Difference equations as models of evolutionary population dynamics
AuthorCushing, J M
AffiliationUniv Arizona, Dept Math, Interdisciplinary Program Appl Math
evolutionary game theory
MetadataShow full item record
PublisherTAYLOR & FRANCIS LTD
CitationJ. M. Cushing (2019) Difference equations as models of evolutionary population dynamics, Journal of Biological Dynamics, 13:1, 103-127, DOI: 10.1080/17513758.2019.1574034
JournalJOURNAL OF BIOLOGICAL DYNAMICS
Rights© 2019 The Author(s).
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at email@example.com.
AbstractWe describe the evolutionary game theoretic methodology for extending a difference equation population dynamic model in a way so as to account for the Darwinian evolution of model coefficients. We give a general theorem that describes the familiar transcritical bifurcation that occurs in non-evolutionary models when theextinction equilibrium destabilizes. This bifurcation results in survival (positive) equilibria whose stability depends on the direction of bifurcation. We give several applications based on evolutionary versions of some classic equations, such as the discrete logistic (Beverton-Holt) and Ricker equations. In addition to illustrating our theorems, these examples also illustrate other biological phenomena, such as strong Allee effects, time-dependent adaptive landscapes, and evolutionary stable strategies.
NoteOpen Access Journal
VersionFinal published version
SponsorsUS National Science Foundation [DMS-1407564]
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