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.     

Residency effects in animal contests

The question of why territorial residents usually win asymmetrical owner-intruder contests is critical to our understanding of animal contest evolution. Game theory suggests that, under certain conditions, residency could be used as an arbitrary means of contest settlement in a manner analogous to tossing a coin. Key empirical support for this idea is provided by a study on the speckled wood butterfly (Pararge aegeria); however, this result has proven controversial. We show conclusively that residency does not serve as an arbitrary cue for contest settlement in this species. By means of a series of manipulative experiments, conducted on two phenotypically divergent populations of P. aegeria, we also rule out the recently presented alternative that contests are settled due to resource-correlated asymmetries in thoracic temperature. Our results instead suggest that more intrinsically aggressive males accumulate as residents and continue to win due to the self-reinforcing effect of prior winning experience. Truly arbitrary contest settlement may be rare or non-existent in the wild.     

The mismeasure of animal contests

Contests between rivals placing similar value on the resource at stake are commonly won by the rival having greater ‘resource holding potential’ (RHP). Mutual assessment of RHP difference between rivals is usually expected as an economical means of resolution; weaker rivals can retreat when they detect their relative inferiority, thereby avoiding costly, futile persistence. Models of contest resolution that entail retreat decisions based on estimates of RHP difference predict that contest duration diminishes as RHP difference between rivals increases because the asymmetry is more readily detected. This prediction appears to have been fulfilled in contests of diverse taxa, generating widespread support for assessment of RHP differences in contests. But few studies have considered alternatives in which each rival simply persists in accord with its own RHP (‘own RHP-dependent persistence’). In contests decided by own RHP-dependent persistence, in which costs accrue only through each rival's own actions, weaker rivals retreat first because they are inherently less persistent, and contest duration depends primarily on the weaker (losing) rival's RHP rather than RHP difference between the rivals. We show here that the analyses most commonly used to detect effects of RHP difference cannot discriminate between these alternatives. Because RHP difference between rivals tends to be correlated with RHP of the weaker rival in a pair, a negative relation between RHP difference and contest duration may be generated even when decisions of retreat are not based on estimated RHP difference. Many studies purporting to show a negative relation between RHP difference and contest duration may actually reflect an incidental association between weaker rival RHP and RHP difference. We suggest statistical and experimental approaches that may help to discriminate between effects of weaker rival RHP and true effects of RHP difference. We also discuss whether ‘true’ negative effects of RHP difference on contest duration always reflect retreat decisions based on estimated RHP differences. Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.      

Information transfer during cricket frog contests

We investigated information transfer during vocal interactions between cricket frogs, Acris crepitans, with a specific focus on information about size and intention. In response to opponents, cricket frogs alter both temporal and spectral (frequency) aspects of their calls. Previous work suggests that males use dominant frequency, which is correlated with size, to provide information about fighting ability, and use temporal call characters, which are independent of size, to provide information about aggressive intent. We tested this hypothesis by investigating the relationship between call characters and contest behaviour. We presented a focal male with a simulated opponent, and categorized his behavioural response as attack, abandon or tolerate. We found that information about opponent size does not appear to influence a male's decision to fight, flee or tolerate an intruder. Whether or not males use the size information that is encoded in call frequency remains unclear. In contrast, changes in call frequency, which are not correlated with size, predicted the outcome of simulated contests, suggesting that male cricket frogs signal information about agonistic intent. Temporal call characters indicated whether or not a resident tolerated an opponent, but they did not predict contest outcome (attack versus abandon). Furthermore, the difference between the temporal call characters of a focal male and the simulated opponent predicted whether the resident tolerated the opponent. We suggest, therefore, that temporal call changes may be a cooperative signal designed to facilitate assessment of size through physical contact in wrestling bouts. Copyright 2002 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.     

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.     

Relationship between attack and skipping in Taekwondo contests

The purpose of this study was to determine the relationship between attack time (AT) and skipping time (ST) during the 2007 Taekwondo World Championship and 2008 Beijing Olympic Games. A total of 22 matches (65 rounds, 13 semifinals, and 8 finals) from the World Championship and 23 matches (63 rounds, 22 rounds with 16 athletes each and 1 quarterfinal round) from the Olympic Games, both in the male category, were assessed using time-motion analysis. The AT was considered as the total time during which the athlete attacked or tried to attack, whereas ST was the total time without attempting to attack. The ratio of AT to ST was ～ 1:7 based on the data pooled from the 2 competitions. The AT/ST ratio was significantly lower for the World Championship than for the Olympic Games (p ≤ 0.05). In the Olympic Games, no consistent differences across weight divisions were found. However, during the World Championship, the heavier weight divisions (>78 kg) exhibited a lower average AT, lower summed AT, lower attack numbers (ANs)and higher average ST than lighter weight divisions (<58 kg, p ≤ 0.05). For both competitions, the ST was lower, and the ANs and AT/ST ratio were higher in round 3 than in round 1 or 2. In conclusion, the results of this study suggest that matches in the Olympic Games were less cadenced than in the World Championship, but that in both competitions, the intensity of the match increased in round 3. Practically, these data suggest that coaches need to structure Taekwondo training sessions in a manner that allows the work/pause ratio to mirror the physical demand imposed during competitions.     

No effect of blue on winning contests in judo

A study by Rowe et al. reported a winning bias for judo athletes wearing a blue outfit relative to those wearing a white one during the 2004 Olympics. It was suggested that blue is associated with a higher likelihood of winning through differential effects of colour on opponent visibility and/or an intimidating effect on the opponent. However, we argue that there is no colour effect on winning in judo. We show that alternative factors, namely allocation biases, asymmetries in prior experience and differences in recovery time are possible confounding factors in the analysis of Rowe et al. After controlling for these factors, we found no difference in blue and white wins. We further analysed contest outcomes of 71 other major judo tournaments and also found no winning bias. Our findings have implications for sports policy makers: they suggest that a white-blue outfit pairing ensures an equal level of play.     

Packaging contests between viral RNA molecules and kinetic selectivity

The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.     

Vocal rate as an assessment process during fallow deer contests

Two types of model propose that strategic decisions during contests are determined either by (i) a mutual-assessment process or (ii) a self-assessment process. Vocal signals are thought to convey information about the competitive abilities of individuals, the ultimate function of which is a reduction in costs associated with fighting consistent with the principle of mutual assessment. Nevertheless, the limited evidence that male ungulates engage in mutual assessment of vocal rates during dyadic contests has been questioned. Therefore, we examined the vocal rates of winners and losers during escalated dyadic contests between male fallow deer in order to further inform on this issue. Our results showed that winners and losers did not differ in vocal rate. The best model fit that accounted for individual vocal rates included a preponderance of factors related to the opponent indicating that contestants were attending to their opponent during fights. Vocal rate was, therefore, dependent on estimates of opponent quality without reference to self, supporting an 'opponent-only' rather than a mutual assessment process.     

Overlapping and matching in the song contests of black-capped chickadees

During vocal contests, animals alter both the timing and the patterning of responses to their opponents. Time-specific responses (such as overlapping an opponent's song) and pattern-specific responses (such as matching the type of an opponent's song) may reveal information about interacting animals. Here we explore the consequences of overlapping and frequency matching during song contests of male black-capped chickadees, Poecile atricapillus. Using interactive playback, we engaged birds of high and low dominance status in vocal interactions with a simulated territorial intruder. The playback intruder either overlapped or avoided overlapping the subjects' songs and either matched or avoided matching the frequency of the subjects' songs. Individuals who were overlapped by the playback intruder showed higher variability in their song length and song timing than individuals who were not overlapped. Individuals who were frequency-matched by the playback intruder responded with more agitated responses (more flights and passes over the speaker and closer distances of closest approach) and spent more time farther away from the loudspeaker. We argue that the timing of song delivery and the choice of song type are distinct functional components of vocal interactions, where overlapping and matching songs are threatening signals that have separate consequences for opponent behaviour and song performance. High-ranking males responded at greater distances from the loudspeaker in all treatments and responded with lower agitation levels than low-ranking males. We demonstrate that males of different quality show different behavioural responses to territorial intruders, where males of high status appear reluctant to engage an intruder as intensely as males of low status.     

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).