Population structure analysis using polygenic traits: estimation of migration matrices

Many studies of subdivided populations have attempted to determine the underlying migration rates that generate observed patterns of genetic differentiation. Most previous analyses have yielded only qualitative inferences about migration. In this paper I present a new method for estimating the full migration matrix from information on polygenic trait variation. The method employs multivariate quantitative genetic theory to provide a matrix formulation of the expected covariance structure in multigenerational subdivided populations for which information is available at different points in the life cycle. I develop a restricted maximum likelihood technique (REML) to take account of this additional life-cycle information and to estimate both the migration matrix and the ratio of effective population size to census size. To make the problem computationally tractable, the migration matrix is modeled as a log-linear function of a few covariates, such as subdivision size and geographic distance. I apply the technique to data on dermatoglyphic ridge counts for 1015 individuals of the Jirel population of east Nepal, considering two different age cohorts. In the adult cohort (individuals over 21 years of age) I examine data by both birthplace and residence and for the subadult cohort (under 21 years of age), by birthplace. Results from the REML technique reveal that the best-fitting migration model is a finite island model with an estimated endemicity of 0.730 +/- 0.105 and an estimated ratio of effective size to census size of 0.287 +/- 0.095. Both estimates are reasonable given known demographic data. In addition, Fst values predicted by the migration model are concordant with REML estimates obtained directly from the dermatoglyphic variation.