Feedback between coevolution and epidemiology can help or hinder the maintenance of genetic variation in host-parasite models.

Antagonistic coevolution has long been suggested to help maintain host genetic variation. Although ecological and epidemiological feedbacks are known to have important consequences on coevolutionary allele-frequency dynamics, their effects on the maintenance of genetic variation remains poorly understood. Here, we extend previous work on the maintenance of genetic variation in a classic matching alleles coevolutionary model by exploring the effects of ecological and epidemiological feedbacks, where both allele frequencies and population sizes are allowed to vary over time. We find that coevolution rarely maintains more host genetic variation than expected under neutral genetic drift alone. When and if coevolution maintains or depletes genetic variation relative to neutral drift is determined, predominantly, by two factors: the deterministic stability of the Red Queen allele-frequency cycles and the chance of allele fixation in the pathogen, as this results in directional selection and depletion of genetic variation in the host. Compared to purely coevolutionary models with constant host and pathogen population sizes, ecological and epidemiological feedbacks stabilize Red Queen cycles deterministically, but population fluctuations in the pathogen increase the rate of allele fixation in the pathogen, especially in epidemiological models. Our results illustrate the importance of considering the ecological and epidemiological context in which coevolution occurs when examining the impact of Red Queen cycles on genetic variation.