A quantitative genetic model of reciprocal altruism: a condition for kin or group selection to prevail.

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Abstract
A condition is derived for reciprocal altruism to evolve to kin or group selection. It is assumed that many additively acting genes of small effect and the environment determine the probability that an individual [animal] is a reciprocal altruist, as opposed to being unconditionally selfish. The particular form of reciprocal altruism considered is TIT FOR TAT, a strategy that involves being altruistic on the 1st encounter with another individual and doing whatever the other did on the previous encounter in subsequent encounters with the same individual. Encounters are restricted to individuals of the same generation belonging to the same kin or breeding group, but 1st encounters occur at random within that group. The number of individuals with which an individual interacts is assumed to be the same within any kin or breeding group. Thereare 1 + .hivin.i expected encounters between 2 interacting individuals. On any encounter, it is assumed that an individual who behaves altruistically suffers a cost in personal fitness proportional to c while improving his partner''s fitness by the same proportion by b. Then, the condition for kin or group selection to prevail is r > {(c/b) - [1 - (c/b)].hivin.i.hivin.C}/{1 + [1 - (c/b)].hivin.i[.hivin.C + (Tb/Vb)]} if group size is sufficiently large and the group mean and the within-group genotypic variance of the trait value (i.e., the probability of being a TIT-FOR-TAT strategist) are uncorrelated. Here, .hivin.C, Vb and Tb are the population mean, between-group variance, and between-group 3rd central moment of the trait value and r is the correlation between the additive genotypic values of interacting kin or of individuals within the same breeding group. The right-hand side of the above inequality is monotone decreasing in .hivin.C if we hold Tb/Vb constant, and kin and group selection become superfluous beyond a certain threshold values of .hivin.C. The effect of finite group size is also considered in a kin-selection model.

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