Social Eavesdropping: A Game-Theoretic Analysis

Here we extend the classic Hawk-Dove model of animal conflict to allow for continuous variation in fighting strengths. Whereas the winner of a fight is chosen at random in the discrete game, in our continuous game, the winner of any fight is the stronger individual, and costs are higher for more evenly matched opponents. We identify the evolutionary stable strength threshold beyond which an animal should be prepared to engage in aggressive behaviour and show that this threshold increases with variance in fighting strength when the costs of aggression are insensitive to the level of strength asymmetry, but decreases with variance when the costs are sensitive to the level of asymmetry. In contrast to the classic discrete game, population-wide aggressive behaviour occurs only when the costs of fighting are zero. It is now known that animals can eavesdrop on the outcome of contests between neighbours and modify their behaviour towards observed winners and losers. We therefore further extend our model to allow for social eavesdropping within networks comprising three individuals. Whereas earlier work showed that eavesdropping increases the frequency of mutually aggressive contests in the discrete game by enhancing the value of victory, here we show that aggression thresholds in the continuous game are always higher with eavesdropping than without it: for sufficiently weak animals, avoiding the costs of challenging an observed winner over-rides the potential benefit of winning, so that eavesdropping reduces the frequency of aggressive encounters. Thus, even though strength is not directly observable, information is extracted from the variation in fighting ability that the classic Hawk-Dove game ignores.     

The coevolution of juvenile play–fighting and adult competition

Although play–fighting is widespread among juvenile mammals, its adaptive significance remains unclear. It has been proposed that play is beneficial for developing skills to improve success in adult contests (motor‐training hypothesis), but the links between juvenile play–fighting and adult aggression are complex and not well understood. In this theoretical study, we investigate the coevolution between juvenile play–fighting and adult aggression using evolutionary computer simulations. We consider a simple life history with two sequential stages: a juvenile phase in which individuals play–fight with other juveniles to develop their fighting skills; and an adult phase in which individuals engage in potentially aggressive contests over access to resources and ultimately mating opportunities, leading to reproductive success. The simulations track genetic evolution in key traits affecting adult contests, such as the level of aggression, as well as juvenile investment in play–fighting, capturing the coevolutionary feedbacks between juvenile and adult decisions. We find that coevolution leads to one of two outcomes: a high‐play, high‐aggression situation with highly aggressive adult contests preceded by a prolonged period of juvenile play–fighting to improve fighting ability, or a low‐play, low‐aggression situation in which adult contests are resolved without fighting and there is minimal investment in play–fighting before individuals mature. Which of these outcomes is favoured depends on the mortality costs and on the type of societal structure: societies with strong reproductive skew, favouring monopolization of resources, show high levels of adult aggression and high investment in juvenile play–fighting, whereas societies with low reproductive skew have both low adult aggression and low levels of play–fighting. A review of empirical evidence, particularly in the primate genus Macaca, highlights some limitations of our model and suggests that other, complementary functional explanations are needed to account for the full range of competitive and cooperative forms of play–fighting. Our study illustrates the power of evolutionary simulations to shed light on the long‐standing puzzle of animal play.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

Can mixed strategies be stable in asymmetric games?

Selten (1980, J. theor. Biol. 84, 93(N)/01) has shown that mixed strategies cannot be evolutionarily stable in asymmetric games. Because every interaction features some asymmetry, this result apparently precludes mixed strategies in an evolutionary setting. In Maynard Smith's Hawk-Dove game (1982, Evolution and the theory of games (UP-Cambridge), for example, Selten's result restricts attention to pure-strategy evolutionarily stable outcomes in which the animals use the ability to condition their actions on asymmetries to coordinate, with one playing Hawk and one playing Dove, and with conflicts in which both animals play Hawk never arising. This result contrasts with the intuition that the mixed equilibrium of the Hawk-Dove game captures important aspects of many animal interactions, including the possibility of conflict. In this paper, we follow Eshel and Sansone (1995, J. theor. Biol. 177, 341-356) in enriching Selten's model to incorporate an important aspect of animal interactions, namely that payoffs and asymmetries may both be imperfectly observed. In the richer model, we find conditions under which effectively mixed strategies are stable in asymmetric games, as well as conditions under which they are not stable. Behavior will be conditioned on asymmetries, leading to pure-strategy equilibria in which conflict is avoided, when there are relatively large, observable asymmetries and small observable variations in payoffs. Under opposite conditions, evolutionarily stable equilibria will appear that are effectively mixed, including the potential for conflict.     

Testing game theory models: fighting ability and decision rules in chameleon contests

Game theory models of animal contests make many non-mutually exclusive predictions, complicating empirical tests. These predictions regard the relationship between contest parameters and fighting ability, for which body size is usually used as a proxy. However, in many systems, body size may be a limited proxy since multiple traits and contextual factors such as experience influence fighting ability. Using contests between male Cape dwarf chameleons, Bradypodion pumilum, I test alternative game theory models of extended contests. I show how the most likely candidate model can be identified through a process of elimination, based on tests of key predictions. In addition, I present a measure of fighting ability based on multiple traits that allows ability to change as experience changes. In dwarf chameleons, persistence is based on loser thresholds rather than assessment of relative ability, ruling out the sequential assessment model. Winners and losers do not match behaviours in early parts of the contest, arguing against all types of war of attrition models. Although the cumulative assessment model remained as the most likely candidate model, not all specific predictions of this model were upheld.     

The energetic costs of fighting in the house cricket, Acheta domesticus L

The cost of performing an agonistic behavior, or tactic, willhave consequences for an individual's rate of cost accrual,the tactic's evolutionary stability if used as an assessmentsignal, and its pattern of use in the behavioral choreographyof a contest. Few studies have attempted to quantify the costsof fighting, particularly with regard to energy expenditure.Flow-through respirometry revealed that house cricket malescan expend energy at relatively high rates when fighting (morethan eight times resting levels) depending on the particulartactic performed. Acoustic signalling (stridulation) constitutedthe least costly of seven measured agonistic tactics, whilewrestling with an opponent, the most energetically costly tactic,consumed oxygen at a net rate more than 40 times that of stridulation.Low-cost tactics are used by opponents more frequently thanmore costly tactics, providing evidence for an escalating tacticalconvention based on energetic costs. The moderate energeticcost of some tactics suggests they may function as reliablesignals in the assessment of wrestling ability. Net energy costsper contest increased linearly with contest duration for bothcontest winners and losers, but winners tended to expend moreenergy per contest than losers. The likely fitness effects ofenergy expended while fighting are discussed. The results ofthis study indicate that energy expenditure is an importantcost shaping contest strategies in Acheta domesticus     

具资源效应的非对称“鹰鸽博弈”进化稳定分析

解释合作行为的演化一直是生命科学及社会学研究的重要问题之一。经典理论研究大都关注于合作双方对等的情况。然而,在合作系统中的合作双方通常是不对等的,由此可带来博弈双方支付的非对称并影响合作双方的合作行为。该文基于经典的"鹰鸽博弈"模型,同时考虑非对称性相互关系和资源压力的影响,建立了具有强弱之分的四策略(实力强且合作、实力强且不合作、实力弱且合作和实力弱且不合作)非对称博弈模型。结合演化博弈理论及动力系统稳定性理论分析发现:在系统达到稳定状态时,四种策略的比例变化显著地依赖于博弈双方的强弱之比、资源压力及冲突的单位成本收益。对模型的进一步分析显示,当资源充足时,实力强且合作的比例与冲突的单位成本收益负相关;而实力强且不合作、实力弱且不合作的比例都与冲突的单位成本收益正相关,并且随着系统强弱对比增加,实力强且合作及实力强且不合作的比例均增加,而实力弱且不合作的比例将减小。当资源短缺时,模型得出一个有趣的结论,即随着博弈双方的强弱之比的变化,经典的"智猪博弈"与"鹰鸽博弈"可相互转化,该结论将能为不同均衡状态之间的相互转化给出一个动力学解释。     

The role of asymmetries in animal contests

This paper contains a game theoretical analysis of animal contest situations which are asymmetric in more than one aspect: two opponents may for example be imagined which differ in ‘ownership status’ as well as in ‘relative fighting ability’. The following question is analysed: which aspect may or must be used for conventional settlement in a population ‘playing’ an evolutionarily stable strategy (ESS)? The contestants are assumed to be fully informed about the asymmetric features. In particular, the assessment of relative fighting ability is supposed to be unambiguous and without cost. This assumption of perfect information allows for a decomposition of the ‘evolutionary game’ into sub-games. Therefore an easy procedure for calculating the ESS's can be presented, and simple models are analysed. It is concluded that payoff-irrelevant aspects may be used for conventional settlement of a conflict even if payoff-relevant asymmetric aspects also exist. One of the aspects may, however, be of such strong relevance that, no matter which ESS is played, animals must base their decisions on that ‘dominant’ aspect. It may also occur that two different asymmetric features are each of strong payoff relevance for either of the opponents, such that they have no escalation-suppressing effect. The particular scenario of a conflict between an ‘owner of a resource’ and an ‘intruder’ is used to derive the more general conclusions.     

Use of energy reserves in fighting hermit crabs

When animals engage in fights they face a series of decisions, which are based on the value of the contested resource and either their relative or their absolute fighting ability. Certain correlates of fighting ability or 'resource holding potential' such as body size are fixed but physiological correlates are expected to vary during the encounter. We examine the role of energy reserves in determining fight outcomes and parameters during 'shell fighting' in hermit crabs. During these fights, the two contestants perform very different roles of attacker and defender. We show that the balance of the total energy pool, in the form of glucose and glycogen, determines the ability of defenders to resist eviction from their shells. Low glucose in evicted defenders is not caused by depletion of energy reserves, rather mobilization of glycogen appears to be the result of a strategic decision about whether to resist effectively, based on the perceived fighting ability of the attacker. Attackers, however, always initiate the fight so such a decision for this role appears unlikely. In addition to influencing decisions and ability during fights, physiological correlates of fighting ability can in turn be influenced by strategic decisions.     

Genetic correlations of fighting ability with somatic cells and longevity in cattle

The success in competitions may be stressful for animals and costly in terms of immune functions and longevity. Focusing on Aosta Chestnut and Aosta Black Pied cattle, selected for their fighting ability in traditional competitions, this study investigated the genetic relationships of fighting ability with udder health traits (somatic cell score and two threshold traits for somatic cells), longevity (length of productive life and number of calvings) and test-day milk, fat and protein yield. Herdbook information and phenotypic records that have been routinely collected for breeding programs in 16 years were used for the abovementioned traits. Data belonged to 9328 cows and 19 283 animals in pedigree. Single-trait animal model analyses were run using a Gibbs sampling algorithm to estimate the variance components of traits, and bivariate analyses were then performed to estimate the genetic correlations. Moderate positive genetic correlations (r_a) were found for fighting ability with somatic cell score (r_a=0.255), suggesting that greater fighting ability is genetically related to a detriment in udder health, in agreement with the theory. The high positive genetic correlation between fighting ability and longevity (average r_a=0.669) suggests that the economic importance of fighting ability (the winning cows get an higher price at selling) had probably masked the true genetic covariances. The genetic correlation between milk yield traits and fighting ability showed large intervals, but the negative values (average r_a=−0.121) agreed with previous research. This study is one of the few empirical studies on genetic correlations for the competitive success v. immune functions and longevity traits. The knowledge of the genetic correlations among productive and functional traits of interest, including fighting ability, is important in animal breeding for a sustainable genetic improvement.     

Game dynamics and evolutionary transitions

An evolutionary model based on the Taylor-Jonker game dynamics is presented. A set of strategies is compatible if there exists a dynamical equilibrium between its members and there is an evolutionary transition to another compatible set if new mutant strategies bring about a passage to another equilibrium. We apply these concepts to supergame strategies, which play repeatedly a given matrix game and at each time step choose their pure strategy according to the preceding moves of the opponent. We investigate the patterns of evolution in zero-sum games, games of partnership, the prisoner's dilemma and the hawkdove game.     

Scent may signal fighting ability in male Iberian rock lizards

Intrasexual competition favours the evolution of conspicuous fighting ability badges. However, in spite of the fact that chemoreception is important in sexual selection of many animals, such as lizards, the role of chemical signals in males' contests is relatively unknown. Here, we show that proportions of cholesterol in femoral gland secretions of male Iberian rock lizards were related to their body size (which confers a competitive advantage in fights). Males discriminated chemically and responded aggressively to cholesterol stimuli presented on swabs. Moreover, we experimentally increased cholesterol in the scent of males, and staged encounters in neutral cages between two unfamiliar and size-matched males. Focal males lost more agonisitic interactions against males manipulated with cholesterol than in control tests. We suggest that differences in scent composition may reliably signal fighting ability in many lizard species, which would help to avoid the costs of fighting.     

一个具有年龄结构的博弈理论模型的研究

考虑一个鹰-鸽博弈的模型.在这个模型里,动物只知道自己的年龄,而不知道对方的年龄.对于这一个博弈模型,将会证明,在进化的平衡点上,存在两个不同的年龄临界点x1和x2(不妨设x1小于x2),并且年龄在这两个临界点之间的动物将会选择鹰策略;而年龄小于x1和年龄大于x2的动物将会选择鸽子策略.在这里,战争发生的可能性大小定义为:当两个个体相遇时,双方都选择鹰策略的概率.进一步,即使动物仅知道自己的年龄,那么在进化稳定性上战争发生的可能性大小也要比标准的鹰-鸽博弈中战争发生的可能性大小要低.     

Effects of physical and social experiences and octopamine receptor agonist on fighting behavior of male crickets Velarifictorus aspersus (Orthoptera: Gryllidae)

Fighting commonly occurs among animals and is very important for resolving conflicts between conspecific individuals over limited resources. The plasticity of fighting strategies and neurobiological mechanisms underlying fighting behavior of insects are not fully understood. In the present study, we examined whether physical and social experiences affected the aggressiveness of males of the cricket Velarifictorus aspersus Walker, and whether an octopamine (OA) receptor agonist could affected the aggressiveness of males exposed to different experiences. We found that flight and winning a fight significantly enhanced male aggressiveness, while losing a fight significantly suppressed male aggressiveness, consistent with the findings of existing studies on other cricket species. We also found that female presence had a stronger enhancing effect on male aggressiveness than flight or winning a fight. These findings demonstrated that physical and social experiences can affect the fighting behavior of male V. aspersus. Topical application of a 0.15?M solution of an OA receptor agonist (chlordimeform, CDM) significantly increased male aggression level, suggesting that OA may play an important role as a neuromodulator in controlling fighting behavior of males of this species. Despite displaying a significantly higher aggression level (level 5 or 6), CDM-treated losers did not escalate to physical combat, while fights between courting males usually resulted in physical escalation. It is likely that fighting behavior is only partly regulated by OA, and additional regulatory pathways may be involved in achieving physical combat.     

Dispersal and fighting in male pollinating fig wasps

For more than two decades, it has been the dogma that the males of pollinating fig wasps do not fight and that they only mate in their native fig. Their extreme degree of local mating leads to highly female biased sex ratios that should eliminate the benefits of fighting and dispersal by males. Furthermore, males sharing a fig are often brothers, and fighting may be barred by kin selection. Therefore, theory supported the presumed absence of fighting and dispersal in pollinating fig wasp males. However, we report here that in pollinating fig wasps, fighting between brothers evolved at least four and possibly six time, and dispersal by males at least twice. This finding supports the idea that competition between relatives can cancel the ameliorating effects of relatedness. The explanation to this evolutionary puzzle, as well as the consequences of male dispersal and fighting, opens the doors to exciting new research.     

Socially stable territories: the negotiation of space by interacting foragers

This article presents a theory of territoriality that integrates optimal foraging and conflict resolution through negotiation. Using a spatially explicit model of a sit-and-wait forager, we show that when resources are scarce, there is a conflict between foragers: there is not enough space for all individuals to have optimal home ranges. We propose that a division of space that solves this conflict over resources is the outcome of a negotiation between foragers. We name this outcome the socially stable territories (SST). Using game theory we show that in a homogenous patch occupied by two interacting foragers, both individuals receive identical energy yields at the socially stable territories; that is, there is economic equity. Economic inequity can arise in a heterogeneous patch or from asymmetries in fighting abilities between the foragers. Opportunity costs play a role in reducing economic inequity. When the asymmetry in fighting abilities is very large, a negotiated division of space is not possible and the forager with lowest fighting ability may be evicted from the habitat patch. A comparison between territories and overlapping home ranges shows that energy yields from territories are generally higher. We discuss why there are instances in which individuals nevertheless overlap home ranges.     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

Knee-clicks and visual traits indicate fighting ability in eland antelopes: multiple messages and back-up signals

Background  

Given the costs of signalling, why do males often advertise their fighting ability to rivals using several signals rather than just one? Multiple signalling theories have developed largely in studies of sexual signals, and less is known about their applicability to intra-sexual communication. We here investigate the evolutionary basis for the intricate agonistic signalling system in eland antelopes, paying particular attention to the evolutionary phenomenon of loud knee-clicking.     

Socially selected ornaments and fitness: Signals of fighting ability in paper wasps are positively associated with survival,reproductive success,and rank

Many animals have ornaments that mediate choice and competition in social and sexual contexts. Individuals with elaborate sexual ornaments typically have higher fitness than those with less elaborate ornaments, but less is known about whether socially selected ornaments are associated with fitness. Here, we test the relationship between fitness and facial patterns that are a socially selected signal of fighting ability in Polistes dominula wasps. We found wasps that signal higher fighting ability have larger nests, are more likely to survive harsh winters, and obtain higher dominance rank than wasps that signal lower fighting ability. In comparison, body weight was not associated with fitness. Larger wasps were dominant over smaller wasps, but showed no difference in nest size or survival. Overall, the positive relationship between wasp facial patterns and fitness indicates that receivers can obtain diverse information about a signaler's phenotypic quality by paying attention to socially selected ornaments. Therefore, there are surprisingly strong parallels between the information conveyed by socially and sexually selected signals. Similar fitness relationships in social and sexually selected signals may be one reason it can be difficult to distinguish the role of social versus sexual selection in ornament evolution.     

Effect of body weight, antler length, resource value and experience on fight duration and intensity in fallow deer

We tested predictions of evolutionary game theory focusing on fight duration and intensity during contests between European fallow deer, Dama dama L. We examined the relation between contest duration and intensity and resource-holding potential (RHP; body weight and antler size), in an effort to reveal the assessment rules used by competing males. We examined other potential determinants of duration and intensity: resource value (the oestrous female) and experience of agonistic interactions. Asymmetry in body weight or antler length of contestants was not correlated with fight duration. Body weight and antler length of the fight winner or loser were also not correlated with fight duration. Neither were the body weight of the heavier or lighter animal or the antler length of the animal that had longer or shorter antlers. A measure of intensity (the jump clash) was positively related to the body weight of the losing animal and the lighter member of the dyad. These results are consistent with the hypothesis that opponents escalate contest intensity based on assessment of their own ability rather than through mutual assessment. There was no evidence that resource value is an important factor in either fight duration or intensity in this population. As the number of fights between pairs of males increased, there was a decrease in fight duration. Fights were longer when at least one member of a competing pair of males had previously experienced a victory.