Models of cooperation

Models serve many possible purposes. The very bestmodels provide insights that revolutionize a field. Afamous case of this is W.D. Hamilton’s (1964) model ofinclusive fitness, or kin selection. This model provoked achange in how social behaviour is studied with a newemphasis on genetic relatedness and kin discrimination(Hamilton, 1964). Hamilton’s derivation was neitherelegant nor all-inclusive, though subsequent work bothmade the derivation more transparent (e.g. Queller,1985, 1992a; Frank, 1998) and expanded the domain ofsocial selection (models cited in Lehmann & Keller,2006). But Hamilton’s powerful result – Hamilton’s rule –has continued to inspire researchers, and not justtheorists. Empirical work has ranged in topic fromaltruism (Hamilton, 1964, 1972) to social insect sexratios (Trivers & Hare, 1976) to siblicide (Mock & Parker,1997) and from microbes (Crespi, 2001) to humans(Alexander, 1979).The model of Lehmann & Keller (2006) will not berevolutionary in this way. Their goal is not to highlight anew principle. Nor is it extreme rigor – the model is builtfrom principles of optimality and inclusive fitness ratherthanbeingbaseddirectlyongenefrequencies.Insteaditisan effort to systematize what we have learned about theforces of social evolution. In some ways their results arenot surprising. They put in relatedness, fitness effects andrepeated interactions, and they get out kin selection,direct benefits and reciprocity (with greenbeard effectstackedon asasortofafterthought).We agreethatthis isanice summary of important forces and that studies basedon these forces will continue to be important. However,we only partially agree with the authors’ main novelclaims: that this is a more comprehensive model thanmost and that the four forces that it defines aresufficientlydistinct, important,and all-inclusivethat theyshould always be the touchstone for other modellers.On the point of comprehensiveness, we would arguethat there is at least one other model (Queller, 1985) thatis as comprehensive, and actually more so. The modelincludes all four of the forces in the Lehmann and Kellermodel, and then some. It shows that a behaviour isfavoured when c þ bcov