A DARWINIAN DYNAMIC MODEL for the EVOLUTION of POST-REPRODUCTION SURVIVAL

J. M. Cushing; Kathryn Stefanko

doi:10.1142/S0218339021400088

A DARWINIAN DYNAMIC MODEL for the EVOLUTION of POST-REPRODUCTION SURVIVAL

J. M. Cushing, Kathryn Stefanko

Mathematics

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12 Scopus citations

Abstract

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

Original language	English (US)
Pages (from-to)	433-450
Number of pages	18
Journal	Journal of Biological Systems
Volume	29
Issue number	2
DOIs	https://doi.org/10.1142/S0218339021400088
State	Published - Jun 2021

Keywords

Allee Effect
Evolutionary Population Dynamics
Life History Strategy
Semelparity

ASJC Scopus subject areas

Ecology
Agricultural and Biological Sciences (miscellaneous)
Applied Mathematics

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10.1142/S0218339021400088

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title = "A DARWINIAN DYNAMIC MODEL for the EVOLUTION of POST-REPRODUCTION SURVIVAL",

abstract = "We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.",

keywords = "Allee Effect, Evolutionary Population Dynamics, Life History Strategy, Semelparity",

author = "Cushing, {J. M.} and Kathryn Stefanko",

note = "Funding Information: This work was supported by NSF grant DMS 1407564. Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

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AU - Cushing, J. M.

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N2 - We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

AB - We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

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KW - Evolutionary Population Dynamics

KW - Life History Strategy

KW - Semelparity

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A DARWINIAN DYNAMIC MODEL for the EVOLUTION of POST-REPRODUCTION SURVIVAL

Abstract

Keywords

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