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

 Title A NOTE ON THE NON-EQUIVALENCE OF A LOTKA-VOLTERRA MODEL AND A CONTINUOUS REPLICATOR Publication Type Journal Article Year of Publication 2017 Authors Slade, PF Journal International Electronic Journal of Pure and Applied Mathematics Volume 11 Issue 2 Start Page 99 Pagination 8 Date Published 04/2017 Type of Article scientific: mathematics ISSN 1314-0744 Keywords evolutionary 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. URL http://www.e.ijpam.eu/contents/articles/201701102003.pdf DOI 10.12732/iejpam.v11i2.3 Refereed Designation Refereed Full Text Editorial Comments: Original publication (2017-04-10). Download file from here. Corrections (2017-04-27).