J. Theor. Biol. (1982) 97,437-480 Evolutionarily Stable Levels of Altruism in Haploid and Diploid Species MICHEL TREISMAN Department of Experimental Psychology, University of Oxford, South Parks Road, Oxford OX1 3UD, England (Received 18 June 1981, and in revised form 8 January 1982) The evolution of altruism has been analysed in terms of “inclusive fitness”, population genetic theory, and game theory. An attempt is made to combine the genetic and game theory approaches to provide an analysis of the evolution of altruism in both haploid and diploid species, A game theory analysis of altruism in a dyad is applied to three models of altruism, in both types of genetic system, both for unrelated individuals and for siblings. In these models Hamilton’s (1963) benefit-cost ratio k does not necessarily determine selection for altruism in all-or-none fashion: at any level of k there may be a corresponding stable level of expression of altruism. Parallels are drawn between the determination of altruism in haploid and diploid dyads, and it is noted that diploid species in which the determination of altruism is recessive may show higher levels of altruism than those with dominant determination. The model is extended to groups of more than two animals, again for both haploid and diploid species, and the stable polymorphisms and evolutionarily stable strategies for these cases are identified. These results qualify the application of the concept of “inclusive fitness”. 1. The Evolution of Altruism The occurrence of altruism IS a central problem in understanding social behavior. The term is applied to behavior which favors the evolutionary success of a recipient member or members of a species at some cost to the actor. It may but need not involve a social interaction. The selective effects of such behavior will depend on the genotypes of the conspecifics affected and so its selection is frequency dependent. Three main approaches have been employed to analyse the evolution of altruism. These are based on the concept of “inclusive fitness”, population genetic analysis, or evolution- ary game theory. Evolution consists in statistical changes in the prevalence of different genetical types in a population. The classical approach, which ascribes Darwinian fitness to individuals of a given genotype, has been used success- fully to analyse the development of characteristics, such as a long neck, 437 0022-5193/82/150437+44$03.00/O @ 1982 Academic Press Inc. (London) Ltd.