Linking biodiversity patterns by autocorrelated random sampling

Biodiversity macroecology deals with the commonly measured variables of abundance, distribution, occupancy, and range size across two scales: the local (or α) and regional (γ). There are ca. 15 patterns consisting of the frequency distributions of the variables, variables as a function of area or sample size, and interrelationships between variables that appear to be very general if not close to universal. A number of links can be drawn between these patterns. In particular, I show that local communities can be seen as random samples of the regional pool, but only as a special form of sampling that is autocorrelated due to the spatial clumping of individuals within a species. I describe two distinct sets of mathematical machinery that can start with the regional species abundance distribution and then predict local species richness, local species abundance distributions, and β-diversity (in the form of species area relationships or decay of similarity with distance). I conclude by examining some of the implications of the fact that biodiversity patterns are linked by autocorrelated sampling.