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In sharp contrast with mammals and birds, many cold-blooded vertebrates present homomorphic sex chromosomes. Empirical evidence supports a role for frequent turnovers, which replace nonrecombining sex chromosomes before they have time to decay. Three main mechanisms have been proposed for such turnovers, relying either on neutral processes, sex-ratio selection, or intrinsic benefits of the new sex-determining genes (due, e.g., to linkage with sexually antagonistic mutations). Here, we suggest an additional mechanism, arising from the load of deleterious mutations that accumulate on nonrecombining sex chromosomes. In the absence of dosage compensation, this load should progressively lower survival rate in the heterogametic sex. Turnovers should occur when this cost outweighs the benefits gained from any sexually antagonistic genes carried by the nonrecombining sex chromosome. We use individual-based simulations of a Muller's ratchet process to test this prediction, and investigate how the relevant parameters (effective population size, strength and dominance of deleterious mutations, size of nonrecombining segment, and strength of sexually antagonistic selection) are expected to affect the rate of turnovers.
According to dominant models of sex-chromosome evolution, the first step in the life of a sex chromosome is taken when an autosomal mutation seizes a leading role in the sex-determining (SD) cascade, such that heterozygotes develop into one sex, and homozygotes into the other (Ohno 1967; Charlesworth et al. 2005). In a second step, sexually antagonistic mutations are expected to accumulate in the vicinity of this gene, benefitting from linkage disequilibrium (Bull 1983; Rice 1996). Arrest of recombination in the heterogametic sex should then amplify the benefits of epistatic interactions between the SD and sexually antagonistic genes. When sex chromosomes evolve from hermaphroditism, two mutations are required (one to suppress the male function, the other to suppress the female function), so that recombination arrest is also selected to prevent the production of neuter individuals (Charlesworth et al. 2005).
As a side effect of recombination arrest, however, all other genes that happen to be trapped in the nonrecombining segment will start to accumulate deleterious mutations, under the combined forces of enhanced drift, background selection, selective sweeps, and Muller's ratchet (i.e., the random loss, through genetic drift, of the haplotypic classes that display the fewest mutations; Muller 1964; Nei 1970; Charlesworth and Charlesworth 2000).
However, in striking contrast with the sex chromosomes of most birds and mammals, those of most cold-blooded vertebrates are homomorphic. Heteromorphism has been documented in only 4% of amphibians investigated so far (Schmid 1991; Eggert 2004). Similar low proportions are found in fish (Devlin and Nagahama 2002). Even recognizing that chromosomes considered as homomorphic by classical cytogenetic methods may show some differentiation when applying more refined techniques such as FISH (e.g., Ross & Peichel 2008), the contrast with warm-blooded vertebrates is striking.
One reason often invoked for this lack of degeneration is a high rate of turnover, during which new SD mutations regularly appear, replacing established sex chromosomes before they have time to degenerate (Volff et al. 2007). Several lineages of fishes seem to have undergone rapid turnover (i.e., high rate of transitions; Mank et al. 2006; Volff et al. 2007; Mank and Avise 2009). All Salmonidae are male heterogametic, but sex is determined by different linkage groups depending on species (Phillips et al. 2001; Woram et al. 2003). Gasterosteidae also experienced nonhomologous transitions (sensu van Doorn and Kirkpatrick 2010; i.e., acquiring new sex-chromosome pairs), sometimes changing the heterogametic sex (Ross et al. 2009). Among Cichlidae, sex determination is associated with at least four different linkage groups: In Tilapiinae, a male-heterogametic system (XY) on LG1 coexists with a female-heterogametic system (ZW) on LG3 (Lee et al. 2004; Cnaani et al. 2008), whereas in Haplochrominae, a male-heterogametic system (XY) on LG7 coexists with a female-heterogametic system (ZW) on LG5 (e.g., Ser et al. 2010). Multiple alleles (X, Y, and W) may also segregate at the same locus, such as found in the Poecilid Xiphophorus maculatus (Kallman 1968). Similar variety exists in reptiles and amphibians (Ezaz et al. 2006). Most Rana frogs are male heterogametic, but sex is determined by different linkage groups in different species or populations (Miura 2007). In Rana rugosa, the same sex-chromosome pair can form either an XY or a ZW system in different populations (heterogametic homologous transition; Miura 2007; Ogata et al. 2008). All of these groups show more sex-chromosome diversity than mammals, despite being much younger: Gasterosteidae, for instance, date back to approximately 20 million years ago (Ross et al. 2009), as compared to 170 million years ago for the mammalian Sry.
Three main hypotheses have been proposed to explain such transitions. The first relies on neutral processes. Different sets of recurrent pairs (sensu Bull and Charnov 1977; Bull 1983; i.e., pairs of genotypes that produce only the same two genotypes when crossed; e.g., XX/XY or WY/YY) are connected by continuous paths of neutral equilibria, consisting of all mixes of genotypes (WX, WY, XX, XY, and YY) that produce even sex ratios in the population (although not necessarily in individual families). Transitions between recurrent pairs may thus occur along such paths just by genetic drift (Scudo 1967; Bull and Charnov 1977).
The third type of hypothesis invokes a fitness advantage for one of the new sex genotypes (Bull and Charnov 1977). A feminizing mutation W, for instance, might invade an XX/XY system if it confers intrinsic benefits on XW females. Transitions will go to completion if the favored genotype is part of an alternative recurrent pair; otherwise, a stable polymorphism is expected, such as the one observed in X. maculatus (Bull and Charnov 1977). Benefits might arise either from pleiotropic effects of the SD locus itself, or, more likely, from linkage disequilibrium with a beneficial mutation. Note that transitions may still occur if the mutation has sexually antagonistic effects, provided the benefits to one sex exceed the costs to the other (van Doorn and Kirkpatrick 2007). Outcomes thus also depend on the recombination rate between the SD and sexually antagonistic genes (van Doorn and Kirkpatrick 2007; Blaser et al. 2011). Such a process has been documented in Cichlidae, where a new ZW system recently invaded an initial XY system, via a mutation on the proto W chromosome conferring a blotched pattern of coloration (nonhomologous heterogametic transition). This mutation is beneficial to females because it confers a cryptic phenotype, but costly to males because it disrupts mating coloration (Roberts et al. 2009).
In the present paper, we propose an additional mechanism for sex-chromosome turnovers. As noted above, deleterious mutations are expected to accumulate on the heterogametic chromosome (Y or W), as a side effect of lack of recombination induced by Y- or W-linked sexually antagonistic genes. This should result in the progressive loss of function of genes in the nonrecombining SD region. In the absence of dosage compensation, this accumulating load will progressively affect some fitness components in the heterogametic sex (e.g., lower its survival to maturity). Turnovers should thus be favored once the fitness loss exceeds the benefits stemming from sexually antagonistic genes established in the nonrecombining region. This mechanism differs from the other selective models outlined above in that it does not rely on new beneficial mutations arising on autosomes (such as sexually antagonistic genes driving turnover; van Doorn and Kirkpatrick 2007, 2010), but emerges as the necessary consequence of the deleterious load accumulating on degenerating sex chromosomes, via Muller's ratchet or other mechanisms.
Outline of the Argument
We consider a male-heterogametic system in which sex chromosomes carry both a SD locus (with subscripts X or Y denoting the different alleles), and a sexually antagonistic locus, where alleles beneficial to one sex are detrimental to the other. Both loci are on a segment that does not recombine in males. This segment can be very short and contain only a few genes. The chromosomes carrying the X and Y allele will be referred to as X and Y chromosomes, respectively. This association between SD and sexually antagonistic genes might be illustrated by the system found in several teleost fishes (Aida 1921; Kallman 1970; Endler 1980; Houde 1992; Kingston et al. 2003), where coloration genes cosegregate with sex. We assume a dominant bright allele A to be fixed on the Y chromosome, such that males (XaYA) are colored, whereas females (XaXa) are cryptic, and recombination to be suppressed in males because sexual selection (via female mate choice) counter-selects dull males, whereas natural selection (via visual predators) counter-selects bright females. Following recombination arrest, deleterious mutations accumulate on the YA.
In addition, we consider an autosomal locus involved in the sex-determination cascade. At the start, all individuals are assumed to have the same allele m, which, however, can mutate to a masculinizing form M. The fitness of XaXamm females and XaYAmm males is given by
where and measure the survival to maturity of XaXa females and XaYA males respectively, b measures female fecundity, and q is male mating success. In our model, survival is function of the deleterious mutations accumulated in the genome, and is thus lower in XaYA males than in XaXa females because of the mutation load fixed in the nonrecombining part of the YA.
The male mating success, on the other hand, is affected by the sexually antagonistic genes tightly linked to the SD locus, which selects against Ya haplotypes. As long as m is fixed, the expected mating success of an XaYA male is given by the number of females per male:
Substituting (2) in (1b) shows that, whatever sex-specific survival, males and females have equal fitness (so that the 1:1 sex ratio is evolutionarily stable):
In this context, a rare mutant male XaXamM would benefit from higher survival to maturity (), but suffer from lower mating success, due to the absence of the bright allele. Assuming that mating success is thereby diminished by a proportion c (with ), the fitness of a rare mutant can be written as
Comparing (4) to (1b) directly shows that this mutant can spread as soon as
In other words, a turnover may occur once the decreased mating success (caused by the absence of the bright allele) is compensated by the increased survival.
Note that our argument is framed in terms of natural and sexual selection purely to illustrate our purpose and link it to our simulations. In more general terms, turnovers should occur whenever the new sex-determination system increases male fitness (i.e., ). Before M appears, the XX genotype has been evolving only in females. Expressing it in males could reduce fitness independent of sexual selection (for example by affecting sperm mobility or viability), which would stabilize the old sex chromosomes.
Simulations were performed to validate the suggestion above, and investigate the dynamics of sex-chromosome transitions driven solely by Muller's ratchet. The genomic model assumed an established sex chromosome and an autosome. The nonrecombining part of the sex chromosome comprised a SD locus with two alleles X and Y (such that, in absence of any masculinizing mutation on the autosome, XX homozygotes developed into females and XY heterozygotes into males), and a sexually antagonistic locus with a female-beneficial allele a fixed on the X chromosome (e.g., an allele for dull coloration) and a male-advantageous allele A fixed on the Y chromosome (such that males lacking A would have a mating success reduced by a proportion c). In addition, we assumed that the nonrecombining segment included 10 evenly spaced functional genes, mutating to a deleterious form at rate μ= 10−4 per generation, such that the survival of homozygotes was decreased by s, and that of heterozygotes by hs. Effects on survival were assumed to be multiplicative, so that
where ns and nhs are, respectively, the numbers of loci homozygous and heterozygous for the deleterious mutations. This segment recombined only in females, with a distance between functional genes arbitrarily set to 10 cM.
The autosome also included one locus involved in the sex-determination cascade, with an initial allele m potentially mutating (with probability 10−5) to a masculinizing allele M (such that XXmM would develop into males), and 10 functional genes regularly dispersed across the chromosome, and mutating at rate μ= 10−4 to deleterious alleles. Individual-based simulations were run with a modified version of quantiNemo 1.0.3 (Neuenschwander et al. 2008; see Appendix 1 for details; data regarding input files are deposited in the Dryad repository: http://dx.doi.org/10.5061/dryad.pk14p).
We varied independently the selection coefficient s (values 0.001, 0.0025, 0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.15, and 0.2) and the dominance coefficient h (values 0.0, 0.1, 0.15, 0.25, 0.5, 0.75, and 1.0). All males were initially XaYAmm, and all females XaXamm, and all functional genes initially had the wild type (nondeleterious) allele. In a first set of simulations, the autosomal m allele was not allowed to mutate, to investigate the dynamics of accumulation of deleterious mutations over the time horizon implemented (105 generations).
In a second set of simulations, we allowed m→M mutation, to investigate the dynamics of turnover under different values of the mating-success parameter c for XaXamM males (c= 0, 0.005, and 0.02, respectively). The effective population size was set at Ne= 103 for most simulations, but we also tested other values (Ne= 102 and 104) for c= 0.005, to evaluate the effect of drift on the accumulation of deleterious mutations and thus on the invasion probability of the masculinization factor M. For the same parameter values (Ne= 103, c= 0.005), we also tested the effects of increasing the nonrecombining segment to 100 loci (each separated by 10 cM on the female map), as well as adding some male recombination, on the accumulation of deleterious mutations and the invasion probability of the M factor. The latter was done by varying genetic linkage between functional genes in males (respectively 0.001, 0.01, and 0.1 cM), while keeping this distance to 10 cM in females.
In the absence of masculinizing mutation and turnover events (first set of simulations), the fate of deleterious mutations depends on the selection and dominance coefficients, accumulating at low hs values, but being eliminated at high hs values (Figs. 1, S1). The shift between these two outcomes occurs at much higher hs values for the Y chromosome than for the X or the autosome (Fig. S1), due to lower Y effective size and its absence of recombination. For the Y chromosome, over all s and h values tested, this shift happened at hs ranging 10−3 to 10−2 (Fig. 1), which amounts to Nehs between 1 and 10, given the effective size assumed (Ne= 103).
In the second set of simulations, the autosomal m allele was allowed to mutate to a masculinizing factor M, and thus potentially to induce turnovers. The proportion of simulations in which turnovers occurred before T= 105 (Fig. 2), and the time taken for turnovers (Fig. S2), varied with the intensity of selection against deleterious mutations on the Y (hs) and the strength of sexually antagonistic selection (c). At low c values (little gain from male-benefitting alleles on the Y), turnovers were frequent under a large range of hs values, and occurred rapidly (Figs. 2, S2). For larger c values (e.g., c= 0.02), turnovers occurred later, less frequently, and at hs values ranging from 10−3 to 10−2 (Figs. 2, S2). Accordingly, the load of deleterious mutations accumulated on the Y at the time of turnover also increased with c (Fig. S3). As predicted by equation (5), turnovers occurred when the fitness of the XaXamM males reached that of XaYAmm males. For instance, at c= 0.02 and hs= 0.0025 (= 10−2.6), turnovers occurred when eight genes on the Y (out of 10) had fixed a deleterious allele (Fig. S3). At this point, the fitness of XaXamM males (1 –c= 0.98) was the same as that of XaYAmm males ((1 – 0.0025)8= 0.98; see also Fig. S4, which illustrates one simulation outcome). No turnovers occurred when c= 0.1 (results not shown), because the cost of deleterious mutations accumulating in 10 genes could not exceed the 10% decrease in mating-success caused by the loss of A.
As expected, purifying selection was more efficient in larger populations (Fig. S5), so that turnovers were less frequent (Fig. S6), occurred later (Fig. S7), and at lower hs values (Figs. S6, S7). Not only did mutations accumulate much faster with lower effective population sizes, but the dynamics were qualitatively different, due to the complex interplay between X and Y chromosomes: Slightly deleterious mutations (hs < 10−3), for instance, also accumulated on the X at small population size (Ne= 100), which in turn induced some purging of deleterious mutations from the Y (Fig. S5).
Assuming a larger nonrecombining segment (100 loci) strongly increased the deleterious load, so that turnovers also occurred with high probability (Fig. S6) and rapidly (Fig. S7) at Ne= 104 for hs values < 10−2. In contrast, very low X–Y recombination rates in males (0.001 cM) were enough to drastically narrow down the range of hs values at which turnovers occurred (without affecting the hs value maximizing turnover probability; Fig. S8). Turnover probability further decreased with increased recombination rate (0.01 cM), vanishing as distance reached 0.1 cM (Fig. S8).
By interfering with the normal expression of genetic networks, such loss-of-function mutations are expected to impact negatively the fitness of the heterogametic sex (Prestel et al. 2010). Muller's ratchet alone has the potential to lower male fitness by several orders of magnitude (e.g., Gordo and Charlesworth 2000b).
HOW TO COPE WITH A DEGENERATING Y?
There are several ways of coping with such potentially deleterious effects. One (as proposed in the present paper, and supported by our simulations) is to get rid of the decaying chromosome (via a sex-chromosome turnover) when the costs of loss-of-function mutations exceed the benefits of nonrecombination. A second one is to allow some X–Y recombination to recurrently purge the Y from its accumulating load (Perrin 2009; Stöck et al. 2011; Grossen et al. 2012; Guerrero et al. 2012). As our simulations also show (Fig. S8), very low X–Y recombination rates are enough to prevent mutation accumulation, and thereby sex-chromosome turnover. Rare sex reversal events (and ensuing X–Y recombination in XY females), occurring, for example, as a side consequence of temperature effects on sex determination, might thus suffice to prevent turnovers mediated by the present mechanism. We recall, however, that our present model assumes recombination to be arrested on a chromosomal segment only, which might be very small. Any inversion on the Y would result in complete but local arrest of recombination, inducing the decay of genes trapped in the inversion. As our simulations show, nonrecombining segments comprising as few as 10 genes may suffice to initiate a turnover.
A third alternative is to accommodate for these losses of function via dosage compensation or similar mechanisms (e.g., Marin et al. 2000). A few lineages did so, including Drosophila, C. elegans, and most mammals. As a consequence, the degenerated sex chromosome has no apparent effect on the fitness of the heterogametic sex (males in these cases). It is worth noting that dosage compensation evolved independently in all three groups, relying on different mechanisms: Upregulation of the single X in Drosophila males, inactivation of one X in female mammals, downregulation of both Xs in C. elegans hermaphrodites. The very fact that such a range of sophisticated mechanisms evolved several times independently underlines the strong selective pressure imposed by these loss-of-function mutations. The taxonomic distribution of dosage compensation and its modalities are still debated, but it may not be widespread (Mank et al. 2011). In vertebrates, there is no evidence for global dosage compensation outside mammals. In birds, compensation varies by tissue and ontogenetically (Mank and Ellegren 2009), occurring on a gene-by-gene basis, when and where balanced transcription is needed (Mank et al. 2011). It seems absent from stickelbacks (Leder et al. 2010).
Another situation in which our hypothesized process may fail to act is when genes are protected against loss. The few genes left on mammalian Y chromosomes, which are mostly involved in testis differentiation and spermatogenesis (e.g., Paria et al. 2011), have no X homolog, and seem to be essential for normal male development (XX males are sterile in humans; Page et al. 1985). They are furthermore protected against loss by YY gene conversion between palindromic sequences (e.g., Rozen et al. 2003; Skaletsky et al. 2003; Marais et al. 2010). Despite this, turnovers have occurred in some mammalian lineages (Fredga 1988; Hoekstra and Edwards 2000; Bianchi 2002; Ortiz et al. 2009; Veyrunes et al. 2010). Overall, however, the situation investigated here seems more likely to apply to fish, amphibians, and reptiles, all lineages in which turnovers appear to be more frequent than in mammals.
Nehs CONDITIONS FAVORING Y DEGENERATION AND TURNOVERS
In addition to effective population size Ne, accumulation also depends on selection and dominance coefficients: Strongly deleterious mutations are more likely to be eliminated, so that increasing hs values induce a shift from a regime of accumulation to one of elimination (Crow and Kimura 1970; Gordo and Charlesworth 2000a). Due to the aforementioned drop in effective population size induced by recombination arrest, the shift occurs at much higher hs values on the Y than on the X or autosomes (Fig. S1).
This shift actually occurs at the hs values that have the highest impact on fitness, and thus provide the highest incentives for turnovers (Fig. 2). Strongly deleterious mutations (high hs values) are eliminated, whereas slightly deleterious ones (very low hs values) have little impact on fitness, despite accumulation. The strongest impact is thus expected from mildly deleterious mutations (Kimura et al. 1963; Pamilo et al. 1987; Lynch and Gabriel 1990; Charlesworth et al. 1993a,b; Gabriel et al. 1993; Lande 1994). In line with these expectations, we found that turnover rate was maximal for hs values ranging from 10−3 to 10−2 (i.e., Nehs: 1–10; Fig. 2). Larger effect mutations (hs > 10−2) were eliminated from the Y (Figs. 1, S1), whereas smaller effect mutations (hs < 10−3) were not deleterious enough to outweigh the benefits of sexually antagonistic genes. In addition, small-effect mutations also accumulated on the X and the autosome (Fig. S1), suppressing selection for turnovers. Assuming codominance (h= 0.5), Lande (1994) analytically showed that the strongest impact of autosomal deleterious mutations is expected at . Given that we are dealing with Y haplotypes (with effective sizes one quarter of autosomal genes), the relationship becomes , a very good fit with our simulations, because, for Ne= 103, the minimum turnover time occurred at (= 10−2.8; Fig. S2).
Effective population sizes also vary widely, from 102 in some vertebrates to 106 or more in Drosophila. It is worth recalling that effective population sizes are often much smaller than census sizes, up to three to five orders of magnitude (e.g., Turner et al. 2002; Hoarau et al. 2005; Gomez-Uchida and Banks 2006). The New Zealand snapper Pagrus auratus, for instance, has a census size of approximately 3 millions, but an Ne of approximately 180; Hauser et al. 2002). The values implemented here (Ne= 102 to 104) fit well within the range documented for many vertebrates: The effective population sizes of fishes and amphibians are commonly below 50, and rarely exceed a few thousands (e.g., Jorde and Ryan 1996; Miller & Kapuchinski 1997; Phillipsen et al. 2011). Thus, Nehs values that facilitate the accumulation of mutations on the Y (1 < Nehs < 10), potentially triggering turnovers, might arise in a large number of vertebrate species.
What about species with larger effective population sizes? With 10 functional loci mutating at rate μ= 10−4, accumulation seems insufficient to induce turnovers at Ne= 104 (Fig. S6c). However, although Muller's ratchet is mostly efficient at low effective population size, it can still significantly affect the accumulation process at larger sizes (in the order of hundreds of thousands), assuming larger (but realistic) mutation rates (Gordo and Charlesworth 2000a,b). The speed and cost of accumulation is actually expected to increase drastically with the size of the nonrecombining segment, due to the increased total rate of mutations and the potential to accumulate a larger load. Accordingly, turnovers occurred with high probabilities at Ne= 104 when the nonrecombining segment encompassed 100 loci (Fig. S6d). This is still a very low and conservative value: In D. melanogaster and C. elegans, the X is home to approximately 15% of the total number of genes.
Whether turnovers occur in our model also depends on c, the cost of having a new SD chromosome lacking male-beneficial alleles. Such costs are difficult to estimate. Sexual selection is known to be strong in sexually dimorphic fish (Endler 1980; Houde 1992; Brooks and Endler 2001; Lindholm and Breden 2002; Kingston et al. 2003), hence the mating success of noncolored males is expected to be much lowered (Bakker 1993; Maan et al. 2004; Maan et al. 2006; Roberts et al. 2009). In our simulations, turnover rates rapidly decreased as c increased, and did not occur for c values in the order of 10%, which may seem surprisingly low. However, the same comment applies as above regarding the number of functional genes implemented in our simulations: Larger nonrecombining segments are expected to boost selective pressure for turnovers.
Our simulations were clearly not aimed at providing quantitative predictions on turnover rates (which are bound to depend on many parameters that are difficult to estimate empirically, including the effective population size, the length of the nonrecombining segment, or the strength of sex antagonistic effects), but essentially at evaluating whether the accumulating deleterious load indeed provides a plausible mechanism to induce turnovers, and at generating qualitative insights on the process. Nevertheless, our model makes specific predictions that should be amenable to empirical tests. First, if the present mechanism plays a significant role (i.e., transitions are regularly driven by the deleterious mutations accumulating on Y chromosomes), then heterogametic transitions should be disfavored, because they lead to the fixation of Y chromosomes (van Doorn & Kirkpatrick 2010). We should therefore expect a strong bias in favor of homogametic transitions (i.e., XY is more likely to turn into another XY, and ZW into ZW, than expected by chance or under alternative scenarios for turnovers).
Second, we expect faster genetic degeneration in male-heterogametic (XY) than in female-heterogametic (ZW) systems, because mutation rates are often higher in males (due to higher numbers of germ line cell divisions; Kirkpatrick and Hall 2004), and because Y chromosomes have lower effective population sizes than W chromosomes (due to higher variance in male reproductive success; Anderssson 1994; Shuster and Wade 2003). In addition, sexual selection is stronger in males than in females, inducing more selective sweeps on Y than on W chromosomes, which can also contribute to genetic degeneration (although strong sexual selection might also cause high c values, if sexual dimorphism results from sex-linked sexually antagonistic genes, rather than from sex-limited autosomal genes). Overall, therefore, we expect more frequent turnovers in male-heterogametic than in female-heterogametic systems.
It would be interesting to test the present model by checking empirically whether transitions indeed affect heterogamety patterns less frequently than expected by chance, and occur more frequently in XY than in ZW systems, provided suitable taxa can be identified (fishes and amphibians seeming a priori to be good candidates).
Associate Editor: L. Moyle
We are grateful to M. Kirkpatrick, S. van Doorn, and an anonymous reviewer for useful discussions and comments on the manuscript, and acknowledge support from the Swiss National Science Foundation (grants 31003A-129894 to NP and 3100A0–138180/1 to Jérôme Goudet) and from the Faculty of Biology and Medicine of the University of Lausanne (Ph.D. fellowship to CG).
IMPLEMENTATION DETAILS FOR SIMULATIONS
Individual-based simulations were run with quantiNemo 1.0.3 (Neuenschwander et al. 2008), with modifications as described in Grossen et al. 2011). We used a simple life cycle with nonoverlapping generations. For each of the Ne offspring, a father and a mother were drawn randomly with replacement (mimicking a promiscuous mating system), with a probability proportional to their individual fitness. For a female, fitness was only affected by survival probability, determined by her genotype at the functional loci (eq. 6). For a male, survival was also weighted by his expected mating success (1 for XaYA males, 1 – c for XaXa males). Because population sizes were kept stable, the realized fitness averaged one for both males and females (i.e., selection was soft). Baring mutations, alleles at all loci were inherited randomly (offspring sex being determined by the allele received from its father at the SD locus), with a fixed probability of recombination r between loci on the same chromosome. All simulations were run over 100,000 generations and each simulation set was repeated 50 times to get average results.