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

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


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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Arabidopsis / genetics
  • Gene Frequency*
  • Genes, Plant
  • Likelihood Functions
  • Models, Theoretical*