PARTITIONING DIVERSITY INTO INDEPENDENT ALPHA AND BETA COMPONENTS
2007/10/01 by Lou Jost · 56 citations
Environmental Science · Computer Science · #Sustainability and Ecological Systems Analysis #Ecology and Vegetation Dynamics Studies #Geochemistry and Geologic Mapping
paper · doi:10.1890/06-1736.1
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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