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

Summary1 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.