Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy

By C. Keylock. 2005

502 citations recorded by the source corpus.

Subfields: Global and Planetary Change, Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cd259651225ffb8e02b9d8c2604ab5e997531d50

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In Global and Planetary Change

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Citations in the corpus

A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity (2010, background): “The term qlg a S i 1p q i p̄ q 1 i ; known as the basic sum, is important because most of the popular species diversity indices can be derived from it (Hill 1973, Keylock 2005).”
Rainfall Shocks, Resilience, and the Effects of Crop Biodiversity on Agroecosystem Productivity (2008, background): “These indices belong to the Hill family of indices, they ‘‘can be linked to a more general information theory’’ and to a generalized formulation of entropy (Keylock 2005).”
Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers (2014, background): “Tsallis, C. 1988.”
Effects of diversity of tree species and size on forest basal area growth, recruitment, and mortality (2007, background): “All three indices are closely related and they can be derived from the same one-parameter family of diversity indices (Patil and Taillie, 1979; Keylock, 2005).”
Combining richness and abundance into a single diversity index using matrix analogues of Shannon's and Simpson's indices (2006, unknown): “Many ecologists (Keylock 2005) use the natural logarithm, base e, but it is not always obvious why.”
Unifying Species Diversity, Phylogenetic Diversity, Functional Diversity, and Related Similarity and Differentiation Measures Through Hill Numbers (2014, unknown): “F o r p er so n al u se o n ly . different disciplines (Havrdra & Charvát 1967, Daróczy 1970, Patil & Taillie 1979, Tsallis 1988, Keylock 2005).”
Partitioning diversity for conservation analyses (2010, methodology): “To find a general formula for such a transformation, we first generalize the traditional additive approach (Lande, 1996) to ‘Tsallis entropies’ of any order of q, which include Shannon entropy and the Gini–Simpson indices as special cases (Keylock, 2005).”
The decomposition of Shannon's entropy and a confidence interval for beta diversity (2012, background): “Decreasing the order of the diversity estimates is conceptually equivalent to enhancing the weight of rare species in the final diversity estimates (Keylock 2005).”
Diet of Yellow-legged Gull (Larus michahellis) chicks along the Spanish Western Mediterranean coast: the relevance of refuse dumps (2008, methodology): “Habitat heterogeneity was estimated using the Shannon– Weaver index (Keylock 2005; Pielou 1967; Shannon and Weaver 1949):”
A unified index to measure ecological diversity and species rarity (2008, background): “Controversy over which index should be used exists in the literature, but some authors have suggested that D performs the best (Lande 1996, Mouillot and Leprête 1999, Keylock 2005).”
Partitioning diversity into independent alpha and beta components. (2007, methodology): “For example, suppose an ecologist applies the additive definition of beta to the Gini-Simpson index (Lande 1996, Veech et al. 2002, Keylock 2005 ) to calculate the beta diversity of two samples of flowering plants from the antarctic tundra.”
Entropy and diversity (2006, unknown): “(Aczel and Daroczy 1975, Tsallis 2001, Keylock 2005).”