PARTITIONING DIVERSITY INTO INDEPENDENT ALPHA AND BETA COMPONENTS

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…