Variation in dominance hierarchies among group-living animals: modeling stability and the likelihood of coalitions

Dominance hierarchies based on resource holding potential (RHP) or age are central to the social structure of many group-living animals. Nonhuman primate females and some other mammals are unusual because ranks can depend on kin support or follow an inverse age-graded pattern independent of kin. Whereas the former hierarchies are mediated by frequent coalitions leading to long-term stability, the latter are unstable due to individualistic contests and occasional revolutionary coalitions. We use mathematical modeling to investigate this variation, based on the interaction of triads, subgroups of the group consisting of 3 individuals. This produces 4 key situations, namely that relationships can be either stable or unstable, and involving coalitionary support or not. Varying the parameter values of our model and applying it to real-world examples, we conclude that the emergence of different dominance hierarchies depends on 6 major factors. In addition to RHP, reproductive skew and demography often suggested previously, we stress the importance of 1) the variance in relatedness; 2) the costs and likelihood of interventions; and 3) the value of resources and rank in different life stages, which might be tightly linked to the life history of a species.