Partial correlation of distance matrices in studies of population structure

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Abstract
Anthropological studies of human population structure commonly compare various monogenic and polygenic (metric) distance matrices to distance matrices obtained from measures of geographical dispersion, linguistic differences, and migration patterns in an attempt to infer something about the effects of evolutionary factors (drift and differential selection, in particular). It is, though, commonly recognized that geography, language, and migration patterns may be intercorrelated due to the common effects of historical and social processes. Previous attempts to deal with the problems of assessing relative effects among such sets of intercorrelated factors using partial correlations have resulted in coefficients that are either not well defined or have no known sampling distribution or both. Here, we outline a general approach to partialling distance matrices that results in well-defined coefficients and valid significance testing procedures. Application of the matrix partialling methods to a variety of distance matrices obtained for a sample of eight ethnolinguistic groups from the Harvard Solomon Islands Expedition (Friedlaender et al., 1986) reveals a close association between language dissimilarity and dermatoglyphics controlling for geography, thus reinforcing earlier suggestions that dermatoglyphics, properly used, reflect historical relationships of groups in this region better than do anthropometry, odontometrics, or small batteries of blood polymorphisms.