The Making and Testing of Geographic Gene-Frequency Maps

Graphic display of a surface by isopleths is frequently useful. This technique has also been used, though not widely, to study the geographic distribution of gene frequencies. We were interested in the development of automatic procedures for this purpose. Three different approaches were tested: (i) a mixed-strategy approach alternating between polynomial surface fitting and local averaging, both weighted by distance and sample size, the choice between the alternatives being based on the local dispersion of data; (ii) the theory of regionalized variables with automatic choice of the degree of the polynomial function representing the generalized covariance distance; (iii) the use in (ii) of current genetic models of covariation of gene frequency with distance. The first method was found to be slightly superior to the second (though not significantly so) by the testing criteria adopted. The third method was definitely less satisfactory, as tested by a variety of criteria. Among them, a 'leaveout-s' technique of jackknifing provided a distribution of x2 values measuring the fit of the map to each data point. Outliers observed were justified on biological grounds. Various aspects and problems of automatic map construction are discussed. Practical results seem quite encouraging.