Subsistence of sib altruism in different mating systems and Haldane arithmetic

Abstract

The moral rule "Risk your life to save your family members" is, at the same time, a biological phenomenon. The prominent population geneticist, J.B.S. Haldane told his friends that he would risk his life to save two drowning brothers, but not one - so the story goes. In biological terms, Haldanes arithmetic claims that sib altruism is evolutionarily rational, whenever by "self-sacrifice" an altruistic gene "rescues", on average, more than one copy of itself in its lineage. Here, we derive conditions for evolutionary stability of sib altruism, using population genetic models for three mating systems (monogamy, promiscuity and polygyny) with linear and non-linear group effect on the siblings survival rate. We show that for all considered selection situations, the condition of evolutionary stability is equivalent to Haldanes arithmetic. The condition for evolutionary stability is formulated in terms of genetic relatedness and the group effect on the survival probability, similarly to the classical Hamiltons rule. We can set up a "scale of mating systems", since in pairwise interactions the chance of evolutionary stability of sib altruism decreases in this order: monogamy, polygyny and promiscuity. Practice of marrying and siblings solidarity are moral rules in a secular world and in various religious traditions. These moral rules are not evolutionarily independent, in the sense that the subsistence of sib altruism is more likely in a monogamous population. HighlightsO_LIHaldanes arithmetic is introduced C_LIO_LIConditions for evolutionary stability of sib altruism are given C_LIO_LIEvolutionary stability is equivalent to Haldanes arithmetic in the studied model C_LIO_LIGeneralized Hamiltons rules are formulated C_LI