Likelihood analysis of geographic variation in allelic frequencies : II. The logit model and an extension to multiple loci.

Likelihood estimation and testing procedures are described for treating geographic variation in allelic frequencies as a logistic function of environmental variables. The basic response curve is sigmoidal, and avoids the necessity of invoking environmental thresholds imposed by a linear response model. The one-locus two-allele, one-locus three-alleles, and two-locus two-allele cases are explicitly treated, and the extensions to multiple alleles and loci are indicated. Three cases of geographic variation in gametic frequencies are analyzed to illustrate the utility of these techniques. A biological rationale is given for a sigmoidal response curve, and the utility of the logit model for univariate and multivariate "analysis of variance" is indicated.