The continuous Sir Philip Sidney game: a simple model of biological signalling.

An analysis of Maynard Smith's two-player, ESS model of biological signalling, the "Sir Philip Sidney game", is presented. The stable strategies of the players in this game are shown to satisfy the conditions of Zahavi's handicap principle. At equilibrium, signals are honest, costly, and costly in a way that is related to the true quality revealed. Further analysis reveals that the level of cost required to maintain stability is inversely related to the degree of relatedness between the players. It therefore seems likely that stable biological signalling systems will feature lower signalling costs when communication occurs between relatives. A three-player, extended version of the model is investigated, in which signals are passed via an intermediate, or "messenger". It is shown that this destabilizes the signalling system, and leads to increased signalling costs. This result suggests that "kin conflict" theories of the evolution of the endosperm in flowering plants require further refinement. The introduction of a novel resource acquisition tissue, which mediates parent-offspring interaction during development, cannot be assumed to limit parent-offspring conflict simply because it carries an extra copy of the maternally inherited genes. The ability to add such complications to the Sir Philip Sidney game and still obtain solutions makes it a very useful modelling tool.     

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.     

Increased signalling effort when survival prospects decrease: male-male competition ensures honesty

For signalling to be honest the handicap principle claims that signals must impose fitness costs so that only the best individuals can afford the most exaggerated signals. The cost of signalling in terms of reduced survival decreases, however, towards the end of an individual's lifetime, which can induce an increase in signalling effort as a terminal effort. I show for the three-spined stickleback, Gasterosteus aculeatus, that a decrease in survival prospects through impaired condition leads to an increase in red nuptial coloration that makes the signal less reliable as an indicator of male parental ability. Males in poor condition with a large signal sometimes cannibalized all the eggs they received, probably to start a new breeding cycle with a higher energy reserve. However, the inclusion of socially imposed costs of signalling through male-male competition during courtship increased the honesty of the signal, as some males in poor condition and of poor parental ability decreased their signal expression. Some cheaters still occurred, but the signalling system was honest on average. This implies that socially imposed costs are important in the maintenance of honest sexual signalling. Dishonesty may occur under favourable conditions when the cost of signalling is reduced. This emphasizes the importance of considering the environmental conditions experienced by individuals when investigating the evolution and maintenance of honest sexual signals. Copyright 2000 The Association for the Study of Animal Behaviour.     

The cost of dishonesty

The handicap principle states that stable biological signals must be honest and costly to produce. The cost of the signal should reflect the true quality of the signaller. Here, it is argued that honest signalling may be maintained although the used signals are not handicaps. A game theoretic model in the form of a game of signalling is presented: all the existing evolutionarily stable strategies (ESSs) are found. Honest and cheap signalling of male quality is shown to be evolutionarily stable if females divorce the mate if it turns out that he has cheated about his quality. However, for this ESS to apply, the cost of lost time must not be too great. The stability of the honest signalling is based on deceivers being prevented from spreading in the population because they suffer from a cost of divorce. Under some fairly strict conditions, a mixed polymorphism of dishonesty and honesty represents another possible ESS.     

Sexual Signals as Advertisers of Resistance to Mistakes

To be evolutionarily stable, sexual signals need to convey information regarding the quality or motivation of individuals. This can be achieved through direct or indirect signal costs that guarantee honest communication or through signal designs that facilitate the assessment of quality. Here, I present the case for an alternative hypothesis: that signalling exposes informative mistakes. Signalling mistakes range from occasional to frequent and from slight distortions of typical signals to grossly atypical signals. Their occurrence may be enhanced by disease or stress, thus revealing individual quality or motivation, and receivers typically respond negatively to them. By this mechanism, honest communication is due to costs of developing resistance to mistakes. Therefore, the hypothesis can function independently of signal design costs, although it can also be enhanced by signal design costs when those increase the occurrence of mistakes. This hypothesis widens the scope of signals expected to be sexually selected and creates new approaches to research in sexual selection and animal communication.     

Signal modulation as a mechanism for handicap disposal

Signal honesty may be compromised when heightened competition provides incentive for signal exaggeration. Some degree of honesty might be maintained by intrinsic handicap costs on signalling or through imposition of extrinsic costs, such as social punishment of low quality cheaters. Thus, theory predicts a delicate balance between signal enhancement and signal reliability that varies with degree of social competition, handicap cost, and social cost. We investigated whether male sexual signals of the electric fish Brachyhypopomus gauderio would become less reliable predictors of body length when competition provides incentives for males to boost electric signal amplitude. As expected, social competition under natural field conditions and in controlled lab experiments drove males to enhance their signals. However, signal enhancement improved the reliability of the information conveyed by the signal, as revealed in the tightening of the relationship between signal amplitude and body length. Signal augmentation in male B. gauderio was independent of body length, and thus appeared not to be curtailed through punishment of low quality (small) individuals. Rather, all individuals boosted their signals under high competition, but those whose signals were farthest from the predicted value under low competition boosted signal amplitude the most. By elimination, intrinsic handicap cost of signal production, rather than extrinsic social cost, appears to be the basis for the unexpected reinforcement of electric signal honesty under social competition. Signal modulation may provide its greatest advantage to the signaller as a mechanism for handicap disposal under low competition rather than as a mechanism for exaggeration of quality under high competition.     

The Handicap Principle: how an erroneous hypothesis became a scientific principle

The most widely cited explanation for the evolution of reliable signals is Zahavi's so‐called Handicap Principle, which proposes that signals are honest because they are costly to produce. Here we provide a critical review of the Handicap Principle and its theoretical development. We explain why this idea is erroneous, and how it nevertheless became widely accepted as the leading explanation for honest signalling. In 1975, Zahavi proposed that elaborate secondary sexual characters impose ‘handicaps’ on male survival, not due to inadvertent signalling trade‐offs, but as a mechanism that functions to demonstrate males' genetic quality to potential mates. His handicap hypothesis received many criticisms, and in response, Zahavi clarified his hypothesis and explained that it assumes that signals are wasteful as well as costly, and that they evolve because wastefulness enforces honesty. He proposed that signals evolve under ‘signal selection’, a non‐Darwinian type of selection that favours waste rather than efficiency. He maintained that the handicap hypothesis provides a general principle to explain the evolution of all types of signalling systems, i.e. the Handicap Principle. In 1977, Zahavi proposed a second hypothesis for honest signalling, which received many different labels and interpretations, although it was assumed to be another example of handicap signalling. In 1990, Grafen published models that he claimed vindicated Zahavi's Handicap Principle. His conclusions were widely accepted and the Handicap Principle subsequently became the dominant paradigm for explaining the evolution of honest signalling in the biological and social sciences. Researchers have subsequently focused on testing predications of the Handicap Principle, such as measuring the absolute costs of honest signals (and using energetic and other proximate costs as proxies for fitness), but very few have attempted to test Grafen's models. We show that Grafen's models do not support the handicap hypothesis, although they do support Zahavi's second hypothesis, which proposes that males adjust their investment into the expression of their sexual signals according to their condition and ability to bear the costs (and risks to their survival). Rather than being wasteful over‐investments, honest signals evolve in this scenario because selection favours efficient and optimal investment into signal expression and minimizes signalling costs. This idea is very different from the handicap hypothesis, but it has been widely misinterpreted and equated to the Handicap Principle. Theoretical studies have since shown that signalling costs paid at the equilibrium are neither sufficient nor necessary to maintain signal honesty, and that honesty can evolve through differential benefits, as well as differential costs. There have been increasing criticisms of the Handicap Principle, but they have focused on the limitations of Grafen's model and overlooked the fact that it is not a handicap model. This model is better understood within a Darwinian framework of adaptive signalling trade‐offs, without the added burden and confusing logic of the Handicap Principle. There is no theoretical or empirical support for the Handicap Principle and the time is long overdue to usher this idea into an ‘honorable retirement’.     

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.     

Energy and predation costs of firefly courtship signals

Animal courtship signals include many highly conspicuous traits and behaviors, and it is generally assumed that such signals must balance the benefits of attracting mates against some fitness costs. However, few studies have assessed the multiple costs potentially incurred by any one courtship signal, so we have limited understanding of the relative importance of different costs. This study provides the first comprehensive assessment of signal costs for Photinus fireflies (Coleoptera: Lampyridae), using controlled experiments to measure both the energy and predation costs associated with their bioluminescent courtship signals. We measured energy required to generate bioluminescent flashes, using differential open-flow respirometry, and found that flash signaling results in only a nominal increase in energy expenditure above resting levels. These results suggest that the energy required to generate bioluminescent flashes represents a minor component of the total cost of firefly courtship. However, controlled field experiments revealed that visually oriented predators imposed major costs on firefly courtship signals, with higher signaling rates significantly increasing the likelihood of predation. Together with previous results demonstrating that female fireflies prefer more conspicuous courtship signals, these results support the importance of multiple-receiver communication networks in driving signal evolution.     

Costs and constraints conspire to produce honest signaling: insights from an ant queen pheromone

Signal costs and evolutionary constraints have both been proposed as ultimate explanations for the ubiquity of honest signaling, but the interface between these two factors is unclear. Here, I propose a pluralistic interpretation, and use game theory to demonstrate that evolutionary constraints determine whether signals evolve to be costly or cheap. Specifically, when the costs or benefits of signaling are strongly influenced by the sender's quality, low-cost signals evolve. The model reaffirms that cheap and costly signals can both be honest, and predicts that expensive signals should have more positive allometric slopes than cheap ones. The new framework is applied to an experimental study of an ant queen pheromone that honestly signals fecundity. Juvenile hormone was found to have opposing, dose-dependent effects on pheromone production and fecundity and was fatal at high doses, indicating that endocrine-mediated trade-offs preclude dishonesty. Several lines of evidence suggest that the realized cost of pheromone production may be nontrivial, and the antagonistic effects of juvenile hormone indicate the presence of significant evolutionary constraints. I conclude that the honesty of queen pheromones and other signals is likely enforced by both the cost of dishonesty and a suite of evolutionary constraints.     

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.     

Signalling of information that is neither cryptic nor private

It is commonly assumed that in order for animal signals to be advantageous, the information being signalled could not have been obtained otherwise, and is therefore ‘cryptic’ or ‘private’. Here, we suggest a scenario in which individuals can gain an advantage by signalling ‘public’ information that is neither cryptic nor private. In that scenario, signalling increases the efficiency with which that ‘public’ information is transmitted. We formalize our idea with a game in which offspring can signal their condition to their parents. Specifically, we consider a resource‐strapped parent who can only invest in one of its two offspring, and we allow offspring the chance to influence parental investment through a signal. A parent in the game seeks to invest in the higher‐quality offspring, which it could identify either through a publicly available cue, such as body size, or by relying on a signal provided by the offspring. We find that if the signal can convey information about offspring quality more efficiently than cues, then signalling of condition between offspring and parents can be favoured by selection, even though parents could potentially have acquired the same information from the cue. Our results suggest that the biological function of signals may be broader than currently considered, and provide a scenario where low cost signalling can be favoured. More generally, efficiency benefits could explain signalling across a range of biological and economic scenarios.     

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.     

Reduction of Total Sample Size and Cost of Sampling in Tests of Hypothesis by Using Unequal Group Sizes

The standard approach in calculating the appropriate sample size required to detect a specified difference in the means of two populations for given type I and II errors assumes equal sample sizes in each group. It is shown here that equal sample sizes are usually sub-optimal with respect to total sample size and with respect to total cost of the experiment. This is may be important in experiments involving animals when costs are measured not only in monetary terms but also in terms of animal suffering or inconvenience.     

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.     

Resource value and the context dependence of receiver behaviour

Many animals use signals of fighting ability to minimize the costs of competition. Theory predicts that signals must be costly to remain reliable indicators of their bearer's abilities, but many signals of fighting ability lack obvious developmental costs. Instead, receivers are thought to maintain signal accuracy by behaving aggressively towards individuals with inaccurate signals (i.e. social costs). Models predict that the evolutionary stability of social cost signals depends on receivers trusting signals in certain contexts and testing signal accuracy in other contexts. Here, I use the signals of agonistic ability in Polistes dominulus wasps to provide the first experimental evidence that receiver responses to social cost signals are context dependent. During contests over low-value resources, wasps trust signals; they avoid patches of food guarded by rivals with elaborate signals. As the value of the resource increases, wasps become more likely to test signal accuracy. In fact, receivers challenge guards regardless of their signal phenotype when the resource is sufficiently valuable. Context-dependent receiver responses are likely to be an important behavioural mechanism underlying the evolution of social costs, as context-dependent responses allow receivers to minimize the costs of conflict while also ensuring signal accuracy.     

Costly signalling theories: beyond the handicap principle

Two recent overviews of costly signalling theory—Maynard-Smith and Harper (2003) and Searcy and Nowicki (2005)—both refuse to count signals kept honest by punishment of dishonesty, as costly signals, because (1) honest signals must be costly in cases of costly signalling, and (2) punishment of dishonesty itself requires explanation. I argue that both pairs of researchers are mistaken: (2) is not a reason to discount signals kept honest by punishment of dishonesty as cases of costly signalling, and (1) betrays too narrow a focus on certain versions of costly signalling theory. In the course of so arguing, I propose a new schema for classifying signal costs, which suggests productive research questions for future conceptual and empirical work on costly signalling.     

Costly signalling: a work in progress

The Evolution of Animal Communication is a detailed examination of a wide variety of animal signalling systems. The main focus of the book is explaining how such signalling systems remain reliable when there is apparent evolutionary pressure to deceive. The principle strategy is to appeal to signal costs: signals remain reliable because the potential benefits of deceit are outweighed by the costs of producing the deceptive signal. In this review I show just how difficult this idea is to test, even in the simplest cases.     

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.     

Breeding density affects the honesty of bird vocal displays as possible indicators of male/territory quality

Vocal displays are supposed to be an honest signal of the phenotypic and genetic quality of individuals and their territory. Moreover, signal interactions are nearly always associated with individuals in aggregations, and their function could in part be explained as social behaviour. Conspecific density has been shown to be a particularly strong proximate and ultimate factor acting on several individual/population features; thus, it may be expected to affect vocal behaviour too. Here, I investigate the hypothesis that, in long‐lived, territorial species, density affects the vocal displays of mated males, masking their honesty as a possible signal of male/territory quality. Each month I listened to the dusk calls of 17 breeding male Eurasian Eagle Owls Bubo bubo during their prelaying period. Nine males bred in a low‐density situation, the other eight in a high‐density one. Conspecific density was found to affect the honesty of call features as signals of male and/or territory quality. The call display as a reliable predictor of male fitness measured as productivity persisted only in situations of high breeding owl density, where male–male competition was stronger. Accommodation of call activity allows individuals to minimize the costs of aggressive calling by adjusting the territoriality threshold to local conditions. The results of this study emphasize the importance, when investigating the evolution and maintenance of honest territorial or sexual signals, of considering the environmental and social context experienced by the individual, thereby corroborating the idea that male–male competition contributes to the maintenance of honest signalling.