Matrix correlation analysis in anthropology and genetics

The comparative analysis of the population variation patterns exhibited by different types of information has long been a genuine anthropological/genetic preoccupation. One of the generic problems attracting repeated attention is the connection between genetic and cultural consequences of population isolation; we expect both patterns and amounts of variation to reflect the same history of group fission and fusion, but what do we see in practice? Numerous techniques have been employed in such work, all based on comparison of different matrices of pairwise distanceslaffinities. A basic difficulty with all of these methods is that the N(N – 1) pairwise elements of an (N × N) matrix cannot be mutually independent. Recently, a versatile test of matrix correlation that allows for this fact, originally developed by Mantel but since extensively modified and extended, has gained popularity in anthropology, as well as geography, ecology, sociology, psychometrics, population biology, and systematics. We present here a general framework for many of these efforts, based on the Mantel test, and then illustrate its use with four examples from our own work and that of our colleagues: (a) genetic affinity and migrational separation in the Bainwa, (b) clinal versus cluster variation in the Yanomama, (c) genetic, linguistic, and geographic affinities among the Chibcha-speaking tribes, and (d) migration and genetic affinity in the Gainj and Kalam. The technique is nonparametric and so general that it is useful for many different types of pattern comparison, even when the connections between different types of information are poorly understood. Greater analytic potential is generally realized when there are definite theoretical connections between the patterns being compared. With theoretical care and a bit of imagination, one can combine the advantages of parametric assumptions with the robustness of nonparametric analysis. Novel analyses and anthropological opportunities are emerging continuously. © 1992 Wiley-Liss, Inc.

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