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Keywords:

  • bet-hedging;
  • copying;
  • mate choice;
  • mating skew;
  • sexual selection

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Mate choice by females may be influenced by both advertizing traits of males, and behaviour of other females. Here, a simple genetic and behavioural model studies the advantages of mate-choice copying. From a genetic point of view, a female preferring to copy others’ mate choice adopts a prudent strategy, because her offspring will inherit the same alleles from their father as the other young in the population. The model predicts that a female should copy others’ mate-choice, unless she encounters a relatively more attractive male than the one she has observed mating, and the attractiveness of the male reflects his genotype. For low or moderate reliability of male signalling, mate-copying is always predicted, even if the newcoming male is more attractive than the first male. This effect is attenuated, however, when the number of females that have already chosen the first male increases.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Mate choice strategies by females may have a strong influence on individual reproductive success and important evolutionary consequences (see Kirkpatrick & Ryan, 1991; Andersson, 1994). Female choice is often based on observable morphological or behavioural characters which may indicate male quality (e.g. Linville et al., 1998). However, it has been shown that in certain cases females do not choose their mate independently, but tend to copy each other (Pomiankowski, 1990). Mate-copying is difficult to demonstrate, because one needs to discriminate, among cues used by females, between those that are linked to male advertizing, and those that are linked to the behaviour of other females (see McComb & Clutton-Brock, 1994). However, experimental evidence exists that in certain species, females do actually copy each other (on fish, see Dugatkin, 1992; Briggs et al., 1996; Grant & Green, 1996; on birds, see Gibson et al., 1991; Höglund et al., 1995; and Galef & White, 1998).

Several studies have addressed the adaptive significance of this particular behaviour. As a possible advantage for mate-copying, Pruett-Jones (1992) proposed that copying females avoid paying the costs of male discrimination. These costs may actually be high, and limit the possibility to visit many males (Forsgren, 1997). Females may also achieve a high reproductive success if they copy the choice of a female with high discriminative ability (Losey et al., 1986). Finally, a gene for mate-copying behaviour may spread in a population as a result of indirect selection, by becoming associated with high fitness genotypes (Servedio & Kirkpatrick, 1996).

Here I present a simple genetic and behavioural model which suggests that mate-copying behaviour could have been selected partly because it reduces genetic risk for breeding females, in the sense that it prevents any particular female from being the only one in the population which has chosen the ‘wrong’ father for her offspring. The model includes three important features:

First, it considers that assessment of male quality and mate-copying are not incompatible. In the wild, females may actually be receptive to both male signalling and behaviour of other females, and their actual choice may depend on these two factors (Dugatkin, 1996, 1998).

Secondly, the model studies whether the probability that a male will be chosen by a particular female depends on the number of females which have already copulated with him. Enhanced tendency among females to copy each other might indeed increase mating skew among males in the breeding area (Wade & Pruett-Jones, 1990).

Finally, female individual success is not measured in terms of net reproductive success, but in terms of relative reproductive success, compared with that of the other females present. It is important to consider that the descendants of a particular female will have to compete with those of the other females, and this may influence the choice of this female (see Wall & Begon, 1985). The paper discusses the extent to which this assumption limits the generality of the model.

The model predicts in which situations females should resort to mate-copying, or avoid it. Its outcomes are discussed in the light of existing experimental evidence.

The model

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Fitness and heritability of characters

For the sake of simplicity, we assume a population of diploid animals for which individual fitness (for example, individual survival rate), is determined by a single gene. In the population, several alleles ai are possible for this particular locus (ai∈{0,1,...,A}). For an individual with genotype (ai, aj), fitness increases with allele values. It is given by: Fitness=eα(A – ai). eα(A – aj)=eα(2A  (ai + aj)), where α is a constant. The choice of an exponential fitness function is arbitrary, but it does not affect the qualitative predictions of the model. We call (ai + aj) the genotypic value of the individual. This value ranges from 0 to 2A, and we see from the equation above that individuals with the highest genotypic value have the highest fitness. We assume that all allelic frequencies in the population are equal, from which we can easily derive the distribution of genotypic values (ai + aj).

Reliability of male signalling

Here we are concerned with the information that the appearance of each male conveys about his genotype. In the model, each male presents a phenotypic value, ranging from 0 to 2A. This value expresses the attractiveness of the male towards females, and it is a more or less honest indicator of his real genotypic value. Honesty of signalling is represented by parameter s, which is the probability that the phenotypic value of the male reflects his true genotypic value. With probability 1 – s, this phenotypic value is not a reliable indicator of his genotypic value. In this case, the genotypic value of the male will be chosen randomly, i.e. according to the distribution of genotypic values in the population.

We note that, even when phenotypic value is a honest indicator of genotypic value (i.e. when s=1), the genetic benefit associated with mating with a particular male is not uniquely determined. First, in a diploid population, the male will transmit only one of his alleles to each of his offspring. Secondly, the genotypic value (ai + aj) of the male does not reveal the value of his alleles. For example, a male with genotypic value 20 could carry alleles ai=10 and aj=10, or ai=0 and aj=20. Hence, we see that, even with this simple genetic representation, the model takes into account both intra- and inter-generational variability inherent in sexual reproduction.

Female reproductive success

Each female has one reproductive bout, during which she produces a fixed number of N offspring. Because we study the influence of male quality on female choice, we will not consider genotypic variability among females. When a female mates with a male of genotype (ai,, aj), she will produce N offspring, X carrying allele ai, and N – X carrying allele aj, where X follows a binomial distribution. These offspring will inherit fitness eα(A – ai) and eα(– aj), respectively, from their father, and therefore the reproductive benefit of the female for choosing this male will be

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Fitness measurement

As a first step, we consider the simple situation where the descendants of the studied female, f, will compete with the descendants of another single female, g. Reproductive benefits resulting from mate-choice for female f and g are called Rf and Rg, respectively. They are computed using eqn (1).

Relative reproductive contribution of female f to the next generation is then given as: Pf=Rf/(Rf + Rg).

As Pf is a random variable, evolutionary theory tells us that fitness associated with a particular behaviour (here, choosing a particular male), should be computed as eqn (2) (Yoshimura & Clark, 1991):

inline image

We consider that female f has to choose between two males, with different phenotypic values. The first male has already copulated with female g, and will father her offspring. We ask whether female f should imitate the choice of female g, or choose the second male. To answer this question we compute numerically fitness value F corresponding to both alternatives, and derive the most profitable behaviour. Computations first require determining the distribution of possible genotypes for both males. These distributions depend on the phenotypic values of the males, and on the reliability of male signalling. These are then used to derive the distributions of possible relative reproductive success for the focal female. We get one distribution for the case where the female chooses to copy another female’s mate-choice, and a second for the case where she chooses the second male. Finally, using these two distributions and eqn (2), we derive fitness value F for both strategies, and identify the optimal strategy as the one associated with highest fitness. Thus we can explore the influence of phenotypic values of both males, and the reliability of these phenotypic values (i.e. parameter s), on the optimal behaviour.

Finally, we extend the model to the case where the first male has already mated with not one, but n females, and ask whether female f should be more tempted to copy the choice of these females. This model is built in a similar way as the preceding one, and still assumes that the descendants of the studied female will have to compete with those of the other females present.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

The model predicts that the choice of the female should depend on the phenotypic value, or attractiveness of both males. For a given phenotype of the first male (the male chosen by the first females), the female should opt for mate-copying if the phenotypic value of the second male is below a certain threshold value, and choose this second male if his phenotypic value is above that value. The curves in Fig. 1 plot this threshold value as a function of coefficient s, which represents the reliability of male signalling, for fixed phenotypic values of the first male. Figure 1a describes the situation where only one female has copulated with the first male, each of the three curves corresponding to a particular phenotypic value for this male. In Fig. 1b, the phenotypic value of the first male is fixed. The upper curve describes the case where only one female has chosen this male (same as Fig. 1a), and the lower curve the case where five females have already copulated with him.

image

Figure 1.  Predicted influence of male phenotypes and reliability of male advertising on the occurrence of mate-copying behaviour. The female has to choose between a first male, which she has observed mating with one or several other females and a second male. For each level of reliability s of male advertizing, the female should choose the second male if his attractiveness, or phenotypic value, is above the curve. If it is below, the female should copy the choice of the other females, and choose the first male. Parameter values: N=5, α=0.5, A=20. (a) The first male has been observed mating with one female. The three curves correspond to different phenotypic values of this male (dotted line: 30 – solid line: 20 – dashed line: 10). (b) The first male has been observed mating with one female (solid line) or five females (dashed line). Phenotypic value of the first male=20.

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Whereas, logically, mate-copying is always predicted if the second male is less attractive than the first, it is also predicted if both males are of equal attractiveness, or if the second male is slightly more attractive than the first one. Females encountering males of apparent similar quality will then tend to copy each other’s choice, as if novelty implies a risk to be avoided.

The reason is that males with similar attractiveness may carry different alleles, either because different combinations of alleles may produce identical phenotypes (see above), or because attractiveness is a poor predictor of male quality. Hence, choosing the second male implies that the descendants of the female may carry poor alleles, alleles that other offspring in the population (i.e., those of the other females) will not carry. The descendants of the female would then have a lower relative fitness during following generations. Therefore choosing the second male is a risky strategy. By contrast, we can call copying a ‘prudent’ strategy, which, in the present example, will be more profitable. Figure 2 presents the distribution of relative reproductive success for both strategies (i.e. copying and choosing the second male), for a given set of parameters. The figure shows that variance is increased when the female chooses not to copy. As a consequence, the probability of having a very low relative reproductive success is relatively high. Note that, in the example represented here, mate-copying is predicted by the model, although the second male is more attractive than the first one.

image

Figure 2.  Distribution of the possible relative reproductive success of the focal female if she chooses to copy the choice of another female (open bars), or if she chooses the newcoming male (shaded bars). Arrows indicate mean values (dashed arrow: mate-copying, plain arrow: choice of the second male). Parameter values: N=5, α=0.5, A=20, s=0.8, phenotypic value of the first male=20, phenotypic value of the second male=25. In the represented case, the model predicts mate-choice copying, although the second male is more attractive than the first one.

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In the situation where phenotypic value is a honest indicator of male quality (i.e. when s=1), the female should choose the second male if he is just a little more attractive than the first one. As honesty of signalling decreases, mate-copying tendency is predicted to increase, and the female will not choose the second male, unless this one is much more attractive than the first one. When s is low, the female should always copy. Here again, prudence is predicted: the female will not take the risk of mating with the second male even if he looks better than the first.

When the female has to choose between a n-times mated male, and a new one, qualitative predictions are the same (see Fig. 1b). The female will tend to copy the choice of the other females if the second male is not much more attractive than the first one, or if male phenotype is a poor indicator of his genetic quality. However, increasing n, i.e. the number of females having chosen the first male, decreases the threshold phenotypic value above which the female prefers not to copy. Surprisingly, as the number of females having chosen the same male increases, the choice of the newcoming focal females should depend more on the attractiveness of the different males. Taking the risk of choosing a new male becomes more advantageous, but still under the conditions that this male is more attractive than the first one and that phenotype is a reliable indicator of quality (i.e. s is high). To explain this non-intuitive result, consider the fitness measure, given by eqn (2): Fitness=E(ln(Rf/(Rf + Rg))). In the case where the female has to choose between a male she has observed mating with n females and a newcoming one, Rg represents the cumulative reproductive success of the n females, and Rf represents her own reproductive success. We suppose that n is large. In this situation, Rf will be small, compared with Rg. We will then have: Fitness=E(ln(Rf/(Rf + Rg))) ≈E(ln(Rf/Rg))=E(ln(Rf)) –E(ln(Rg)). The optimal strategy is then the strategy which maximizes E(ln(Rf))., independent of Rg (i.e. independent of the choice of the other females). As n increases, the female will then rely more on male attractiveness (provided it is somewhat reliable), and less on the other females’ mate choice.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

As soon as male advertizing conveys some information about his genetic value, a female will have, on average, a better reproductive success if she chooses the most attractive male (Nicoletto, 1995). The present model predicts that in certain circumstances she will nonetheless choose a less attractive male, if she sees him mating with one or several females. This result stems from the assumption that her descendants will live and compete with those of the other females during the following generation, and it is the expression of a ‘bet-hedging’ strategy (Slatkin, 1974; Cooper & Kaplan, 1982). Bet-hedging theory predicts that, in stochastic environments, selected strategies should be those that, although permitting relatively high mean reproductive success, minimize the variance of this success (Gillespie, 1977). In other words, bet-hedging strategies will minimize the probability of having a very poor reproductive success. Animals will then adopt risk-avoidance strategies (Yoshimura & Clark, 1991), even if this also reduces the probability of having a very high reproductive success (Boyce & Perrins, 1987).

In the present example, reproductive success for a female is the outcome of a stochastic process, as male advertizing is not always honest, and which allele the male will transmit to her offspring is unpredictable. From a genetic point of view, choosing a new male is a risk-prone strategy, because it implies the possibility that the offspring of the female will inherit very poor alleles that only they will carry. This is reflected by an increased variance in relative reproductive success for non-copying females (Fig. 2). Prudence, and therefore mate-copying behaviour, is then the best strategy. Choosing a new male will be worthwhile only if this male is more attractive than the first one, and attractiveness is an honest signal of genetic quality (Fig. 1). In this situation, taking the genetic risk pays, because the expected mean reproductive success is increased. Genetic bet-hedging and avoidance of genetic risk has already been proposed as a factor influencing female reproductive behaviour. It could be the reason why certain females prefer to mate with several males (Ligon & Zwartjes, 1995). Losey et al. (1986) already suggested that mate-copying behaviour could be a bet-hedging strategy. It is also known that sometimes, dominant females prevent subordinate females from mating with the best males (see Pomiankowski, 1990). This might indicate that females do actually consider which males will father the other young in the population, and justifies the approach taken in this paper.

Pruett-Jones (1992) has shown that the cost of male assessment could account for mate-copying behaviour. The present model suggests that the risk of error in assessing male quality might enhance this tendency. Discrimination errors in the wild must have important consequences on the reproductive success of males and females (see Getty, 1996; Johnstone & Earn, 1999). Independently, the inheritance of male quality may be unpredictable for strictly genetic reasons. For simplicity’s sake I used a monogenic determinism for fitness. Introducing a more realistic polygenic determinism would make the inheritance of male quality more predictable and offspring quality less variable. It could then, to a certain extent, decrease the pay-off of mate-copying behaviour.

In recent studies, Dugatkin (1996, 1998) observed mate-copying behaviour in guppies, Poecilia reticulata. This author showed that, whenever encountering two males with unequal coloration patterns, a female prefers to mate with the male she has observed mating with another female. This effect vanishes, however, if the second male is much more coloured than the first one. In this situation, the second male will be chosen. These experiments show that both male signalling and behaviour of other females influence mate choice by females, and their results agree with the predictions of the present model. The model also predicts that initial preference order for a female may be reversed if she observes that the drabber male is chosen by another female. This reversal in behaviour has been observed in guppies by Dugatkin & Godin (1992).

I found no evidence in the ecological literature that the tendency of females to copy each other decreases as the number of them having chosen a particular male increases. By contrast, Dugatkin (1998) has shown that letting one female observe a male being visited by two females increases the probability that she will choose this male. This result seems to contradict the predictions of the model. However, a female observing a male being courted twice can also increase her confidence that this male will sire some of the animals of the next generation (Dugatkin, 1998). In this case, mate-copying is predicted by the model. The present model shows that, in general, choosing a novel male should pay off more if the number of females having chosen another male increases. If this affects female behaviour, it should reduce the mating skew engendered by mate-copying behaviour (Wade & Pruett-Jones, 1990).

Although it was not the subject of the present model, one may ask if the tendency to copy others should depend on the state, or genotype, of the female. An additional analysis, whose results are not presented here, shows that females with low reproductive potential should be less tempted to copy others. Consider, for example, a female with a poor genotype, or which is in a bad physiological state. On average, this female will have a low reproductive success. Reducing relative reproductive success decreases the tendency to copy others’ mate-choice. Low quality females should then rely less on the prudent strategy of mate-choice copying than higher quality females, and try to acquire better than average genes from their mates.

In testing the present predictions with experimental data, it must be borne in mind that the hypotheses of the model somewhat reduce its generality. In the model, the driving force for mate-copying behaviour is competition between the offspring of the different females; thus the model will not apply to species with widely dispersing offspring. The offspring of females that reproduce synchronously and in the same place will more often compete with each other, at least for some part of their life. For example, the offspring of fishes spawning close to each other are likely to join the same shoal. In other species (e.g. lekking birds), offspring of the different females may compete as adults on breeding grounds.

The explanation proposed in this paper relies on stochastic effects of genotype transmission during sexual reproduction, but it is not restricted to small populations. Consider, for example, that all males present in a breeding area and belonging to a polygynous species have similar phenotypes, or that real quality of males cannot be assessed from their phenotype. In this case, the model predicts that females will prefer to choose males they observe mating, irrespectively of the size of the population. This will result in only a few males participating in reproduction, and a strong mating skew. Hence, the present model shows that avoidance of genetic risk may play a role in the natural selection of mate-copying behaviour, even in large populations, and especially when the risk of error in assessing male quality is high.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

I thank two referees and the editor for helpful comments on the manuscript.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  • 1
    Andersson, M. 1994. Sexual Selection. Princeton University Press, Princeton.
  • 2
    Boyce, M. & Perrins, C.M. 1987. Optimizing great tit clutch size in a fluctuating environment. Ecology 68: 142153.
  • 3
    Briggs, S.E., Godin, J.G., Dugatkin, L.A. 1996. Mate-choice copying under predation risk in the Trinidadian guppy (Poecilia reticulata). Behav. Ecol. 7: 151157.
  • 4
    Cooper, W.S. & Kaplan, R.H. 1982. Adaptive ‘coin-flipping’: a decision-theoretic examination of natural selection for random individual variation. J. Theoret. Biol. 94: 135151.
  • 5
    Dugatkin, L.A. 1992. Sexual selection and imitation: females copy the mate choice of others. Am. Nat. 139: 13841389.
  • 6
    Dugatkin, L.A. 1996. Interface between culturally based preferences and genetic preferences: female mate choice in Poecilia reticulata. Proc. Natl. Acad. Sci. USA 93: 27702773.
  • 7
    Dugatkin, L.A. 1998. Genes, copying and female mate choice: shifting thresholds. Behav. Ecol. 9: 323327.
  • 8
    Dugatkin, L.A. & Godin, J.G. 1992. Reversal of female choice by copying in the guppy (Poecilia reticulata). Proc. R. Soc. Lond. Series B 249: 179184.
  • 9
    Forsgren, E. 1997. Mate sampling in a population of sand gobies. Anim. Behav. 53: 267276.DOI: 10.1006/anbe.1996.0374
  • 10
    Galef, B.G. & White, D.J. 1998. Mate-choice copying in Japanese quail, Coturnix coturnix japonica. Anim. Behav. 55: 545552.DOI: 10.1006/anbe.1997.0616
  • 11
    Getty, T. 1996. Mate selection by repeated inspection: more on flycatchers. Anim. Behav. 51: 739745.DOI: 10.1006/anbe.1996.0078
  • 12
    Gibson, R.M., Bradbury, J.W., Vehrencamp, S.L. 1991. Mate choice in lekking sage grouse revisited: the roles of vocal display, female site fidelity, and copying. Behav. Ecol. 2: 165180.
  • 13
    Gillespie, J.H. 1977. Natural selection for variance in offspring numbers: a new evolutionary principle. Am. Nat. 111: 10101014.
  • 14
    Grant, J.W. & Green, L.D. 1996. Mate copying versus preferences for actively courting males by female Japanese medaka (Oryzias latipes). Behav. Ecol. 7: 165167.
  • 15
    Höglund, J., Alatalo, R.V., Gibson, R.M., Lundberg, A. 1995. Mate-choice copying in the black grouse. Anim. Behav. 49: 16271633.
  • 16
    Johnstone, R.A. & Earn, D.J.D. 1999. Imperfect female choice and male mating skew on leks of different sizes. Behav. Ecol. Sociobiol. 45: 277281.DOI: 10.1007/s002650050562
  • 17
    Kirkpatrick, M. & Ryan, M.J. 1991. The evolution of mating preferences and the paradox of the lek. Nature 350: 3338.
  • 18
    Ligon, J.D. & Zwartjes, P.W. 1995. Female red junglefowl choose to mate with multiple males. Anim. Behav. 49: 127135.
  • 19
    Linville, S.U., Breitwisch, R., Schilling, A.J. 1998. Plumage brightness as an indicator of parental care in northern cardinals. Anim. Behav. 55: 119127.DOI: 10.1006/anbe.1997.0595
  • 20
    Losey, G.S. Jr, Stanton, F.G., Teleky, T.M., Tyler, W.A. III & the Zoology, 691 Graduate Seminar Class. 1986. Copying others, an evolutionary stable strategy for mate choice: a model. Am. Nat. 128: 653664.
  • 21
    McComb, K. & Clutton-Brock, T. 1994. Is mate choice copying or aggregation responsible for skewed distribution of females on leks? Proc. R. Soc. Lond. Series B 255: 1319.
  • 22
    Nicoletto, P.F. 1995. Offspring quality and female choice in the guppy, Poecilia reticulata. Anim. Behav 49: 377387.DOI: 10.1006/anbe.1995.0050
  • 23
    Pomiankowski, A. 1990. How to find the top male. Nature 347: 616617.
  • 24
    Pruett-Jones, S.G. 1992. Independent versus non-independent mate choice: do females copy each other? Am. Nat. 140: 10001009.
  • 25
    Servedio, M.R. & Kirkpatrick, M. 1996. The evolution of mate choice copying by indirect selection. Am. Nat. 148: 848867.
  • 26
    Slatkin, M. 1974. Hedging one’s evolutionary bet. Nature 250: 704705.
  • 27
    Wade, M.J. & Pruett-Jones, S.G. 1990. Female copying increases the variance in male mating success. Proc. Natl. Acad. Sci. USA 87: 57495753.
  • 28
    Wall, R. & Begon, M. 1985. Competition and fitness. Oikos 44: 356360.
  • 29
    Yoshimura, J. & Clark, C.W. 1991. Individual adaptations in stochastic environments. Evol. Ecol. 5: 173192.