Discrete-time population dynamics of spatially distributed semelparous two-sex populations

Horst R. Thieme

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Spatially distributed populations with two sexes may face the problem that males and females concentrate in different parts of the habitat and mating and reproduction does not happen sufficiently often for the population to persist. For simplicity, to explore the impact of sex-dependent dispersal on population survival, we consider a discrete-time model for a semelparous population where individuals reproduce only once in their life-time, during a very short reproduction season. The dispersal of females and males is modeled by Feller kernels and the mating by a homogeneous pair formation function. The spectral radius of a homogeneous operator is established as basic reproduction number of the population, R. If R< 1 , the extinction state is locally stable, and if R> 1 the population shows various degrees of persistence that depend on the irreducibility properties of the dispersal kernels. Special cases exhibit how sex-biased dispersal affects the persistence of the population.

Original languageEnglish (US)
Article number18
JournalJournal Of Mathematical Biology
Volume83
Issue number2
DOIs
StatePublished - Aug 2021

Keywords

  • Basic turnover number
  • Eigenfunctional
  • Extinction
  • Integral projection models
  • Integro-difference equations
  • Net reproductive value
  • Ordered normed vector spaces
  • Population growth factor
  • Spectral radius of homogeneous operators
  • Stability
  • Uniform persistence
  • compact attractor

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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