ARMA models both on univariate time series of abundances and on the aggregated series of diversity profiles. A Monte Carlo simulation is performed in order to test the goodness of forecasts obtained applying the three different methods proposed.

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Diversity as a Concept and its Measurement

Cited by 239 publications

References 0 publications

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Generalized entropy indices to measure α- and β-diversities of macrophytes

VAR-models for Predicting Biodiversity

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