Allee effects in an iteroparous host population nd in host-parasitoid interactions

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Abstract

We investigate a stage-structured model of an iteroparous popu-lation with two age classes. The population is assumed to exhibit Allee effects hrough reproduction. The asymptotic dynamics of the model depend on the aximal reproductive number of the population. The population may per-sist if the maximal reproductive number is greater than one. There exists a pulation threshold in terms of the unstable interior equilibrium. The host opulation will become extinct if its initial distribution lies below the threshold nd the host population can persist indefinitely if its initial distribution lies bove the threshold. In addition, if the unstable equilibrium is a saddle point nd the system has no 2-cycles, then the stable manifold of the saddle point rovides the Allee threshold for the host. Based on this host population sys-em, we construct a host-parasitoid model to study the impact of Allee effects pon the population interaction. The parasitoid population may drive the host o below the Allee threshold so that both populations become extinct. On the ther hand, under some conditions on the parameters, the host-parasitoid sys-tem may possess an interior equilibrium and the populations may coexist as n interior equilibrium.

Original languageEnglish
Pages (from-to)113-135
Number of pages23
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume15
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Allee effects
  • Monotone map
  • Population threshold
  • Stable manifold

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