A model for within-group coalitionary aggression among males

Abstract

Perhaps the most common form of cooperation among primates is the formation of coalitions. Competition among males within a group concerns a constant quantity of the limiting resource (fertilizations). Contest competition over fertilizations is known to produce payoffs that are distributed according to the priority-of-access model, and hence show an exponential decline in payoff with rank. We develop a model for rank-changing, withingroup coalitions among primate males. For these coalitions to occur, they must be both profitable (i.e. improve fitness) for all coalition members and feasible (i.e. be able to beat the targets). We assume that the value of the coalition is the sum of the payoffs of the partners in their original ranks. We distinguish three basic coalition configurations, depending on the dominance ranks of the coalition partners relative to their target. We predict five basic coalition types. First, all-up, rank-changing coalitions targeting individuals ranking above all coalition partners; these are expected to involve coalition partners ranking just below their target, concern top rank, and be small, just two or three animals. Second, bridging, rankchanging coalitions, where higher-rankers support lowerrankers to rise to a rank below themselves; these are expected to be most common where a high-ranking male in a despotic system can support a low-ranking relative.Third, bridging non-rank-changing coalitions; these are expected to be common whenever high-ranking males have low-ranking close relatives. Fourth, non-rankchanging coalitions by high-rankers against lower-ranking targets; these are expected to serve to counteract or prevent the first type. Fifth, non-rank-changing, leveling coalitions, in which all partners rank below their target and which flatten the payoff distribution; these are expected to be large and mainly involve lower-ranking males. Bridging, rank-changing coalitions are expected in situations where contest is strong, all-up rank-changing coalitions where contest is intermediate, and leveling coalitions where contest is weak. We review the empirical patterns found among primates. The strong predictions of the model are confirmed by observational data on malemale coalitions in primates.

Coalitions in theory and reality: a review of pertinent variables and processes

“…This theory aims to predict coalitionary strategies that maximize individual fitness given a particular (ecological) situation, the costs and benefits of different actions, and the information available to individuals. Most existing models of coalition formation in animals belong to this general framework, which overlaps with evolutionary game theory (Noë, 1990(Noë, , 1992(Noë, , 1994Pandit & van Schaik, 2003;van Schaik et al, 2004van Schaik et al, , 2006Mesterton-Gibbons & Sherratt, 2007;Broom et al, 2009;Okasha, 2009). We will discuss a number of these models in more detail below.…”

“…Using a similar approach, van Schaik and colleagues (Pandit & van Schaik, 2003;van Schaik et al, 2004van Schaik et al, , 2006 aimed to predict the type of coalitions formed (i.e., all-up, bridging, or all-down; rank-changing or levelling) in a group of males competing for fertilization opportunities. They considered primate males living in groups of an arbitrary size, where individuals ranked in a linear hierarchy compete over increases in ranks.…”

“…They considered primate males living in groups of an arbitrary size, where individuals ranked in a linear hierarchy compete over increases in ranks. van Schaik et al (2004van Schaik et al ( , 2006 assumed: (a) that the relationship between the rank and fitness pay-off is exponential, (b) that coalitions are formed only against a single target, (c) that coalition strength is given by a sum of the strengths of its participants, and (d) that the stronger party always wins. Using an idealized cost parameter, van Schaik et al (2004van Schaik et al ( , 2006 identified regions of parameter space where coalitions were both feasible (i.e., are stronger than the target) and profitable.…”

“…van Schaik et al (2004van Schaik et al ( , 2006 assumed: (a) that the relationship between the rank and fitness pay-off is exponential, (b) that coalitions are formed only against a single target, (c) that coalition strength is given by a sum of the strengths of its participants, and (d) that the stronger party always wins. Using an idealized cost parameter, van Schaik et al (2004van Schaik et al ( , 2006 identified regions of parameter space where coalitions were both feasible (i.e., are stronger than the target) and profitable. Building on these results, van Schaik et al (2004Schaik et al ( , 2006) made a number of testable predictions.…”

“…Using an idealized cost parameter, van Schaik et al (2004van Schaik et al ( , 2006 identified regions of parameter space where coalitions were both feasible (i.e., are stronger than the target) and profitable. Building on these results, van Schaik et al (2004Schaik et al ( , 2006) made a number of testable predictions. For example, they predicted that all-up rank-changing coalitions should (a) arise only in groups with a medium degree of despotism, (b) be a small coalition (two or three members), (c) target the top individual, and (d) involve individuals ranking just below the target.…”