Kinship, reciprocity and synergism in the evolution of social behaviour

There are two ways to model the genetic evolution of social behaviour. Population genetic models using personal fitness^{1 -9} may be exact and of wide applicability, but they are often complex and assume very different forms for different kinds of social behaviour. The alternative, inclusive fitness models^{10 -12}, achieves simplicity and clarity by attributing all fitness effects of a behaviour to an expanded fitness of the actor. For example, Hamilton's rule states that an altruistic behaviour will be favoured when -c + rb>0, where c is the fitness cost to the altruist, b is the benefit to its partner, and r is their relatedness. But inclusive fitness results are often inexact for interactions between kin^1-5, and they do not address phenomena such as reciprocity^13-15 and synergistic effects^7,8,16 that may either be confounded with kinship or operate in its absence. Here I develop a model the results of which may be expressed in terms of either personal or inclusive fitness, and which combines the advantages of both; it is general, exact, simple and empirically useful. Hamilton's rule is shown to hold for reciprocity as well as kin selection. It fails because of synergistic effects, but this failure can be corrected through the use of coefficients of synergism, which are analogous to the coefficient of relatedness.