The Hawk—Dove game revisited: Effects of continuous variation in resource-holding potential on the frequency of escalation

Summary The classic Hawk—Dove game is extended to deal with continuous variation in resource-holding potential or RHP, when RHP is observable (via any sensory modality) but RHP difference is less than perfectly reliable as a predictor of the outcome of an escalated contest. The relationship between sensory and physical magnitudes of RHP is assumed to be governed by Fechner's psychophysical law, whose effect is that contestants interact as if they had perfect information about their relative RHP (as opposed to RHP difference). Thus, an animal is aggressive if its RHP exceeds a certain fraction, called its threshold, of its opponent's RHP and otherwise is non-aggressive; and the classic Hawk and Dove strategies correspond to zero and infinite thresholds, respectively. For RHPs drawn at random from an arbitrary Gamma distribution there is a unique evolutionarily stable strategy or ESS, which depends on a parameter measuring the reliability of RHP as a predictor of the outcome of a fight, on the ratio of the valueV of winning to the costC of losing (both measured in units of reproductive fitness) and on the mean µ and variance ² of the RHP distribution. In a population at this ESS, ifV/C < 1 then the threshold is 1 and there is no fighting. AsV/C increases beyond 1 to a second critical value , however, the threshold decreases steadily from 1 to 0 and remains 0 forV/C > ; is an increasing function of , but a decreasing function of ². That a lower variance of RHP can imply a lower escalation frequencyp is a novel insight of the analysis. The prediction is at first counterintuitive, because if the aggression threshold were fixed then larger variance would imply lowerp (dispersion effect of variance). When natural selection acts on the threshold, however, increasing the variance not only reduces the probability that an animal with larger RHP will be attacked by an animal with lower RHP at the existing threshold, but also reduces the expected costs of adopting that particular threshold, so that a mutant with a somewhat lower threshold can invade the population (selection effect of variance). Forp, the selection effect dominates toward the upper end of the interval 1 V/C .     

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.     

Can transitive inference evolve in animals playing the hawk-dove game?

What should an individual do if there are no reliable cues to the strength of a competitor when fighting with it for resources? We herein examine the evolutionarily stable strategy (ESS) in the hawk-dove game, if the opponent's resource-holding potential (RHP) can only indirectly be inferred from the outcome of past interactions in the population. The strategies we examined include the classical mixed strategy in which no information on past games is utilized, the 'imprinting' strategy in which a player increases/decreases its aggressiveness if it wins/loses a game, the 'immediate inference' strategy in which a player can infer the strength of those opponents it fought before, and the 'transitive inference' strategy in which a player can infer the strength of a new opponent through a third party with which both players have fought before. Invasibility analysis for each pair of strategies revealed that (i) the transitive-inference strategy can always invade the mixed strategy and the imprinting strategy, and itself refuses invasion by these strategies; (ii) the largest advantage for transitive inference is achieved when the number of games played per individual in one generation is small and when the cost of losing an escalated game is large; (iii) the immediate inference, rather than the transitive inference, can be an ESS if the cost of fighting is small; (iv) a strong linear ranking is established in the population of transitive-inference strategists, though it does not perfectly correlate to the ranking by actual RHPs. We found that the advantage of the transitive inference is not in its ability to correct a misassessment (it is actually the worst in doing so), but in the ability of quickly lining up either incorrect or correct assessments to form a linear dominance hierarchy.     

A test of the sequential assessment game: the effect of increased cost of sampling

The sequential assessment game describes a fight between twoconspecifics as a statistical sampling process, allowing forspecific predictions about fight duration and number of repetitionsof a behavioral element depending on relative fighting ability.Fight duration and number of repetitions of a behavioral elementcorrelate moderately to relative fighting ability. Variationin real contests depends on differences between the contestantsin the ability to incur cost and the value of the contestedresource. I hypothesized that an additional source of variationis differences between individuals in their perception of howdangerous it is to fight. To investigate this, I used the riskof predation to study the effect on the use of different agonisticbehaviors in fights between males of the cichlid fish Nannacaraanomala. In the group subjected to predation risk, the time untilthe most escalated behavior (mouth wrestling) was more variableand increased significantly on average. In addition, the durationof fights was significantly longer. In the predator treatmentthe use of visual assessment and tail beating varied more thanin the control, giving a significant positive relationship betweenthe use of low-intensity behaviors and time to mouth wrestlingacross the group. These relationships were less pronounced in thecontrol group. The effect of predation risk on optimal information transferis discussed based on the behavioral mechanism suggested bythe sequential assessment game.     

Fighting for shells: how private information about resource value changes hermit crab pre-fight displays and escalated fight behaviour

Pre-fight displays typically provide honest, but sometimes dishonest, information about resource holding potential and may be influenced by assessment of resource value and hence motivation to acquire the resource. These assessments of potential costs and benefits are also predicted to influence escalated fight behaviour. This is examined in shell exchange contests of hermit crabs in which we establish an information asymmetry about a particularly poor quality shell. The poor shell was created by gluing sand to the interior whereas control shells lacked sand and the low value of the poor shell could not be accurately assessed by the opponent. Crabs in the poor shell showed changes in the use of pre-fight displays, apparently to increase the chances of swapping shells. When the fights escalated, crabs in poor shells fought harder if they took the role of attacker but gave up quickly if in the defender role. These tactics appear to be adaptive but do not result in a major shift in the roles taken or outcome. We thus link resource assessment with pre-fight displays, the roles taken, tactics used during escalation and the outcome of these contests.     

Effects of resource holding potential and resource value on tenure at nest sites in sand gobies

Over a broad range of animal systems, male reproductive successdepends on resource holding potential (RHP) and resource quality.In a field study, we randomly combined males of different sizeswith nests of different sizes to investigate the relative roleof resource holding potential and resource quality in determininga sand goby, Pomatoschistus minutus, male's nest tenure. Individuallymarked small and large males were given either small or largeflowerpots for nests in isolation and were exposed to intrudersafter they had built nests. We found that nest tenure was longerfor big males and owners of big nests. In most cases (34 of51) the original nest owner was replaced by a bigger male. Thesereplacements by larger males were probably due to takeoversby stronger intruders. Replacement males were larger at bignests. Our results support resource defense theory, as individualswith higher RHP and more valuable resources defended their nestfor longer. On nine occasions males abandoned their nests. Ownersof these nests were larger than the nest owners that were replaced.Hence, our results may provide an example of a situation inwhich sand goby males are able to judge the reproductive valueof their current situation and act accordingly.     

Effects of resource variation during early life and adult social environment on contest outcomes in burying beetles: a context-dependent silver spoon strategy?

Good early nutritional conditions may confer a lasting fitness advantage over individuals suffering poor early conditions (a ‘silver spoon’ effect). Alternatively, if early conditions predict the likely adult environment, adaptive plastic responses might maximize individual performance when developmental and adult conditions match (environmental-matching effect). Here, we test for silver spoon and environmental-matching effects by manipulating the early nutritional environment of Nicrophorus vespilloides burying beetles. We manipulated nutrition during two specific early developmental windows: the larval environment and the post-eclosion environment. We then tested contest success in relation to variation in adult social environmental quality experienced (defined according to whether contest opponents were smaller (good environment) or larger (poor environment) than the focal individual). Variation in the larval environment influenced adult body size but not contest success per se for a given adult social environment experienced (an ‘indirect’ silver spoon effect). Variation in post-eclosion environment affected contest success dependent on the quality of the adult environment experienced (a context-dependent ‘direct’ silver spoon effect). By contrast, there was no evidence for environmental-matching. The results demonstrate the importance of social environmental context in determining how variation in nutrition in early life affects success as an adult.     

The Impact of Exploitation on Freshwater Mussels (Bivalvia: Hyriidae) in the Tocantins River,Brazil

Freshwater mussels in the Tocantins River are exploited for their shells to make buttons. Data were collected on mussel density, size frequency distribution, habitat and exploitation level at five sites. The most abundant species is Paxyodon syrmatophorus (Meuschen, 1781) and is preferred by fishermen. Mean harvested shell size is larger than that of randomly sampled mussels for all species. No individuals below 30 mm were found among harvested shells. Exploitation level varied among sites. Mussel density and mean shell size were correlated with exploitation level and with some habitat parameters. The results are discussed in relation to strategies for the management of existing stocks. Bivalves de água doce no rio Tocantins são explorados pelas conchas para a confecção de bot[otilde]es. Em cinco sítios, dados foram obtidos sobre densidade, distribuição em tamanho, hábitat e nível de exploração dos moluscos. O bivalve mais abundante e mais preferido pelos coletadores de conchas foi Paxyodon syrmatophorus (Meuschen, 1781). O tamanho em média das conchas coletadas é maior do que o das conchas amostradas aleatóriamente. Só indivíduos acima de 30 mm em tamanho foram encontrados entre conchas coletadas. O nível de exploração variou entre sítios. Densidade e tamanho média das conchas foram relacionados com o nível de exploração e alguns parâmetros de hábitat. Os resultados são discutidos em relação às estratégias de manejo dos estoques já existentes.     

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.     

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.     

Strong but variable associations between social dominance and clutch sex ratio in a colonial corvid

We studied primary sex ratio of clutches in relation to socialdominance for 6 years in a colony of free-living jackdaws, asmall corvid. Social dominance was strongly associated withclutch sex ratio, with the difference in clutch sex ratio betweenthe most and least dominant pairs being 30–40%. To ourknowledge, this is the first demonstration of an associationbetween social dominance and sex allocation in birds. However,the direction of this effect varied between years. Dominantjackdaws produced more sons during the first years of the studybut fewer sons during the last years. Offspring sex was notrelated to laying order within a clutch, and the effect of socialdominance on sex ratio was similar on eggs laid first, middle,or last. We investigated the effect of 2 factors (laying dateand parental condition) that could have mediated the shift inthe effect of social dominance on sex allocation in the courseof the study. Laying date was positively associated with theproportion of males, but this effect was independent of socialdominance. Maternal condition (residual mass over tarsus andegg volume) was related to social dominance but not to clutchsex ratio. Paternal condition (residual mass over tarsus) wasnot related to clutch sex ratio. We discuss how spatial or temporalvariation in effects of variables such as social dominance onsex allocation can contribute to our understanding of the evolutionof sex allocation in species with complex life histories.