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Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes |
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| Authors: | Tao Yi R Cressman B Brooks |
| Institution: | (1) Center for Animal Ecology and Conservational Biology, Institute of Zoology, Academia Sinica, 19 Zhongguancun Lu, Haidian, Beijing, 100080, P.R. China, CN;(2) Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada, CA;(3) Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada, CA |
| Abstract: | The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes. Received: 22 October 1998 |
| Keywords: | : Discrete diploid dynamic Natural selection ESS Period-doubling bifurcation Chaos |
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