Biological signals as handicaps

An ESS model of Zahavi's handicap principle is constructed. This allows a formal exposition of how the handicap principle works, and shows that its essential elements are strategic. The handicap model is about signalling, and it is proved under fairly general conditions that if the handicap principle's conditions are met, then an evolutionarily stable signalling equilibrium exists in a biological signalling system, and that any signalling equilibrium satisfies the conditions of the handicap principle. Zahavi's major claims for the handicap principle are thus vindicated. The place of cheating is discussed in view of the honesty that follows from the handicap principle. Parallel signalling models in economics are discussed. Interpretations of the handicap principle are compared. The models are not fully explicit about how females use information about male quality, and, less seriously, have no genetics. A companion paper remedies both defects in a model of the handicap principle at work in sexual selection.     

Modelling and the fall and rise of the handicap principle

The story of the fall and rise of Zahavi??s handicap principle is one of a battle between models. Early attempts at formal modeling produced negative results and, unsurprisingly, scepticism about the principle. A major change came in 1990 with Grafen??s production of coherent models of a handicap mechanism of honest signalling. This paper??s first claim is that acceptance of the principle, and its dissemination into other disciplines, has been driven principally by that, and subsequent modeling, rather than by empirical results. Secondly, there is a vast literature on biological signalling but few studies that make all of the observations necessary to diagnose the handicap mechanism. My final claim is that many of the applications of ??costly signalling theory?? in other disciplines are conceptually confused. Misinterpretations of what is meant by ??costly signalling?? are common. Demonstrating that a signal is costly is insufficient and is not always necessary in order to prove that, and explain why, a signal is honest. In addition to the biological modelling of signals, there is an economic literature on the same subject. The two run in parallel in the sense that they have had little mutual interaction. Additionally, it is the biological modelling that has been picked up, and often misapplied, by other disciplines.     

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.     

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’.     

ARE WARNING COLORS HANDICAPS?

The handicap theory, in which the cost of waste guarantees honest advertising, is being used increasingly in solutions to the problems of biological signal evolution. However, it is usually applied to systems which are insufficiently understood to allow testing against alternative theories. In particular, the ability of the handicap theory to explain the design of signals has never been properly tested. We test its ability to explain signal design features in an unusually well studied area of biological signalling: warning coloration and mimicry. Since a full handicap model proves immediately unrealistic, we modify the model to incorporate realistic assumptions about predator learning. Using this model we explicitly compare the handicap theory with a purely “conventional” signalling model and with a null model. Predictions relating to three key design features (conspicuousness, pattern similarity, and Batesian mimicry) are compared, and tested against available data. Although many predictions remain to be tested adequately, we conclude that: (i) conspicuousness is most plausibly explained by the conventional signalling theory that ascribes the function of conspicuous coloration to signal efficacy rather than waste; (ii) pattern similarity, within and between species, is unlikely to be the result of the need to produce similar degrees of conspicuousness, as predicted by the handicap theory, but is plausibly explained as the result of pattern generalization amongst discriminating predators, as predicted by the conventional signalling theory; and (iii) Batesian mimicry is predicted by the conventional signalling theory, but not the handicap theory. Therefore the handicap theory fails to provide an adequate explanation of the main design features of at least one major signalling system.     

The rise and fall of handicap principle: a commentary on the “Modelling and the fall and rise of the handicap principle”

The honesty of animal communication is in the spot lights in the last 30 years. During most of this time the field was dominated by one explanation: Zahavi’s handicap principle (Zahavi, J Theor Biol 67:603–605, 1975; Grafen, J Theor Biol 144:517–546, 1990). Grose (Biol Philos 2011) embarks to explain both the success of the theory and the empirical difficulties that exist despite this success. While I wholeheartedly agree with the criticism offered by Grose and with almost all the claims he makes, the treatment of the issue is far from complete and it still leaves much to be explained. Accordingly, my commentary consist of six sections: in the first section I clear up some technical issues left unexposed, most importantly the role of strategic cost in handicap signalling; in the second section I relate this to empirical testing; in the next section I comment on the historical development of the handicap principle; in the fourth section I review the biological models that came up with conclusions that contradict the handicap principle; in the fifth section I discuss the reasons behind the success of the handicap theory; finally, in the last section I discuss the application of the handicap theory to anthropology and human sciences.     

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.     

Indirect selection and individual selection in sociobiology: my personal views on theories of social behaviour

This is the story of my involvement in sociobiological studies. I first discuss group selection models, which were common in the 1950s. I then move on to kin selection and reciprocity models, which were developed to replace group selection models and are still being used by many sociobiologists, even though I argue that they contain the same weaknesses that led group selection to be rejected. As an alternative, I present the handicap principle, an essential component in all signalling. The handicap principle is useful in understanding many components of social systems, not the least of which is why individuals invest in the benefit of other members of a social system (altruism). Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.     

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.     

Signal verification can promote reliable signalling

The central question in communication theory is whether communication is reliable, and if so, which mechanisms select for reliability. The primary approach in the past has been to attribute reliability to strategic costs associated with signalling as predicted by the handicap principle. Yet, reliability can arise through other mechanisms, such as signal verification; but the theoretical understanding of such mechanisms has received relatively little attention. Here, we model whether verification can lead to reliability in repeated interactions that typically characterize mutualisms. Specifically, we model whether fruit consumers that discriminate among poor- and good-quality fruits within a population can select for reliable fruit signals. In our model, plants either signal or they do not; costs associated with signalling are fixed and independent of plant quality. We find parameter combinations where discriminating fruit consumers can select for signal reliability by abandoning unprofitable plants more quickly. This self-serving behaviour imposes costs upon plants as a by-product, rendering it unprofitable for unrewarding plants to signal. Thus, strategic costs to signalling are not a prerequisite for reliable communication. We expect verification to more generally explain signal reliability in repeated consumer–resource interactions that typify mutualisms but also in antagonistic interactions such as mimicry and aposematism.     

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.     

Shade avoidance and Zahavi's handicap principle in dense plant populations

I propose that tall plants 'show off' and that the shade avoidance syndrome is a case of spectral communication among plants in dense populations, enabling the operation of Zahavi's handicap principle in plants. The costly signal triggering shade avoidance is composed of: (1) the far-red (FR) irradiation that plants emit as a by-product of photosynthesis, and (2) the phytochromes and the down-stream factors that respond to phytochrome signalling that evolved to analyse the FR emission and respond. This is a special case of a complex system serving as a signal. Because various types and levels of shade avoidance are common in most, if not all, dense plant populations, it seems that the operation of Zahavi's handicap principle in plants is a common phenomenon. Although plants do not see, they can use light for interplant communication about their relative strength. Unlike the many types of species-specific operations of Zahavi's handicap principle in animals, the handicap signal in plants is not species-specific, like prey–predator interactions. This difference probably stems from the fact that plants are sessile, have no animal-like vision, and compete with individuals of many other species.   © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 84 , 313–319.     

Begging and bleating: the evolution of parent-offspring signalling

The evolution of biological signalling in the face of evolutionary conflicts of interest is an active area of evolutionary ecology, and one to which Maynard Smith has made important contributions. We explore the major theoretical challenges in the field, concentrating largely on how offspring signal to their parents when there is the potential for parent-offspring conflict. Costly offspring solicitation (begging etc.) has been interpreted in terms of a Zahavi Grafen honest handicap signal, but this has been challenged on the grounds of' the costs of signalling. We review this controversy and also explore the issue of pooling versus separating signalling equilibrium. An alternative explanation for costly begging is that it is due to sibling competition, and we discuss the relationship between these ideas and signalling models in families with more than one offspring. Finally we consider signal uncertainty, how signalling models can be made dynamic, and briefly how they may be tested experimentally.     

By‐product information can stabilize the reliability of communication

Although communication underpins many biological processes, its function and basic definition remain contentious. In particular, researchers have debated whether information should be an integral part of a definition of communication and how it remains reliable. So far the handicap principle, assuming signal costs to stabilize reliable communication, has been the predominant paradigm in the study of animal communication. The role of by‐product information produced by mechanisms other than the communicative interaction has been neglected in the debate on signal reliability. We argue that by‐product information is common and that it provides the starting point for ritualization as the process of the evolution of communication. Second, by‐product information remains unchanged during ritualization and enforces reliable communication by restricting the options for manipulation and cheating. Third, this perspective changes the focus of research on communication from studying signal costs to studying the costs of cheating. It can thus explain the reliability of signalling in many communication systems that do not rely on handicaps. We emphasize that communication can often be informative but that the evolution of communication does not cause the evolution of information because by‐product information often predates and stimulates the evolution of communication. Communication is thus a consequence but not a cause of reliability. Communication is the interplay of inadvertent, informative traits and evolved traits that increase the stimulation and perception of perceivers. Viewing communication as a complex of inadvertent and derived traits facilitates understanding of the selective pressures shaping communication and those shaping information and its reliability. This viewpoint further contributes to resolving the current controversy on the role of information in communication.     

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.     

Accounting for robustness in modeling signal transduction responses

Abstract

A classical question in systems biology is to find a Boolean model which is able to predict the observed responses of a signaling network. It has been previously shown that such models can be tailored based on experimental data. While fitting a minimum-size network to the experimentally observed data is a natural assumption, it can potentially result in a network which is not so robust against the noises in the training dataset. Indeed, it is widely accepted now that biological systems are generally evolved to be very robust. Therefore, in the present work, we extended the classical formulation of Boolean network construction in order to put weight on the robustness of the created network. We show that our method results generally in more relevant networks. Consequently, considering robustness as a design principle of biological networks can result in more realistic models.     

Sibling competition stabilizes signalling resolution models of parent-offspring conflict

Young of altricial birds use conspicuous displays to solicit food from their parents. There is experimental evidence that the intensity of these displays is correlated with the level of food deprivation of young, and that parents respond to increased levels of solicitation by increasing the rate of food delivery to the nest. Game-theoretical models based on the handicap principle show that, when solicitation is costly, there is a signalling equilibrium at which there is a one-to-one correspondence between the condition of the young and the intensity of their display. Parents use this information to adjust their levels of investment on the current offspring. However, the models also have a non-signalling equilibrium, and computer simulations show that only the non-signalling equilibrium is stable. Here I show that when direct sibling competition is introduced into the model, in such a way that parents have control on the amount of food provided to the nest, but not on the way the food is allocated among siblings, the non-signalling equilibrium disappears and the signalling equilibrium becomes stable.     

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.     

The origin of autumn colours by coevolution

We lack an adaptive explanation for a striking phenomenon, that of bright colours displayed in autumn by the leaves of many deciduous trees. The usual explanation is that it is simply a non-adaptive secondary effect of leaf senescence. A game-theoretic model of biological signalling provides an adaptive hypothesis for autumn colours showing that they can be the result of a process of coevolution between insects and trees: if leaf colour acts as a warning indicator of the tree's vigour to autumn parasite insects, trees can gain advantage from the reduction of parasite load and insects can gain advantage from location of the most profitable hosts to lay their eggs. The results of the model are consistent with Zahavi's handicap principle. Possible explanations for the origin of the system and evidence from natural history are discussed.     

Sexually selected signals are not similar to sports handicaps

The handicap principle is a simple but powerful metaphor that has had a major impact on how biologists study and understand sexual selection. Here, I show that its application to signalling in sexual selection is not a valid generalization from its roots in economics. Although some signalling systems, with additive costs and benefits, have solutions that resemble sports handicaps, the signalling in sexual selection has multiplicative costs and benefits, and solutions that do not resemble sports handicaps. The sports analogy is technically incorrect, metaphorically misleading and a poor guide for empirical research on the signalling in sexual selection. The evolution of sexually selected signals is not a missing piece of Darwin's puzzle; it is an integral piece of the process of evolution by natural selection, and it should be approached with the same tools that we bring to bear on the evolution of other correlated traits involved in social interactions.