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Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the habitats population size distribution from a general stochastic dynamic within each habitat, using a deterministic approximation which becomes exact for an infinite number of habitats. Fragmented populations are usually thought to be characterized by a separation of time scale between, on the one hand, colonization and extinction of habitats and, on the other hand, the local population dynamics within each habitat. The analysis in this paper suggests an alternative view: the effective population dynamic stems from a law of large numbers, where stochastic fluctuations in population size of single habitats are buffered through the dispersal pool so that the global population dynamic remains approximately smooth. For illustration, the deterministic approximation is compared to simulations of a stochastic model with density dependent local recruitment and mortality. The article is concluded with a discussion of the general implications of the results, and possible extensions of the method.
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain changes in co
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. W
The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings--despite the fact that many bacteria inhabit complex a
This paper develops a quasispecies model that incorporates the SOS response. We consider a unicellular, asexually replicating population of organisms, whose genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome. We assume tha
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in ecology,