The logic of asymmetric contests

A theoretical analysis is made of the evolution of behavioural strategies in contest situations. It is assumed that behaviour will evolve so as to maximize individual fitness. If so, a population will evolve an ‘evolutionarily stable strategy’, or ESS, which can be defined as a strategy such that, if all members of a population adopt it, no ‘mutant’ strategy can do better. A number of simple models of contest situations are analysed from this point of view. It is concluded that in ‘symmetric’ contests the ESS is likely to be a ‘mixed’ strategy; that is, either the population will be genetically polymorphic or individuals will be behaviourally variable. Most real contests are probably asymmetric, either in pay-off to the contestants, or in size or weapons, or in some ‘uncorrelated’ fashion; i.e. in a fashion which does not substantially bias either the pay-offs or the likely outcome of an escalated contest. An example of an uncorrelated asymmetry is that between the ‘discoverer’ of a resource and a ‘late-comer’. It is shown that the ESS in asymmetric contests will usually be to permit the asymmetric cue to settle the contest without escalation. Escalated contests will, however, occur if information to the contestants about the asymmetry is imperfect.     

The evolution of traits that determine ability in competitive contests

Summary We analyse mathematical models of the evolution of a trait that determines ability in contest competition. We assume that the value of the competitive trait affects two different components of fitness, one measuring the benefit of winning contests and the other measuring the cost of developing the competitive trait. Unlike previous analyses, we include the population dynamical consequences of larger competitive trait values. Exaggeration of the competitive trait reduces the mean probability of survival during the non-competitive stage of the life cycle. The resulting lower population density reduces competition and, therefore, reduces the advantages of greater competitive ability. Models without population dynamics often predict dimorphism in the competitive trait when resource possession is decided by interactions with many other individuals. If the competition involves a contest with a single other individual, models without population dynamics often predict cycles of increase and collapse in the trait or a continual increase, possibly resulting in extinction. When population dynamics are included, both of these results become less likely and a single stable trait value becomes more likely. Population dynamics also make it possible to have dimorphism when individuals have a single pairwise contest and alternative stable trait values when an individual has many contests. Increases in the value of the resource being contested may increase or decrease the evolutionarily stable size of the trait. Competition between very differently sized species will often decrease size in the larger species (character convergence).     

Kleptoparasitic Melees��Modelling Food Stealing Featuring Contests with Multiple Individuals

Kleptoparasitism is the stealing of food by one animal from another. This has been modelled in various ways before, but all previous models have only allowed contests between two individuals. We investigate a model of kleptoparasitism where individuals are allowed to fight in groups of more than two, as often occurs in real populations. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable challenging strategies. We find that there is always at least one ESS, but sometimes there are two or more, and discuss the circumstances when particular ESSs occur, and when there are likely to be multiple ESSs.     

Evolutionarily stable kleptoparasitism: consequences of different prey types

We present two elaborations of the model of Broom and Ruxtonthat found evolutionarily stable kleptoparasitic strategiesfor foragers. These elaborations relax the assumption that thedistribution of times required to handle discovered food itemsis exponential. These changes increase the complexity of themodel but represent a significant improvement in biologicalrealism. In one elaboration, handling takes a fixed interval,t_h, at the end of which the whole value of the food item isobtained. We liken this to peeling then consuming a small orange.The other elaboration also assumes that handling takes a fixedinterval, t_h, but this time the reward from the food item isextracted continuously throughout the handling period. We likenthis to eating an apple. Both models predict that increasingfood density, the ease with which food items can be discovered,or the length of aggressive contests all act to make kleptoparasitismless common. The difference between the evolutionarily stablestrategy solutions of the apple and orange models provides aclear prediction of our theory. When prey items require handlingbefore yielding a lump sum at the end, then kleptoparasiticattacks will be focused on prey items near the end of theirhandling period. However, if prey items yield reward continuouslyduring handling, then attacks should be biased toward newlydiscovered food items. Another key difference between the modelpredictions is that kleptoparasitism increases with foragerdensity in the apple model, but decreases in the orange model.     

Evolutionarily stable stealing: game theory applied to kleptoparasitism

We present an individual-based model of a group of foraginganimals. Individuals can obtain food either by discovering itthemselves or by stealing it from others (kleptoparasitism).Given that challenging another individual for a discovered fooditem costs time (which could otherwise be spent searching foran undiscovered item), attempting to steal from another maynot always be efficient We show that there is generally a uniquestrategy that maximizes uptake rate—always or never challengingothers. For any combination of parameter values, we can identifywhich strategy is appropraite. As a corollary to this, we predictthat small changes in ecolgical conditions can, under some circumstances,cause a dramatic change in the aggressive behavior of individuals.Further, we investigate situations where searching for undiscoveredfood and searching for potential opportunities for stealingare mutually exclusive activities (i.e., success at one canonly be improved at the expense of the other). Using game theory,we are able to find the evolutionarily stable strategy for investmentin these two activities in terms of the ecological parametersof the model.     

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.     

All by myself? Meta‐analysis of animal contests shows stronger support for self than for mutual assessment models

Since the 1970's, models based on evolutionary game theory, such as war of attrition (WOA), energetic war of attrition (E‐WOA), cumulative assessment model (CAM) and sequential assessment model (SAM), have been widely applied to understand how animals settle contests. Despite the important theoretical advances provided by these models, empirical evidence indicates that rules adopted by animals to settle contests vary among species. This stimulated recent discussions about the generality and applicability of models of contest. A meta‐analysis may be helpful to answer questions such as: (i) is there a common contest rule to settle contests; (ii) do contest characteristics, such as the occurrence of physical contact during the fight, influence the use of specific contest rules; and (iii) is there a phylogenetic signal behind contest rules? To answer these questions, we gathered information on the relationship between contest duration and traits linked to contestants' resource holding potential (RHP) for randomly paired rivals and RHP‐matched rivals. We also gathered behavioural data about contest escalation and RHP asymmetry. In contests between randomly paired rivals, we found a positive relationship between contest duration and loser RHP but did not find any pattern for winners. We also found a low phylogenetic signal and a similar response for species that fight with and without physical contact. In RHP‐matched rivals, we found a positive relationship between contest duration and the mean RHP of the pair. Finally, we found a negative relation between contest escalation and RHP asymmetry, even though it was more variable than the other results. Our results thus indicate that rivals settle contests following the rules predicted by WOA and E‐WOA in most species. However, we also found inconsistencies between the behaviours exhibited during contests and the assumptions of WOA models in most species. We discuss additional (and relatively untested) theoretical possibilities that may be explored to resolve the existing inconsistencies.     

Resistance is useless?—Extensions to the game theory of kleptoparasitism

We extend the game theoretic model of kleptoparasitism introduced by Broom and Ruxton (1998, Behav. Ecol. 9, 397–403) in two ways: we allow for asymmetric contests, where the probability α of the challenger winning can take any value from 0 to 1; and we allow the handler to choose not to resist the challenge, but to immediately concede and relinquish its food to the challenger. We find, in general, three possible evolutionarily stable strategies—challenge-and-resist (Hawk), challenge-but-do-not-resist (Marauder) and do-not-challenge-but-resist (Retaliator). When α = 1/2, we find that Hawk and Marauder are the only ESS’s, in contrast to the result of the original model; we also find an overlap region, in parameter space, where two different ESS’s are possible, depending on initial conditions. For general α, we see that all three ESS are possible, depending on different values of the environmental parameters; however, as the average time of a contest over food becomes long, then the Marauder strategy becomes more and more prevalent. The model makes a potentially significant prediction about animal behaviour in the area of kleptoparasitism, that a searcher, when it meets a handler, will only decline to attack that handler when α < 1/2 i.e.when the defender is more likely to win. One possible converse of this statement, that a handler whose probability of success is greater than 1/2 should always resist a challenge, is not true.     

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.     

Modulation of aggressive behaviour by fighting experience: mechanisms and contest outcomes

Experience in aggressive contests often affects behaviour during, and the outcome of, later contests. This review discusses evidence for, variations in, and consequences of such effects. Generally, prior winning experiences increase, and prior losing experiences decrease, the probability of winning in later contests, reflecting modifications of expected fighting ability. We examine differences in the methodologies used to study experience effects, and the relative importance and persistence of winning and losing experiences within and across taxa. We review the voluminous, but somewhat disconnected, literature on the neuroendocrine mechanisms that mediate experience effects. Most studies focus on only one of a number of possible mechanisms without providing a comprehensive view of how these mechanisms are integrated into overt behaviour. More carefully controlled work on the mechanisms underlying experience effects is needed before firm conclusions can be drawn.Behavioural changes during contests that relate to prior experience fall into two general categories. Losing experiences decrease willingness to engage in a contest while winning experiences increase willingness to escalate a contest. As expected from the sequential assessment model of contest behaviour, experiences become less important to outcomes of contests that escalate to physical fighting.A limited number of studies indicate that integration of multiple experiences can influence current contest behaviour. Details of multiple experience integration for any species are virtually unknown. We propose a simple additive model for this integration of multiple experiences into an individual's expected fighting ability. The model accounts for different magnitudes of experience effects and the possible decline in experience effects over time.Predicting contest outcomes based on prior experiences requires an algorithm that translates experience differences into contest outcomes. We propose two general types of model, one based solely on individual differences in integrated multiple experiences and the other based on the probability contests reach the escalated phase. The difference models include four algorithms reflecting possible decision rules that convert the perceived fighting abilities of two rivals into their probabilities of winning. The second type of algorithm focuses on how experience influences the probability that a subsequent contest will escalate and the fact that escalated contests may not be influenced by prior experience. Neither type of algorithm has been systematically investigated.Finally, we review models for the formation of dominance hierarchies that assume that prior experience influences contest outcome. Numerous models have reached varied conclusions depending on which factors examined in this review are included. We know relatively little about the importance of and variation in experience effects in nature and how they influence the dynamics of aggressive interactions in social groups and random assemblages of individuals. Researchers should be very active in this area in the next decade. The role of experience must be integrated with other influences on contest outcome, such as prior residency, to arrive at a more complete picture of variations in contest outcomes. We expect that this integrated view will be important in understanding other types of interactions between individuals, such as mating and predator-prey interactions, that also are affected significantly by prior experiences.     

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.     

Contest outcome in a territorial butterfly: the role of motivation

In many butterfly species, males compete over areas advantageous for encountering females. Rules for contest settlement are, however, largely unknown and neither morphological nor physiological traits can reliably predict the contest outcome. Here, we test the hypothesis that contests are settled in accordance with a motivation asymmetry. We staged contests between males of Pararge aegeria and after removing the resident, the non-resident was allowed (i) either to interact with a non-receptive female for 30 min (n = 30) or (ii) to spend 30 min alone in the cage (n = 30), after which the initial resident was reintroduced. The results show that males that had interacted with a female had a higher probability of becoming dominant and reversing contest outcome. Moreover, males that were faster to take over a vacant territory when the resident was removed were more likely to become dominant. Here, we show for the first time, to our knowledge, that frequent encounters with a mated female can increase male motivation to persist in a territorial contest in a butterfly. Further, we suggest that variation in intrinsic motivation reflects male eagerness to take over vacant territory. This study indicates that variation in resource value and motivational asymmetries are important for settling contests in butterflies.     

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.     

Hierarchical models of intra-specific competition: scramble versus contest

Hierarchical structured models for scramble and contest intraspecific competition are derived. The dynamical consequences of the two modes of competition are studied under the assumption that both populations divide up the same amount of a limiting resource at equal population levels. A comparison of equilibrium levels and their resiliences is made in order to determine which mode of competition is more advantageous. It is found that the concavity of the resource uptake rate is an important determining factor. Under certain circumstances contest competition is more advantageous for a population while under other circumstances scramble competition is more advantageous.Supported by NSF grant DMS-9306271     

Contest Duration and Dynamics are Affected by Body Size in a Potentially Subsocial Crayfish (Crustacea: Decapoda)

Fighting is a costly behavior, consuming both time and energy. As a result, the benefits of acquiring resources must outweigh these costs. Resource value will thus influence willingness to invest in a contest through its objective (the intrinsic properties of the resource) and subjective value (context/state dependent). In burrowing crayfish, subjective resource value may vary with life stage: adults, subadults, and juveniles differ in their ability to obtain resources. As juveniles cannot dig their own burrows, we hypothesize that earlier life stages will exhibit lower aggression than later life stages. To test this, we evaluated contests between paired individuals according to their cephalothorax length (CL), encompassing different life stages of Parastacus brasiliensis. To quantify aggression levels, we recorded contest duration, the frequency of low and highly aggressive behaviors, the time to escalate to highly aggressive behaviors, the probability of initiating contests with highly aggressive behaviors, and the latency to initiate a contest. We examined the relationship between these dependent variables and CL (independent variable) using GLMs to test how aggressive behaviors develop. Contest duration increased with pair mean, winner's and loser's CL. Frequency of low aggressive behaviors increased with CL, whereas highly aggressive behaviors, latency, and time to reach highly aggressive behaviors were unrelated to CL. Smaller individuals had a higher probability of initiating contests with highly aggressive behaviors. Self‐assessment explains the contest dynamics of P. brasiliensis, with smaller individuals giving up sooner, probably due to lower energy and time budgets.     

Lifetime resource utilization,flight physiology,and the evolution of contest competition in territorial insects

Adaptationist analyses of animal contests have contributed much to our understanding of behavioral evolution. One class of contest, however, the war of attrition, has proven difficult to interpret. In wars of attrition involving aerial displays, there is evidence that asymmetries in performance parameters such as flight energetics may be important determinants of contest resolution. This paradigm is not universal, however, and we presently lack a framework for understanding why certain biophysical parameters are important only in some cases. One possibility is that the relevance of these parameters is determined by evolutionarily conserved life-history-scale patterns of resource allocation and acquisition. We evaluated this hypothesis by investigating the correlates of competitive success in two territorial insects that exemplify markedly different lifetime patterns of resource utilization. We found that in the bot fly Cuterebra austeni, an extreme capital breeding species that depends entirely on energy acquired during its immature stages, territorial residency was most strongly correlated with a size-independent measure of energetic availability. In contrast, residency in the tarantula hawk wasp Hemipepsis ustulata was best predicted by variation in body size per se. Adult H. ustulata are able to supplement their larval-derived nutrient capital in the manner of an income breeder, and fuel reserves were independent of age and actually correlated negatively with residency in this species. These results underscore how the study of sexually selected phenomena may be enriched by an explicit consideration of life-history principles.     

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.     

Pure Self‐Assessment of Size During Male–Male Contests in the Parasitoid Wasp Nasonia vitripennis

During contest competition, a competitor may persist in a given contest based on information regarding its own fighting ability (resource‐holding potential, RHP), or that of its opponent. Although a number of models formalize the ways in which competitors are hypothesized to use RHP‐related information to determine their persistence in contests, we focused on pure self‐assessment and mutual assessment models in this study. According to pure self‐assessment models, a competitor uses only information regarding its own RHP to determine its persistence in a contest. In contrast, according to mutual assessment models, persistence is based on information regarding a competitor's RHP relative to that of its opponent and therefore requires assessment between competitors. In this study, using size as a proxy for RHP, we tested whether the parasitoid wasp Nasonia vitripennis utilizes pure self‐assessment or mutual assessment during pairwise, male–male contests. When we examined competitors of varied sizes, we found that the losing male's size was positively related to contest duration, but the winning male's size was uncorrelated with contest duration. When we examined contests in which competitors were size‐matched, we found that the mean size of paired competitors was positively related to contest duration. These results suggest that male N. vitripennis engage in pure self‐assessment during contests.     

Effects of body size and resource value on fighting behaviour in a jumping spider

Fights between male Euophrys parvula, a New Zealand salticid spider, consist of a number of discrete ‘stages’, of increasing intensity. Two aspects of these contests were investigated: (1) relative body size of the two opponents, and (2) the presence of a ‘resource’ (a female model). In 92% of all contests where a size difference existed, the larger of the two opponents won. Contest intensity (measured as the highest intensity behaviour elicited during the contest) was inversely correlated with relative body size of the two opponents (measured as carapace width). Contests escalated further when the female model was present. No relationship was found between contest duration and either relative body size or the presence of the model. It is suggested that for contests in which a number of behaviours of different intensity are used, contest intensity may be a better estimate of contest cost than duration. The results are discussed in terms of theoretical models of contest behaviour.     

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.