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Keywords:

  • approximate Bayesian computation;
  • homomorphic sex chromosomes;
  • Hyla;
  • recombination suppression

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Sex chromosomes are expected to evolve suppressed recombination, which leads to degeneration of the Y and heteromorphism between the X and Y. Some sex chromosomes remain homomorphic, however, and the factors that prevent degeneration of the Y in these cases are not well understood. The homomorphic sex chromosomes of the European tree frogs (Hyla spp.) present an interesting paradox. Recombination in males has never been observed in crossing experiments, but molecular data are suggestive of occasional recombination between the X and Y. The hypothesis that these sex chromosomes recombine has not been tested statistically, however, nor has the X-Y recombination rate been estimated. Here, we use approximate Bayesian computation coupled with coalescent simulations of sex chromosomes to quantify X-Y recombination rate from existent data. We find that microsatellite data from H. arborea, H. intermedia and H. molleri support a recombination rate between X and Y that is significantly different from zero. We estimate that rate to be approximately 105 times smaller than that between X chromosomes. Our findings support the notion that very low recombination rate may be sufficient to maintain homomorphism in sex chromosomes.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Recombination determines the fate of sex chromosomes. Suppressed recombination between the X and Y (or Z and W) chromosomes facilitates their divergence, ultimately leading to the degeneration of the Y (or W) (Charlesworth & Charlesworth, 2000). Recombining regions of sex chromosomes, on the other hand, remain homomorphic and show little or no signs of degeneration. In general, sex chromosomes are expected to evolve towards suppression of recombination favoured by the interaction between the sex-determining locus and sex-specific selection on neighbouring genes (reviewed in Otto et al. (2011)). This reduction in recombination and subsequent degeneration can happen rapidly after the origin of the sex chromosome pair (Bachtrog et al., 2008). Many homomorphic sex chromosomes are young [e.g. in medaka (Kondo et al., 2001) and stickleback (Peichel et al., 2004)], and in these cases, there may not yet have been enough time for the X and Y to diverge. Other homomorphic sex chromosomes, however, are old. Some culicid mosquitoes (Rai, 2010), boid snakes (Ohno, 1967) and ratite birds (Janes et al., 2009) show no signs of divergence between the sex chromosomes, even though they are tens to hundreds of millions of years old. In these cases, ongoing recombination is thought to prevent the sex chromosomes from diverging (Janes et al., 2009).

Some sex chromosomes, nonetheless, remain homomorphic even in the apparent absence of recombination. This may be the case of the European tree frogs (Hyla spp.). Crossing experiments have never detected recombination in males (Berset-Brändli et al., 2008). Karyotype studies are not able to distinguish the X and Y (Anderson, 1991), however, despite the fact that this X-Y system is at least 5 million years old (Stöck et al., 2011). Recent molecular data present an unexpected pattern: the X and Y chromosomes within a species seem to be more similar than the X chromosomes or the Y chromosomes from different species (Stöck et al., 2011). This result suggests that the sex chromosomes have recombined since the speciation events, an implication at odds with the lack of recombination observed in male frogs.

A possible solution to this apparent paradox is that the X and Y in fact do recombine occasionally, producing Y chromosomes purged of deleterious mutations. These ‘rejuvenated’ Y chromosomes then sweep through the population, maintaining the homomorphism between the sex chromosomes. One mechanism by which recombination between X and Y might happen is the ‘fountain of youth’ hypothesis (Perrin, 2009). Under this hypothesis, recombination is always suppressed in males, but occasionally sex-reversed XY females appear and produce gametes with recombined sex chromosomes. This idea is supported by evidence for sex reversal in Hyla japonica (Kawamura & Nishioka, 1977) and by data from Rana temporaria showing that recombination depends on an individual's phenotypic, not genetic, sex (Matsuba et al., 2010). Alternatively, it is possible that recombination happens in males at very low rates that have not been detected in laboratory crosses. Simulation results suggest that recombination rates as low as 10−5 could allow the purge of deleterious mutation and maintenance of homomorphy (Grossen et al., 2012). Therefore, even though hundreds of meiosis events have been observed (Berset-Brändli et al., 2008; Stöck et al., 2011), these may not have been enough to detect such low rates.

Regardless of the mechanism by which it may happen, how much X-Y recombination is consistent with the molecular data in Hyla? The available molecular markers can be used to infer X-Y recombination, as they may hold signatures left by this process (Fig. 1). In the absence of genetic exchange, sex chromosomes within species will diverge just as chromosomes from different species do. If recombination has been suppressed since the origin of the sex-determination system, the X and Y within one species are expected to be as diverged as the X in that species and the Y in another species. A different pattern is expected when X and Y recombine. In this case, divergence within species is inhibited and the sex chromosomes within species can be more similar to each other relative to those of closely related species. In Hyla, qualitative patterns consistent with recombination have been found. No rigorous test, however, has been carried out to determine whether there is statistically significant evidence for recombination. If there were, a quantitative estimate for its rate would suggest how much recombination might be sufficient to maintain X-Y homology.

image

Figure 1. The effect of recombination on the gene trees from samples in X and Y chromosomes of two species. In the absence of recombination (left), X and Y start diverging at the origin of the sex-determining region (SDR), whereas gametologs diverge later (at speciation). X-Y recombination (right) inhibits divergence between opposite sex chromosomes, so they appear more similar to each other than to their gametologs from sister species.

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Here, we use a novel approach to infer X-Y recombination from population-genetic data. Our goal is to estimate the rate of X-Y recombination relative to that between X chromosomes in three species of European tree frogs (Hyla arborea, H. intermedia and H. molleri). For these three species, we have samples from seven sex-linked microsatellite markers at known positions in the genetic map of the X chromosome. We analyse these data using approximate Bayesian computation, or ABC (reviewed in Beaumont (2010)). The results provide strong statistical support for the hypothesis that there is recombination between X and Y. We estimate that its rate is about 105 times smaller than between X chromosomes.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Our main interest is to estimate α, the factor by which recombination between X and Y chromosomes is reduced relative to its rate between two X chromosomes. For this purpose, we assume an evolutionary model for the phylogeny, the recombination pattern for the sex chromosomes and the evolution of microsatellite loci. This model includes seven parameters that specify, for example, the X-Y recombination rate, the ages of the speciation events and the microsatellite mutation rates. We then generate a large number of simulations under this model using a large number of parameter values. Next, we determine which of these simulations produce patterns that most closely resemble those seen in the real data. The parameter values used in the best simulations (the 0.1% closest to the data) give us the estimated posterior distributions for all parameters, including (and most importantly) α. We now describe the three components of our approach: the evolutionary model, a brief account of the data and the estimation using ABC.

Evolutionary model

We built a coalescent-based model to simulate the gene trees of neutral sites linked to sex chromosomes in three species with known phylogeny (Fig. 2). These sex chromosomes originated from an autosomal pair in the common ancestor species TY generations ago (i.e. there is no initial X-Y divergence). Two speciation events follow at times T1 and T2, giving rise to the three species. We assume these species do not hybridize [an assumption supported by molecular data (Verardi et al., 2009; Stöck et al., 2012)], and they each have a constant population size N. The chromosomes evolve under the standard neutral model for recombining sex chromosomes (Kirkpatrick et al., 2010). The sex-determining region (SDR) is at an unknown position xSDR on the genetic map of females, and it behaves as a single locus with two alleles (X, Y). For a pair of loci that recombine at a rate r in females (XX), their recombination rate in males (XY) is αr. Our model makes no assumption about the mechanism by which recombination happens, however. It is therefore also possible to think of α as the rate of sex reversal in XY individuals (which would, as females, recombine at rate r). We assume there are no selected sites on the sex chromosomes.

image

Figure 2. Schematic of the assumed coalescent model. Before the origin of the SDR (at TY), the ancestral population is composed of N autosomes. At time TY, a single mutation gives rise to the new Y chromosome, subdividing the population. Two speciation events give origin to our three studied species. Through time, the X and Y chromosomes recombine at a constant rate.

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After the gene tree has been simulated, we simulate the occurrence of mutations along its branches. Mutation rates are locus specific with mean μ and gamma distributed, Γ(aa/μ), where a is the shape parameter. We assume the generalized stepwise mutation model of microsatellites (reviewed in Estoup et al. (2002)), which allows for varying step sizes. In this mutation model, the size of each mutation is a random variable drawn from a geometric distribution. This distribution is described by p, the last parameter in our model. The value of p gives the fraction of mutations that are a single step (e.g. at = 0.78, 78% of mutations are one step, 13% are two steps, etc.), and it ranges from zero to unity. We make the simplifying assumption that mutation rates are equal in males and females.

Data

We used a data set of seven microsatellite markers previously published by Stöck et al. (2011). The samples come from H. arborea (= 49 X and 13 Y), H. intermedia (= 72 X and 24 Y) and H. molleri (= 17 X and 13 Y). The observed distributions of alleles for these microsatellite markers are shown in Fig. 3.

image

Figure 3. Allele frequencies at the sex-linked microsatellite markers. The columns show the seven loci. Frequencies on X chromosomes are the filled bars, and those on Y chromosomes are open bars. The stars denote groups for which all chromosomes have a null allele at the given marker.

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Estimation of α using ABC

The approximate Bayesian computation consists of three steps. First, we produce a large set of simulations under an assumed evolutionary model with parameter values drawn from prior distributions. Second, we use summary statistics to compare the simulations to the observed frog chromosome data. Third, we take those simulations that most closely resemble the data to produce a posterior distribution for the parameters of interest.

Our model has a total of nine parameters: T1, T2, TY, N, xSDR, μ, a, p and our parameter of interest, α. Our prior for T1 is a normal distribution (mean = 2.75 × 106, SD = 106) truncated between 7.5 × 105 and 6 × 106. This distribution is based on the estimated species divergence time and credible interval (Stöck et al., 2011), and assuming 2 years per generation. The prior for TY is a uniform distribution between 1 and 5 × 106 generations before T1 (which we denote as TY ~ U[1, 5 × 106] + T1). Population size is unknown for these species, so we set a wide uninformative prior: log10(N) ~ U[2.5, 5], which corresponds to an exponential distribution truncated at 102.5 (= 316) and 105. The position of the SDR is also unknown, so we allow it to vary uniformly along the consensus genetic map for the X. The prior for the mean mutation rate, μ, is log10(μ) ~ U[−6, −3], and the prior for the shape parameter is a ~ U[8, 15]. These values produce mutation rate distributions similar to those observed in nature (Seyfert et al., 2008).

We set a prior for the relative recombination rate, α, after evaluating the amount of recombination present in a preliminary set of simulations. For this purpose, we executed 106 simulations with log10(α) ~ U[−11, −7] and other priors as described above, and recorded the number of recombination events that happened in each simulation. In this preliminary set, only simulations with α > 2.5 × 10−10 had one or more recombination events, implying that α is effectively zero at about this value. Consequently, we assume the prior for log10(α) ~ U[−10, −2] in the main body of our simulations.

The last two parameters in the model, T2 and p, are treated as fixed values. Experience shows that ABC has difficulty converging as the number of free parameters increases (Beaumont, 2010). Preliminary analyses indicated that T2 and p have little impact on the estimate of α (Supplemental Fig. S1). For this reason, we fix T2 = ½ T1 and = 0.78 [based on estimates of the microsatellite step-size distributions from humans (Dib et al., 1996)].

Our summary statistic for the ABC analyses measures the amount of X-Y divergence within species relative to X-Y between species:

  • display math

where δij is the square of the difference in mean allele length between X of species i and the Y of species j at a given locus. The δij are a natural choice here because their expected values increase linearly with the time since divergence under a simple random walk model for microsatellite evolution. High levels of recombination will slow the divergence of X and Y within species (as in the right-hand side of Fig. 1), leading to values of Dij that approach zero. On the other hand, suppressed recombination allows the X and Y to diverge. If recombination is completely suppressed and the sex chromosomes are very much older than the speciation events, we expect Dij to approach unity. In principle, divergence between the X and Y within species may be greater than between species, making it possible to have Dij > 1.

We can calculate a value of Dij for each locus between each pair of species. With three species and seven markers, it is possible to calculate 21 values. Some loci in some species are null or uninformative, however, which reduces the number of Dij values that we can compute to twelve. We further reduce the number of statistics by using the mean of H. intermedia and H. molleri in their comparison with H. arborea for three markers (5–22, M2 and M3). After these reductions, we have a total of nine Dij summary statistics for our ABC analyses (Fig. 4).

image

Figure 4. Nine observed summary statistics, Dij, from seven microsatellite markers along the sex chromosomes of three Hylid frogs. Small values of Dij reflect lower X-Y divergence within species, indicative of X-Y recombination. The positions (in cM) of each marker on the consensus genetic map for the X chromosomes are shown below the horizontal axis.

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By their very nature, summary statistics discard some of the information in the data. For example, ours discard information about variation at the microsatellite loci within species. Although additional summary statistics could be added, including a large number of summary statistics tends to increase the variance of estimators and introduce bias (Wegmann et al., 2009). We therefore elected to limit ours to Dij statistics, which quantify the key features of the pattern of interest.

We estimated α by the rejection sampling ABC algorithm (Tavare et al., 1997) implemented in the ABCtoolbox software (Wegmann et al., 2010). We used the ABC-REG algorithm described by Wegmann et al. (2009), which executes a post-sampling regression adjustment before estimating the posterior distribution. We simulated a total of 107 runs using parameter values drawn from the priors described above. This number of simulations was chosen after preliminary analyses showed that 5 million runs were adequate to obtain convergence on the posterior distribution of α (Supplemental Fig. S1). We use the nine Dij summary statistics to calculate the Euclidean distance between the simulated and observed data sets and retain the best 104 simulations. From this retained set, we estimate the posterior distribution of α. To validate our model, we inspected the distributions of the Dij statistics in the retained simulations and verify that the observed Dij values for Hyla are within the simulated range (Supplemental Fig. S2).

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Our main interest is in α, the relative recombination rate of X and Y chromosomes. Its posterior distribution is shown in Fig. 5. The mode, median and mean are 4.6 × 10−6, and the 99% highest posterior density interval (HPDI) is [1.1 × 10−7, 1.4 × 10−4] (Fig. 5). This interval does not include the value estimated to be effective zero recombination (2.5 × 10−10); therefore, we conclude that α is significantly different from zero. Using the mode of α, the length of the Y chromosome is approximately 0.0008 cM. This implies that recombination between X and Y will happen about once among 105 individuals. With population sizes smaller than that number, several generations may pass between recombination events.

image

Figure 5. Posterior distribution of α, the relative X-Y recombination rate in three species of Hylid frogs (black curve). The distribution of α in simulations retained for ABC estimation (before post-sampling adjustment) is shown in light grey. The horizontal band represents the 99% highest posterior density interval (HPDI), and the horizontal dashed line indicates the prior distribution. The arrow indicates the point at which X-Y recombination is effectively zero in the simulations (α = 2.5 × 10−10).

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The nine Dij statistics observed in Hyla suggest a pattern of heterogeneous divergence along the chromosome (Fig. 4). Towards the centre of the genetic map, we observe the highest levels of divergence in X and Y within species (showing values of Dij close to and greater than unity). As we move towards the end of the chromosome, we find the lower divergence between X and Y, and the last marker (A-103) has the lowest Dij value. This pattern allows some speculation about the position of the SDR, probably around the 82 cM mark in the X chromosome. It is not surprising that our estimate for xSDR is close to that position (although with very low confidence; Supplemental Table S1, Supplemental Fig. S3).

To confirm the conclusion that α is significantly greater than zero, we carried out one more set of analyses. We first ran 105 simulations fixing α = 0 while leaving the prior distributions for the other parameters unchanged. We took each of these simulations as independent observed data sets and carried out 105 new ABC estimations (as described for our main analysis and reusing the set of 107 simulations for the computation). The purpose is to evaluate how likely is it to obtain a value of α = 4.6 × 10−6 (our estimated mode for Hyla) when in fact there is no X-Y recombination. Given that in only 0.01% of the cases we obtained modes of α > 4.6 × 10−6, we can safely reject the possibility of falsely concluding α > 0 from the observed data.

To assess potential biases in our estimation, we carried out a test of the coverage properties of our posterior estimates (as recommended by Wegmann et al. (2009)). For this purpose, we simulated 1000 data sets drawn from the prior distribution and carried out an ABC estimation for each set (reusing the 107 runs from the main analysis). We then obtain the distribution of posterior quantiles (i.e. the quantile in the posterior distribution where the real value of the parameter lies). If the parameter estimates are not biased, this quantile distribution is expected to be uniform (Wegmann et al., 2009). In the case of α, we did not find any deviations from a uniform distribution (Kolmogorov–Smirnov test, = 0.26), indicating that there is no evidence of bias in our estimate.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

We estimate X-Y recombination in H. arborea, H. intermedia and H. molleri to be significantly greater than zero, confirming the previous suggestion by Stöck et al. (2011). Our analyses, however, imply that recombination events will be difficult to observe directly. We estimate that recombination occurs only in about 1 of 105 XY individuals. The findings further suggest that very low recombination rates might be sufficient to prevent degeneration of the Y and maintain the homomorphism observed in the Hylid sex chromosomes.

The upper bound for the map length of the Y chromosome is 0.025 cM, which is at least an order of magnitude smaller than the recombining regions of sex chromosomes observed in other species (reviewed in Otto et al. (2011)). The pseudo-autosomal region of the mosquito Culex tarsalis, for example, is about 12 cM in heterogametic and 50 cM in homogametic individuals (implying α = 0.24).

Our findings are consistent with the fountain of youth hypothesis, which posits that rare X-Y recombination events in XY sex-reversed individuals rejuvenate the Y chromosome (Perrin, 2009). Our analysis is not, however, a test of that hypothesis. We have evidence for recombination of the Y, but can make no inference about whether that results from sex reversal (as envisioned in the hypothesis) or from some other mechanism.

Although our model assumes that the X and Y are evolving neutrally, it is certain that some form of selection acts at some loci on these chromosomes. Although selection would affect the quantitative estimate, we suggest that our qualitative conclusion that X and Y recombine is robust. In this regard, consider three types of selection that could be at work. The first is background selection, which occurs when deleterious mutations cause a reduction in the effective population size of Y chromosomes and hence lead to a reduction in diversity at neutrally evolving loci (reviewed in Charlesworth (2012)). The neutral diversity expected on the sex chromosomes therefore depends not only on the rate of X-Y recombination, but also on the intensity of background selection and the positions of sites under selection. As these last two quantities are unknown, it is not possible to make clear predictions about how selective forces might change our estimate for the X-Y recombination rate. The changes in neutral diversity, however, should not lead to the observed pattern of similarity between X and Y within each species. Consequently, the conclusion that these chromosomes recombine seems robust to the presence of background selection.

Selective sweeps on the Y driven by positive selection, which are envisioned in the fountain of youth hypothesis, are a second way in which the neutrality assumption in our model might be violated. Sweeps of recombinant Y chromosomes would strongly reduce divergence between X and Y. In this case, a smaller recombination rate than what we estimated would suffice to produce the patterns in the data. Nevertheless, recombination is still needed to explain the basic pattern observed.

Third, these sex chromosomes may carry balanced polymorphisms maintained by sex-specific selection (Kidwell et al., 1977; Rice, 1984; Otto et al., 2011). This type of selection will increase neutral divergence between recombining X and Y chromosomes (M. Kirkpatrick & R.F. Guerrero, unpublished). The result would be to cause our model to underestimate the recombination rate between the X and Y, making our estimate conservative.

It might seem possible to make further quantitative inferences using patterns of neutral diversity observed at the microsatellite loci within each sex chromosome and each species (recall that our summary statistics discard this information.) Berset-Brandli et al. (2007) found that molecular diversities on Y, X and autosomes in H. arborea fall roughly in the ratio 1:3:4. Such ratios are expected for neutrally evolving sex chromosomes that do not recombine. As we have just discussed, however, these chromosomes do recombine and are very likely under some form(s) of selection. Therefore, it seems difficult to draw further quantitative conclusions without additional data.

Several caveats apply to our results. We assume a constant recombination rate for the three species through time. These species, however, have evolved independently for a considerable time and differences in present recombination rates are plausible. This possibility is perhaps not such a concern, given that female genetic maps do not differ between species (Stöck et al., 2011). The X-Y recombination rate could also vary along the chromosome, through chromosomal inversions or other local recombination modifiers. The data available, though, do not provide us with enough power to implement more complex models.

Our results suggest the possibility that very low rates of recombination suffice to prevent the Y chromosome from degenerating. Grossen et al. (2012) used simulations to study the purging of deleterious mutations on the Y by occasional recombination events with the X, and how this process might prevent the X and Y from diverging. They found that recombination rates on the order of 10−4 (or smaller, depending on the population size) are enough to keep sex chromosomes homomorphic. Intriguingly, this value is not too far from what we estimate. It is impossible to make direct comparisons between our results and that model, however, because they are based on such different assumptions. The question of how much recombination is adequate to maintain homomorphic sex chromosomes certainly warrants further study.

The current data paint but a coarse picture of the evolution of the whole sex chromosome. It is possible that strong background selection is acting on the Y chromosome and that genes under sex-specific selection have accumulated in this region. These two forces combined set the stage for the fountain of youth hypothesis, the mechanism that could be responsible for the ongoing X-Y recombination we observe. To explore these possibilities and expand on the simple model presented here, however, it is necessary to obtain genomic data along with complementary approaches that inform us about the function of genes that reside on the sex chromosomes.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

We thank two anonymous reviewers for helpful comments on the manuscript. We are grateful for funding from the US National Science Foundation (grant DEB-0819901 to MK) and from the Swiss National Science Foundation (grant 31003A-129894 to NP).

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References
  9. Supporting Information

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

FilenameFormatSizeDescription
jeb2591-sup-0001-FigS1-S3-TableS1.pdfapplication/PDF257KFigure S1 Effect of the age of one speciation node, T2 (left), and the p parameter (right) on the posterior distribution for α estimated by ABC. Figure S2 Distributions of Dij summary statistics in the simulations retained for ABC. Figure S3 Histograms for nuisance parameter values from simulations retained in ABC. Table S1 Posterior characteristics of seven parameters estimated by ABC.

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