Abstract: More than half a century has now elapsed since coalition or alliance formation theory (CAFT) was first developed. During that time, researchers have amassed a vast amount of detailed and high-quality data on coalitions or alliances among primates and other animals. But models have not kept pace, and more relevant theory is needed. In particular, even though CAFT is primarily an exercise in polyadic game theory, game theorists have devoted relatively little attention to questions that motivate field research, and much remains largely unexplored. The state of the art is both a challenge and an opportunity. In this review we describe a variety of game-theoretic and related modelling approaches that have much untapped potential to address the questions that field biologists ask.

Abstract: Grooming networks among adult female monkeys exhibit two similar features across a number of different species. High-ranking animals receive more grooming than others, and the majority of grooming occurs between females of adjacent rank. A theoretical model which duplicates these features is presented, and the properties of the model are used to explain the possible causation and function of female grooming behaviour. The model illustrates how relatively simple principles governing the behaviour of individuals may be used to explain more complex aspects of the social structure of non-human primate groups.

Abstract: A genetical mathematical model is described which allows for interactions between relatives on one another's fitness. Making use of Wright's Coefficient of Relationship as the measure of the proportion of replica genes in a relative, a quantity is found which incorporates the maximizing property of Darwinian fitness. This quantity is named “inclusive fitness”. Species following the model should tend to evolve behaviour such that each organism appears to be attempting to maximize its inclusive fitness. This implies a limited restraint on selfish competitive behaviour and possibility of limited self-sacrifices.
Special cases of the model are used to show (a) that selection in the social situations newly covered tends to be slower than classical selection, (b) how in populations of rather non-dispersive organisms the model may apply to genes affecting dispersion, and (c) how it may apply approximately to competition between relatives, for example, within sibships. Some artificialities of the model are discussed.

Abstract: The view is examined that the adaptive value of conventional aspects of fighting behaviour is for assessment of relative RHP (resource holding power) of the combatants. Outcomes of aggressive disputes should be decided by each individual's fitness budget available for expenditure during a fight (determined by the fitness difference between adoption of alternative strategies, escalation or withdrawal without escalation) and on the rate of expenditure of the fitness budget if escalation occurs (determined by the RHPs of the combatants). Thus response thresholds for alternative strategies (“assessments”) will be determined by natural selection on a basis of which opponent is likely to expend its fitness budget first, should escalation occur. This “loser” should retreat (before escalation) and the winner should stay in possession of the resource. Many aggressive decisions depend on whether one is a resource holder, or an attacker. Assuming the RHP of the combatants to be equal, there are many instances of fitness pay-off imbalances between holder and attacker which should weight the dispute outcome in favour of one or other opponent by allowing it a greater expendable fitness budget. Usually the weighting favours the holder; the attacker therefore needs a correspondingly higher RHP before it may be expected to win. This is not invariably the case, and much observed data fits the predictions of this sort of model. If assessments are perfect and budget expenditure rates exactly predictable, then there would never seem to be any case for escalation. Escalation can be explained in terms of injury inflictions (expenditures) occurring as discrete events; i.e. as “bouts” won or lost during fighting. Assessment can give only a probabilistic prediction of the outcome of a bout. A simple model is developed to investigate escalation situations. Each combatant assesses relative RHP; this correlates with an absolute probability of winning the next bout (cabs). The stake played for is infliction of loss of RHP and is determined by the fitness budgets of the opponents. (Each individual plays for the withdrawal of its opponent.) This defines a critical probability of winning (ccrit) for each combatant, above which escalation is the favourable strategy (cabs > ccrit) and below which withdrawal is favourable (cabs < ccrit). Escalation should occur only where cabs-ccrit is positive for both combatants. This model gives predictions compatible with the observations, indicating that RHP loss alone can be adequate to explain withdrawal: escalation behaviour. Withdrawal tendency will be increased by low searching costs. Escalations should be restricted to closely matched RHP opponents if RHP disparity is the major imbalance. Outside the “escalation range” of a given individual, the higher RHP individual wins and the lower one loses (i.e. it should withdraw after conventional display). RHP disparity and holder: attacker imbalance should both interact to shape the observed pattern, though their relative importances will depend on species and situation. In some instances selection may favour immediate withdrawal from an occupied territory even without assessment of RHP.

Abstract: There is growing evidence that macaque social systems represent sets of coadapted traits in which strength of hierarchies and degree of nepotism covary. A framework is developed to explain the link between dominance and kinship phenomena, assuming that power brought by alliances among non-kin is allometrically related to those involving relatives. This can account for the type of social relationships observed in “despotic” systems vs. “egalitarian” ones. When social bonds are mostly founded on kinship, lineages are closed and social power generated by coalitions among relatives may reach high levels; social power frequently outweighs the fighting abilities of single individuals, and asymmetry of dominance between group members may be marked. When lineages are more open, social bonds and alliances are less kin-biased, social relationships are more equal, and as the influence of coalitions is less important, the individual retains a certain degree of freedom in relation to the power of kin-networks. Acknowledging that the balance between individual and social power is not set at the same level across different species can explain a number of variations in rules of rank inheritance and relative dominance of males and females among macaques. The framework illustrates how epigenetic processes may shape complex features of primate social systems, and offers opportunities for testing.