Limiting Relationships Between Selection and Recombination

It is difficult to directly observe processes like natural selection at the genetic level, but relatively easy to estimate genetic frequencies in populations. As a result, genetic frequency data are widely used to make inferences about the underlying evolutionary processes. However, multiple processes can generate the same patterns of frequency data, making such inferences weak. By studying the limits to the underlying processes, one can make inferences from frequency data by asking how strong selection (or some other process of interest) would have to be to generate the observed pattern. Here we present results of a study of the limits to the relationship between selection and recombination in two-locus, twoallele systems in which we found the limiting relationships for over 30 000 sets of parameters, effectively covering the range of two-locus, two-allele problems. Our analysis relates Tmin—the minimum time for a population to evolve from the initial to the final conditions—to the strengths of selection and recombination, the amount of linkage disequilibrium, and the Nei distance between the initial and final conditions. Tmin can be large with either large disequilibrium and small Nei distance, or the reverse. The behavior of Tmin provides information about the limiting relationships between selection and recombination. Our methods allow evolutionary inferences from frequency data when deterministic processes like selection and recombination are operating; in this sense they complement methods based entirely on drif