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A NOTE ON THE NON-EQUIVALENCE OF A LOTKA-VOLTERRA MODEL AND A CONTINUOUS REPLICATOR

TitleA NOTE ON THE NON-EQUIVALENCE OF A LOTKA-VOLTERRA MODEL AND A CONTINUOUS REPLICATOR
Publication TypeJournal Article
Year of Publication2017
AuthorsSlade, PF
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume11
Issue2
Start Page99
Pagination8
Date Published04/2017
Type of Articlescientific: mathematics
ISSN1314-0744
Keywordsevolutionary game theory, inter-species competition, predator-prey model
Abstract
The equivalence of a continuous-time replicator equation for $n$ strategies with a Lotka-Volterra equation for $n-1$ competing species, under a suitable transformation of variables, is disproven. The correction relates to the parametric conversion corresponding to a transformation of variables between these two models suggested widely in the literature of mathematical biology. An alternative approach shown here is purely algebraic instead of the heuristic calculus with which the earlier equivalence result was obtained. The particular and unavoidable non-linearity that arises to prevent the conversion is unambiguously identified. Consequently, it is shown that no such bridge exists between these foundational equations of evolutionary game theory and theoretical ecology, bearing on evolutionary properties of multi-species communities.
URLhttp://www.e.ijpam.eu/contents/articles/201701102003.pdf
DOI10.12732/iejpam.v11i2.3
Refereed DesignationRefereed
Full Text
Editorial Comments: Original publication (2017-04-10). Download file from here. Corrections (2017-04-27).