Green beards in the light of indirect genetic effects.

The green-beard effect is one proposed mechanism predicted to underpin the evolution of altruistic behavior. It relies on the recognition and the selective help of altruists to each other in order to promote and sustain altruistic behavior. However, this mechanism has often been dismissed as unlikely or uncommon, as it is assumed that both the signaling trait and altruistic trait need to be encoded by the same gene or through tightly linked genes. Here, we use models of indirect genetic effects (IGEs) to find the minimum correlation between the signaling and altruistic trait required for the evolution of the latter. We show that this correlation threshold depends on the strength of the interaction (influence of the green beard on the expression of the altruistic trait), as well as the costs and benefits of the altruistic behavior. We further show that this correlation does not necessarily have to be high and support our analytical results by simulations.