title: Partitioning diversity into independent alpha and beta components.
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.
authors.affiliation: loujost@yahoo.com
authors.forename: Lou
authors.initials: L
authors.lastname: Jost
mesh_terms: D000818:Animals; D044822:Biodiversity; D017753:Ecosystem; D004777:Environment; D015233:Models, Statistical; D011156:Population Density; D011157:Population Dynamics