A STRONG ALLEE EFFECT AND PARASITOID AGGREGATION IN A DISCRETE HOST–PARASITOID SYSTEM

Abstract

We study a discrete-time model of host–parasitoid interactions, where the host is subject to a strong Allee effect and the parasitoid is aggregated. The system may have multiple coexisting steady states and there are two host population thresholds. The hosts become extinct if it is below the Allee threshold. The other threshold depends on the Allee threshold beyond which the host also becomes extinct due to overcompensated density dependence. When the initial host population size is between the two thresholds, we derive a critical parasitoid population size above which both populations become extinct. The critical size depends on the degree of aggregation of parasitoids. It is shown that both populations are more likely to become extinct if parasitoid aggregation is increased. Numerical simulations reveal that a strong Allee effect on the host can stabilize the host–parasitoid interactions on one hand but may drive both populations to extinction on the other hand. Further, aggregation of the parasitoid can promote population persistence when the host is subject to a strong Allee effect with a large Allee threshold. However, a more aggregated parasitoid population is more vulnerable to extinction if the growth rate of hosts is large.