Play and the evolution of fairness: a game theory model

Bekoff [J. Consci. Stud. 8 (2001) 81] argued that mammalian social play is a useful behavioral phenotype on which to concentrate in order to learn more about the evolution of fairness. Here, we build a game theoretical model designed to formalize some of the ideas laid out by Bekoff, and to examine whether ‘fair’ strategies can in fact be evolutionarily stable. The models we present examine fairness at two different developmental stages during an individual's ontogeny, and hence we create four strategies—fair at time 1/fair at time 2, not fair at time 1/not fair at time 2, fair at time 1/not fair at time 2, not fair at time 1/fair at time 2. Our results suggest that when considering species where fairness can be expressed during two different developmental stages, acting fairly should be more common than never acting fairly. In addition, when no one strategy was evolutionarily stable, we found that all four strategies we model can coexist at evolutionary equilibrium. Even in the absence of an overwhelming database from which to test our model, the general predictions we make have significant implications for the evolution of fairness.     

Antibiotic resistance and the evolution of group-beneficial traits. II: a metapopulation model

Inspired by the evolution of antibiotic resistance in bacteria, we have developed a model that examines the evolution of "producers" (who secrete a substance that breaks down antibiotics) and non-producers. In a previous study, we found that frequency-dependent selection could favor an intermediate frequency of producers in a single, large population. Here we develop a metapopulation model that examines the evolution of producers and non-producers. Our results indicate that in a metapopulation with many groups, each of size N, the equilibrial frequency of producers decreases with group size. Even when N is high (e.g. 150 individuals/group), however, a significant frequency of producers is still predicted. We also found that the equilibrial frequency of producers increases as the minimum numbers of producers necessary to provide protection to non-producers increases. Lastly, increasing the benefit/cost ratio (b/c) for producers increases their equilibrial frequency.     

Individual recognition, dominance hierarchies and winner and loser effects

Winner and loser effects are defined as an increased probability of winning an aggressive interaction at time T, based on victories at time T-1, T-2, etc., and an increased probability of losing at time T, based on losses at time T-1, T-2, etc., respectively. Prior theoretical work on dominance hierarchy formation has demonstrated that when players are not capable of individual recognition, loser effects always produce a clear top-ranked (alpha) individual, but all other ranks in a group remain unclear; whereas winner effects always produce strict linear hierarchies in which the rank of each individual is clear. Paradoxically, however, when individual recognition--a phenomenon long thought to stabilize hierarchies--is possible, winner and loser effects have no impact on the probability of forming strict linear hierarchies.     

Tendency to inspect predators predicts mortality risk in the guppy (Poecilia reticulata)

Although predator inspection behavior in fishes has become amodel system for examining game theoretical strategies suchas Tit for Tat, the direct costs of inspection behavior havenot been quantified. To begin quantifying such costs, I conductedan experiment that examined mortality due to predation as afunction of predator inspection in the guppy (Poecilia reticulata).Before being subjected to a "survivorship" experiment, guppieswere assayed for their tendency to inspect a predator. Groupswere then composed of six guppies that differed in their tendencyto inspect. These groups were placed into a pool containinga predator, and survivorship of guppies with different inspectiontendencies was noted 36 and 60 h later. Results indicate thatindividuals that display high degrees of inspection behaviorsuffer greater mortality than their noninspecting shoalmates.     

N-person games and the evolution of co-operation: a model based on predator inspection in fish

Two N-person game theoretical models examining the evolution of co-operation during predator inspection in fish are presented. Predator inspection occurs in small shoals of fish, in which one to a few individuals, the "inspectors" (co-operators) break away from the shoal and cautiously approach a predator to obtain information on this potential danger. In the models presented here, remaining with the shoal and not inspecting is considered an act of defection. Both model I and II produce a stable internal polymorphism of inspectors and noninspectors. While the equilibrial frequency of inspectors can be low (i.e. less than 10%) at large shoal size, the proportion of shoals containing any inspectors--and therefore exhibiting the inspection behavior--is much greater. Both models presented here, and N-person games in general are equivalent to intrademic group selection models of evolution in structured populations, in which shoals are trait groups and co-operation evolves by between-shoal selection. While the results are cast in terms of predator inspection, the model itself is general and applies to any multi-group scenario where co-operators benefit entire groups at their own expense. The results presented here add to the mounting theoretical and empirical evidence that co-operation is frequently not a pure evolutionarily stable strategy, and that many metapopulations should be polymorphic for both co-operators and defectors.     

Altruism,tit for tat and ‘outlaw’ genes

Summary In a prior study we combined game theory and inclusive fitness models to examine whether the guarded altruism that can evolve among non-relatives (tit for tat, TFT) might also evolve among close relatives, supplanting unconditional altruism. In most cases, TFT replaced unconditional altruism in family-structured models. Even when TFT is selected at a single locus, however, by withholding altruism from non-reciprocating relatives it may qualify as an outlaw from the standpoint of modifier genes at other loci. Here we examine this possibility with a series of haploid, two-locus models in which a modifier gene transforms TFT into unconditional altruism. The modifier allele spreads to fixation whenever Hamilton's Rule is satisfied, resulting in an unconditional altruist replacing the TFT strategy. As such, TFT may be regarded as an outlaw vulnerable to suppression by alleles at other loci.     

Can altruism evolve in purely viscous populations?

Summary Limited dispersal is often thought to facilitate the evolution of altruism by increasing the degree of relatedness among interacting individuals. Limited dispersal can have additional effects, however, such as local population regulation, that inhibits the evolution of altruism. Many models of structured populations assume that a viscous stage of the life cycle alternates with a global mixing stage, which allows the advantages of interactions among close relatives without the disadvantages of local population regulation. Here we analyse a computer simulation model of pure population viscosity, in which offspring are always deposited close to parents and no global mixing stage exists. As expected, limited dispersal generates a high coefficient of relatedness among interacting individuals. Patches of altruists, however, are unable to export their productivity to other regions of the landscape and are easily invaded by selfish types from neighbouring patches. Unlike models of alternating viscosity, in which high relatedness and local population regulation can be decoupled, these two opposing effects are inextricably linked in purely viscous populations, which therefore are not conducive to the evolution of altruistic traits.     

Female mate copying in the guppy {Poecilia reticulata): age-dependent effects

Virtually all studies of mate choice to date have assumed thatfemales choose mates independent of one another. Social cues,however, such as the mate choice of conspecifics, may also playan important role in such decisions. Previous work has shownthat female guppies of similar age copy each other's choiceof mates. Here we examine the effect of relative age on matechoice copying in the guppy, Poecilia reticulata, and examinewhether younger individuals are more likely to copy the matechoice of older conspecifics than vice versa. Results indicatethat younger females copy the mate choice of older females,but older individuals do not appear to be influenced by themate choice of younger individuals.     

Group fusion: the impact of winner, loser, and bystander effects on hierarchy formation in large groups

We present the results of a series of computer simulations thatexamined the impact of winner, loser, and bystander effectson hierarchy formation in fused groups. These effects and theirimplications for hierarchy structure and aggressive interactionswere first examined in small four-member groups. Subsequentto this, the two small groups were fused into a single largergroup. Further interactions took place in this fused group,generating a new hierarchy. Our models demonstrate clearly thatwinner, loser, and bystander effects strongly influence boththe structure and types of interactions that emerge from thefusion of smaller groups. Four conditions produced results inwhich the same general patterns were uncovered in pre- and postfusiongroups: (1) winner effects alone, (2) bystander loser effectsalone, (3) winner and bystander winner effects operating simultaneously,and (4) all four effects in play simultaneously. Outside thisparameter space, hierarchy structure and the nature of aggressiveinteractions differed in pre- and postfusion groups. When onlyloser effects were in play, one of the two clear alphas fromthe prefused groups dropped in rank in the eight-member fusedgroup. When bystander winner effects were in play, it was difficultto rank any of the eight individuals in the fused group, andplayers interacted almost exclusively with those that were notin their original four-member group. When loser and bystanderloser effects operated simultaneously, two top-ranking individualsemerged in the fused groups, but the relative rank of the otherplayers was difficult to assign.     

Extrinsic effects, estimating opponents' RHP, and the structure of dominance hierarchies

We examined the impact of winner and loser effects on dominance hierarchy formation when individuals are capable of estimating their opponent's resource holding power (RHP). The accuracy of such estimates was a variable in our simulations, and we considered cases in which all individuals err within the same bounds, as well as cases in which some individuals consistently overestimate, while others consistently underestimate their opponent's fighting RHP. In all cases, we found a clearly defined linear hierarchy. In most simulations, the vast majority of interactions were 'attack-retreats', and the remainder of interactions were almost all 'fights'. Error rates had no effect on the linearity of the hierarchy or the basic attack-retreat nature of interactions, and consistent over and underestimation did not affect the ultimate position of an individual in a hierarchy.