Darwinian dynamics of a juvenile-adult model

Jim M Cushing, Simon Maccracken Stump

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The bifurcation that occurs from the extinction equilibrium in a basic discrete time, nonlinear juvenile-adult model for semelparous populations, as the inherent net reproductive number R0 increases through 1, exhibits a dynamic dichotomy with two alternatives: an equilibrium with overlapping generations and a synchronous 2-cycle with non-overlapping generations. Which of the two alternatives is stable depends on the intensity of competition between juveniles and adults and on the direction of bifurcation. We study this dynamic dichotomy in an evolutionary setting by assuming adult fertility and juvenile survival are functions of a phenotypic trait u subject to Darwinian evolution. Extinction equilibria for the Darwinian model exist only at traits u* that are critical points of R0 (u). We establish the simultaneous bifurcation of positive equilibria and synchronous 2-cycles as the value of R0 (u*) increases through 1 and describe how the stability of these dynamics depend on the direction of bifurcation, the intensity of between-class competition, and the extremal properties of R0 (u) at u*. These results can be equivalently stated in terms of the inherent population growth rate r (u).

Original languageEnglish (US)
Pages (from-to)1017-1044
Number of pages28
JournalMathematical Biosciences and Engineering
Volume10
Issue number4
DOIs
StatePublished - Aug 2013

Fingerprint

Bifurcation
Population Growth
Dichotomy
extinction
Extinction
Fertility
Reproductive number
Overlapping Generations
Cycle
Alternatives
population growth
Model
Population
Critical point
Discrete-time
Direction compound

Keywords

  • Bifurcation
  • Darwinian dynamics
  • Dynamic dichotomy
  • Equilibrium
  • Evolutionary game theory
  • Juvenile-adult population model
  • Semelparity
  • Structured population dynamics
  • Synchronous cycles

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

Darwinian dynamics of a juvenile-adult model. / Cushing, Jim M; Stump, Simon Maccracken.

In: Mathematical Biosciences and Engineering, Vol. 10, No. 4, 08.2013, p. 1017-1044.

Research output: Contribution to journalArticle

Cushing, Jim M ; Stump, Simon Maccracken. / Darwinian dynamics of a juvenile-adult model. In: Mathematical Biosciences and Engineering. 2013 ; Vol. 10, No. 4. pp. 1017-1044.
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