Evolutionary genetics of sex-limited traits under fluctuating selection
K. Reinhold Institut für Evolutionsbiologie und Ökologie der Universität Bonn, An der Immenburg 1, D-53121 Bonn, Germany. Tel: +49 228 73 51 19; fax: +49 228 73 51 29; e-mail: Kreinhold@evolution.uni-bonn.de
Ultimately based on the different gamete size and the resulting sex roles, most animal species have acquired traits that occur only in one of the sexes. For those sex-limited traits the impact of a single selection event is reduced, because the genes coding for these traits also occur unexpressed in the other sex and are therefore partly hidden to selection. All sex-limited traits thus show a storage effect analogous to a seed bank. This storage effect has to be considered when measuring the effect of fluctuating selection on sex-limited traits. Here, I develop appropriate equations to measure the ability of an allele to invade a population when fluctuating selection acts on sex-limited traits. A comparison of the equations for X-chromosomal and autosomal traits gives the following result: the evolution of traits limited to the heterogametic sex should preferentially involve X-chromosomal genes and the evolution of traits limited to the homogametic sex should preferentially involve autosomal genes. This difference between the sexes may contribute to explain (1) the large effect of X-chromosomal genes in causing hybrid sterility in the heterogametic sex and (2) the large effect of X-chromosomal genes on sexually selected traits in heterogametic males.
In most animal species there are two different sexes, males and females, that often differ extensively in phenotype. In extreme cases males and females are so dissimilar that they have been described as members of different taxa. But even in species with less sexual dimorphism many morphological or behavioural characters differ between males and females. Males and females are defined according to the size of gametes they produce: females produce macrogametes and males produce microgametes. As a consequence of the different investment in zygotes, differences in the reproductive roles of males and females have evolved (Trivers, 1972; Bell, 1982). These differing reproductive roles have led to sexually dimorphic characters in addition to the differences in reproductive organs necessary for the production of micro- and macrogametes (Thornhill & Alcock, 1983; Fairbairn, 1997).
If parental care is provided to the offspring, the sexes differ in the extent of care and as a consequence males and females usually differ in morphological, behavioural or physiological adaptations for brooding, feeding or defending the offspring (Clutton-Brock, 1991). Males of most animal species show sex-specific courtship behaviour and often use specialized morphological traits for advertisement (Eberhard, 1985; Andersson, 1994). Females, on the other hand, also often show sex-specific behaviour towards courting males: they attract males with olfactorial, visual or acoustic stimuli, they select mating partners based on the males’ advertisement signalling and they have evolved mechanisms to control fertilization (Eberhard, 1991, 1996; Andersson, 1994). Maximum reproductive rates usually are larger in males than in females (Clutton-Brock & Vincent, 1991) and therefore contests within one sex are usually stronger between males than between females (Andersson, 1994). As a consequence males of many animal species have evolved specialized weaponry. Overall, there are large differences between the sexes and many characters occur only in one sex and are thus sex-limited.
According to the above arguments, selection will lead to sex-limitation of many characters. To achieve sex-limited phenotypes, genes coding for these characters have to have sex-limited expression. Such sex-limited expression has consequences on the impact of selection on these traits. Within a single generation, selection on sex-limited traits can only affect the reproductive success of the sex that expresses this trait. In the other sex, genes are hidden to selection because they are not expressed. Some proportion of the alleles coding for sex-limited traits is thus shielded from selection. A similar absence of selection that occurs when part of the population stays in a seed bank had been termed ‘storage-effect’. When selection fluctuates in time, such a storage effect can have profound influence on the outcome of selection (Ellner & Hairston, 1994; Ellner & Sasaki, 1996). It is therefore important to know whether sex-limited traits are likely to be influenced by fluctuating selection.
Evolution of sex-limited characters is extensively studied with experimental and theoretical approaches (Andersson, 1994; Eberhard, 1996; Fairbairn, 1997). Selection on sex-limited traits is usually assumed to be directional or stabilizing. However, environmental fluctuations leading to temporal fluctuations in the direction of selection are probably widespread and should occur in most environments (e.g. Merell & Rodell, 1968; Heath, 1974; Lynch, 1987; Hairstone & Dillon, 1990; Forsman, 1993; Borash et al., 1998). And, fluctuating selection has been assumed to play an important role for the evolution of female choice (Hamilton & Zuk, 1982; Iwasa & Pomiankowski, 1995).
Temporal fluctuations in population density that occur in many animal species can be viewed as the result of fluctuating environmental conditions. On the other hand, fluctuations in population density will also cause fluctuating selection on sex-limited traits, e.g. sexually selected traits (Conner, 1989; Clutton-Brock et al., 1997). With decreasing population density the reproductive success of attractive males may decrease when females have fewer opportunities to choose among males. When, as an effect of low population density, predation pressure on attractive males is increased at the same time, the intensity of fluctuating selection on sexually selected traits can be magnified in the considered case. Empirical evidence shows that selection on weaponry, size and other sexually selected traits changes direction with fluctuations in population density (Conner, 1989; French & Cade, 1989; Wikelski & Trillmich, 1997). Fluctuating selection thus seems to be almost universal and sex-limited traits should be especially prone to temporal changes in environmental conditions.
Under fluctuating selection, the geometric mean fitness of the heterozygote phenotype is often used as the best measure for the ability of an allele to invade a population (Gillespie, 1973; Ritland & Jain, 1984; Bulmer, 1985; Boyce & Perrins, 1987). The reason why the geometrical mean instead of the arithmetic mean is appropriate can be shown with the following example: assume that individuals heterozygotic for a rare allele have zero fitness in one of 100 years but have above average fitness in the other 99 years so that the arithmetic mean of their fitness is above 1. Such an allele will nevertheless be lost from the population, at least when it is expressed in all heterozygotes (see Haldane & Jayakar, 1963). Under fluctuating selection, the geometric mean fitness, being 0 in the above example, is a good predictor for the direction of evolution.
For a sex-limited trait, however, a single year with no descendants of those individuals showing the trait will not necessarily lead to the elimination of the allele responsible for the expression of that trait, since this allele also occurs unexpressed in the other sex. In the following, I develop an appropriate estimator to measure whether a given allele with sex-limited expression can invade when selection fluctuates. This estimator takes into consideration that sex-limited alleles are not expressed in one sex.
The proportion of a sex-limited allele that is exposed to selection depends on whether the allele is on the autosomes or on the sex-chromosomes. And, for sex-linked alleles the proportion of a sex-limited allele exposed to selection differs between the sexes. These differences are proposed to cause a bias of sex-limited traits towards the autosomes in the homogametic sex and towards the X-chromosome in the heterogametic sex.
The following model assumes a diploid organism with chromosomal sex determination, discrete generations and infinite population size. The two sexes are assumed to be determined by an XX–XY sex determination system: individuals that have one X- and one Y-chromosome besides the autosomes develop into the heterogametic sex, individuals with two X-chromosomes into the homogametic sex. The effects of fluctuating environmental conditions are examined for a one-locus two-allele system with a common allele C, and a rare allele R. The frequency of R is assumed to be small so that R can be treated as if it occurs only in heterozygotes. Both alleles are assumed to influence the expression of a sex-limited trait and thus cause sex-limited effects on reproductive success. The fitness effect f of the rare allele is defined here as the relative reproductive success of individuals heterozygotic for the rare allele. An f of 1.5 thus means that individuals expressing R because they are heterozygotic for R have 1.5 times the reproductive success than same sex individuals expressing C. If f is always larger than 1, R will invade, and when f is always smaller than 1, R cannot invade. For the more complicated case, when f is sometimes smaller and sometimes larger than 1 – that is when there is fluctuating selection – it is necessary to analyse the long-term growth rate of allele R. For a low frequency of allele R, the long-term growth rate allows us to estimate the ratio between the frequency of R in zygotes of generation n + 1 and the frequency of R in zygotes in generation 1. The long-term growth rate of allele R thus gives a measure for the impact of fluctuating selection on allele frequency and allows us to estimate whether allele R can invade. When the long-term growth rate is smaller than 1, R will not be able to invade, and when it is larger than 1, R will be able to invade.
In the model, random environmental fluctuations are assumed to influence the fitness of individuals expressing the alleles under consideration. The relative fitness of the rare phenotype is assumed to be fi in generation i. Owing to fluctuating environmental conditions and hence fluctuating selection on the trait under consideration f will fluctuate between generations.
Long-term effects of selection on sex-limited traits
With sex-limited expression of an allele only a fraction of the allele is exposed to selection because it is expressed in only one of the two sexes. Considering the proportion p of allele R that is exposed to selection and the relative reproductive success f of individuals heterozygotic for R, one can calculate the change in the frequency of R that will result. When in one generation individuals that express R have twice the reproductive success than individuals that express C (f = 2), the frequency of R will increase. Since the reproductive success of those individuals that carry R but do not express it is not increased, the increase in the frequency of R will be less than 2. In the considered case with f = 2, when half of the R alleles are expressed (P = 0.5), R will increase by a factor of 1.5. For all values of f and p, the effect of selection on the frequency of R will be the weighed average effect of allele R on reproductive success in all individuals that carry R. Accordingly, the long-term growth rate F of a rare allele under fluctuating selection can be given as
The proportion of an allele that is exposed to selection differs between autosomes and sex-chromosomes and between the sexes. In the following the equations are considered separately for the homogametic and the heterogametic sex.
An autosomal trait limited to the homogametic sex is expressed in all heterozygous homogametic individuals carrying it when it is at least partially dominant (h ≠ 0). But it is not expressed in individuals of the heterogametic sex. Thus 50% of such a sex-limited autosomal allele is exposed to selection when it is rare. Using this proportion of 0.5 and inserting it in eqn 1 thus gives eqn 2 as a measure for the long-term growth rate of an autosomal allele under fluctuating selection.
In contrast, an X-chromosomal allele expressed only in the homogametic sex is to a larger extent exposed to selection. Since the homogametic sex has two X- chromosomes and the heterogametic sex only one, two-thirds of all X-chromosomes will be exposed to selection. The appropriate measure for the long-term growth rate of an X-chromosomal allele under fluctuating selection is given in eqn 3.
A rare autosomal sex-limited allele expressed only in the heterogametic sex is expressed in all heterozygous heterogametic individuals carrying it, when it is at least partially dominant (h ≠ 0). But it is not expressed in any individuals of the homogametic sex. Thus, only 50% of an autosomal sex-limited allele is exposed to selection. Since this is the same value as for autosomal alleles in the homogametic sex, eqn 2, giving the long-term growth rate (FA) of an autosomal allele subject to fluctuating selection, is also valid for the heterogametic sex.
In comparison with an autosomal allele, an X-chromosomal allele expressed only in the heterogametic sex is to a smaller extent exposed to selection. Since there are two X-chromosomes in the homogametic sex and only one in the heterogametic sex, an X-chromosomal allele coding for a trait limited to the heterogametic sex is only to one-third expressed and thus exposed to selection. The appropriate equation for the long-term growth rate of an X-chromosomal allele subject to fluctuating selection is given in eqn 4.
Y-chromosomal alleles can, per definition, only code for sex-limited traits. Since Y-chromosomal alleles do not occur unexpressed in the other sex, the geometric mean fitness (eqn 5) is appropriate for Y-chromosomal alleles under fluctuating selection.
Equations 2–5 allow us to estimate the long-term effect of fluctuating selection on allele frequency for rare autosomal, X-chromosomal and Y-chromosomal alleles in the homogametic and the heterogametic sex. In large populations where drift is not important the allele R can be expected to invade whenever F > 1. In contrast, the allele R can be expected not to invade for any values of F < 1.
Comparing alleles differing in expression
In the following I will analyse whether p, the proportion of an allele that is expressed, does influence the ability of an allele to invade a population. Assume, there are two rare alleles S and T that have identical fitness effects but differ in the extent of expression. The proportions of these alleles that are expressed and thus exposed to selection are given by s and t (1 > s, t > 0). And, allele T is assumed to be expressed to a larger extent than allele S (0 < s < t < 1). Then, one can compare the effect of fluctuating selection on the alleles S and T:
Each single factor within the large brackets in eqn 6 can be shown to have a global minimum of 1 at fi = 1. Whenever there is fluctuating selection, that is if there are fi different from 1, then Yst will always be larger than 1. This means (1) that FS is larger than FT when FT is smaller than 1, (2) that FS is larger than 1 when FT is equal to 1 and (3) that FS is larger than one whenever FT is larger than 1. It also follows from eqn 6 that (4) FT is smaller than 1 when FS is equal to 1 and (5) FT is smaller than 1 whenever FS is smaller than 1.
Together, this means that depending on the fi values either none of the two alleles, both of the alleles or only allele S will be able to invade a given population. The combination of fitness effects that will lead to an increase of allele S are thus wider than those for allele T. With increasing frequency and strength of fluctuating selection, Yst will increase. This means that the combination of fitness effects that will lead to the invasion of allele S but not of allele T can be expected to become wider with increasing strength of fluctuating selection.
Comparison between chromosomes
Fifty per cent of a rare autosomal allele that codes for a trait limited to the homogametic sex is exposed to selection. In contrast, two-thirds of an X-chromosomal allele will be expressed and thus exposed to selection. According to the previous section, such a difference in expression does influence whether an allele can invade when selection fluctuates in time. Whenever an X-chromosomal allele can invade, an autosomal allele with identical fitness effects will also be able to invade. Whenever an autosomal allele is unable to invade, an X-chromosomal allele with identical fitness effects will always be unable to invade, too. But, there are sets of fluctuating environmental conditions that lead to the increase of an autosomal allele but to a decrease of an X-chromosomal allele with identical fitness effects. This means that the set of possible phenotypes that will allow the invasion of a rare allele is wider for autosomal alleles than for X-chromosomal alleles.
The following proportions of an allele coding for a trait limited to the heterogametic sex are exposed to selection: one-third for X-chromosomal alleles, one-half for autosomal alleles and 100% for Y-chromosomal alleles. Using the conclusions derived from eqn 6 the long-term effects of fluctuating selection on X-chromosomal, Y-chromosomal and autosomal genes can be compared in the heterogametic sex. In comparison with the homogametic sex the relationship between autosomal and X-chromosomal alleles is reversed in the heterogametic sex. There are sets of fluctuating environmental conditions that lead to the increase of an X-chromosomal allele but to a decrease of an autosomal allele with identical fitness effects. This means that the set of possible phenotypes that will allow the invasion of a rare allele in the heterogametic sex is wider for X-chromosomal alleles than for autosomal alleles. Including the Y-chromosome into the analysis gives the following order for the ease of invasion of alleles: X-chromosome > autosome > Y-chromosome.
When selection on sex-limited characters fluctuates in time, in each generation some proportion of the alleles coding for these characters is not exposed to selection because they occur unexpressed in the other sex. This storage effect has to be considered when estimating the long-term fate of a sex-limited allele under fluctuating selection. Here, I develop equations for the long-term growth rate of a rare allele that is influenced by fluctuating selection and expressed only in the homogametic or in the heterogametic sex. Since sex-chromosomal and autosomal alleles differ in the extent of expression, appropriate equations are given for alleles on all types of chromosomes. The comparison of these equations revealed (1) that rare alleles on the autosomes or sex-chromosomes have a different chance to invade a population and (2) that there are differences between the sexes. In the homogametic sex, autosomal alleles are more likely to increase in frequency than X-chromosomal alleles; in the heterogametic sex, autosomal alleles are less likely to increase in frequency than X-chromosomal alleles. This difference should lead to a preferential linkage of traits limited to the homogametic sex towards the autosomes. And, traits limited to the heterogametic sex can be expected to be linked preferentially to the X-chromosome.
Is there any empirical evidence for the hypothesis that genes coding for sex-limited traits tend to be X-chromosomal in the heterogametic sex and autosomal in the homogametic sex? The location of genes responsible for sex-limited morphological and behavioural traits involved in sexual selection fits to the expected pattern. In butterflies, where females are heterogametic, X-chromosomal genes have a surprisingly large influence on traits limited to females (Sperling, 1994; Ritchie & Philips, 1998). In animals with heterogametic males, the X-chromosome does play a special role in traits limited to the heterogametic sex but not in traits shown in both sexes (Reinhold, 1998). And, of those traits limited to homogametic females in Drosophila, none has a significant X-chromosomal contribution though the X-chromosome constitutes a large proportion of the genome (Allemand & David, 1984; Coyne, 1989, 1992, 1996; Moreteau et al., 1994; Ruiz-Dubreuil & Köhler, 1994). Hybrid sterility is often limited to the heterogametic sex (Haldane, 1922; Coyne, 1994), and it is therefore thought that the involved genes are sex-limited in their expression. In accordance with the hypothesis presented here, X-chromosomal genes have been shown to be important in causing hybrid sterility in the heterogametic sex (e.g. Coyne & Orr, 1989; Johnson & Wu, 1993; Coyne, 1994; True et al., 1996; Khadem & Krimbas, 1997; Turelli & Begun, 1997; but see Wu et al., 1996).
The preferential linkage of sex-limited traits of heterogametic males to the X-chromosome may, however, also be explained by other theories concerning the evolutionary speed of X-chromosomal traits. When there is sexually antagonistic selection, sex-chromosomal genes will be more likely to evolve, because their expression in males and females already differs (Rice, 1984). Charlesworth et al. (1987) have argued that X-chromosomal genes can be expected to evolve faster than autosomal alleles. When mutations are usually recessive, there is a difference between X-chromosomal and autosomal alleles: rare X-chromosomal alleles are always expressed in the heterozygotic sex. Recessive autosomal alleles, on the other hand, need to increase by drift until their frequency is large enough for homozygotes to occur. The proposed faster evolutionary speed of X-chromosomal traits thus will be especially strong for traits limited to the heterogametic sex but there should also be a substantial influence of X-chromosomal genes on traits expressed in both sexes. In contrast to the expectation, such an influence is absent in empirical data (Reinhold, 1998). The larger evolutionary speed of X-chromosomal genes proposed by Charlesworth et al. (1987) thus cannot fully explain the observed sex-linkage of sex-limited traits.
If there is a difference in hybrid sterility between the sexes it is the heterogametic sex where hybrid sterility is more severe and more frequent. This pattern, named Haldane's rule, was found long ago (Haldane, 1922), but the causes behind it are still debated (Coyne, 1994; True et al., 1996; Wu et al., 1996; Turelli & Begun, 1997). According to the hypothesis presented here, the X-chromosome can be expected to be preferentially involved in the evolution of traits limited to the heterogametic sex. Many of the genes involved in the production of gametes will be sex-limited in expression. In the heterogametic sex these genes should therefore preferentially be linked to the X-chromosome. Epistatic interactions between X-chromosomal genes and allospecific autosomal genes may then lead to hybrid dysgenesis in gamete production and thus hybrid sterility. In accordance with the preferential linkage of male sterility factors to the X-chromosome, True et al. (1996) have shown, by using introgression of allospecific genes into Drosophila simulans, that male sterility factors evolve about 50% faster at the X-chromosome. Thus the proposed effect of fluctuating selection on traits limited to the heterogametic sex – preferential involvement of X-chromosomal genes – may contribute to explain Haldane's rule and the role of X-chromosomal genes in causing hybrid sterility.
In conclusion, fluctuating selection on sex-limited characters should lead to differential linkage in the sexes: in the heterogametic sex X-chromosomal genes and in the homogametic sex autosomal genes can be expected to code preferentially for sex-limited traits. This expectation seems to be in accordance with empirical data on the genetics of sex-limited traits. The expected linkage of alleles with sex-limited expression might also contribute to Haldane's rule and especially to the large effect of X-chromosomes in hybrid sterility.
I am grateful to Leif Engqvist, Richard Gomulkiewicz, Thomas Hoffmeister, Bob Holt, Yikweon Jang, Joachim Kurtz, Bernhard Misof and Helge Ritter for discussions and their helpful comments on previous drafts of the manuscript. Special thanks go to Michael Doebeli for his outstanding advice as a reviewer.