Is There Only One Type of Male Handicap?Author(s): Sarah CollinsSource: Proceedings: Biological Sciences, Vol. 252, No. 1335 (Jun. 22, 1993), pp. 193-197Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/49880 .

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Is there only one type of male handicap?

SARAH COLLINSt

Edward Grey Institute, Zoology Department, Oxford University, South Parks Road, Oxford OX] 3PS, U.K.

SUMMARY

The handicap principle has been one of the most important developments in sexual selection theory. Numerous theoretical papers have considered whether extreme male ornaments could have arisen through female choice by being handicaps to the male. These models have been defined as belonging to one of three categories: (i) Zahavi's (J. theor. Biol. 53, 205 (1975)); (ii) the revealing; or (iii) the condition- dependent handicap. Here I discuss whether the division is still helpful for empirical purposes, or whether handicaps are not best considered as being condition dependent. I argue that in fact the revealing and condition-dependent handicaps are indistinguishable empirically, and that the 'Zahavi' handicap models arose due to a misunderstanding of what Zahavi originally proposed, which was in fact a condition- dependent handicap.

1. INTRODUCTION

Darwin (1871) was the first to suggest that the existence of extreme and elaborate ornaments in some male birds was due to female mating preference for males with these traits. However, he did not explain why females should prefer these males. It was Fisher (1915, 1930) who first suggested a possible mechanism for the evolution of female preference for males with exag- gerated traits. Fisher stated that in a population where some females prefer males with an exaggerated trait, males possessing the trait will obtain relatively more matings than those males without the trait. The sons of females expressing a preference will inherit the exag- gerated trait, and will obtain more matings as a consequence. This mechanism gives rise to 'runaway selection' of the male trait and the female preference for it. Several population genetics models have con- firmed that the 'Fisher Process' can work (O'Donald 1962, 1967; Lande 1981; Kirkpatrick 1982: but see Kirkpatrick 1985).

Following Fisher's paper there were few new ideas on the problem of sexual selection until Zahavi (1975, 1977) proposed the handicap principle as a possible mechanism for the evolution of female preference for male ornaments. The ornament is assumed to be costly in terms of survivorship, and therefore a handicap, and to reflect the viability of the possessor. The cost of the handicap is at the basis of the assumption that low- viability males cannot 'afford' to produce such a large handicap as high-viability males. Therefore, females can use the size of the ornament to discriminate between males of different viability; by choosing a mate with a large handicap a female will select a male of high viability. Both male and female offspring of

t Present address: Central Science Laboratory, London Road, Slough SL3 7HJ, U.K.

discriminating females obtain the gene for the or- nament, which may be expressed if the individual is male, with its survival cost and possible mating advantage, and the 'good genes' (Trivers 1972) of the high-viability father. At evolutionary equilibrium, the cost of the handicap to a male is compensated for by the mating advantage he obtains. The second paper by Zahavi (1977) stressed the condition-dependent nature of the handicap principle by stating that male handicaps are 'honest signals' of their quality.

Theoretical papers investigating the evolution of elaborate traits have been divided over the importance of the handicap principle (Maynard Smith 1976, 1978; Bell 1978; Eshel 1978; Kirkpatrick 1986; Pomian- kowski 1987a, b). Two recent papers have modelled the evolution of male ornaments through an 'honest signalling' mechanism (Grafen 1990a, b; Pomian- kowski et al. 1991). In these models the evolutionary stable strategies of males and females, in terms of handicap production and mate preference, are investi- gated theoretically. The handicap is treated as a signal of the viability of the possessor, with the honesty of the signal ensured by its cost (as Zahavi (1977) suggested).

In 1985, Maynard Smith defined the models of the handicap principle as belonging to one of three categories: (i) Zahavi's handicap (Zahavi 1975); (ii) the revealing handicap (Hamilton & Zuk 1982); and (iii) the condition-dependent handicap (West- Eberhard 1979; Andersson 1982 b). Subsequent papers have continued to treat the three types of handicap as distinct theoretical models (Pomiankowski 1988; Read 1990; Pomiankowski et al. 1991). In a recent paper Maynard Smith (1991) again classified models of the handicap principle into three types, but the Zahavi handicap was renamed as the fixed handicap. How- ever, although Maynard Smith's distinction is useful, in that it allows us to categorize previous papers, I believe a new approach is needed. I suggest that the

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194 S. Collins Is there only one male handicap?

revealing handicap is simply a special case of the condition-dependent handicap, and Zahavi's handicap is based on biologically unrealistic assumptions. Indeed the assumptions of the 'Zahavi handicap' (Maynard Smith 1985), or fixed handicap (Maynard Smith 1991) are not those that Zahavi (1975) originally proposed. The original Zahavi handicap is more properly considered as a condition-dependent handicap (also suggested by Pomiankowski et al. 1991). I propose to look at the three different handicap models and show that there is in fact only one type of handicap. I shall then consider the implications of the 'honest signal' models for the importance of the handicap mechanism.

2. ZAHAVI'S HANDICAP

Zahavi (1975) stated that 'the size of the character serves as a mark of quality', and that 'females select males with the most developed character'. He also stated that the character is an effective tool of sexual selection because it increases the ability of the selecting sex to detect quality in the selected, and that good quality males 'spend' more to pass the test of female choice. The above shows that Zahavi considered the handicap as being condition dependent. In this situation, high-viability males produce large handi- caps, low-viability males produce smaller handicaps for the same cost in terms of survival rate. Differences in the size of the handicap are indicators of differences in male viability.

Zahavi's handicap (1975, 1977) is in fact a condition- dependent handicap, i.e. the expression of the handicap is dependent upon the condition of the individual. However, the Zahavi handicap, as explained by Maynard Smith (1985), assumes that all the indi- viduals who carry the handicap allele develop the same level of handicap, but that low-viability males suffer a greater cost of producing the trait than high-viability males. Handicapped, low-viability males have a lower survival rate than handicapped, high-viability males. After selection, ornamented males are more likely to have high viability than non-ornamented males. Females who prefer ornamented males have a greater probability of choosing a high-viability male than females who mate randomly.

Theoretical papers showed that Zahavi's handicap can give rise to an increase in the frequency of preference and trait, but only under extreme conditions such as if low-viability males suffer a considerably reduced survival rate as a consequence of possessing the handicap (Eshel 1978). All models of Zahavi's handi- cap have followed Maynard Smith's (1976, 1985) definition and assumptions. However, the assumption of the models, that low-viability males produce the same size handicap as high-viability males and that these low-viability males have a low survivorship, is not assumed by Zahavi.

The mistake has arisen because in his 1975 paper Zahavi states that low-viability males producing a large handicap are selected against. The mathematical expression of this idea in subsequent models was a situation where all males produce equal-sized handi-

caps, but the cost to low-viability males is greater than for high-viability males. Therefore, low-viability males suffer decreased survival rates, i.e. are selected against. However, Zahavi saw this as being a situation that would give rise to a positive correlation between handicap size and viability, and not as a fixed attribute of the handicap. Low-viability males who produced large handicaps would be selected against leaving only low-viability males that produce small handicaps. Zahavi did not express his idea mathematically, which is probably the reason for the confusion about the details of the handicap.

3. CONDITION-DEPENDENT AND REVEALING HANDICAP: EVOLUTION

Let us first consider the attributes of the above types of handicap during their evolution. Both models assume that there are four genotypes of male, as in Zahavi's handicap, and that choosy females prefer ornamented males. The major difference between assumptions of the revealing and condition-dependent handicaps concerns the expression of the trait amongst low-viability males. Models of the condition-dependent handicap assume that low-viability males do not express the trait, even if they possess the allele for this trait. Models of the revealing handicap assume that both low- and high-viability males possessing the trait allele develop the trait; however, the low viability of a male has a detrimental effect on the expression of the handicap, allowing females to discriminate against these males. In the case of the revealing handicap the relation between trait and viability is multiplicative; the fitness of a male is reduced by some proportion if the male possesses a handicap. The relation in the condition-dependent handicap is additive; the fitness of the male is reduced by a fixed amount if he possesses a handicap.

If males express a condition-dependent handicap only high-viability males develop the trait, and in the case of the revealing handicap choosy females can discriminate against low-viability males expressing the trait. In both cases choosy females mate with relatively more high-viability males than females who mate randomly. Therefore, under certain circumstances, the frequency of both trait and preference can increase (Andersson 1986; Pomiankowski 1987b, 1988). The results obtained from modelling the condition- dependent handicap are qualitatively identical to those obtained modelling the revealing handicap (Maynard Smith 1985; Pomiankowski 1987a).

One problem with the condition-dependent, the revealing and 'Zahavi' handicap is that the strong directional selection for high-viability genes causes variation in heritable viability to be exhausted (this may be less of a problem in the case of the condition- dependent handicap, because of the large array of characters upon which condition is based (Halliday 1990)). If female choice is costly, and there is evidence that it is (Slagsvold et al. 1988; Gibson & Bachman 1992), then there will be selection on the preference. If there are no longer viability differences amongst males,

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Is there only one male handicap? S. Collins 195

it is of no benefit to a female to choose between males, therefore female choice will decline (Pomiankowski 1987 b). As the preference decreases in frequency so will the expression of the trait. The Hamilton & Zuk theory (1982) postulates a mechanism whereby heritable viability differences may be maintained. Low-viability males are assumed to be those males who lack resistance to the strain of parasites currently infecting the population, whereas high-viability males are resistant to these parasites. The expression of the trait by a male is detrimentally affected if he is infected with disease. Thus, the size of the ornament reflects differences in resistance to disease. The parasites and host resistance alleles coevolve, and variation in viability, specifically variation in resistance to parasites, is maintained. Males will always differ in their resistance to parasites, therefore there is always variation in viability upon which females can choose. The Hamilton & Zuk hypothesis has been assumed in many models to be synonymous with the revealing handicap.

4. CONDITION-DEPENDENT AND REVEALING HANDICAP: EQUILIBRIUM

In both these types of handicap the expression of the ornament is assumed to correlate with male viability, and females prefer males with the largest traits. The condition-dependent handicap has been described as the situation where 'the development of the male ornament depends upon the general "viability" of the individual' (Pomiankowski 1987 a). The revealing handicap is defined as the situation where 'the condition of the ornament accurately and directly reveals whether the male has high or low "viability"' (Pomiankowski 1987 a). A closer look at the definitions reveals that the two are interchangeable. In the case of the condition-dependent handicap the ornament ' reveals' something about male viability, and the development of an ornament ' depends upon the condition' of the male if it is a revealing handicap.

One common example used to differentiate between the two types of handicap is the following: attendance at a lek is a condition-dependent handicap whereas display rate on the lek is a revealing handicap. In the case of the former, a male only visits the lek if he possesses a certain fitness, his absence or presence 'depends' upon his condition. In the latter case the frequency of a male's display at a lek is limited by his fitness and so ' reveals' his quality. However, the reverse could equally well apply. The presence of a male on a lek 'reveals' his fitness to a female who visits the lek over several days. The female observes not the absence or presence of the male, but his absence or presence over a number of days. The number of days of attendance is correlated with the condition of the male. Furthermore, the frequency of the male's display 'depends' upon the fitness of the male.

The only situation where a handicap could truly be said to be revealing rather than condition dependent is where there is no differential cost of the handicap to low- and high-viability males, for example, the coloured throat sacs of sage grouse. These sacs reveal the presence of haematomas (Boyce 1990), which are

caused by ectoparasites; all males possess the sacs and production of the sac could be assumed have an equal cost to each male. Females are not choosing for the sac per se, but for the condition of the sac. However, this trait is actually a direct indicator of male parasite load. Handicaps are traits which reveal male quality to the female when this quality cannot be measured directly.

5. WHY THREE HANDICAPS?

In considering models of the handicap principle, I have shown that the 'Zahavi' or fixed handicap (Maynard Smith 1985, 1991) should be dismissed, as models have consistently shown that it does not work and it is not what Zahavi originally outlined; I consider the original Zahavi handicap to be a condition-dependent handicap. The revealing handi- cap and the condition-dependent handicap are best treated as one, in both theoretical models and experimental investigations. The Hamilton & Zuk or revealing handicap can be treated as a mechanism whereby heritable variation is maintained in a popu- lation which expresses a condition-dependent handi- cap. The assumptions of the condition-dependent and revealing handicap models are so similar that a common modelling approach seems sensible, with the expression of the trait in males being determined by viability, which includes the effects of disease.

6. HONEST SIGNAL MODEL

One problem with many of the theoretical models of the handicap principle is that a discontinuous dis- tribution of trait and viability is assumed during evolution (exceptions being Kirkpatrick 1986; Iwasa et al. 1991), whereas experimental data suggest that the trait (Andersson 1982 a; Petrie et al. 1991) and viability are continuously distributed in present populations (Moller 1988, 1989). The advantage of considering the handicap as an 'honest signal' is that the trait and viability are assumed to be continuously distributed in the theoretical models.

Grafen (1 990 a, b) used an 'honest signal' model to investigate Zahavi's handicap theory, which he called the 'strategic-choice' handicap. This name was prob- ably chosen as the size of the handicap is assumed to be the outcome of a 'strategic choice' by the male of the size of handicap to produce given his viability. The first paper used a game theory model, in which the rule that males use to produce an ornament varies amongst individuals, and females follow different preference rules. Grafen then looked for the combination of rules which produced an ESS. He found that a situation in which high-viability males produce more costly adver- tisements than low-viability males, and where females prefer to mate with males who have costly adver- tisements, was an ESS. This only occurs when the marginal cost of advertising is less for high-viability males, i.e. the cost of a small increase in handicap size is less for high- than for low-viability males.

In the second model, Grafen (1990b) used a genetic model of ' honest signalling '. The genetic model produced the same outcome, in terms of the nature of

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196 S. Collins Is there only one male handicap?

the ESS, as the game theory model. In both cases the size of the ornament varies with male quality and females prefer more ornamented males. The 'strategic- choice' (Grafen 1990 a, b) handicap differs from models of the revealing and condition-dependent handicaps in that low-viability males may produce large and 'dishonest' handicaps during evolution, but will suffer an increased cost in terms of survival. Signalling is honest because 'dishonesty is disadvantageous' (Grafen 1990a). In this model Fisher's process has no effect on the outcome, and neither do the genetics of the population, in that the assumptions about the in- heritance of the trait and preference have no effect.

The above model shows that, given the assumptions stated above, males express a handicap which is an honest signal of quality, and females choose males upon the basis of the size of the ornament they possess. This is the strongest theoretical support, so far, for the evolution of handicaps as defined by Zahavi (1975, 1977). It seems that Maynard Smith's (1 99 1) definition of models as being genetic or 'honest signalling' is somewhat misleading in that the 'honest signal' is a handicap and therefore genetic.

Grafen (1990b) believes that the condition-depen- dent and revealing handicaps are simple versions of the ' strategic choice' model, in that a discontinuous distribution of trait and viability is modelled. Early genetic models of the condition-dependent handicap simplified the process of evolution by using a dis- continuous distribution of trait size and viability. Grafen's model uses a continuous distribution which is biologically more realistic, and is the way forward for modelling the evolution of male ornaments.

The predictions of both the ' honest signalling' models and the condition-dependent models are identical. In effect, males use a kind of optimality rule, such that for different male viabilities there is an associated optimal ornament size; this is similar to the conclusion of Parker (1983). If all handicap models are condition dependent, and the condition-dependent handicap model is a simple version of the 'strategic- choice' handicap model, then there is in fact only one type of handicap. Relating evolution, as shown in the theoretical models, to the present situation is best done through the more complex 'honest signal' models.

7. FISHER'S PROCESS

The next question is whether male ornaments evolved through the handicap mechanism, Fisher's process, or a combination of both. However, it is probable that the outcome from the above processes of evolution would be identical. Whatever the path of evolution there would be an optimally sized ornament given a particular fitness; a male would trade the cost of the advertisement against the mating benefit to be obtained from having that level of advertisement. If we observed that males of higher fitness produce larger traits, and that males with larger traits were preferred as mates by females, it would be consistent with both Fisher's and the 'honest signal' hypotheses. The only way to distinguish between the two processes would be to show that the ornament is not costly to produce; if

this were true the ornament could not be a handicap. However, a costly ornament could have arisen through either 'Fisher's' process or the Handicap principle. It seems likely that most characters will be energetically expensive, such as male calls, male displays or the scent marking of territories (Halliday 1987).

Considering male handicaps simply as 'honest' signals is the way forward for empirical studies of the relation between male ornaments, male viability and female preference, rather than attempting to test between different types of handicap.

I am extremely grateful to Julee Greenough, with whom I had very helpful discussions on the problem of handicap theory and who commented upon earlier drafts of this paper. I also thank Dr T. R. Halliday for his helpful comments when refereeing the manuscript. Professor J. R. Krebs en- couraged me to develop the idea put forward in this paper. I was supported by an NERC studentship.

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Received 25 February 1993; accepted 22 March 1993

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