Abstract
Coalition formation has been documented in a diverse array of taxa, yet there has been little formal analysis of polyadic interactions such as coalitions. Here, we develop an optimality model which examines the role of winner and loser effects in shaping coalition formation. We demonstrate that the predicted patterns of alliances are strongly dependent on the way in which winner and loser effects change with contestant strength. When winner and loser effects decrease with the resource-holding power (RHP) of the combatants, coalitions will be favoured between the strongest members of a group, but not between the weakest. If, in contrast, winner and loser effects increase with RHP, exactly the opposite predictions emerge. All other things being equal, intervention is more likely to prove worthwhile when the beneficiary of the aid is weaker (and its opponent is stronger), because the beneficiary is then less likely to win without help. Consequently, intervention is more probable when the impact of victory on the subsequent performance of a combatant increases with that individual's strength because this selects for intervention in favour of weaker combatants. The published literature on hierarchy formation does not reveal how winner and loser effects actually change with contestant strength and we therefore hope that our model will spur others to collect such data; in this light we suggest an experiment which will help to elucidate the nature of winner and loser effects and their impact on coalition formation in animals.