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KEY WORDS Genetic variation, Demic diffusion, Language, Computer simulation Allele frequency distributions were generated by computer simulation of five models of microevolution in European populations. Genetic distances calculated from these distributions were compared with observed genetic distances among Indo-European speakers. The simulated models differ in complexity, but all incorporate random genetic drift and short-range gene flow (isolation by distance). The best correlations between observed and simulated data were obtained for two models where dispersal of Neolithic farmers from the Near East depends only on population growth. More complex models, where the timing of the farmers' expansion is constrained by archaeological time data, fail to account for a larger fraction of the observed genetic variation; this is also the case for a model including late Neolithic migrations from the Pontic steppes. The genetic structure of current populations speaking Indo-European languages seems therefore to largely reflect a Neolithic expansion. This is consistent with the hypothesis of a parallel spread of farming technologies and a proto-Indo-European language in the Neolithic. Allele-frequency gradients among Indo-European speakers may be due either to incomplete admixture between dispersing farmers, who presumably spoke proto-Indo-European, and pre-existing hunters and gatherers (as in the traditional demic diffusion hypothesis), or to founder effects during the farmers' dispersal. By contrast, successive migrational waves from the East, if any, do not seem to have had genetic consequences detectable by the present comparison of observed and simulated allele frequencies.

From 420 records of ethnic locations and movements since 2000 B.C., we computed vectors describing the proportions which peoples of the various European language families contributed to the gene pools within 85 land-based 5 X 5-degree quadrats in Europe. Using these language family vectors, we computed ethnohistorical affinities as arc distances between all pairs of the 85 quadrats. These affinities are significantly correlated with genetic distances based on 26 genetic systems, even when geographic distances, a common causative factor, are held constant. Thus, the ethnohistorical distances explain a significant amount of the genetic variation observed in modern populations. Randomizations of the records by chronology result in loss of significance for the observed partial correlation between genetics and ethnohistory, when geography is held constant. However, a randomization of records by location only results in reduced significance. Thus, while the historical sequence of the movements does not seem to matter in Europe, their geographic locations do. We discuss the implications of these findings.

Dow and Cheverud (Am. J. Phys. Anthropol. 68:367-373, 1985) have published a statistical test for comparing any three similarity matrices. Using both simulations and analytical arguments, I establish that the presence of spatial autocorrelation, a common feature of geographically based anthropological and biological data, causes this test to reject too often. Increasing the spatial autocorrelation increases the spurious rejection rate. About 20% of the papers that reference Dow and Cheverud's paper have used their test with spatially autocorrelated data. Mantel's (Cancer Res. 27:209-220, 1967) method, when used as a test of spatial autocorrelation, is unaffected by these considerations, since its null hypothesis is that the data are uncorrelated. [C] 1992 Wiley-Liss, Inc.