A Separation-of-Timescales Approach to the Coalescent in a Continuous Population

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Abstract
This article presents an analysis of a model of isolation by distance in a continuous, two-dimensional habitat. An approximate expression is derived for the distribution of coalescence times for a pair of sequences sampled from specific locations in a rectangular habitat. Results are qualitatively similar to previous analyses of isolation by distance, but account explicitly for the location of samples relative to the habitat boundaries. A separation-of-timescales approach takes advantage of the fact that the sampling locations affect only the recent coalescent behavior. When the population size is larger than the number of generations required for a lineage to cross the habitat range, the long-term genealogical process is reasonably well described by Kingman's coalescent with time rescaled by the effective population size. This long-term effective population size is affected by the local dispersal behavior as well as the geometry of the habitat. When the population size is smaller than the time required to cross the habitat, deep branches in the genealogy are longer than would be expected under the standard neutral coalescent, similar to the pattern expected for a panmictic population whose population size was larger in the past.
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