Gadgil, Sulochana and Nanjundiah, Vidyanand and Gadgil, Madhav (1980) On evolutionarily stable compositions of populations of interacting genotypes. In: Journal of Theoretical Biology, 84 (4). pp. 737-759.
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Consider an organism in which the genetic fitness of an individual depends to a large extent on its social interactions. Assuming the genotypes to differ only in the choice of strategies they adopt in social interactions, and equating the variation in genetic fitness to the mean payoff to an individual averaged over all possible encounters, we develop a dynamical model for the evolution of genotypic frequencies in such a population. Such a system is characterised by frequency dependent selection, and depending on the initial composition, the population evolves towards one of several possible compositions. We term as evolutionarily stable compositions (ESC) any such composition towards which a population can evolve and which is stable against small fluctuations in the frequencies of existing genotypes as well as to invasions by any other postulated genotype. We state the necessary and sufficient conditions for the identification of all possible ESC's for any number of interacting genotypes. Our results conform to those derived earlier in connection with the concept of evolutionarily stable strategies only in the case of two interacting genotypes; when more than two genotypes interact the conditions under which various ESC's exist become far richer. We consider interactions with mixed strategists and show that in a conflict with pure strategists the optimal mixed strategist will be the only one to ultimately survive. We illustrate our approach by considering the specific case of a primitively social wasp.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Centre for Theoretical Studies|
|Date Deposited:||05 Nov 2009 09:00|
|Last Modified:||22 Feb 2014 05:18|
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