Relatedness in trait group models of social evolution

Genetic relatedness is a central concept in the study of social evolution. Though originally defined in terms of genealogy, the modern version of relatedness accommodates genetic similarity of any origin. This paper examines relatedness in group structured modes, in which a trait affects the fitness of all group members. Such traits can be divided into two types, based on whether their group fitness effects encompass all group members including the actor ("whole-group traits"), or only group members other than the actor ("other-only traits"). Both trait types are common in nature as well as in theoretical models, but they have rarely been distinguished clearly. The average relatedness of recipients to actors differs for the two trait types within the same population and even the same individual, leading to different selection pressures and evolutionary outcomes. Total relatedness in group-structured models can be partitioned into two components: structural relatedness due to the size and number of groups in the population, and assortative relatedness due to the distribution of genotypes among groups. Each component differs for whole-group vs. other-only traits, both in terms of their values and the factors that influence them. Some key differences include: positive relatedness requires positive assortment for other-only but not for whole-group traits; negative relatedness is possible for other-only but not whole-group traits; relatedness depends on average group size for whole-group but not other-only traits, and non-random assortment into groups affects relatedness more strongly for other-only than whole-group traits. Recognizing the distinction between these trait types resolves some apparent contradictions in the literature, and clarifies the limits of some previous results.