The evolution of respect for property.

Although possession is 'nine-tenths of the law', respect for ownership is widespread in the animal kingdom even without third-party enforcement. Thus, the first individuals to find objects are frequently left unchallenged by potential competitors and tend to win contests when disputes arise. Game theory has shown that respect for ownership ('Bourgeois' behaviour) can arise as an arbitrary convention to avoid costly disputes. However, the same theory predicts that a paradoxical respect for lack of ownership ('anti-Bourgeois' behaviour) can evolve under the same conditions and in some cases is the only stable outcome. Despite these predictions, anti-Bourgeois behaviour is rare in nature, whereas respect for ownership is frequently not absolute. Here, we review extensions of the classic models involving repeated interactions, confusion over roles, strategic coordination of behaviour ('secret handshakes'), owner-intruder asymmetries and continuous control of fighting investment. Confusion over roles and owner-intruder asymmetries in fighting ability may explain why respect for ownership is often partial. Moreover, although most model extensions facilitate the evolution of Bourgeois-like behaviour, secret handshakes and continuous control of fighting investment render the alternative anti-Bourgeois convention unstable. We develop these insights to highlight several key areas for future investigation.

A polymorphic effect of sexually differential production costs when one parent controls the sex ratio.

R. A. Fisher's sex ratio theory predicts that if sons and daughters cost fixed amounts of resources to raise and parents have fixed amounts to invest, then the numerical sex ratio of a panmictic population will evolve to be inversely proportional to relative cost. However, the theory assumes control by both parents. We show that allowing one parent to control the sex ratio biases it further from parity than Fisher's theory predicts. Quantitatively, the additional bias towards the cheaper sex depends only very weakly on which sex is in control. Qualitatively, however, the effect is very strong: a monomorphic, mixed-brood strategy evolves only if the more expensive sex is in control. If the controlling sex is cheaper to raise, then the sex ratio is instead achieved through a polymorphism of single-sex broods. Such polymorphisms are seldom observed in nature, generating the prediction that wherever the sexes are not equally costly, sex ratio is usually either under biparental control or under uniparental control by the more expensive sex. However, such polymorphisms do occur, and some of them may be explained by our model.

On sperm competition games: raffles and roles revisited.

In principle there are two approaches to modelling a trade-off between the positive and negative outcomes of a behavior: after suitably defining a value for the behavior in the absence of any trade-off, one can either multiply that value by an appropriate discount or subtract an appropriate cost. In a prospective analysis of sperm competition, Parker (Proc. Roy. Soc. Lond. B (1990) 242, 120-126) adopted the multiplicative approach to model the trade-off between the value of a mating and the cost of its acquisition. He obtained two paradoxical results. First, if two males 'know' whether they are first or second to mate, but these roles are assigned randomly, then sperm numbers should be the same for both males whether the 'raffle' for fertilization is fair or unfair. Second, if mating order is constant, then a favored male should expend less on sperm. His results are puzzling not only in terms of intuition about nature, but also in terms of his model's consistency. In other words, they present both an external and an internal paradox. Parker assumed the fairness of the raffle to a disfavored male to be independent of how much sperm a favored male deposits. This article both generalizes Parker's analysis by allowing fairness to decrease with sperm expenditure by the favored male and compares Parker's results to those obtained by the additive approach. In many respects, results are similar. Nevertheless, if the costs of mating are assumed to increase with sperm expenditure but not to depend on the role in which sperm is expended, as Parker assumed, then the additive approach is more fundamentally correct. In particular, Parker's constant-role paradox is an artifact of his approach. His random-role paradox is internally rationalized in terms of standard microeconomic theory. When fairness decreases, however slightly, with sperm expenditure by the favored male, both models demonstrate that the evolutionarily stable strategy is for more sperm to be deposited during a favored mating than during a disfavored mating. The lower the costs, the greater the divergence. Thus a possible resolution of the external paradox is that fairness is not constant in nature.

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

The persistence of linear dominance hierarchies is often attributed to higher probabilities of a win after a win or a loss after a loss in agonistic interactions, yet there has been no theory on the evolution of such prior-experience effects. Here an analytic model, based on the idea that contests are determined by subjective perceptions of resource-holding potential (RHP) which animals may revise in the light of experience, demonstrates that winner and loser effects can evolve through round-robin competition among triads of animals drawn randomly from their population, and that the probability of a hierarchy increases with the strength of the combined effect. The effects 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 strength of an effect is unmodified by the RHPs of particular individuals, but depends on the distribution of RHP among the population at large. The greater the difference between an individual's and its opponent's RHP perception, the more likely it is to win a contest; however, if it overestimates its 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 effect can exist alone, or it can coexist with a winner effect; however, there cannot exist a winner effect without a loser effect.

Cooperation and the Prisoner's Dilemma: towards testable models of mutualism versus reciprocity

For the purpose of distinguishing between mutualism and reciprocity in nature, recent work on the evolution of cooperation has both oversimplifed and undersimplified the distinction between these two categories of cooperation. This article addresses the resulting issues of model testability, clarifies the role of time and argues that the category of 'pseudo-reciprocity' is an unnecessary complication.1997The Association for the Study of Animal Behaviour

On the war of attrition and other games among kin.

Evolutionarily stable strategies or ESSs of games among kin have been calculated in the literature by both "personal-fitness" and "inclusive-fitness" methods. These methods were compared by Hines and Maynard Smith (1979) for games with bilinear payoffs. Although Hines and Maynard Smith regarded the first method as correct, they regarded the second method as useful because the inclusive-fitness conditions for an ESS gave necessary conditions for a personal-fitness ESS in the class of games they considered. In general, however, satisfying the inclusive-fitness conditions is neither necessary nor sufficient for satisfying the inclusive-fitness conditions, although the two methods may often yield identical ESSs. This result is established by reformulating the classic war-of-attrition model to allow variation in energy reserves, assumed to have a Gamma distribution. For this game, the two methods may disagree for intermediate values of relatedness. By the correct method, if the coefficient of variation in energy reserves is sufficiently high, then the game has a unique ESS in pure strategies at which populations with higher coefficients of variation or relatedness display for shorter times. Unrelated contestants are prepared to expend at least half of their reserves. For populations with lower variation coefficients, the ESS exists only if the cost of displaying per unit time is low compared to the rate at which remaining reserves translate into expected future reproductive success for the victor. The critical variation coefficient, below which the ESS exists regardless of cost, decreases from 0.52 to 0 as the coefficient of relatedness increases from 0 to 1. Although there is no assessment, contests are always won by the animal with greater energy reserves in a population at the ESS.

Cooperation among unrelated individuals: reciprocal altruism, by-product mutualism and group selection in fishes.

Cooperation among unrelated individuals can evolve not only via reciprocal altruism but also via trait-group selection or by-product mutualism (or some combination of all three categories). Therefore the (iterated) prisoner's dilemma is an insufficient paradigm for studying the evolution of cooperation. We replace this game by the cooperator's dilemma, which is more versatile because it enables all three categories of cooperative behavior to be examined within the framework of a single theory. Controlled studies of cooperation among fish provide examples of each category of cooperation. Specifically, we describe reciprocal altruism among simultaneous hermaphrodites that swap egg parcels, group-selected cooperation among fish that inspect dangerous predators and by-product mutualism in the cooperative foraging of coral-reef fish.