2014
DOI: 10.1371/journal.pone.0090289
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Generalization of the Partitioning of Shannon Diversity

Abstract: Traditional measures of diversity, namely the number of species as well as Simpson's and Shannon's indices, are particular cases of Tsallis entropy. Entropy decomposition, i.e. decomposing gamma entropy into alpha and beta components, has been previously derived in the literature. We propose a generalization of the additive decomposition of Shannon entropy applied to Tsallis entropy. We obtain a self-contained definition of beta entropy as the information gain brought by the knowledge of each community composi… Show more

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Cited by 59 publications
(65 citation statements)
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“…This approach, which assumes that community species follow multinomial distributions (Marcon et al 2012(Marcon et al , 2014, enables us to correct sampling biases and compare 95% confidence intervals between corresponding size classes of the two forest types, and among size classes within each forest type.…”
Section: Discussionmentioning
confidence: 99%
“…This approach, which assumes that community species follow multinomial distributions (Marcon et al 2012(Marcon et al , 2014, enables us to correct sampling biases and compare 95% confidence intervals between corresponding size classes of the two forest types, and among size classes within each forest type.…”
Section: Discussionmentioning
confidence: 99%
“…This approach which assumes that community species follow multinomial distributions [31], [32] enables us to correct sampling biases and compare 95% confidence intervals between the two forest types.…”
Section: Methodsmentioning
confidence: 99%
“…Hill's numbers have advantages: they can be interpreted as the number of effective species; they are members of a more general family of diversities (Leinster and Cobbold 2012; Chao et al 2014a); and reduced-bias estimators are available (Chao and Jost 2015). Marcon et al (2014a) showed that the Hill numbers are the deformed exponential of Tsallis entropy (Tsallis 1988), whereas they are the exponential of Rényi's entropy (Patil and Taillie 1982). The relation between Tsallis entropy and the Hill numbers is continuous and strictly increasing (Jost 2006), so a bijective relation exists between entropy and diversity.…”
Section: Diversity Profilesmentioning
confidence: 99%