Geographic range, turnover rate and the scaling of species diversity

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Abstract
The study of the relative roles of local and regional processes in determining the scaling of species diversity is a very active field in current ecology. The importance of species turnover and the species‐range‐size frequency distributions in determining how local and regional species diversity are linked has been recognised by recent approaches. Here we present a model, based on a system of fully nested sampling quadrats, to analyse species diversity at several scales. Using a recursive procedure that incorporates increasingly smaller scales and a multiplicative formula for relating local and regional diversity, the model allows the simultaneous depiction of alpha, beta and gamma diversity in a single “species‐scale plot”. Species diversity is defined as the number of ranges that are intersected by sampling quadrats of various sizes. The size, shape and location of individual species ranges determine diversity at any scale, but the average point diversity, measured at hypothetical zero‐area localities, is determined solely by the size of individual ranges, regardless of their shape and location. The model predicts that if the species‐area relationship is a power function, then beta diversity must be scale invariant if measured at constant scale increments. Applying the model to the mammal fauna of four Mexican regions with contrasting environmental conditions, we found that: 1) the species‐range‐size frequency distribution at the scale of the Mexican regions differs from the log‐normal pattern reported for the national and continental scales. 2) Beta diversity is not scale‐invariant within each region, implying that the species‐area relationship (SAR) does not follow a power function. 3) There is geographic variation in beta diversity. 4) The scaling of diversity is directly linked to patterns of species turnover rate, and ultimately determined by patterns in the geographic distribution of species. The model shows that regional species diversity and the average distribution range of species are the two basic data necessary to predict patterns in the scaling of species diversity.