The distribution and abundance of populations limited at multiple spatial scales

1. We use mathematical programming to explore long-term equilibrium population distribution and abundance effects arising from a single-patch reaction-diffusion model when ecological factors limit carrying capacity at two different spatial scales. Both homogeneous and heterogeneous habitat patches are investigated under passive diffusion conditions. Capacity limits, reproduction and dispersal rates, and habitat preferences are individually varied. 2. When landscape-scale habitat factors are strongly limiting, and reproduction and dispersal processes are less so, suitable population arrangements can be either clustered or highly fragmented. 3. Population clustering also occurs when strong habitat preferences are introduced, even though few members of the clusters may actually occupy the preferred sites. 4. As reproduction or dispersal rates become increasingly limiting in the system (i.e. as the parameters approach extinction thresholds), population clustering within a habitat patch is required to reach long-term equilibrium population levels. 5. These results offer a potential explanation for why species–habitat association studies have been characterized by high variability.