The need for richness‐independent measures of turnover when delineating biogeographical regions

Abstract Delineating biogeographical regions is one of the primary steps when analysing biogeographical patterns. In their proposed quantitative framework, Kreft & Jetz (2010, Journal of Biogeography , 37 , 2029–2053) recommended the use of the β sim index to delineate biogeographical regions because this turnover measure is weakly affected by differences in species richness between localities. A recent study by Carvalho et al . (2012, Global Ecology and Biogeography , 21 , 760–771) critiziced the use of β sim in ecological and biogeographical studies, and proposed the β ‐3 index. Here we used simple numerical examples and an empirical case study (European freshwater fishes) to highlight potential pitfalls associated with the use of β ‐3 for bioregionalization. We show that β ‐3 is not a richness‐independent measure of species turnover. We also show that this index violates the ‘complementarity’ property, namely that localities without species in common have the largest dissimilarity, which is an essential prerequisite for beta diversity studies.