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Transactional concession models of social evolution explain the reproductive skew within groups by assuming that a dominant individual completely controls the allocation of reproduction to other group members. The models predict when the dominant will benefit from donating parcels of reproduction to other members in return for peaceful cooperation. Using linear programming methods, we present a 'majority-rules' model in which the summed actions of all society members, each with equal power, completely determine the reproductive share of any single member. The majority-rules model predicts that, despite the diffusion of power, a 'virtual dominant' (a dominant lacking special behavioural power) will emerge and that the reproductive skew will be exactly that predicted if the virtual dominant were to control completely the group's reproductive partitioning. The virtual dominant is the individual to which group members have the maximum average genetic relatedness. This result greatly broadens the applicability of transactional models of reproductive skew to social groups of any size, such as large-colony eusocial insects, and explains why queens in such colonies can achieve reproductive domination without any behavioural enforcement. Moreover, the majority-rules model unifies transactional-skew theory with models of worker policing and even generates a new theory for the cooperation among somatic cells in a multicellular organism.

From individual control to majority rule: extending transactional models of reproductive skew in animal societies