Geographic range, turnover rate and the scaling of species diversity

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.

Species Diversity and Distribution in Presence‐Absence Matrices: Mathematical Relationships and Biological Implications

“…Because beta Whittaker's diversity and the fill of the matrix depend on the number of sites that are used to describe the distribution of species, they are sensitive to changes in the scale of analysis (Arita and Rodriguez 2002). However, the mathematical constraints that we have deduced are universal to any presence-absence matrix.…”

“…However, at smaller scales and for different taxa, other kinds of frequency distributions are possible, responding to a variety of environmental and biological factors (McGeoch and Gaston 2002;Mora and Robertson 2005). In fact, this variation in frequency distributions determines different patterns in the scaling of species diversity (Arita and Rodriguez 2002). Therefore, if both diversity and distribution vary with scale, we should expect different forms of rangediversity plots for different combinations of taxa and scale.…”

Mapping More of Terrestrial Biodiversity for Global Conservation Assessment

“…However, as we demonstrate below, there is much to be gained by working directly with turnover itself in conservation assessment, as this approach retains more information on the pattern of complementarity (sensu Margules and Pressey 2000) between areas. Several recent ecological papers on the partitioning of regional biodiversity into components of alpha and beta diversity have helped to provide a strong theoretical foundation for the richness-turnover view of biodiversity adopted here (Arita andRodriguez 2002, Gering et al 2003).…”

Linking global turnover of species and environments

“…Broad-scale diversity patterns have been found previously to be contingent on the geographic range sizes of species (11). Given the direct link between size of ranges and their average turnover in space (24), much of the cross-taxon variation in turnover may be because of this component. We investigate whether the approximately fourfold difference in geographic range sizes between amphibians and birds can account for differential rates of turnover.…”