A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena

The present two-part review aims to put the different phenomena that have been called "beta diversity" over the years into a common conceptual framework and to explain what each of them measures. The first part (Tuomisto 2010) discussed basic definitions of "beta diversity". Each arises from a different way of combining a definition of "diversity" with a definition of its alpha component and with a mathematical relationship between the alpha and gamma components. This second part assumes that an appropriate basic definition of a beta component (which may or may not be true beta diversity) has been chosen, and the focus here will be on how to quantify it for a given dataset. About twenty different approaches have been used for this purpose. It turns out that only two of these approaches accurately quantify the selected beta component: one does so for the entire dataset, and the other for two sampling units at a time. The other approaches actually quantify other phenomena, such as mean species turnover between sampling units, compositional gradient length (with or without reference to an external gradient), distinctness of a focal sampling unit, rate of species accumulation with increasing sampling effort, rate of compositional turnover along an external gradient, or the rate of decay in compositional similarity with increasing geographical distance. Although most of these phenomena can be expressed as a function of a beta component of diversity, they do not equal a beta component of diversity. Many of these derived variables are not even numerically correlated with the beta component on which they are based, which needs to be taken into account when interpreting the results. The effects of sampling decisions when results are extrapolated beyond the available data will also be discussed.