Dynamics of an age-structured population with allee effects and harvesting

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Abstract

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depend on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.

Original languageEnglish
Pages (from-to)409-427
Number of pages19
JournalJournal of Biological Dynamics
Volume4
Issue number4
DOIs
StatePublished - Jul 2010

Keywords

  • Age-structure
  • Allee effects
  • Harvesting
  • Population threshold

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