Host phenology regulates parasite–host demographic cycles and eco‐evolutionary feedbacks

Parasite–host interactions can drive periodic population dynamics when parasites overexploit host populations. The timing of host seasonal activity, or host phenology, determines the frequency and demographic impact of parasite–host interactions, which may govern whether parasites sufficiently overexploit hosts to drive population cycles. We describe a mathematical model of a monocyclic, obligate‐killer parasite system with seasonal host activity to investigate the consequences of host phenology on host–parasite dynamics. The results suggest that parasites can reach the densities necessary to destabilize host dynamics and drive cycling as they adapt, but only in some phenological scenarios such as environments with short seasons and synchronous host emergence. Furthermore, only parasite lineages that are sufficiently adapted to phenological scenarios with short seasons and synchronous host emergence can achieve the densities necessary to overexploit hosts and produce population cycles. Host‐parasite cycles also generate an eco‐evolutionary feedback that slows parasite adaptation to the phenological environment as rare advantageous phenotypes can be driven extinct due to a population bottleneck depending on when they are introduced in the cycle. The results demonstrate that seasonal environments can drive population cycling in a restricted set of phenological patterns and provide further evidence that the rate of adaptive evolution depends on underlying ecological dynamics.