A dynamic game theory model of a diploid genetic system

The dynamic game theory model developed previously for asexual organisms is extended to randomly mating diploid populations where the strategy used is determined by a single locus. Any number of strategies may be considered in the model, but only the case of hierarchical dominance is treated. An algorithm is given for determining all equilibria in any given game, and for checking these equilibria for local stability. Many of the stability properties found in our previous paper for asexual populations also apply to diploid populations, but, in contrast to asexual populations, diploid populations with no evolutionarily stable points (ESPs) can exhibit stable oscillations.

[1]  B. Thomas.  Genetical ESS-models. II. Multi-strategy models and multiple alleles. , 1985, Theoretical population biology.

[2]  Richard L. W. Brown.  Evolutionary game dynamics in diploid populations , 1983 .

[3]  G. Rowe.  Mutations, mixed strategies and game theory , 1985 .

[4]  W. G. S. Hines.  Strategy stability in complex randomly mating diploid populations , 1982 .

[5]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[6]  W. Hines,et al.  Evolutionarily stable strategies in diploid populations with general inheritance patterns , 1983, Journal of Applied Probability.

[7]  W. Hines,et al.  Can and will a sexual diploid population attain an evolutionary stable strategy , 1984 .

[8]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[9]  B. Noble.  Applied Linear Algebra , 1969 .

[10]  B. Thomas.  Genetical ESS-models. I. Concepts and basic model. , 1985, Theoretical population biology.

[11]  On the local stability of an evolutionarily stable strategy in a diploid population , 1984 .

[12]  L. Ginzburg.  Theory of natural selection and population growth , 1983 .

[13]  PLAYER I. TWO-SPECIES HAPLOID OR RANDOMLY MATING DIPLOID , 1985 .

[14]  Constancy of mean strategy versus constancy of gene frequencies in a sexual diploid population , 1986 .

[15]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[16]  G. Rowe,et al.  The essential properties of evolutionary stability , 1985 .