Authors: Yuanyuan Huang Zhijun Wu
Publish Date: 2012/03/21
Volume: 74, Issue: 7, Pages: 1469-1484
Abstract
Game theoretic models along with replicator equations have been applied successfully to the study of evolution of populations of competing species including the growth of a population the reaching of the population to an equilibrium state and the evolutionary stability of the state In this paper we analyze a game model proposed by Gore et al Nature 456253–256 2009 in their recent study on the codevelopment of two mixed yeast strains We examine the mathematical properties of this model with varying experimental parameters We simulate the growths of the yeast strains and compare them with the experimental results We also compute and analyze the equilibrium state of the system and prove that it is asymptotically and evolutionarily stableWe would like to thank Prof Jeff Gore for kindly giving us the Matlab code for generating some of the graphical results in their paper and for providing helpful suggestions and advices for how to proceed in our computation This work is partially supported by the NIH/ /NIGMS grants R01GM072014 and R01GM081680 and by the NSF/ /DMS grant DMS0914354
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