Game theory in biology: 50 years and onwards

Game theory in biology gained prominence 50 years ago, when Maynard Smith & Price formulated the concept of an evolutionarily stable strategy (ESS). Their aim was to explain why conflicts between animals of the same species usually are of a 'limited war' type, not causing serious injury. They emphasized that game theory is an alternative to previous ideas about group selection, which were used by ethologists to explain limited aggression. Subsequently, the ESS concept was applied to many phenomena with frequency dependence in the evolutionary success of strategies, including sex allocation, alternative mating types, contest behaviour and signalling, cooperation, and parental care. Both the analyses of signalling and cooperation were inspired by similar problems in economics and attracted much attention in biology. Here we give a perspective on which of the ambitions in the field have been achieved, with a focus on contest behaviour and cooperation. We evaluate whether the game-theoretical study of the evolution of cooperation has measured up to expectations in explaining the behaviour of non-human animals. We also point to potentially fruitful directions for the field, and emphasize the importance of incorporating realistic behavioural mechanisms into models. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Agonistic interactions with asymmetric body size in two adult-age groups of the annual killifish Millerichthys robustus (Miller & Hubbs, 1974)

In this study, the author evaluated two adult age groups of the Mexican rivulus Millerichthys robustus with body size asymmetries to determine the strategies used by an annual killifish during agonistic interactions of different ontogenetic stages. To achieve this goal, the author first characterized the ethogram of agonistic interactions of M. robustus composed of seven behavioural units in males and five behavioural units in females. The author then analysed agonistic interaction strategies used by males and females with body size asymmetries in two groups of different adult ages that represent different ontogenetic stages: (a) just after sexual maturity was reached, at 5 weeks of age, and (b) near natural death, at 24 weeks of age. The agonistic behaviour patterns of M. robustus were compatible with the logic of mutual assessment. Large males had an advantage during their interactions in both age groups, winning all of the encounters. Nonetheless, there was more aggression in 5-week-old fish encounters. In addition, small 24-week-old fish were more aggressive than small 5-week-old fish. These changing strategies may be because of the cost-benefits required during a fight at each ontogenetic stage. In the female encounters, size did not predict winners, as both small and large fish won a similar number of encounters, and some contests remained unresolved regardless of age group. There was a tendency for small females of any age to risk more than males in fights to maintain reproductive fitness.

A Brain Module for Scalable Control of Complex, Multi-motor Threat Displays

Threat displays are a universal feature of agonistic interactions. Whether threats are part of a continuum of aggressive behaviors or separately controlled remains unclear. We analyze threats in Drosophila and show they are triggered by male cues and visual motion, and comprised of multiple motor elements that can be flexibly combined. We isolate a cluster of ∼3 neurons whose activity is necessary for threat displays but not for other aggressive behaviors, and whose artificial activation suffices to evoke naturalistic threats in solitary flies, suggesting that the neural control of threats is modular with respect to other aggressive behaviors. Artificially evoked threats suffice to repel opponents from a resource in the absence of contact aggression. Depending on its level of artificial activation, this neural threat module can evoke different motor elements in a threshold-dependent manner. Such scalable modules may represent fundamental "building blocks" of neural circuits that mediate complex multi-motor behaviors.

Behavioural dominance of the invasive red-billed leiothrix (Leiothrix lutea) over European native passerine-birds in a feeding context

Behavioural dominance and aggressiveness may be crucial traits facilitating the establishment of invasive species. Few studies considered agonistic interactions between exotic and native bird species in feeding contexts, particularly when the exotic has social habits. We aimed to know if individuals of a social invasive species, the red-billed leiothrix Leiothrix lutea, are: more aggressive; the initiators of the first interaction; and dominant (i.e., won most interactions) over native opponents in a feeding context. We performed an experiment in a closed environment forcing dyadic interactions between an individual of a native species facing a leiothrix individual. We found that the leiothrix was the initiator in most experiments, being apparently dominant over natives. However, the invader was not more aggressive than natives. This can increase the risk of injury for natives because the leiothrix has a relatively larger body size. We discuss possible negative impacts of the leiothrix on native species.

Fighting cichlids: Dynamic of intrasexual aggression in dyadic agonistic encounters

Aggression is an extremely complex behaviour and female aggression is understudied when compared to males. Despite the fact that it has been suggested that conflict among females may be more frequently resolved peacefully, in many species females show high levels of aggression. We used Cichlasoma dimerus to describe dynamics and conflict outcome in intrasexual agonistic encounters. We performed encounters of two sex-matched animals in a neutral arena and we recorded agonistic interactions during one hour. All aggressive and submissive behaviours were described and quantified to perform the ethogram. Encounters followed three phases: pre-contest, contest and post-resolution. Latency, time of resolution and frequency of aggressive displays did not differ between sexes. Relative variations in size between female opponents better explained aggression outcome in each contest, since higher levels of aggression occurred in dyads of more similar fish. However, this was not observed in males, suggesting that probably morphological characteristics could be less relevant in male conflict resolution. Altogether these results suggest that in this ethological context, C. dimerus females are as aggressive as males and that they have similar motivation towards territorial aggression, emphasizing the need of deepening the study of aggression in females and not only in males.

Appraisal of unimodal cues during agonistic interactions in Maylandia zebra

Communication is essential during social interactions including animal conflicts and it is often a complex process involving multiple sensory channels or modalities. To better understand how different modalities interact during communication, it is fundamental to study the behavioural responses to both the composite multimodal signal and each unimodal component with adequate experimental protocols. Here we test how an African cichlid, which communicates with multiple senses, responds to different sensory stimuli in a social relevant scenario. We tested Maylandia zebra males with isolated chemical (urine or holding water coming both from dominant males), visual (real opponent or video playback) and acoustic (agonistic sounds) cues during agonistic interactions. We showed that (1) these fish relied mostly on the visual modality, showing increased aggressiveness in response to the sight of a real contestant but no responses to urine or agonistic sounds presented separately, (2) video playback in our study did not appear appropriate to test the visual modality and needs more technical prospecting, (3) holding water provoked territorial behaviours and seems to be promising for the investigation into the role of the chemical channel in this species. Our findings suggest that unimodal signals are non-redundant but how different sensory modalities interplay during communication remains largely unknown in fish.

Self-Construals, Anger Regulation, and Life Satisfaction in the United States and Japan

Previous studies have reported evidence that indicates differences between Western and East Asian cultures in anger regulation and its psychological consequences. However, many of these studies have focused on a specific anger regulation strategy and its relation with a psychological consequence. Here, we developed an integrated model that can comprehensively examine three different anger regulation strategies (anger suppression, expression, and control), independent and interdependent self-construals as the psychological antecedent, and life satisfaction as the psychological consequence. We estimated the model using large samples of American and Japanese adults to examine the associations between the two self-construals, three anger regulation strategies, and life satisfaction. We compared the difference in the patterns of relationships among the key constructs between the American and Japanese samples. The results confirmed previously suggested cultural differences while also discovering new culturally different paths. The results generally suggest that individual-level self-construals matter more when anger is a culturally condoned emotion (vs. condemned). The implications and limitations of the integrated model are discussed.

A Simple Behavioral Model Predicts the Emergence of Complex Animal Hierarchies

Social dominance hierarchies are widespread, but little is known about the mechanisms that produce nonlinear structures. In addition to despotic hierarchies, where a single individual dominates, shared hierarchies exist, where multiple individuals occupy a single rank. In vertebrates, these complex dominance relationships are thought to develop from interactions that require higher cognition, but similar cases of shared dominance have been found in social insects. Combining empirical observations with a modeling approach, we show that all three hierarchy structures-linear, despotic, and shared-can emerge from different combinations of simple interactions present in social insects. Our model shows that a linear hierarchy emerges when a typical winner-loser interaction (dominance biting) is present. A despotic hierarchy emerges when a policing interaction is added that results in the complete loss of dominance status for an attacked individual (physical policing). Finally, a shared hierarchy emerges with the addition of a winner-winner interaction that results in a positive outcome for both interactors (antennal dueling). Antennal dueling is an enigmatic ant behavior that has previously lacked a functional explanation. These results show how complex social traits can emerge from simple behaviors without requiring advanced cognition.

Expression of anger and ill health in two cultures: an examination of inflammation and cardiovascular risk

Expression of anger is associated with biological health risk (BHR) in Western cultures. However, recent evidence documenting culturally divergent functions of the expression of anger suggests that its link with BHR may be moderated by culture. To test this prediction, we examined large probability samples of both Japanese and Americans using multiple measures of BHR, including pro-inflammatory markers (interleukin-6 and C-reactive protein) and indices of cardiovascular malfunction (systolic blood pressure and ratio of total to HDL cholesterol). We found that the link between greater expression of anger and increased BHR was robust for Americans. As predicted, however, this association was diametrically reversed for Japanese, among whom greater expression of anger predicted reduced BHR. These patterns were unique to the expressive facet of anger and remained after we controlled for age, gender, health status, health behaviors, social status, and reported experience of negative emotions. Implications for sociocultural modulation of bio-physiological responses are discussed.

Arch displays signal threat intentions in a fission–fusion flock of the red-crowned crane

Ritualised displays are used by group-living animals in various contexts, such as when individuals join a group or flock. Only a few quantitative studies of the function of displays in species with fission–fusion social dynamics have been conducted to date. Here, we examined the arch display in red-crowned cranes (Grus japonensis) immediately after joining a flock. Behavioural observations indicated that the arch functions as a signal of both threat motivation and individual strength. Singletons had disadvantages in terms of competition over resources and were, therefore, expected to have higher threat motivation than pairs or families. Indeed, singletons performed the arch more frequently than did pairs or families. Performance of the arch was related to dominance: males and adults were more likely to perform the arch than females and sub-adults. The likelihood of performing the arch was positively associated with local group density, indicating that joiners arched in more competitive situations. Contextual analyses indicated that subsequent behaviour by a joiner was more aggressive and that nearby individuals more frequently showed behavioural responses when a joiner arched than when it did not. Together, this study shows that cranes demonstrate functional displays to potential competitors, and represents a rare example of the functional analysis of ritualised signals in non-songbird species with fission–fusion social dynamics.

Confidence sharing: an economic strategy for efficient information flows in animal groups

Social animals may share information to obtain a more complete and accurate picture of their surroundings. However, physical constraints on communication limit the flow of information between interacting individuals in a way that can cause an accumulation of errors and deteriorated collective behaviors. Here, we theoretically study a general model of information sharing within animal groups. We take an algorithmic perspective to identify efficient communication schemes that are, nevertheless, economic in terms of communication, memory and individual internal computation. We present a simple and natural algorithm in which each agent compresses all information it has gathered into a single parameter that represents its confidence in its behavior. Confidence is communicated between agents by means of active signaling. We motivate this model by novel and existing empirical evidences for confidence sharing in animal groups. We rigorously show that this algorithm competes extremely well with the best possible algorithm that operates without any computational constraints. We also show that this algorithm is minimal, in the sense that further reduction in communication may significantly reduce performances. Our proofs rely on the Cramér-Rao bound and on our definition of a Fisher Channel Capacity. We use these concepts to quantify information flows within the group which are then used to obtain lower bounds on collective performance. The abstract nature of our model makes it rigorously solvable and its conclusions highly general. Indeed, our results suggest confidence sharing as a central notion in the context of animal communication.

Cooperative groups are abundant on all scales of the biological world. Despite much empirical evidence on a wide variety of natural communication schemes, there is still a growing need for rigorous tools to quantify and understand the information flows involved. Here, we borrow techniques from information theory and theoretical distributed computing to study information sharing within animal groups. We consider a group of individuals that integrate personal and social information to obtain improved knowledge of their surroundings. We rigorously show that communication between such individuals can be compressed into simple messages that contain an opinion and a corresponding confidence parameter. While this algorithm is extremely efficient, further reduction in communication capacity may greatly hamper collective performances.

Temporal and frontal lobe initiation and regulation of the top-down escalation of anger and aggression

The widespread, across-species strategy of stagewise escalation of aggression in agonistic encounters can be understood in terms of resource capture and control with least risk and cost. Human anger likely follows similar principles. As an adaptive phenomenon, escalation may involve particular neural circuitry. To advance beyond a standard view that the frontal lobe tonically inhibits subcortical circuits of aggression, a model is proposed which starts with the general rostrally directed flow of information in the brain. Earlier stage processing of visual and auditory input is transmitted from posterior and middle temporal cortices to anterior temporal lobe where rudimentary appraisals of threat and provocation are developed. These directly but diffusely activate cortical/subcortical anger/aggression response systems. At the same time, the anterior temporal loci transmit the modality-specific perceptual information to orbito-frontal cortex where it is integrated with information about, e.g., the opponent's relative dominance/social status and evaluated for likelihood of potential rewards and punishments associated with different modes of responding and so forth. These frontal areas then impose an inhibitory gating or modulation and focusing of activity initiated by the anterior temporal loci through their projections to GABAergic interneurons in the same cortical/subcortical circuits. Escalation occurs as the inhibition imposed by the frontal areas is progressively lifted. Exploration of the implications, applications and hypotheses flowing from this model will improve our understanding of the biologically important and socially significant phenomena of escalation.

Putting information back into biological communication

At the heart of many debates on communication is the concept of information. There is an intuitive sense in which communication implies the transfer of some kind of information, probably the reason why information is an essential ingredient in most definitions of communication. However, information has also been an endless source of misunderstandings, and recent accounts have proposed that information should be dropped from a formal definition of communication. In this article, we re-evaluate the merits and the internal logic of information-based vs. information-free approaches and conclude that information-free approaches are conceptually incomplete and operationally hindered. Instead, we propose a functional notion of information that follows logically from previous adaptationist accounts. The ensuing definition of communication provides a wider, more inclusive theoretical scope that reflects more accurately the evolutionary scenario shaping animal signals. Additionally, it is a definition better equipped to deal with the extraordinary diversity of animal signals, facilitates the distinction of honest and deceptive signals at a proximate level and accommodates a number of conceptual and practical issues (e.g. redundancy, alerting components) that are lost when we fail to acknowledge the informative content of animal signals.

Androgens and dominance: sex-specific patterns in a highly social fish (Neolamprologus pulcher)

In most vertebrates, aggression and dominance are tightly linked to circulating testosterone. Fish, however, have two androgens (testosterone, T and 11-ketotestosterone, 11KT) that influence aggression and dominance. To date, few studies have compared the relationship between androgen levels and the outcome of aggressive contests in both females and males of the same species. To investigate sex differences in androgens we staged size-matched, limited-resource (territory) contests with 14 female-female and 10 male-male pairs of the highly social cichlid Neolamprologus pulcher. We then examined androgen levels in recently established dominants, who won the contest and subsequently acquired a territory (for 3h), and subordinates, who lost and did not acquire a territory. Newly dominant females had higher plasma T but similar 11KT levels to newly subordinate females. In contrast, newly dominant males had higher 11KT but similar T levels to subordinate males. The ratio of 11KT to T, which demonstrates physiological importance of T conversion to 11KT, was positively correlated with submissive behavior in female winners, and correlated weakly with aggressive behavior in male winners (p=0.05). These findings provide support for the hypothesis that different androgens play equivalent roles in female versus male dominance establishment, and suggest that relative levels of 11KT and T are implicated in female dominance behavior and perhaps behavior of both sexes.

Sequence and priming in 15 month-olds' reactions to brief arm restraint: evidence for a hierarchy of anger responses

Brief, gentle arm restraint is widely used in experimental studies of children's anger, but the pattern of responses generated by such restraint has been incompletely described. We now describe a hierarchy of responses within trials as well as an escalation across trials that have both methodological and theoretical significance. Mothers of 87 15-month olds prevented them from playing with a toy by restraining their arms on two consecutive 30 sec trials. Physical struggling was the first and most frequent response; children who struggled were significantly more likely to vocalize, and those who vocalized were significantly more likely to show facial expressions of anger. The children's responses became more probable, rapid, and intense during Trial 2 restraint. Overall, the hierarchy was orderly enough to meet criteria for Guttman scalability. The particular sequence observed suggests situational, as opposed to bio-energetic, ordering of responses. Methodologically, the two trial paradigm is a simple, ecologically valid model for studying anger escalation that parallels the "attack priming" of aggression in other species. The magnitude and persistence of anger priming may provide novel measures of anger regulation. Theoretically, the existence of an orderly response hierarchy is consistent with previous observations suggesting that, within a situational context, the sequential appearance of specific behaviors may indicate progressive increases in anger intensity.

Phenotypic plasticity, sexual selection and the evolution of colour patterns

When a population comes to occupy a new environment, phenotypically plastic responses alter the distribution of phenotypes, and hence affect both the direction and the intensity of selection. Rates of evolution can be accelerated or retarded compared to what would happen in the absence of plasticity. Plastic responses in one trait result in novel selection pressures on other traits, and this can lead to evolution in completely different directions than predicted in the absence of plasticity. In this paper I use the concept of the adaptive surface in order to identify conditions under which the various different outcomes are expected. I then discuss differences between sexually and naturally selected traits. Sexually selected traits are often expected to be plastic in their expression, with individuals in high condition developing greater elaboration. As examples of sexually selected traits I review the evolution of colour patterns in birds with a view to assessing the magnitude of plastic responses in their development, and to ask how such responses may have influenced genetic evolution. The common colour pigments in birds are carotenoids and melanins. Both are used in social signaling, and consequently are expected to evolve to be phenotypically plastic indicators of an individual's quality. Perhaps partly because they are condition indicators, the quantity of carotenoids in the plumage can be strongly influenced by diet. Examples are described where alterations of carotenoids in the diet are thought to have altered the phenotype, driving genetic evolution in novel directions. Melanin patterns seem to be less affected by diet, but the intensity of melanization after moult is affected by social interactions during the moult and by raising birds in humid conditions. Hormonal manipulations can have dramatic effects on both the kinds of melanin produced (eumelanin or phaeomelanin) as well as the patterns they form. Differences between species in melanin patterns resemble differences produced by environmental manipulations, as well as those produced by simple modulations of parameters in computer simulations of pattern formation. While phenotypic plasticity is one way that genetic change in plumage patterns (and other traits) could be driven, there are others, including the appearance of major mutations and selection on standing variation whose distribution is not altered in the new environment. I consider some evidence for the different alternatives, and ask when they might lead to qualitatively different evolutionary outcomes.

Threat displays are not handicaps

Within a general framework of handicap signalling it was proposed that threat displays are handicaps, they can work only if they put the signaller at a disadvantage, which is only acceptable to honest signallers. The aim of the present article is to investigate this proposal with the help of a simple game-theoretical model. It was found: (1) that the use of cost-free signals is an ESS against the invasion of handicapped signals even if cheating is played as part of a mixed strategy in the population; (2) that the use of handicaps may be an ESS against cost-free signals but only if we assume that the invading cost-free signal is not accepted by weak individuals as a signal of strength; (3) that the establishment of a handicapped signal in the first place is an unresolved problem, because both cost free signals and negative-handicaps are evolutionarily stable against the invasion of handicaps; (4) that in contrast to handicaps the use of negative-handicaps can invade a population using cost-free signals (a negative-handicap is a signal which may serve other functions as well); (5) that negative-handicaps are ESS against cost-free signals as well as against handicaps; and (6) thus, the most likely evolutionary end point is that the biggest negative-handicap would be used as a threat display. This is a posture, which prepares the animal most efficiently to fight; hence, most probably it is the initial position of the fighting technique of the given species. (7) Finally, the investigation of the threat displays of well-studied taxa (great tit, cats, dogs, and hoofed mammals) confirms that threat displays are indeed negative-handicaps. They do not put the user into a disadvantaged position, instead the initial position of the species specific fighting technique is used as a threat display as predicted by the present model.