Distributions of habitat suitability and the abundance-occupancy relationship

Positive abundance-occupancy relationships (a relationship between the number of sites a species occupies and the average density of individuals in occupied sites) are widespread through a range of taxa. The simplest model for this is the "vital rates" model, which proposes that habitat suitability varies spatially; increasing average habitat quality thus leads to simultaneous increases in average densities within occupied areas, as well as the total area that is habitable. This model has not been tested. We develop a general analytical version of this model and show that it predicts that the skewness of population size or aggregation of individuals within sites should vary systematically with density and occupancy, depending on the distribution of habitat suitability, and that the variance in occupancy should be highest at low densities. We compare these predictions with data from the British Trust for Ornithology's Common Birds Census, and we find systematic changes in both variance and skewness of density, both intra- and interspecifically.