A problem with synthetic maps

Synthetic maps of human gene frequencies, which are maps of principal compo nent scores based on correlations of interpolated surfaces, have been popul arized widely by L. Cavalli-Sforza, P. Menozzi, and A. Piazza. Such maps ar e used to make ethnohistorical inferences or to support various demographic or historical hypotheses. We show from first principles and by analyses of real and simulated data that synthetic maps are subject to large errors an d that apparent geographic trends may be detected in spatially random data. We conclude that results featured as synthetic maps should be approached w ith considerable caution.