Variance in Species Richness, Species Association, and Niche Limitation

A low variance in species richness, relative to a null model, has been proposed as evidence for niche limitation in ecologicaI communities. We demonstrate that niche limitation does not inevitably lead to low variance in species richness. Furthermore. low variance in species richness can be caused by physical limits to the number of individuals in a sample, and by spatial dependence. Two methods (the rotation/ reflection method and the random shifts method) for creating spatially-explicit null models are proposed to correct for spatial dependence in transect-based and grid-based sampling schemes. These methods can also be used to correct for measures of association between species. The rotation/reflection method is not as powerful as the random shifts method, but the latter requires some simplifying assumptions about the nature of spatial patterns. A new sampling design, the trainsect, is proposed to eliminate the need for spatial assumptions