On the Relationship between Abundance and Distribution of Species

There appears to be a general relationship between abundance and distribution that has two parts. First, within species, population density tends to be greatest in the center of the range and to decline gradually toward the boundaries. This pattern holds over a range of spatial scales from steep environmental gradients within local regions to the entire geographic range. Exceptions include: (1) abrupt changes in abundance that usually correspond to sharp, discontinuous changes in single environmental variables; and (2) multimodal patterns of abundance that are caused by environmental patchiness. The second general relationship is that among closely related, ecologically similar species spatial distribution is positively correlated with average abundance. Again this pattern holds over a variety of spatial scales from local regions to entire geographic ranges. These empirical patterns have already been reported in the literature, but their generality is demonstrated by analysis of additional data for diverse kinds of organisms. A single general theory accounts for these observations and follows logically from three assumptions. First, the abundance and distribution of each species are limited by the combination of physical and biotic environmental variables that determines the multidimensional niche. Second, spatial variation in these environmental variables is somewhat stochastic but autocorrelated, so that nearby sites tend to have more similar environmental conditions than more distant ones. Third, closely related, ecologically similar species differ in no more than a very few niche dimensions. A more formal model can be developed that predicts that under these assumptions the distribution of population density over space should approximate a normal probability density distribution. Most exceptions to this predicted pattern can be explained as cases in which assumptions of the model are clearly violated. This paper represents an example of a statistical approach that should be useful for investigating complex ecological systems comprised of many components, such as species of many individuals or communities of many species. The general relationships between abundance and distribution developed here eventually should contribute to our understanding of the biogeography, population genetics, and evolution of species as well as the ecological attributes of populations and communities.