Limits of Hamilton's rule

The evolution of cooperation is a fundamental problem in evolutionary biology. Over the last decades a wealth of models and mechanisms have been proposed for explain- ing how cooperators can thrive under Darwinian selec- tion. At the same time, discussions of the conceptual connections between the different approaches have often been neglected. The synthesis proposed by Lehmann & Keller (2006) is therefore a welcome contribution to the literature on the evolution of cooperation. Their frame- work for understanding the evolution of cooperative traits is based on the fitness gradient. A particular mechanism is said to favour cooperation if it generates a positive fitness gradient towards higher values of the cooperative trait. The proposed framework is based on an extension of Hamilton's rule that is obtained by adjusting and reinterpreting costs, benefits and genetic relatedness. While such an approach may be useful in many circum- stances, we would like to point out that if selection on cooperation is frequency-dependent, the classification given by Lehmann & Keller (2006) is not applicable in an interesting class of evolutionary scenarios.