Genetic relatedness and group size in an aggregation economy

Summary We use Hamilton's Rule to investigate effects of genetic relatedness on the predicted size of social groups. We assume an aggregation economy; individual fitness initially increases with group size, but in sufficiently large groups each member's individual fitness declines with further increments in the size of the group. We model two processes of group formation, designated free entry and group-controlled entry. The first model assumes that solitary individuals decide to join groups or remain alone; group size equilibrates when solitaries no longer choose to join. The second model allows group members to regulate the size of the group, so that the predicted group size results from members' decisions to repel or accept intruding solitaries. Both the Nash equilibrium group size and any change in the equilibrium caused by varying the level of relatedness depend on the particular entry rule assumed. The largest equilibrium group size occurs when solitaries choose between joining or not joining and individuals are unrelated. Increasing genetic relatedness may reduce and can never increase, equilibrium group size when this entry rule applies. The smallest equilibrium group size occurs when group members choose between repelling or accepting intruders and individuals are unrelated. Under this entry rule, increasing genetic relatedness can increase and can never decrease, equilibrium group size. We extend the models' predictions to suggest when individuals should prefer kin vs non-kin as members of the same group.