1 November 2009 Likelihood-Based Inference in Isolation-By-Distance Models Using the Spatial Distribution of Low-Frequency Alleles
John Novembre, Montgomery Slatkin
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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 ρσ2, the product of population density (ρ) and the variance of the dispersal displacement distribution (σ2). 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 ρσ2. 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.

© 2009 The Society for the Study of Evolution.
John Novembre and Montgomery Slatkin "Likelihood-Based Inference in Isolation-By-Distance Models Using the Spatial Distribution of Low-Frequency Alleles," Evolution 63(11), 2914-2925, (1 November 2009). https://doi.org/10.1111/j.1558-5646.2009.00775.x
Received: 2 November 2008; Accepted: 1 May 2009; Published: 1 November 2009

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importance sampling
intraallelic genealogy
low-frequency alleles
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