  The role of epistatic interactions among loci is a central question in
evolutionary biology and is increasingly relevant in the genomic age. While the
population genetics of compensatory substitution have received considerable
attention, most studies have focused on the case when natural selection is very
strong against deleterious intermediates. In the biologically-plausible
scenario of weak to moderate selection there exist two alternate pathways for
compensatory substitution. In one pathway, a deleterious mutation becomes fixed
prior to occurrence of the compensatory mutation. In the other, the two loci
are simultaneously polymorphic. The rates of compensatory substitution along
these two pathways and their relative probabilities are functions of the
population size, selection strength, mutation rate, and recombination rate. In
this paper these rates and path probabilities are derived analytically and
verified using population genetic simulations. The expected time durations of
these two paths are similar when selection is moderate, but not when selection
is weak. The effect of recombination on the dynamics of the substitution
process are explored using simulation. Using the derived rates, a phylogenetic
substitution model of the compensatory evolution process is presented that
could be used for inference of population genetic parameters from interspecific
data.
