Large-scale population dynamics, abundance-occupancy relationships and the scaling from local to regional population size

1. We explore the relationship between patch occupancy and local abundance in a general model for regional population dynamics. We vary colonization ability and key demographic and habitat characteristics in order to explore the effects on abundance-occupancy relationships. 2. In populations in which colonization rates are very high, new habitat is rapidly colonized and there is a simple asymptotic relationship between occupancy and abundance, assuming that habitat quality and abundance are linked. 3. If colonization rates are moderate to low, as in metapopulations, there is similarly a positive relationship between occupancy and abundance, but there is a minimum abundance below which the metapopulation becomes extinct. 4. These responses are modulated by the occurrence of Allee effects, demographic stochasticity or depensatory effects: when such effects are significant, the metapopulation rescue effect becomes important, and regional occupancy becomes more sensitive to changes in local density. 5. Finally, in populations in which colonization rates are very low, there is no relationship between occupancy and abundance. 6. Our results emphasize two aspects of large-scale ecology as being key in generating positive abundance-occupancy relationships: (i) a relationship between average habitat quality and the proportion of habitat that is habitable; and (ii) the nature of colonization. It is important to note that colonization is a function of dispersal, fecundity, and local processes such as Allee effects, as well as the availability and isolation of habitat patches. 7. When an abundance-occupancy relationship exists there is typically a non-linear scaling from local to total population sizes at low population densities, and we discuss how this may be detected in real data, as well as its implications.