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Evolution. 2009 Nov;63(11):2914-25. doi: 10.1111/j.1558-5646.2009.00775.x. Epub 2009 Jul 16.

Likelihood-based inference in isolation-by-distance models using the spatial distribution of low-frequency alleles.

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Department of Ecology and Evolutionary Biology, Interdepartmental Program in Bioinformatics, University of California Los Angeles, Los Angeles, California 90095, USA.


Estimating dispersal distances from population genetic data provides an important alternative to logistically taxing methods for directly observing dispersal. Although methods for estimating dispersal rates between a modest number of discrete demes are well developed, methods of inference applicable to "isolation-by-distance" models are much less established. Here, we present a method for estimating rhosigma(2), the product of population density (rho) and the variance of the dispersal displacement distribution (sigma(2)). The method is based on the assumption that low-frequency alleles are identical by descent. Hence, the extent of geographic clustering of such alleles, relative to their frequency in the population, provides information about rhosigma(2). We show that a novel likelihood-based method can infer this composite parameter with a modest bias in a lattice model of isolation-by-distance. For calculating the likelihood, we use an importance sampling approach to average over the unobserved intraallelic genealogies, where the intraallelic genealogies are modeled as a pure birth process. The approach also leads to a likelihood-ratio test of isotropy of dispersal, that is, whether dispersal distances on two axes are different. We test the performance of our methods using simulations of new mutations in a lattice model and illustrate its use with a dataset from Arabidopsis thaliana.

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