On the relationship between range size and local abundance: Back to basics

In many taxa, the sizes of species' geographic ranges and their average local abundances at sites where they occur are positively correlated. We develop a simple population model that predicts this relationship which does not rely upon spatial dynamics. The simple, but fundamental, fact which should link distribution and abundance is that the distribution of species i is given by the number of sites at which its intrinsic rate of increase, r(i) > 0, whereas its equilibrium local abundance should often vary directly with r(i). Any factor which tends to increase r(i) across all sites will simultaneously enlarge the number of sites potentially occupied, and increase abundance at each occupied site. If species differ principally in their response to density-independent factors influencing birth and death rates, but are similar in density-dependence, then in a broad range of circumstances one should observe a range-abundance correlation. The model also predicts particular circumstances in which there is no, or even a negative, correlation between range and abundance. The general occurrence of this correlation in a broad range of taxa may reflect the operation of a number of distinct mechanisms.