DISEQUILIBRIUM, SELECTION, AND RECOMBINATION: LIMITS IN TWO-LOCUS, TWO-ALLELE MODELS

Alan Hastings ¹

¹ Department of Mathematics, University of California, Davis, California 95616

All possible combinations of equilibria and fitnesses in two-locus, two-allele, deterministic, discrete-generation selection models are enumerated. This knowledge is used to obtain limits (which can be calculated to arbitrary precision) to the relationships among disequilibrium, selection and recombination for fixed values of allele frequencies. In all cases, the inequality|rD| < s/10 holds, where r is recombination and D is disequilibrium, and all selection coefficients lie between 1 - s and 1 + s times that of the double heterozygote. Linear programming techniques are used to calculate the minimum strength of selection needed to explain several observed nonzero values of D reported in the literature. One conclusion is that the failure to observe nonzero values of D is not surprising.