Rarity, commonness, and the contribution of individual species to species richness patterns.

Common species have a greater effect on observed geographical patterns of species richness than do rare ones. Here we present a theory of the relationship between individual species occurrence patterns and patterns in species richness, which allows purely geometrical and statistical causes to be distinguished from biological ones. Relationships between species occupancy and the correlation of species occurrence with overall species richness are driven by the frequency distribution of species richness among sites. Moreover, generally positive relationships are promoted by the fact that species occupancy distributions are mostly right skewed. However, biological processes can lead to deviations from the predicted pattern by changing the nestedness of a species' spatial distribution with regard to the distributions of other species in an assemblage. We have applied our theory to data for European birds at several spatial scales and have identified the species with significantly stronger or weaker correspondence with the overall richness pattern than that predicted by the null model. In sum, whereas the general macroecological pattern of a stronger influence of common species than of rare species on species richness is predicted by mathematical considerations, the theory can reveal biologically important deviations at the level of individual species.