Sex Ratio Theory is a Contradiction, Not an Extension, of Kin Selection

Kin selection and sex ratio theory employ gene-centric models with coefficients of relatedness to explain the evolution of altruism in the social Hymenoptera. Central to both theories is the fact that Hymenoptera organisms are haplodiploid, a condition that creates an asymmetry in relatedness among siblings. This paper exposes the fact that sex ratio theory is a contradiction, not an extension, of kin selection. In kin selection, Hamilton developed the coefficient of relatedness as a probability fraction. Hamilton’s altruists must help a small number of close relatives or a large number of distant relatives to ensure that one copy of their altruistic genes are propagated into the next generation. In sex ratio theory, Trivers and Hare modeled the coefficient of relatedness as an arithmetic fraction rather than a probability fraction. As a result, their altruists help a large number of close relatives and a small number of distant relatives, the opposite of Hamilton’s altruists. Gene-centric modelers must clarify which relatedness coefficient, arithmetic or probability, they are using to frame their predictions.