Detecting and comparing the direction of gene-frequency gradients

TLDR: An approach to quantifying the orientation of a cline is put forward, based on description of gene-frequency variance as a function of distance between populations, by means of directional variograms.

Abstract: Directional gene flow between genetically differentiated populations leads to parallel gene-frequency gradients at various loci; processes of differential selection are not expected to result in equally oriented patterns of gene frequencies. Therefore, inferences on the mechanisms maintaining genetic diversity can be drawn by comparing the directions of clines at different loci. An approach to quantifying the orientation of a cline is put forward here. The method is based on description of gene-frequency variance as a function of distance between populations, by means of directional variograms. The mean axis of the cline is then computed by averaging the directional components of variation; it can be regarded as the axis along which the frequencies of an allele vary showing the maximum degree of order. The significance of the mean axis can be tested, and the directions of two clines can be compared, using techniques developed in circular statistics. An example of application of this method to human gene frequencies is presented. Discordant clines are observed at six electrophoretically polymorphic loci in Eurasian populations. Only a fraction of such clines can be accounted for by the Neolithic radiation of early farmers in the Middle East and Europe.