One dimensional maps as population and evolutionary dynamic models

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

I discuss one dimensional maps as discrete time models of population dynamics from an extinction-versus-survival point of view by means of bifurcation theory. I extend this approach to a version of these population models that incorporates the dynamics of a single phenotypic trait subject to Darwinian evolution. This is done by proving a fundamental bifurcation theorem for the resulting two dimensional, discrete time model. This theorem describes the bifurcation that occurs when an extinction equilibrium destabilizes. Examples illustrate the application of the theorem. Included is a short summary of generalizations of this bifurcation theorem to the higher dimensional maps that arise when modeling the evolutionary dynamics of a structured population.

Original languageEnglish (US)
Title of host publicationApplied Analysis in Biological and Physical Sciences - ICMBAA 2015
PublisherSpringer New York LLC
Pages41-62
Number of pages22
Volume186
ISBN (Print)9788132236382
DOIs
StatePublished - 2016
EventInternational Conference on Recent Advances in Mathematical Biology, Analysis and Applications, ICMBAA 2015 - Aligarh, India
Duration: May 25 2016May 29 2016

Other

OtherInternational Conference on Recent Advances in Mathematical Biology, Analysis and Applications, ICMBAA 2015
CountryIndia
CityAligarh
Period5/25/165/29/16

Keywords

  • Allee effects
  • Bifurcations
  • Difference equations
  • Discrete time dynamics
  • Equilibria
  • Evolutionary dynamics
  • Population dynamics
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)

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