Separating equilibria in continuous signalling games

Much of the literature on costly signalling theory concentrates on separating equilibria of continuous signalling games. At such equilibria, every signaller sends a distinct signal, and signal receivers are able to exactly infer the signaller's condition from the signal sent. In this paper, we introduce a vector-field solution method that simplifies the process of solving for separating equilibria. Using this approach, we show that continuous signalling games can have low-cost separating equilibria despite conflicting interests between signaller and receiver. We find that contrary to prior arguments, honesty does not require wasteful signals. Finally, we examine signalling games in which different signallers have different minimal-cost signals, and provide a mathematical justification for the argument that even non-signalling traits will be exaggerated beyond their phenotypic optimum when they are used by other individuals to judge condition or quality.     

The limits to cost-free signalling of need between relatives

Theoretical models have demonstrated the possibility of stable cost-free signalling of need between relatives. The stability of these cost-free equilibria depends on the indirect fitness cost of cheating and deceiving a donor into giving away resources. We show that this stability is highly sensitive to the distribution of need among signallers and receivers. In particular, cost-free signalling is likely to prove stable only if there is very large variation in need (such that the least-needy individuals stand to gain much less than the most-needy individuals from additional resources). We discuss whether these conditions are likely to be found in altricial avian breeding systems--the most intensively studied instance of signalling of need between relatives. We suggest that cost-free signalling is more likely to prove stable and will provide parents with more information during the earlier phases of chick growth, when parents can more easily meet the demands of a brood (and chicks are more likely to reach satiation). Later, informative yet cost-free signalling is unlikely to persist.     

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.     

Error-proneness as a handicap signal

This paper describes two discrete signalling models in which the error-proneness of signals can serve as a handicap signal. In the first model, the direct handicap of sending a high-quality signal is not large enough to assure that a low-quality signaller will not send it. However, if the receiver sometimes mistakes a high-quality signal for a low-quality one, then there is an indirect handicap to sending a high-quality signal. The total handicap of sending such a signal may then still be such that a low-quality signaller would not want to send it. In the second model, there is no direct handicap of sending signals, so that nothing would seem to stop a signaller from always sending a high-quality signal. However, the receiver sometimes fails to detect signals, and this causes an indirect handicap of sending a high-quality signal that still stops the low-quality signaller of sending such a signal. The conditions for honesty are that the probability of an error of detection is higher for a high-quality than for a low-quality signal, and that the signaller who does not detect a signal adopts a response that is bad to the signaller. In both our models, we thus obtain the result that signal accuracy should not lie above a certain level in order for honest signalling to be possible. Moreover, we show that the maximal accuracy that can be achieved is higher the lower the degree of conflict between signaller and receiver. As well, we show that it is the conditions for honest signalling that may be constraining signal accuracy, rather than the signaller trying to make honest signals as effective as possible given receiver psychology, or the signaller adapting the accuracy of honest signals depending on his interests.     

The evolution of index signals to avoid the cost of dishonesty

Animals often convey useful information, despite a conflict of interest between the signaller and receiver. There are two major explanations for such ‘honest’ signalling, particularly when the size or intensity of signals reliably indicates the underlying quality of the signaller. Costly signalling theory (including the handicap principle) predicts that dishonest signals are too costly to fake, whereas the index hypothesis predicts that dishonest signals cannot be faked. Recent evidence of a highly conserved causal link between individual quality and signal growth appears to bolster the index hypothesis. However, it is not clear that this also diminishes costly signalling theory, as is often suggested. Here, by incorporating a mechanism of signal growth into costly signalling theory, we show that index signals can actually be favoured owing to the cost of dishonesty. We conclude that costly signalling theory provides the ultimate, adaptive rationale for honest signalling, whereas the index hypothesis describes one proximate (and potentially very general) mechanism for achieving honesty.     

Can behavioural constraints alter the stability of signalling equilibria?

In traditional models of signalling one class of individual, the signaller, presents a signal which another class of individual, the receiver, examines. Receivers are typically assumed to have fitness returns that depend on their ability to determine the utility of the signaller to them. Each signaller must decide what level to signal at, which is a function of the quality of the signaller. In addition, a signaller's quality is assumed to be synonymous with the signaller's utility to a receiver. However, there is no reason to believe that signalling costs are incurred in the same currency as the receivers are paid and, thus, no reason to believe that the relationship between signaller quality and utility is linear or even increasing. For instance, in signalling between prey and predators, the utility of a prey item may be its fat reserves, whereas an individual prey pays for signalling (and thus measures quality) in terms of increased risk of capture; quality and utility are synonymous only if a high risk of capture is associated with high fat reserves. In addition, several recent studies have documented increased signalling as utility decreases. If utility and quality are decoupled, so that increasing quality does not always mean increasing utility, then traditional signalling models predict that no signalling equilibrium will exist. I show that if receiver fitness is modelled by a set of behavioural responses, which have both costs and benefits, then a signalling equilibrium can sometimes be recovered. An example of signalling between mates is presented in order to demonstrate this equilibrium.     

Linking signal fidelity and the efficiency costs of communication

The handicap principle has been the overarching framework to explain the evolution and maintenance of communication. Yet, it is becoming apparent that strategic costs of signalling are not the only mechanism maintaining signal honesty. Rather, the fidelity of detecting signals can itself be strongly selected. Specifically, we argue that the fidelity of many signals will be constrained by the investment in signal generation and reception by the signaller and perceiver, respectively. Here, we model how investments in signal fidelity influence the emergence and stability of communication using a simple theoretical framework. The predictions of the model indicate that high‐cost communication can be stable whereas low‐cost intermediates are generally selected against. This dichotomy suggests that the most parsimonious route to the evolution of communication is for initial investment in communicative traits to be driven by noncommunicative functions. Such cues can appeal to pre‐existing perceptual biases and thereby stimulate signal evolution. We predict that signal evolution will vary between systems in ways that can be linked to the economics of communication to the two parties involved.     

The evolution of strategic male mating effort in an information transfer framework

Sperm competition theory predicts that males should use cues indicating the risk and intensity of sperm competition to tailor their sperm investment accordingly. Rival males are an important source of social information regarding sperm competition risk. However, revealing such information may not be in the rival males' interest. Here, we use a theoretical approach based on informed and uninformed games to investigate when information transfer about sperm competition risk to competitors is beneficial for a male, and when it is not. The results show that signalling to potential future mates that a female has already mated is beneficial when the signalling male has a sperm competition disadvantage, whereas it is unfavourable when the signaller has an advantage. The reason for this counterintuitive result is that the rival males' optimal response is to reduce sperm investment when the signaller has a disadvantage and, conversely, to increase investment when the signaller has an advantage. Furthermore, we analysed scenarios where males use alternative reproductive tactics. In this situation, signalling the awareness of sperm competition risk rarely pays; instead, it is beneficial to maintain an information advantage. Thus, it may be beneficial for bourgeois males to accept cuckoldry instead of revealing their sperm competition awareness to reproductive parasites. These results provide new insight into the evolution of communication between rivals in the context of sperm competition.     

Do aggressive signals evolve towards higher reliability or lower costs of assessment?

It has been suggested that the evolution of signals must be a wasteful process for the signaller, aimed at the maximization of signal honesty. However, the reliability of communication depends not only on the costs paid by signallers but also on the costs paid by receivers during assessment, and less attention has been given to the interaction between these two types of costs during the evolution of signalling systems. A signaller and receiver may accept some level of signal dishonesty by choosing signals that are cheaper in terms of assessment but that are stabilized with less reliable mechanisms. I studied the potential trade‐off between signal reliability and the costs of signal assessment in the corncrake (Crex crex). I found that the birds prefer signals that are less costly regarding assessment rather than more reliable. Despite the fact that the fundamental frequency of calls was a strong predictor of male size, it was ignored by receivers unless they could directly compare signal variants. My data revealed a response advantage of costly signals when comparison between calls differing with fundamental frequencies is fast and straightforward, whereas cheap signalling is preferred in natural conditions. These data might improve our understanding of the influence of receivers on signal design because they support the hypothesis that fully honest signalling systems may be prone to dishonesty based on the effects of receiver costs and be replaced by signals that are cheaper in production and reception but more susceptible to cheating.     

Tactics of evasion: strategies used by signallers to deter eavesdropping enemies from exploiting communication systems

Eavesdropping predators, parasites and parasitoids exploit signals emitted by their prey and hosts for detection, assessment, localization and attack, and in the process impose strong selective pressures on the communication systems of the organisms they exploit. Signallers have evolved numerous anti-eavesdropper strategies to mitigate the trade-off between the costs imposed from signal exploitation and the need for conspecific communication. Eavesdropper strategies fall along a continuum from opportunistic to highly specialized, and the tightness of the eavesdropper–signaller relationship results in differential pressures on communication systems. A wide variety of anti-eavesdropper strategies mitigate the trade-off between eavesdropper exploitation and conspecific communication. Antagonistic selection from eavesdroppers can result in diverse outcomes including modulation of signalling displays, signal structure, and evolutionary loss or gain of a signal from a population. These strategies often result in reduced signal conspicuousness and in decreased signal ornamentation. Eavesdropping enemies, however, can also promote signal ornamentation. While less common, this alternative outcome offers a unique opportunity to dissect the factors that may lead to different evolutionary pathways. In addition, contrary to traditional assumptions, no sensory modality is completely ‘safe’ as eavesdroppers are ubiquitous and have a broad array of sensory filters that allow opportunity for signal exploitation. We discuss how anthropogenic change affects interactions between eavesdropping enemies and their victims as it rapidly modifies signalling environments and community composition. Drawing on diverse research from a range of taxa and sensory modalities, we synthesize current knowledge on anti-eavesdropper strategies, discuss challenges in this field and highlight fruitful new directions for future research. Ultimately, this review offers a conceptual framework to understand the diverse strategies used by signallers to communicate under the pressure imposed by their eavesdropping enemies.     

Receivers limit the prevalence of deception in humans: evidence from diving behaviour in soccer players

Deception remains a hotly debated topic in evolutionary and behavioural research. Our understanding of what impedes or facilitates the use and detection of deceptive signals in humans is still largely limited to studies of verbal deception under laboratory conditions. Recent theoretical models of non-human behaviour have suggested that the potential outcome for deceivers and the ability of receivers to discriminate signals can effectively maintain their honesty. In this paper, we empirically test these predictions in a real-world case of human deception, simulation in soccer. In support of theoretical predictions in signalling theory, we show that cost-free deceit by soccer players decreases as the potential outcome for the signaller becomes more costly. We further show that the ability of receivers (referees) to detect deceptive signals may limit the prevalence of deception by soccer players. Our study provides empirical support to recent theoretical models in signalling theory, and identifies conditions that may facilitate human deception and hinder its detection.     

Body postures and patterns as amplifiers of physical condition

The question of why receivers accept a selfish signaller's message as reliable or 'honest' has fuelled ample controversy in discussions of communication. The handicap mechanism is now widely accepted as a potent constraint on cheating. Handicap signals are deemed reliable by their costs: signallers must choose between investing in the signal or in other aspects of fitness. Accordingly, resources allocated to the signal come to reflect the signaller's fitness budget and, on average, cheating is uneconomic. However, that signals may also be deemed reliable by their design, regardless of costs, is not widely appreciated. Here we briefly describe indices and amplifiers, reliable signals that may be essentially cost free. Indices are reliable because they bear a direct association with the signalled quality rather than costs. Amplifiers do not directly provide information about signaller quality, but they facilitate assessment by increasing the apparency of pre-existing cues and signals that are associated with quality. We present results of experiments involving a jumping spider (Plexippus paykulli) to illustrate how amplifiers can facilitate assessment of cues associated with physical condition without invoking the costs required for handicap signalling.     

Evolutionarily stable communication between kin: a general model

At present, the most general evolutionary theory of honest communication is Grafen''s model of Zahavi''s ''handicap'' signalling system, in which honesty of signals about the signaller''s quality (e.g. mate suitability or fighting ability) is maintained by the differentially high cost of signals to signallers having lower quality. The latter model is here further generalized to include any communication between signallers and receivers that are genetically related (e.g. parents and begging offspring, cooperative or competing siblings). Signalling systems involving relatives are shown to be evolutionarily stable, despite a potential pay-off for false signalling, if the Zahavian assumption of differential signal costs holds and there are diminishing reproductive returns to the signaller as the receiver''s assessed value of its attribute increases, or if, regardless of whether the Zahavian assumption holds, signallers with high values of the attribute benefit more from a given receiver assessment than signallers with low values (e.g. begging chicks that are hungrier benefit more from being fed). In stable systems of signalling among kin, it is also shown to be generally true that (i) levels of signalling and thus observed signal costs will decline as relatedness increases or as the receiver''s reproductive penalty for erroneous assessment increases, and (ii) receivers will consistently, altruistically overestimate the true value of the signalled attribute.     

Are aposematic signals honest? A review

We explore the relevance of honest signalling theory to the evolution of aposematism. We begin with a general consideration of models of signal stability, with a focus on the Zahavian costly signalling framework. Next, we review early models of signalling in the context of aposematism (some that are consistent and some inconsistent with costly honest signalling). We focus on controversies surrounding the idea that aposematic signals are handicaps in a Zahavian framework. Then, we discuss how the alignment of interests between signaller and predator influences the evolution of aposematism, highlight the distinction between qualitative and quantitative honesty and review theory and research relevant to these categories. We also review recent theoretical treatments of the evolution of aposematism that have focused on honest signalling as well as empirical research on a variety of organisms, including invertebrates and frogs. Finally, we discuss future directions for empirical and theoretical research in this area.     

Do great tits assess rivals by combining direct experience with information gathered by eavesdropping?

Animals frequently use signals that travel further than the spacing between individuals. For every intended recipient of a given signal there are likely to be many other individuals that receive information. Eavesdropping on signalling interactions between other individuals provides a relatively cost-free method of assessing future opponents or mates. Male great tits (Parus major) extract relative information from such interactions between individuals unknown to them. Here, we show that male great tits can take information gathering a stage further and obtain more information about a previously unencountered intruder, by the hitherto unknown capability of combining information gathered by eavesdropping with that derived from their own direct interaction with an individual. Prior experience with an intruder (A) was achieved by subjecting a focal male to different levels of intrusion simulated using interactive playback. This intruder (A) then took part in a simulated interaction with an unknown male (B) outside the territorial boundary of the focal males. In response to subsequent intrusion by the second male (B), focal males showed low song output in response to males that had lost to a male that the subject was able to beat. Males of known high quality, or those about which information was ambiguous, elicited a high level of song output by focal males. We discuss the implications of this finding for the evolution of communication and social behaviour.     

Signalling among relatives. I. Is costly signalling too costly?

Zahavi''s handicap principle,originally proposed as an explanation for sexual selection ofelaborate male traits, suggests that a sufficient cost to dishonest signals can outweigh the rewards of deception and allow individuals to communicate honestly. Maynard Smith (1991) and Johnstone and Grafen (1992) introduce the Sir Philip Sidney game in order to extend the handicap principle to interactions among related individuals, and to demonstrate that stable costly signalling systems can exist among relatives.In this paper we demonstrate that despite the benefits associated with honest information transfer, the costs incurred in a stable costly signalling system may leave all participants worse off than they would be in a system with no signalling at all. In both the discrete and continuous forms of the Sir Philip Sidney game, there exist conditions under which costly signalling among relatives, while stable, is so costly that it is disadvantageous compared with no signalling at all. We determine the factors which dictate signal cost and signal benefit in a generalized version of this game, and explain how signal cost can exceed signal value. Such results raise concerns about theevolutionary pathways which could have led to the existence of signalling equilibria in nature. The paper stresses the importance of comparing signalling equilibria with other possible strategies, beforedrawing conclusions regarding the optimality of signalling.     

Attention-Seeking Displays

Animal communication abounds with extravagant displays. These signals are usually interpreted as costly signals of quality. However, there is another important function for these signals: to call the attention of the receiver to the signaller. While there is abundant empirical evidence to show the importance of this stage, it is not yet incorporated into standard signalling theory. Here I investigate a general model of signalling - based on a basic action-response game - that incorporates this searching stage. I show that giving attention-seeking displays and searching for them can be an ESS. This is a very general result and holds regardless whether only the high quality signallers or both high and low types give them. These signals need not be costly at the equilibrium and they need not be honest signals of any quality, as their function is not to signal quality but simply to call the attention of the potential receivers. These kind of displays are probably more common than their current weight in the literature would suggest.     

Proportional processing of a visual mate choice signal in the green swordtail,Xiphophorus hellerii

During mate choice, receivers often assess the magnitude (duration, size, etc.) of signals that vary along a continuum and reflect variation in signaller quality. It is generally assumed that receivers assess this variation linearly, meaning each difference in signalling trait between signallers results in a commensurate change in receiver response. However, increasing evidence shows receivers can respond to signals non-linearly, for example through Weber's Law of proportional processing, where discrimination between stimuli is based on proportional, rather than absolute, differences in magnitude. We quantified mate preferences of female green swordtail fish, Xiphophorus hellerii, for pairs of males differing in body size. Preferences for larger males were better predicted by the proportional difference between males (proportional processing) than the absolute difference (linear processing). This demonstration of proportional processing of a visual signal implies that receiver perception may be an important mechanism selecting against the evolution of ever-larger signalling traits.     

Do Mechanical Effectiveness and Recipient Species Influence Intentional Signal Laterality in Captive Chimpanzees (<Emphasis Type="Italic">Pan troglodytes</Emphasis>)?

Studying the relationships between the directions of brain lateralization for handedness and language can shed light on mechanisms underlying hemispheric specialization for manipulation and signalling functions. We investigated the influence of manipulation and communication functions and of recipient species (conspecific- versus human-directed communication) on manual laterality in signalling context, taking several factors into account simultaneously. We assessed laterality in 39 chimpanzees (Pan troglodytes), including 4 manipulators (mechanically effective social actions used to get things done) and 18 gestures (mechanically ineffective social actions implying that the signaller takes the recipient’s response into account). We focused on the following factors: interactional context components (e.g., visual fields of both interactants), degree of use of signals (“rare” for signals performed by only a few subjects in the population or “common” for signals performed by many subjects), mechanical effectiveness, subjects’ sociodemographic characteristics (e.g., age and hierarchy), and recipient species. We found a significant population-level right-hand bias for one type of human-directed gesture (slap hand). Mechanical effectiveness influenced laterality: right-hand use was more pronounced for conspecific-directed gestures than for conspecific-directed manipulators. The laterality of conspecific-directed gestures overall did not differ from that of human-directed gestures. However, we found an indirect influence of recipient species on laterality as conspecific- and human-directed gestural lateralities were modulated differently by the position of the recipient in the signaller’s visual field and by signaller’s age. We hypothesize that the communication nature of gestures might have developed from manipulators. Manipulators may have contributed to the emergence and the evolution of the left-lateralized communication system in primates.     

Decoupling vigour and quality in the autumn colours game: Weak individuals can signal, cheating can pay

According to the coevolution theory, autumn colours are a warning signal to insects, signalling the level of chemical defences or availability of nutrients. Because in the original model tree vigour and defences were positively correlated, it is not clear whether signalling would still be stable when they are decoupled, and the fact that weak trees often display bright autumn colours is usually presented as evidence against the coevolution theory. I show that in a theoretical model of insect-tree coevolution, signalling is still stable when vigour and defences are decoupled. Weak trees can signal. Moreover, partial cheating is possible. The different equilibria depend on the importance of vigour and defences against insect attack, of vigour in the production of the signal, and of pleiotropic effects between colour and defences. These results provide precise predictions that can be used for planning future empirical test.