Abstract
The establishment of a population into a new empty habitat outside of its initial niche is a phenomenon akin to evolutionary rescue in the presence of immigration. It underlies a wide range of processes, such as biological invasions by alien organisms, host shifts in pathogens, or the emergence of resistance to pesticides or antibiotics from untreated areas. We derive an analytically tractable framework to describe the evolutionary and demographic dynamics of asexual populations in a source-sink system. We analyze the influence of several factors on the establishment success in the sink, and on the time until establishment. To this aim, we use a classic phenotype-fitness landscape (Fisher's geometrical model in n dimensions) where the source and sink habitats have different phenotypic optima. In case of successful establishment, the mean fitness in the sink follows a typical four-phases trajectory. The waiting time to establishment is independent of the immigration rate and has a "U-shaped" dependence on the mutation rate, until some threshold where lethal mutagenesis impedes establishment and the sink population remains so. We use these results to get some insight into possible effects of several managementstrategies.
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