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

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...

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Bibliographic Details
Published in:Journal of mathematical biology 2021-08, Vol.83 (2), p.18-18, Article 18
Main Author: Thieme, Horst R.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Dispersal
Dispersion
Females
Kernels
Males
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Pair bond
Population
Population dynamics
Populations
Reproduction
Sex
Species extinction
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Summary: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 0 . If R 0 < 1 , the extinction state is locally stable, and if R 0 > 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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-021-01649-4