PARTITIONING DIVERSITY INTO INDEPENDENT ALPHA AND BETA COMPONENTS
2007/10/01 by Lou Jost · 2,296 citations
Computer Science · Environmental Science · Mathematics · #Alpha (finance) #Alpha diversity #BETA (programming language) #Beta diversity #Biodiversity #Biology #Cluster analysis #Computer science #Ecology #Ecology and Vegetation Dynamics Studies #Gamma diversity #Geochemistry and Geologic Mapping #Jaccard index #Mathematics #Multiplicative function #Species diversity #Statistics #Sustainability and Ecological Systems Analysis
paper · doi:10.1890/06-1736.1
published in Ecology 88(10), 2427-2439 (Wiley)
openalex publication_date 2007/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
Existing general definitions of beta diversity often produce a beta with a hidden dependence on alpha. Such a beta cannot be used to compare regions that differ in alpha diversity. To avoid misinterpretation, existing definitions of alpha and beta must be replaced by a definition that partitions diversity into independent alpha and beta components. Such a unique definition is derived here. When these new alpha and beta components are transformed into their numbers equivalents (effective numbers of elements), Whittaker's multiplicative law (alpha x beta = gamma) is necessarily true for all indices. The new beta gives the effective number of distinct communities. The most popular similarity and overlap measures of ecology (Jaccard, Sorensen, Horn, and Morisita-Horn indices) are monotonic transformations of the new beta diversity. Shannon measures follow deductively from this formalism and do not need to be borrowed from information theory; they are shown to be the only standard diversity measures which can be decomposed into meaningful independent alpha and beta components when community weights are unequal.
Citations
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