«To cite this version: Sylvain Billiard, Charlotte Faurie, Michel Raymond. Maintenance of handedness polymorphism in humans: A frequency-dependent ...»
Maintenance of handedness polymorphism in humans: A
frequency-dependent selection model
Sylvain Billiard, Charlotte Faurie, Michel Raymond
To cite this version:
Sylvain Billiard, Charlotte Faurie, Michel Raymond. Maintenance of handedness polymorphism
in humans: A frequency-dependent selection model. Journal of Theoretical Biology, Elsevier,
2005, 235, pp.85-93. 10.1016/j.jtbi.2004.12.021. halsde-00184539
HAL Id: halsde-00184539
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Maintenance of handedness polymorphism in humans:
A frequency-dependent selection model1 Sylvain Billiard1, Charlotte Faurie1,* and Michel Raymond1 1 The authors contributed equally and are listed in alphabetical order.
1 Institute of Evolutionary Sciences of Montpellier, France.
* Corresponding author. Institute of Evolutionary Sciences University of Montpellier II – CC 065 Place Eugène Bataillon F 34095 Montpellier cedex 5 Telephone: +33 467 144 632 Fax: +33 467 143 622 E-mail: firstname.lastname@example.org Abstract Frequency-dependent selection is an important process in the maintenance of genetic variation in fitness. In humans, it has been proposed that the polymorphism of handedness is maintained by negative frequency-dependent selection, through a strategic advantage of left-handers in fighting interactions. Using simple mathematical models, we explore: 1°) whether it is possible to predict the range of left-handedness frequencies observed in human populations by the frequency and the violence of fighting interactions;
2°) the consequences of the sex differences in the probability of transmission of hand preference to offspring. We show that a wide range of values of the frequency of lefthanders can be obtained with realistic changes of the parameters values. Our models reinforce the idea that negative frequency dependence may have played a role in maintaining left-handedness in human populations, and provide further support for the importance of fighting interactions in the evolution of hand preference. Moreover, they suggest an explanation for the occurrence of left-handedness among women in this context, namely an indirect selective advantage through their male offspring.
Keywords: Human evolution, polymorphism, frequency-dependence, handedness.
1 This article was published in Journal of Theoretical Biology (235) Billiard S., Faurie, C., Raymond M., Maintenance of handedness polymorphism in humans: a frequency-dependent selection model, Pages 85– 93, © 2005, and is posted with permission from Elsevier. JOURNAL OF THEORETICAL BIOLOGY
A polymorphism for a non-neutral trait can be observed in a population when there is a balance of selective forces. This can occur either if this trait is under frequency-dependent selection, or if there is a spatial or temporal heterogeneity of selective pressures (Maynard Smith, 1989). If different values of the trait are associated to a frequency-dependent selective cost, or advantage, then stable coexistence will result. The most widespread and dramatic genetic polymorphism, that of sexual dimorphism, is certainly maintained by negative frequency-dependent selection (Fisher, 1958). Negative frequency-dependent selection is a potentially important process in the maintenance of genetic variation in fitness traits, as has been described for the maintenance of the polymorphism of courtship in Drosophila (Ayala and Campbell, 1974), color morphs in lizards, fishes and plants (Endler, 1988; Gigord, Macnair and Smithson, 2001; Sinervo and Lively, 1996), mouth morphology in scale-eating fishes (Hori, 1993), bill crossing morphs in crossbills (Benkman, 1996), cytoplasmic male-sterility factors in gynodioecious plant (Städler and Delph, 2002), major histocompatibility complex in mammals (Meyer and Thomson, 2001), etc.
In humans, handedness is one of the traits for which the maintenance of a polymorphism is probably due to negative frequency-dependent selection (Vallortigara and Rogers, in press). Hand preference is heritable (see e.g. Francks et al., 2002; McKeever, 2000; McManus, 1991; Sicotte, Woods and Mazziotta, 1999), and a handedness polymorphism is detected in early human populations (Faurie and Raymond, 2004) and observed in all contemporary populations as well (Faurie et al., 2005; Raymond and Pontier, 2004). However, left-handedness seems to be associated with several fitness costs, such as a lower height or a reduced longevity (e.g. Aggleton, Kentridge and Neave, 1993; Coren and Halpern, 1991; Gangestad and Yeo, 1997; McManus and Bryden, 1991). The costs reported in the literature are not likely to be frequency-dependent. A frequencydependent advantage is therefore required to explain the maintenance of the polymorphism.
(Raymond et al., 1996) have proposed a negative frequency-dependent selection mechanism related to fighting interactions. As left-handers are less frequent, one is more likely to be confronted with a right-handed opponent in a physical fight. Left-handers would thus be more accustomed to righthanded competitors than vice versa. Therefore, they might enjoy a negatively frequency-dependent strategic advantage in fights when rare, relative to right-handers. This frequency-dependent superiority of left-handers in interactive contests would confer them fitness advantages, directly and indirectly. It could have historically influenced survival, but also social status and reproductive success (see, e.g., Archer, Holloway and McLoughlin, 1995; Chagnon, 1988; Hill, 1984).
The action of a negative frequency-dependent advantage of left-handers in physical fights is strongly suggested by the study of interactive sports, which can be considered as a form of fighting interaction. Indeed, left-handers are significantly more frequent among competitors in these sports than in the general population or among non-interactive sport competitors (Aggleton and Wood, 1990; Raymond et al., 1996; Wood and Aggleton, 1989). In sports where the interaction is direct, the frequency of left-handers is almost reaching one half, and it is lower when the interaction is less direct (Grouios et al., 1999). Game-theoretic modelling of handedness in both batting and pitching in baseball has found that models incorporating frequency dependence provide a good fit to historical data on handedness (Goldstein and Young, 1996). Similarly, in cricket, left-handed batsmen have a strategic advantage that decreases as left-handers become more common in competition, which is consistent with frequency-dependent rather than uniform benefits of lefthandedness in interactive contests (Brooks et al., 2003). Another empirical support of the fighting hypothesis is the cross-cultural positive correlation found in traditional societies between the rate of homicides and the frequency of left-handedness (Faurie and Raymond, 2005). This correlation is predicted by the fighting hypothesis, as an increased level of violence (and thus of dual fights) provides a greater fitness advantage to left-handers, which thus increase in frequency. Physical fights could therefore be involved in the selection pressures acting on the frequency of left-handers in human populations. This hypothesis is essentially developed as a verbal argument, and does not formally consider inheritance processes, sex differences, and frequency dependence.
2 The primary aim of the article was to determine the range of parameters values to consider to be able to predict the whole range of the left-handedness frequencies observed in human populations. Furthermore, there is a problematic issue in the context of this hypothesis. As male/male aggression in humans is much more frequent than aggression involving females (e.g.
Manning and Taylor, 2001; Mesquida and Wiener, 1999), the fighting advantage should concern mostly left-handed men. Considering that the costs apply to both sexes, the mere existence of lefthanded women is puzzling. Nevertheless, the frequency of left-handers among women is close to the frequency among men (although generally lower) (Annett, 1985; Porac and Coren, 1981). We investigated whether the probabilities of transmission of hand preference to offspring could reflect the proximal mechanism for this phenomenon. Indeed, the probability for a child to be left-handed increases when one of his/her parents is left-handed and, more remarkably, this increase is higher when the mother is left-handed than when the father is left-handed (e.g. McKeever, 2000;
McManus, 1991; Porac and Coren, 1981). There are thus stronger maternal effects than paternal effects upon offspring handedness. Such a finding could result from a sex-related genetic effect, or from a greater social influence on the child likely to be exerted by the mother.
In the first section of this article, a simple mathematical model of frequency-dependent selection is presented; it serves as a basis for the models of the following sections. In the second section, we investigate whether the frequency of left-handers at equilibrium in a population may be predicted by the frequency and the violence of fighting interactions. We study the influence of different parameters, representing the underlying mechanisms of the frequency-dependent advantage in fighting. These parameters are: probability of fighting during an individual’s life, probability of death during a fight, cost of being left-handed, and the frequency-dependent advantage of left-handers in fights. We also consider in this section the influence of the costs and advantages associated to involvement in fights. In the third section, we investigate the consequences of the sex differences in the probability of transmission of hand preference to offspring. All computations were performed using Mathematica version 4 (Wolfram Research, Inc.
1. The basic negative frequency-dependent selection model of the evolution of hand preference
3 We see in equation (2) that the frequency of left-handers tends towards 0 when c goes to 1 and that limδ →∞ f L° =1/ 2. As shown on Figure 1, the frequency reaches high values for a small δ.
The range of values found in the literature for the frequency of left-handedness across human populations is reported also in Figure 1. No estimation of the global cost of left-handers is available in the literature, but whatever the value of c chosen here, the model can predict the whole range of frequencies. Moreover, under this kind of selection, relatively small variations in the value of the advantage are sufficient to explain the observed variations in the prevalence of left-handedness. In other words, it is not necessary that the advantage of left-handers be large to obtain high frequencies at equilibrium.
2. Effects of fights on the frequency of left-handed males at equilibrium
In this section, we use a specific mechanism to describe the frequency-dependent advantage of left-handed males in fights. Hence, we only consider males’ handedness. Fitness is assumed to be the probability of survival until age of maturity, and depends on hand preference.
The survival probability is decomposed into two components: the probability to be killed in fights and the probability to die before reproduction because of intrinsic reasons (this second component is introduced to take into account the cost of left-handers). Therefore, if we note k the probability to be killed in fights, and c the probability for left-handers to die before reproduction for intrinsic reasons, the total survival probability of left-handers is (1 - k)(1 - c).
We suppose that each male has a probability Pfight to be involved in a fight during his life.
When a fight occurs between two right-handed males, each male has a probability Pdeath to be killed by the other. When a fight occurs between a right-hander and a left-hander, the right-hander has a probability Pdeath (1 + Δ) and the left-hander a probability Pdeath (1 - Δ) to be killed, because of the fighting advantage of left-handers, who are less frequent than right-handers are. The advantage Δ is defined as in the first section.
All males who have survived until age of maturity are assumed to have the same probability to reproduce and the same amount of offspring: resources for reproduction, including females, are not limiting. All males die after reproduction. As the population is considered infinite, the occurrence of deaths during fights does not change the frequency of right- and left-handed males within a generation.
Under these assumptions, the probability for a left-handed male to survive until
reproduction at generation t is:
WL (t ) = Pfight ( f R (t )(1 − Pdeath (1 − Δ)) + f L (t )(1 − Pdeath ))(1 − c) + (1 − Pfight )(1 − c) (3)
The frequency of left-handers at equilibrium is 0 when V = 0 and 1/2 when c = 0, as expected. When c and δ are small, say c and δ are of the same order as a small parameter ε, we have c (1 − V) + Ο (ε ) (where О(ε) represents a term of the same order as ε), f Lo = 1 − 2δ V + 2 c (1 − V) 2 which shows that the frequency at equilibrium increases with violence. A remarkably large range of frequencies of left-handers can be obtained with small variations of the parameters (see Figure 2).
For example, with c = 0.1, i.e. the survival of left-handed males until age of reproduction is 4 decreased by a factor 10% (due to the intrinsic cost of left-handedness), and δ = 0.05, which leads to a very low advantage in fights, the frequency of left-handers varies between f Lo =0.01 for V ≈0.043 and f Lo =0.1 for V ≈0.355. It is important to note that the form of the curve depends mostly on the value of the modulator of the advantage δ (see Figure 2).