Using distance matrices to choose between competing theories and an application to the origin of modern humans

This paper examines competing theories for cases in which both the data and the hypotheses can be represented as distance matrices. A test due to Dow & Cheverud has been used for such comparisons in anthropology, but when data are spatially, temporally, or phylogenetically autocorrelated, this test may be far too liberal. We examine a classification procedure based on ratios of probabilities obtained from Mantel tests of the competing hypotheses and find that design matrices describing only lag-one connections and those eliminating common connections of competing hypotheses are the most informative. We apply this method to simulated gene-frequency data in a 7 x 7 chessboard representing a stepping-stone model and discriminate between alternative theories with a 7% misclassification rate. We also apply these techniques to the current controversy concerning the origin of anatomically modern humans by testing design matrices representing regional continuity and single African origins. The outcome for lag-one matrices and those showing only unique lag-one differences indicate that the single African origin of anatomically modern humans fits the distance matrix based on 165 characters of 83 fossil crania better than the competing theory. However, we also tested a design matrix describing single origin out of southwest Asia. This design matrix was clearly most similar to the data in all tested cases. These results make the regional-continuity theory a less likely explanation for the observed cranial differences than the two single-origin theories. Of these, single southwest Asian origins seems the more likely interpretation of the data.