Diversity partitioning without statistical independence of alpha and beta.

Diversity partitioning has become a popular method for analyzing patterns of alpha and beta diversity. A recent evaluation of the method emphasized a distinction between additive and multiplicative partitioning and further advocated the use of multiplicative partitioning based on a presumed independence between alpha and beta. Concurrently, additive partitioning was criticized for producing dependent alpha and beta estimates. Until now, the issue of statistical independence of alpha and beta (in either type of partitioning) has not been thoroughly examined, partly due to confusion about the meaning of statistical independence. Here, we adopted a probability-based definition of statistical independence that is essentially identical to the definition found in any statistics textbook. We used a data simulation approach to show that alpha and beta diversity are not statistically independent in either additive or multiplicative partitioning. However, the extent of the dependence is not so great that it cannot be overcome by using appropriate statistical techniques to control it. Both additive and multiplicative partitioning are statistically valid and logically sound approaches to analyzing diversity patterns.