Scramble competitions can rescue endangered species subject to strong Allee effects

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

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.

A host-parasitoid system with predation-driven component Allee effects in host population

Allee effects and parasitism are common biological phenomena observed in nature, which are believed to have significant impacts in ecological conservation programmes. In this article, we investigate population dynamics of a discrete-time host-parasitoid system with component Allee effects induced by predation satiation in host to study the synergy effects of Allee effects and parasitism. Our model assumes that parasitism attacks the host after the density dependence of the host. The interactions of component Allee effects and parasitism can lead to extremely rich dynamics that include but are not limited to extinction of both species due to Allee effects at their low population density, multiple attractors, strange interior attractors and even crisis of strange attractor due to high parasitism. We perform local and global analysis to study the number of equilibria and their stability; and study the extinction and permanence of our host-parasitoid system. One of the most interesting results shows that the combination of strong Allee effects and parasitism may promote the coexistence of both host and parasite at their high population density. In addition, component Allee effects may destroy interior equilibrium under different values of parameters' ranges.