Independence of alpha and beta diversities.

Though Veech and Crist’s paper (Veech and Crist 2010) deals primarily with species richness, ecologists partitioning diversity generally use multiple diversity measures and compare the beta values among them (e.g., Gering et al. 2003, Summerville et al. 2003, 2006, Couteron and Pelissier 2004, Stendera and Johnson 2005, Ribiero et al. 2008). This paper therefore takes a more general perspective and treats all standard measures, not just species richness. Veech and Crist rightly note that I do not mention ‘‘statistical independence’’ in Jost (2007). Statistical independence of alpha and beta is neither necessary nor desirable. Statistical independence between alpha and beta is primarily an empirical question; it depends on nature and on our sampling scheme. In some kinds of ecosystems, it is conceivable that high differentiation is associated with high within-group diversity. The reverse is also conceivable. If nature has these regularities, we would want our measures of alpha and beta to be able to reflect them. We would not want a definition of beta that predetermined the kind of regularities we could observe.