Several empirical examples and theoretical models suggest that the greenbeard effect may be an important mechanism in driving the evolution of altruism. However, previous theoretical models rely on assumptions such as spatial structure and specific sets of pleiotropic loci, the importance of which for the evolution of altruism has not been studied. Here, we develop a population-genetic model that clarifies the roles of extrinsic assortment (e.g., due to population viscosity) and pleiotropy in the maintenance of altruism through the greenbeard effect. We show that, when extrinsic assortment is too weak to promote the evolution of altruism on its own, the greenbeard effect can only promote altruism significantly if there is a pleiotropic locus controlling both altruism and signaling. Further, we show that indirect selection via genetic associations is too weak to have a noticeable impact on altruism evolution. We also highlight that, if extrinsic assortment is strong enough to promote the evolution of altruism on its own, it also favors the spread of alleles encoding the other functions of a greenbeard trait (signaling and discriminatory behavior), as well as genetic associations. This occurs despite the fact that the greenbeard effect did not favor the evolution of altruism in the first place. This calls for caution when inferring the causality between greenbeard traits and the evolution of altruism.
