title: 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 composition. We propose a correction of the estimation bias allowing to estimate alpha, beta and gamma entropy from the data and eventually convert them into true diversity. We advocate additive decomposition in complement of multiplicative partitioning to allow robust estimation of biodiversity.
authors.affiliation: AgroParisTech, UMR Écologie des Forêts de Guyane, Kourou Cedex, France.
authors.forename: Eric
authors.initials: E
authors.lastname: Marcon
authors.affiliation: INRA, UMR Écologie des Forêts de Guyane, Kourou Cedex, France.
authors.forename: Ivan
authors.initials: I
authors.lastname: Scotti
authors.affiliation: CIRAD, UMR Écologie des Forêts de Guyane, Kourou Cedex, France.
authors.forename: Bruno
authors.initials: B
authors.lastname: Hérault
authors.affiliation: CIRAD, UMR Écologie des Forêts de Guyane, Kourou Cedex, France.
authors.forename: Vivien
authors.initials: V
authors.lastname: Rossi
authors.affiliation: AgroParisTech, UMR 518 Math. Info. Appli., Paris, France; INRA, UMR 518 Math. Info. Appli., Paris, France.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Lang
mesh_terms: D000465:Algorithms; D000818:Animals; D044822:Biodiversity; D017753:Ecosystem; D019277:Entropy; D004777:Environment; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D013045:Species Specificity