A model of kin selection not invoking coefficients of relationship

Abstract

The pioneering work of Hamilton assumed the coefficient of relationship easy to compute and used it to predict the direction of selection acting on “genes for altruism” in a theoretical model. A similar model is presented here which does not require the coefficient of relationship as explicit data, in order to predict the direction of selection. The model presented implicitly defines the coefficient of relationship and is reducible to two equations. Inverting one of these produces an explicit formula for the coefficient of relationship. This formula has a domain of input beyond traditional formulae for the coefficient of relationship. These include: 1. (1) Populations undergoing selection during half dominance and populations not undergoing selection while altruism is either dominant or recessive. 2. (2) Populations undergoing selection on an altruism gene while that gene is either dominant or recessive. The formula agrees with Hamilton's regression coefficient of relatedness when dealing with the category (1) populations, but not when dealing with the category (2) populations. The biological significance of the model is mainly: 1. (a) Traditional coefficients of relationship apply in the absence of selection only when: (i) the gene for altruism, or its alternate allele, is infinitesimally rare; (ii) half dominance prevails i.e. the heterozygote uses half of its resources selfishly and the other half altruistically; (iii) the beneficiary's fitness is only infinitesimally augmented by the altruism, e.g. when the beneficiary would have had an infinite number of children anyway. 2. (b) At other times in the absence of selection the coefficient of relationship alters so as to: (i) deviate most from traditional coefficients when the frequency of the altruism gene is approximately one-half; (ii) favour selection for the dominant allele; (iii) account for the fact that increasing the number of offspring which the beneficiary has anyway, always helps the recessive allele. Rapid selection against a dominant altruism gene causes the coefficient of relationship, as defined here, to approach unity as the frequency of the altruism gene approaches zero. This result and all departures of the coefficient defined here frum Hamilton's regression coefficient, during selection with gene dominance, can be accounted for as a hysteresis effect due to the fact there is no selection in the males. This model may be generalized to one which sheds light on the selective advantages of sexual reproduction and it is proposed here that self-dilution (which includes altruism and sexual reproduction) may be as important an asset to the animal as self-replication in evolution. The significance of this on existing definitions of altruism is discussed.