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

Abstract

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 ra- tio theory is a contradiction, not an extension, of kin selection. In kin selection, Hamilton developed the coefficient of re- latedness 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 the- ory, 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 Ham- ilton's altruists. Gene-centric modelers must clarify which relatedness coefficient, arithmetic or probability, they are using to frame their predictions.