Detection of differential gene flow from patterns of quantitative variation.

A major goal in anthropological genetics is the assessment of the effects of different microevolutionary forces. Harpending and Ward (1982) developed a model that aids in this effort by comparing observed and expected heterozygosity within populations in a local region. The expected heterozygosity within a population is a function of the total heterozygosity of the entire region and the distance of the population from the regional mean centroid of allele frequencies. Greater than average gene flow from an external source will result in a population having greater heterozygosity than expected. Less than average gene flow from an external source will result in a population having less heterozygosity than expected. We extend the Harpending-Ward model to quantitative traits using an equal and additive effects model of inheritance. Here the additive genetic variance within a population is directly proportional to heterozygosity, and its expectation is directly proportional to the genetic distance from the centroid. Under certain assumptions the expectations for phenotypic variances are similar. Observed and expected genetic or phenotypic variance can then be compared to assess the effects of differential external gene flow. When the additive genetic covariance matrix or heritabilities are not known, the phenotypic covariance matrix can be used to provide a conservative application of the model. In addition, we develop new methods for estimation of the genetic relationship matrix (R) from quantitative traits. We apply these models to two data sets: (1) six principal components derived from twenty dermatoglyphic ridge count measures for nine villages in Nepal and (2) ten anthropometric measurements for seven isolated populations in western Ireland. In both cases both the univariate and multivariate analyses provide results that can be directly interpreted in terms of historically known patterns of gene flow.