Comparison of distance matrices in studies of population structure and genetic microdifferentiation: quadratic assignment.

Questions concerning the relative effects of various evolutionary forces in molding the genetic variability exhibited by groups of human populations have typically been investigated by comparing a variety of genetic and cultural/historical "distance" matrices. A major methodological difficulty has been the lack of formal testing procedures with which to assess the degree of confirmation or disconfirmation of an estimated measure of relationship between such matrices. In this paper, we examine a very flexible matrix combinatorial procedure which generates statistical significance levels for correlational measures of pattern similarity between distance matrices. A recent generalization of the basic procedure to the three-matrix case allows questions concerning which of two matrices best fits a third matrix to be formally tested. Applications of these hypothesis testing and inference procedures to two separate sets of genetic, geographic, and cultural distance matrices illustrates their potential for finally solving a long-standing problem in anthropological genetics.