Abstract
We investigate a stage-structured model of an iteroparouspopulation with two age classes. The population is assumed toexhibit Allee effects through reproduction. The asymptoticdynamics of the model depend on the maximal reproductive number ofthe population. The population may persist if the maximalreproductive number is greater than one. There exists a populationthreshold in terms of the unstable interior equilibrium. The hostpopulation will become extinct if its initial distribution liesbelow the threshold and the host population can persistindefinitely if its initial distribution lies above thethreshold. In addition, if the unstable equilibrium is a saddlepoint and the system has no $2$-cycles, then the stable manifoldof the saddle point provides the Allee threshold for the host.Based on this host population system, we construct ahost-parasitoid model to study the impact of Allee effects uponthe population interaction. The parasitoid population may drivethe host to below the Allee threshold so that both populationsbecome extinct. On the other hand, under some conditions on theparameters, the host-parasitoid system may possess an interiorequilibrium and the populations may coexist as an interiorequilibrium.
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