Role assessment,reserve strategy,and acquisition of information in asymmetric animal conflicts

It was formerly argued that alternative evolutionarily stable strategies (ESSs) are possible for animal contests characterized by some asymmetry that can be perceived with perfect accuracy. Where roles A and B refer to the asymmetry between opponents, ESSs are: ‘fight when A, retreat when B’, and vice versa. Either can be an ESS, but only if the ‘reserve strategy’ (=what an animal does when it fights) is sufficiently damaging. We examine the ‘war of attrition’ (winner = opponent that persists longer). In a population at either ESS, reserve strategy is never normally shown; it is therefore subject to drift unless the selective action of rare individuals which break the convention is considered. These could arise either by mutation or by mistakes in role assessment. When mutations and mistakes simply specify that occasionally an animal fights when it ‘should’ retreat, selection adjusts reserve strategy to a level where only one ESS (the ‘commonsense’ ESS) is possible, if the asymmetry is relevant to payoff. Thus for asymmetries in fighting ability or resource value, the individual with the lower score will retreat. However, we are particularly concerned with cases where both payoff-relevant aspects (fighting ability and resource value) are asymmetric. If opponents sustain contest costs at rates K_A and K_B, and their resource values are V_A and V_B, an ‘optimal assessor’ strategy defined by the interaction between the two asymmetries, is a unique ESS. It obeys the rule ‘fight on estimating role A, where V_A/K_A>V_B/K_B; retreat in B’. If mistakes can occur in both roles, but are very rate, the ESS is not fundamentally altered though there will be infinitesimal tendencies for persisting in role B. Selection to improve assessment abilities intensifies as abilities improve, but is weak if roles A and B are rather similar. Over a range of similarity between roles, an ‘owner wins’ convention may be adopted if ownership correlates positively with role A and an individual cannot tell when it would otherwise pay him to break the convention. We also examine a contest in which information about roles can be acquired only during a contest itself, and at a cost. Much depends on the rate at which information is acquired relative to the rate at which costs are expended, and on whether contests normally escalate in intensity, remain at the same level, or de-escalate. Selection favours short contests when costs are high relative to resource value, where the outcome of a round contains much information about fighting ability, and where the actual disparity in fighting ability is large.     

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.     

The theory of games and the evolution of animal conflicts

The evolution of behaviour patterns used in animal conflicts is discussed, using models based on the theory of games. The paper extends arguments used by Maynard Smith &; Price (1973) showing that ritualized behaviour can evolve by individual selection. The concept of an evolutionarily stable strategy, or ESS, is defined. Two types of ritualized contests are distinguished, “tournaments” and “displays”; the latter, defined as contests without physical contact in which victory goes to the contestant which continues longer, are analyzed in detail. Three main conclusions are drawn. The degree of persistence should be very variable, either between individuals or for the same individual at different times; a negative exponential distribution of persistence times is predicted. Individuals should display with constant intensity, independent of how much longer they will in fact continue. An initial asymmetry in the conditions of a contest can be used to settle it, even if it is irrelevant to the outcome of a more protracted conflict if one were to take place.     

Ecotypic variation in the asymmetric Hawk-Dove game: When is Bourgeois an evolutionarily stable strategy?

Summary This paper develops a mathematical model of an iterated, asymmetric Hawk-Dove game with the novel feature that not only are successive pairs of interactants — in the roles of owner and intruder contesting a site — drawn randomly from the population, but also the behaviour adopted at one interaction affects the role of a contestant in the next. Under the assumption that a site is essential for reproduction, the evolutionarily stable strategy (ESS) of the population is found to depend on the probability, w, that the game will continue for at least a further period (which is inversely related to predation risk), and five other parameters; two of them are measures of site scarcity, two are measures of fighting costs, and the last is a measure of resource holding potential (RHP). Among the four strategies — Hawk (H), Dove (D), Bourgeois (B) and anti-Bourgeois (X) — only D is incapable of being an ESS; and regions of parameter space are found in which the ESS can be only H, or only X, or only B; or either H or X; or either X or B; or either H or B; or any of the three. The scarcer the sites or the lower the costs of fighting, or the lower the value of w, the more likely it is that H is an ESS; the more abundant the sites or the higher the costs of fighting, or the higher the value of w, the more likely it is that X or B is an ESS. The different ESSs are interpreted as different ecotypes. The analysis suggests how a non-fighting population could evolve from a fighting population under decreasing risk of predation. If there were no RHP, or if RHP were low, then the ESS in the non-fighting population would be X; only if RHP were sufficiently high would the ESS be B, and the scarcer the sites, the higher the RHP would have to be. These conclusions support the thesis that if long-term territories are essential for reproduction and sites are scarce, then ownership is ruled out not only as an uncorrelated asymmetry for settling disputes in favour of owner, but also as a correlated asymmetry.     

Female and male Texas cichlids (Herichthys cyanoguttatum) do not fight by the same rules

Selection usually acts differently on males and females duringintrasexual competition for resources and/or mates. Nevertheless,agonistic behavior has been examined both theoretically andempirically mostly in males. Our research questions whethermales and females follow the same rules of engagement in intrasexualcontests as predicted by the sequential assessment model (SAM).The SAM predicts negative correlations between contest intensityand duration and the magnitude of asymmetry in resource holdingpower (RHP) between the contestants, such that the most escalatedcontests are those between similarly endowed individuals. Westaged male and female intrasexual contests with varying degreesof body size asymmetry under a round robin design using themonogamous Texas cichlid fish (Herichthys cyanoguttatum) asa study case. We used Mantel's matrix analysis to compare howthe behavioral content, duration, structure, and outcome ofmale and female contests were affected by the relative bodysize of the contestants. In the case of males, relative sizein each contest predicted outcome, duration, and frequency ofconventional and escalated behaviors according to prevailingtheory. Female contest structure and outcome, however, werenot predicted by the relative size of contestants. We discussour results in terms of other asymmetries that might be importantin structuring female contests, and we propose potential approachesto study female–female aggression.     

Evolutionarily stable strategies for a finite population and a variable contest size

This paper presents a generalization of Maynard Smith's concept of an evolutionarily stable strategy (ESS) to cover the cases of a finite population and a variable contest size. Both equilibrium and stability conditions are analysed. The standard Maynard Smith ESS with an infinite population and a contest size of two (pairwise contests) is shown to be a special case of this generalized ESS. An important implication of the generalized ESS is that in finite populations the behaviour of an ESS player is "spiteful", in the sense that an ESS player acts not only to increase his payoff but also to decrease the payoffs of his competitors. The degree of this "spiteful" behaviour is shown to increase with a decrease in the population size, and so is most likely to be observed in small populations. The paper concludes with an extended example: a symmetric two-pure-strategies two-player game for a finite population. It is shown that a mixed strategy ESS is globally stable against invasion by any one type of mutant strategist. The condition for the start of simultaneous invasion by two types of mutant is also given.     

Aggression and RHP in the Northern Swordtail Fish, Xiphophorus cortezi: The Relationship Between Size and Contest Dynamics in Male–Male Competition

Current theory predicts that contest outcome, as well as decisions on whether to initiate a contest, escalate during a contest or retreat are decided by asymmetries in resource holding potential (RHP) and/or expected payoffs between contestants. In this investigation, dyadic contests were staged between male swordtail fish (Xiphophorus cortezi) where individuals were paired based on cumulative fight records and were ranked at the end of the trials in order to approximate RHP. Size was the only asymmetry that I did not attempt to control for and as a result, I was able to determine the relationships between size, contest initiation, escalation and outcome. Individuals changed their contest initiation strategy based on their size relative to that of their opponents, and contrary to predictions, the smaller of the two males in each contest was more likely to initiate the conflict than was the larger male. However, the larger of the two males was more likely to win and standard length proved to be a moderate predictor of an individual's final rank. Regardless of size, initiators fared poorly, winning only 31% of the contests. In instances where the smaller males won the contests, they were no more likely to initiate the encounter than was the larger male. However, when small males did win, fights lasted longer, suggesting that in some cases smaller males may be able to outlast their opponents.     

Payoffs and strategies in territorial contests: ESS analyses of two ecotypes of the spiderAgelenopsis aperta

Summary Game-theoretic analyses were completed on the territorial contest behavior of two populations of a desert spider that exhibit markedly different levels of within-species competition. Numerical payoff matrices were constructed from field data collected on the behavior and demography of each population. Payoffs were expressed in terms of expected future egg production. Three behavior patterns that a spider might exhibit following assessment of its weight relative to that of its opponent and the value of the site were considered: withdraw, display, or escalate. The model predicts for the more harsh grassland habitat an evolutionarily stable strategy (ESS) that makes ownership decisive in settling contests between opponents with small weight differences, whereas it otherwise assigns victory to the heavier opponent. Whereas the empirical data collected for this grassland population closely approximates the predicted ESS, that for a population occupying a more favorable riparian habitat deviates significantly. The ESS prediction for this latter population is that an intruding spider will withdraw from a contest if it is similar in weight to the web-owner. Withdrawal is common in this population, but so are display and threat and these actions were not predicted. We hypothesize that gene flow from surrounding habitats is preventing the riparian population from completely adapting to its local environment.     

The ESS in an asymmetric generalized war of attrition with mistakes in role perception

We derive the ESS for the generalized asymmetric war of attrition, where payoffs to contestants may vary in time and may depend on some characteristic, called the "role" of an individual. We use the same approach as Hammerstein & Parker (1982), who examined an asymmetric war of attrition. We consider two roles, A and B. Role A is assumed to be favoured with respect to payoffs. It is assumed that there is always a true asymmetry, so in each contest one individual has role A and the other has role B. It is assumed that roles are assigned to contestants at random and that they can make mistakes in role perception. It is shown that, under certain assumptions about shapes of payoff functions and probabilities of making mistakes, there is an ESS which can be characterized by two probability distributions with non-overlapping support. Individuals who perceive their role as A should choose larger persistence times. This ESS structure is similar to that in the asymmetric war of attrition. In that model, the resource values and the cost rates are constant. We consider situations where all these values may change in time and where rewards and costs may be equal after some finite time. Such shapes of payoff functions arise naturally in competitive patch depletion (Sjerps & Haccou, 1994a,b). As a result, the probability density functions that specify the conditional strategies are no longer necessarily negative exponentials (as in the war of attrition), but may have very different shapes. Furthermore, under some conditions there is a maximum persistence time, at which there can be an atom of probability. We give explicit expressions as well as numerical approximations for the ESS.     

ESS equations sometimes do not specify an ESS

The equations used to find an evolutionarily stable strategy in the basic game theory model (Maynard Smith, 1974, 1982; Maynard Smith & Price, 1973), and in sexual conflict models (Maynard Smith, 1977; Parker, 1979) do not, in fact, specify an ESS when the expected number of contests entered is not the same for each strategy. This means that the conclusions of many game theory models may be incorrect. This is particularly likely to be true when the mean durations of contests for different strategies are not the same, or when the probability that an individual enters a contest is not the same for all strategies. New ESS equations are developed which incorporate the expected number of contests entered.     

Individual Recognition Affects Aggression and Dominance Relations in Rainbow Trout,Oncorhynchus mykiss

In this study, the hypothesis that individual recognition is used as a cue to reduce the cost of contesting resources in rainbow trout Oncorhynchus mykiss, was addressed. The predictions were that the second contest between familiar individuals should be settled with less aggression, and lower probability of status reversal, than a contest between strangers. To test these predictions, similar-sized juvenile rainbow trout were subjected to two dyadic dominance contests in one of four treatment groups: in half of the pairs, the initially subordinate and dominant individuals were staged against an unfamiliar opponent (of opposite rank to their own) in a second contest, while in the other the initial pair was reunited for the second contest. Further, in half of the pairs, contestants were separated for 3 d between contests, while in the other the second contest was staged immediately after the first. Levels of aggression in contests between familiar individuals were lower than in contests between strangers, which supports the hypothesis that individual recognition reduces aggression. Dominance status was reversed in 31% of the 62 tested pairs. Although the probability of status reversal was not significantly affected by individual recognition, the degree of change in competitive success appeared to be lower in familiar pairs. Separation interacted with familiarity so that the effect of individual recognition generally was less pronounced when pairs were separated between contests, suggesting that the ability to remember opponents is time/limited. In natural streams, salmonids may use individual recognition to reduce the cost of contesting resources within groups, to reduce aggression between territory neighbours and to distinguish ‘cheaters’ from honest signallers.     

Individual-based simulations of the War of Attrition

The War of Attrition model of John Maynard Smith predicts a single, mixed evolutionarily stable strategy (ESS) for animal contests which are settled by conventional displays with no assessment of the opponent's fighting ability. We test the predictions of the model by simulating the evolution of strategies in a finite population of animals under various assumptions on how possible strategies are coded and mutated. While our simulations for the most part confirm the predictions of the model, we also discovered some significant deviations from the theoretically predicted ESS. Specifically, we found that if inheritance of strategies is somewhat imprecise, then a population can evolve that achieves on average a higher payoff than a population at the theoretically predicted ESS. Moreover, if the ESS is realized as a polymorphism of fixed persistence times, then for small populations, sufficiently stringent statistical tests will reject the hypothesis that these times are distributed as theoretically predicted.     

Game theory and the evolution of behaviour.

How far can game theory account for the evolution of contest behaviour in animals? The first qualitative prediction of the theory was that symmetric contests in which escalation is expensive should lead to mixed strategies. As yet it is hard to say how far this is borne out, because of the difficulty of distinguishing a 'mixed evolutionarily stable strategy' maintained by frequency-dependent selection from a 'pure conditional strategy'; the distinction is discussed in relation to several field studies. The second prediction was that if a contest is asymmetric (e.g. in ownership) then the asymmetry will be used as a conventional cue to settle it. This prediction has been well supported by observation. A third important issue is whether or not information about intentions is exchanged during contests. The significance of 'assessment' strategies is discussed.     

Post-contest behaviour in black-capped chickadees (<Emphasis Type="Italic">Poecile atricapillus</Emphasis>): loser displays,not victory displays,follow asymmetrical countersinging exchanges

Victory displays are behaviours that occur after the conclusion of a signaling contest, performed solely by the contest winner. Victory displays may reinforce the dominance of the winner either to the loser or to other conspecifics within signaling range. Victory displays are poorly studied despite the significant consequences that post-conflict behaviour may have on the individuals involved. We examined the period immediately following 50 territorial countersinging contests between males in 10 neighbourhoods of black-capped chickadees (Poecile atricapillus) of known dominance rank. We characterized the post-contest singing behaviour of chickadees and evaluated whether post-contest behaviour is consistent with victory displays. Using a 16-microphone acoustic location system to simultaneously record entire neighbourhoods of breeding chickadees, we isolated 50 dyadic countersinging contests and measured the vocal behaviour of the contestants in the minutes following each interaction. Eighty-six percent of contests were followed by a period of solo singing by one of the contestants, while 14% were followed by silence. The post-contest singer was most often the contestant who held a subordinate dominance position in the previous winter’s dominance hierarchy; dominant males performed post-contest song bouts significantly less often. Asymmetry in overlapping between contestants did not predict which bird sang a post-contest bout. However, in a significant majority of cases, the post-contest singer was pitch-matched by his opponent during the contest more than he pitch-matched his opponent. Our results indicate that male chickadees do not perform acoustic victory displays after countersinging contests. In contrast, the post-contest behaviour of territorial chickadees is more consistent with a “loser display”.     

A generalized war of attrition

In the “War of Attrition” model of animal conflict, introduced by Maynard Smith, a reward is obtained by whichever of two opponents displays longer, each individual incurring a cost associated with the length of the contest. This model is generalized to allow more general reward and cost functions, and restrictions on the length of contest permitted. This permits unification of the “War of Attrition” model and the “Graduated Risks” model, and also the extension to models in which contests may end either due to injury, or to retreat.In each case it is demonstrated that either (i) there is no evolutionary stable strategy (ESS) or (ii) there is a unique ESS, which is fully specified. In the case where only a finite number of pure strategies are available, global convergence to the ESS is shown.A variety of interesting conclusions of biological relevance emerge, perhaps the most striking being the occurrence of a dichotomous behavioural pattern in an essentially continuous conflict.     

Dynamics of intersexual conflict over precopulatory mate guarding in two populations of the isopod Idotea baltica

Aggressiveness during intersexual conflicts is predicted to depend on its costs, the value of winning and the power asymmetry of the contestants, all of which may vary between populations. In the marine isopod Idotea baltica (Pallas) a conflict occurs as females resist the attempts by males to start precopulatory mate guarding. We analysed contest dynamics with respect to female maturity stage, that is, to time left to reproductive moult, with which the payoffs of guarding for males and females change. We did this in two populations that differ in synchrony of reproduction, sex ratio and the degree of sexual dimorphism. The intensity and dynamics of contests differed between populations: in the more size-dimorphic population, females, the smaller sex, resisted less by forceful flexing but more by hooking their body than in the other population. Male aggressiveness stayed at a constant level with respect to female maturity. In the less size-dimorphic population, female resistance by flexing was intense and it decreased, while male persistence increased, with the approaching reproductive moult. Contests were more intense with small than with large males. These results fit well with the predictions from models of conflict behaviour. Assessment of the payoffs of winning versus contest costs, coadaptation of the level of aggressiveness to the other traits affecting contest outcome, and counteradaptations by the sexes to each other largely explain the dynamics and between-population differences of these contests. Copyright 2000 The Association for the Study of Animal Behaviour.     

Arms races in evolution—An ESS to the opponent-independent costs game

The opponent-independent cost game is an animal contest in which the bigger and more heavily-armed opponent wins a disputed resource without significant fighting costs. A strategy is a choice of investment level in armament. Increasing armament is assumed to have fitness costs that are unrelated to contests; i.e. the cost of an individual's investment in arms is independent of the strategy played by an opponent.Previous work with this model showed that no ESS exists if a strategy prescribes an arms level exactly. This is equivalent to the notion that there is no environmental variation in the arms level attained by a given strategy. If environmental variation is introduced, a pure ESS can generally exist. A strategy is assumed to prescribe an exact investment cost, but this is translated into a probability distribution of arms levels attained, rather than an exact arms level. Increasing investment increases the mean of the arms level distribution. The ESS investment level depends both on how environmental factors distribute arms levels, and on the shape of the cost function (i.e. on the way that costs increase with investment); in some instances there is no ESS. Two types of model are investigated; in one fitness is additive (benefit-cost), in the other it is multiplicative (benefit × survivorship). The multiplicative model is likely to apply to the case where contests are between males for access to females. Here the ESS investment level (an ESS degree of risk that a male sustains as a result of armament) increases as fewer individuals guard the available resources. Thus sexual size dimorphism (male/female size) and relative male armament should increase as harem size increases. The ESS investment level will also be highest if most individuals are small and poorly armed, as would often be the case where size increases throughout life.The model can be applied to coevolutionary arms races between two classes of opponent, such as prey and predator, or parent and offspring. Here the ESS is likely to be a pair of ESS arms levels, one for each class of opponent.     

Asymmetrical Resource Ownership Increases Owners’ and Reduces Non‐Owners’ Motivation to Fight in the Mangrove Rivulus,Kryptolebias marmoratus

Resource ownership often increases an individual's aggressiveness and its probability of defeating a competitor. Individuals contesting resource owners could therefore incur higher costs, making individuals reluctant to compete with owners. We tested the hypothesis that animals use asymmetry in resource ownership as a cue for contest costs and adjust contest decisions accordingly. Using a mangrove rivulus fish (Kryptolebias marmoratus), we staged (1) contests with a randomly assigned asymmetry in resource ownership (one fish was provided with a shelter) and (2) contests in which neither fish had a shelter. Owners that were in their shelters at the contest start showed a greater tendency to fight and won more contests than their intruder opponents; those outside the shelter at the start did not. Compared with fish in contests with no shelters at stake, shelter owners had a higher tendency to fight whether or not they were in their shelters at the start; intruders, however, had a lower tendency to fight only against owners that were inside the shelter at the start. These results demonstrate (1) that ownership status influences both owners’ and intruders’ contest decisions (and in opposite directions), producing a detectable ownership advantage and (2) that intruders required confirmation of their opponents’ ownership status before retreating without challenging them. Ownership status per se is therefore important to the fish's contest decisions.     

Properties of a mixed ESS candidate in continuous strategy sets

An evolutionarily stable strategy (ESS) is a strategy that if almost all members of the population adopt, then this population cannot be invaded by any mutant strategy. An ESS is not necessarily a possible end point of the evolutionary process. Moreover, there are cases where the population evolves towards a strategy that is not an ESS. This paper studies the properties of a unique mixed ESS candidate in a continuous time animal conflict. A member of a group sized three finds itself at risk and needs the assistance of another group member to be saved. In this conflict, a player's strategy is to choose the probability distribution of the interval between the beginning of the game and the moment it assists the player which is at risk. We first assume that a player is only allowed to choose an exponential distribution, and show that in this case the ESS candidate is an attracting ESS; the population will always evolve towards this strategy, and once it is adopted by most members of the population it cannot be invaded by mutant strategies. Then, we extend the strategy sets and allow a player to choose any continuous distribution. We show that although this ESS candidate may no longer be an ESS, under fairly general conditions the population will tend towards it. This is done by characterizing types of strategies that if established in the population, can be invaded by this ESS candidate, and by presenting possible paths of transition from other types of common strategies to this ESS candidate.     

Evolution of kleptoparasitism as a war of attrition

Previous models of kleptoparasitism (resource stealing) assume that contests over resource items are of fixed duration. Here we suggest that such contests will often be well represented as a war of attrition, with the winner being the individual who is prepared to contest for the longer time. Given that time spent in contests cannot be used to search for other resource items, we provide an analytical expression for the evolutionarily stable distribution of contest times. This can be used to investigate the circumstances under which we would expect kleptoparasitism to evolve. In particular, we focus on situations where searching for conspecifics to kleptoparasitize can only be achieved at a cost of reduced resource discovery by other means; under such circumstances we show that kleptoparasitism is not evolutionarily stable.