# American Institute of Mathematical Sciences

January  2011, 15(1): 113-135. doi: 10.3934/dcdsb.2011.15.113

## Allee effects in an iteroparous host population and in host-parasitoid interactions

 1 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States

Received  December 2009 Revised  May 2010 Published  October 2010

We investigate a stage-structured model of an iteroparous population with two age classes. The population is assumed to exhibit Allee effects through reproduction. The asymptotic dynamics of the model depend on the maximal reproductive number of the population. The population may persist if the maximal reproductive number is greater than one. There exists a population threshold in terms of the unstable interior equilibrium. The host population will become extinct if its initial distribution lies below the threshold and the host population can persist indefinitely if its initial distribution lies above the threshold. In addition, if the unstable equilibrium is a saddle point and the system has no $2$-cycles, then the stable manifold of the saddle point provides the Allee threshold for the host. Based on this host population system, we construct a host-parasitoid model to study the impact of Allee effects upon the population interaction. The parasitoid population may drive the host to below the Allee threshold so that both populations become extinct. On the other hand, under some conditions on the parameters, the host-parasitoid system may possess an interior equilibrium and the populations may coexist as an interior equilibrium.
Citation: Sophia R.-J. Jang. Allee effects in an iteroparous host population and in host-parasitoid interactions. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 113-135. doi: 10.3934/dcdsb.2011.15.113
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