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Game Dynamic Model for Yeast Development

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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 456:253–256, 2009) in their recent study on the co-development 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 stable.

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Acknowledgements

We 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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  1. Department of Mathematics, Program on Bioinformatics and Computational Biology, Iowa State University, Ames, IA, 50011, USA

    Yuanyuan Huang & Zhijun Wu

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  1. Yuanyuan Huang
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  2. Zhijun Wu
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Correspondence to Yuanyuan Huang.

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Huang, Y., Wu, Z. Game Dynamic Model for Yeast Development. Bull Math Biol 74, 1469–1484 (2012). https://doi.org/10.1007/s11538-012-9721-5

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  • DOI: https://doi.org/10.1007/s11538-012-9721-5

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