A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity

The term beta diversity has been used to refer to a wide variety of phenomena. Although all of these encompass some kind of compositional heterogeneity between places, many are not related to each other in any predictable way. The present two-part review aims to put the different phenomena that have been called a beta component of diversity into a common conceptual framework, and to explain what each of them measures. In this first part, the focus is on defining beta diversity. This involves deciding what diversity is and how the observed total or gamma diversity (gamma) is partitioned into alpha (alpha) and beta (beta) components. Several different definitions of "beta diversity" that result from these decisions have been used in the ecological literature. True beta diversity is obtained when the total effective number of species in a dataset (true gamma diversity gamma) is multiplicatively partitioned into the effective number of species per compositionally distinct virtual sampling unit (true alpha diversity alpha(d)) and the effective number of such compositional units (beta(Md)=gamma/alpha(d)). All true diversities quantify the effective number of types of entities. Because the other variants of "beta diversity" that have been used by ecologists quantify other phenomena, an alternative nomenclature is proposed here for the seven most popular beta components: regional-to-local diversity ratio, two-way diversity ratio, absolute effective species turnover (=regional diversity excess), Whittaker's effective species turnover, proportional effective species turnover, regional entropy excess and regional variance excess. In the second part of the review, the focus will be on how to quantify these phenomena in practice. This involves deciding how the sampling units that contribute to total diversity are selected, and whether the entity that is quantified is all of "beta diversity", a specific part of "beta diversity", the rate of change in "beta diversity" in relation to a given external factor, or something else.