Gene-culture coevolution: models for the evolution of altruism with cultural transmission

Models of sexual haploids under kin selection are constructed. The trait of altruism is transmitted vertically from parent to child, but not in a strictly genetic manner. Two systems of altruism are considered: parent-to-offspring and sib-to-sib. In the former case it is shown that even when Hamilton's conditions for the success of genetically determined altruism are met, genes that increase the transmission of altruism may not invade the population. With sib-to-sib altruism, such genes will always increase initially.