Maximum Likelihood Fit of a Gradual Admixture Model to Clines of Gene Frequencies in the Main Islands of Japan.

Abstract

The hypothesis was tested that the observed clines of gene frequencies in the main islands of Japan (Kyushu, Shikoku, and Honshu) were produced by a two-phase episode of immigration and admixture. In the first phase, an intrusive population occupies the western part of the main islands, causing a temporary discontinuity in the geographical distribution of the gene frequency at each locus. In the second phase, gradual admixture occurs by the random migration of both immigrants and indigenes, leading to the formation of a cline. Under the assumption that the population density is uniform in space at all times, the process is modelled mathematically as a simple diffusion on a finite linear habitat with reflecting boundaries. The discontinuous gene frequency distribution is approximated by a step function. Maximum likelihood estimates of the parameters of the model are obtained by Marquardt's method, and the chisquare statistic is used to test goodness-of-fit. The model does not give a satisfactory fit at the ABO blood group locus. It does give an acceptable fit at the group-specific component and haptoglobin loci, whether the model fitting is done at each locus separately, or at both loci simultaneously. Moreover, the maximum likelihood estimates of the elapsed time since beginning of admixture are compatible with the proposal that the immigrants arrived at the end of the Jomon period. On the other hand, the maximum likelihood estimates of the eastern limit of initial occupation appear to be too large.