Coevolution fails to maintain genetic variation in a host-parasite model with constant finite population size

Coevolutionary negative frequency-dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the temporal dynamics of genetic variation have not been examined in a matching-alleles model (MAM) with a finite population size relative to the expectation under neutral genetic drift alone. The dynamics of the MA coevolution in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. By comparing host heterozygosity to the expectation in a single-species model of neutral genetic drift we find that while this is also largely true in finite populations two additional phenomena arise. First, reciprocal natural selection acting on stochastic perturbations in host and pathogen allele frequencies results in a slight increase or decrease in genetic variation depending on the parameter conditions. Second, following the fixation of an allele in the parasite, selection in the MAM becomes directional, which then rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.