Inferring selective history from multilocus frequency data: Wright meets the Hamiltonian.

We describe a method to study characteristics of the dynamics of multilocus population genetic models without specifying the form of selection a priori. Our approach consists of specifying initial and final genotypic frequencies (either completely or partially) and then determining the minimum time to go from the initial condition to the final condition according to a continuous time genetic model, with arbitrary constraints on the strength and possibly the form of selection. In analyzing a two-locus, two-allele model with this approach, we show that--so long as r is not much larger than s--substantial linkage disequilibrium can be generated from an initial state of linkage equilibrium in a few hundred generations. We also show that unless recombination is much larger than selection, there is only weak dependence on r of the minimum time to reach a specified state. Thus, similar strengths of selection can lead to similar levels of disequilibrium over a fixed time and a range of small recombination rates. This implies that, within the level of a single gene, selection cannot in general be assumed to lead to any particular relationship between recombination rate and levels of disequilibrium. We indicate a number of other ways in which our method can be useful in asking theoretical questions and in interpreting data.