The form of density-dependence in host growth impacts parasitoid-driven host suppression

Leveraging the discrete-time formalism of the Nicholson-Bailey model, we investigate the ecological population dynamics of host-parasitoid interactions with an arbitrary form of density-dependence in the host growth rate, and map out regimes allowing stable coexistence of the consumer (parasitoid) and the resource (host). If the parasitoid-free host population dynamics is stable, we provide sufficient conditions that ensure stability is maintained with the inclusion of the parasitoid irrespective of the level of parasitism. When parasitoids parasitize hosts at a constant rate, high parasitism levels are shown to always destabilize the population dynamics. This results in a limit of host suppression that we quantify using the ratio of host density (just before stability is lost for high parasitism levels) and the host's parasitoid-free carrying capacity. We systematically examine this limit for different types of intrinsic self-limitations in host growth. Our analysis shows that for both Ricker and Beverton-Holt-type host population dynamics, this parasitoid-driven host suppression limit is 33% for slow-growing hosts and 10-20% for fast-growing hosts. Moreover, our results reveal that these limits can be much higher for Hill-type density-dependence in host growth rate. In summary, this contribution characterizes the impact of coupling different forms of intrinsic host population dynamics with and without additional stabilizing factors (such as a fraction of hosts protected from parasitism). These results have important implications for using parasitoids as natural enemies against arthropod pest populations, and the success of such biological control is inherently tied to the form of self-limitation in host growth.