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.

中文翻译：

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离散宿主-寄生虫系统中的强等位基因效应和寄生虫聚集

我们研究了宿主 - 寄生蜂相互作用的离散时间模型，其中宿主受到强烈的 Allee 效应并且寄生蜂聚集。该系统可能有多个共存的稳态，并且有两个宿主种群阈值。如果宿主低于 Allee 阈值，则宿主将灭绝。另一个阈值取决于 Allee 阈值，超过该阈值宿主也会由于过度补偿的密度依赖性而灭绝。当初始宿主种群大小介于两个阈值之间时，我们得出一个临界寄生蜂种群大小，超过该种群大小，两个种群都会灭绝。临界大小取决于寄生蜂的聚集程度。结果表明，如果寄生蜂聚集增加，这两个种群更有可能灭绝。数值模拟表明，对宿主的强烈 Allee 效应一方面可以稳定宿主 - 寄生生物的相互作用，但另一方面可能会导致两个种群灭绝。此外，当宿主受到具有大 Allee 阈值的强 Allee 效应时，寄生蜂的聚集可以促进种群持久性。但是，如果寄主的增长率很大，则更聚集的寄生蜂种群更容易灭绝。