Premium
The decomposition of Shannon's entropy and a confidence interval for beta diversity
Author(s) -
Marcon Eric,
Hérault Bruno,
Baraloto Christopher,
Lang Gabriel
Publication year - 2012
Publication title -
oikos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.672
H-Index - 179
eISSN - 1600-0706
pISSN - 0030-1299
DOI - 10.1111/j.1600-0706.2011.19267.x
Subject(s) - gamma diversity , biodiversity , estimator , diversity index , mathematics , alpha diversity , statistics , ecology , beta diversity , entropy (arrow of time) , confidence interval , rényi entropy , diversity (politics) , principle of maximum entropy , biology , species richness , sociology , physics , quantum mechanics , anthropology
Beta diversity is among the most employed theoretical concepts in ecology and biodiversity conservation. Up to date, a self‐contained definition of it, with no reference to alpha and gamma diversity, has never been proposed. Using Kullback‐Leibler divergence, we present the explicit formula of Shannon's β entropy, a bias correction for its estimator and a confidence interval. We also provide the mathematical framework to decompose Shannon diversity into several hierarchical nested levels. From botanical inventories of tropical forest plots in French Guiana, we estimate Shannon diversity at the plot, forest and regional level. We believe this is a complete and usefulness toolbox for ecologists interested in partitioning biodiversity.