On the evolution of pure winner and loser effects: A game-theoretic model

The persistence of linear dominance hierarchies is often attributed to high er probabilities of a win after a win or a loss after a loss in agonistic i nteractions, yet there has been no theory on the evolution of such prior-ex perience effects. Here an analytic model, based on the idea that contests a re determined by subjective perceptions of resource-holding potential (RHP) which animals may revise in the light of experience, demonstrates that win ner and loser effects can evolve through round-robin competition among tria ds of animals drawn randomly from their population, and that the probabilit y of a hierarchy increases with the strength of the combined effect. The ef fects are pure, in the sense that a contestant observes neither its own RHP nor its opponent's RHP or RHP perception or win-loss record; and so the st rength of an effect is unmodified by the RHPs of particular individuals, bu t depends on the distribution of RHP among the population at large. The gre ater the difference between an individual's and its opponent's RHP percepti on, the more likely it is to win a contest; however, if it overestimates it s RHP, then the cost of fighting increases with the overestimate. A winner or loser effect exists only if the fitness gain of the beta individual in a hierarchy, relative to that of the alpha, is less than 0.5. Then a loser e ffect can exist alone, or it can coexist with a winner effect; however, the re cannot exist a winner effect without a loser effect. (C) 1999 Society fo r Mathematical Biology.