Sex-Averaged Recombination and Mutation Rates on the X Chromosome: A Comment on Labuda et al.
2010; Elsevier BV; Volume: 86; Issue: 6 Linguagem: Inglês
10.1016/j.ajhg.2010.03.021
ISSN1537-6605
AutoresKirk E. Lohmueller, Jeremiah D. Degenhardt, Alon Keinan,
Tópico(s)Genetic and Clinical Aspects of Sex Determination and Chromosomal Abnormalities
ResumoTo the Editor: A recent paper by Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar used patterns of linkage disequilibrium (LD) among SNPs from the HapMap data on the X chromosome and the autosomes to estimate the female-to-male breeding ratio in human populations (β=Nf/Nm). This approach was of considerable interest to us because two recent papers2Hammer M.F. Mendez F.L. Cox M.P. Woerner A.E. Wall J.D. Sex-biased evolutionary forces shape genomic patterns of human diversity.PLoS Genet. 2008; 4: e1000202Crossref PubMed Scopus (100) Google Scholar, 3Keinan A. Mullikin J.C. Patterson N. Reich D. Accelerated genetic drift on chromosome X during the human dispersal out of Africa.Nat. Genet. 2009; 41: 66-70Crossref PubMed Scopus (102) Google Scholar using SNP diversity and frequency patterns to study sex-biased demography differed in their conclusion as to whether the effective population size of the X chromosome was larger than expected. A larger than expected effective population size on the X chromosome could be due to a larger female than male effective population size (β>1). Because neither of the previous studies used information contained within LD patterns, the study of Labuda et al.,1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar in principle, could provide independent estimates of β. They find evidence that β is slightly larger than 1 but still smaller than the value reported by Hammer et al.2Hammer M.F. Mendez F.L. Cox M.P. Woerner A.E. Wall J.D. Sex-biased evolutionary forces shape genomic patterns of human diversity.PLoS Genet. 2008; 4: e1000202Crossref PubMed Scopus (100) Google Scholar Thus, Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar concluded that there is little evidence for polygyny, or a larger female than male effective population size, throughout human history. However, errors in their analytical derivations affect most of their analyses, and correction of these errors leads to different conclusions. In deriving Equation 4, Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar state that the sex-averaged recombination rate on the X chromosome, rX, depends on the female-to-male breeding ratio of the population through the expression rX=(2β/(1+2β))rfX, in which rfX is the female recombination rate. However, rX=(2/3)rfX and is independent of β because each offspring is produced from a male-female mating, regardless of the sex ratio in the population. Therefore, because recombination on the X chromosome can occur only in females (rmX=0), only two of the three potentially transmitted X chromosomes can be the product of a recombination event. Deviations from an equal number of breeding males and females in the population will change the relationship between the effective population sizes of the X chromosome (NeX) and the autosomes (NeA), but will not change the fact that each mating will still consist of a single male parent and a single female parent (Figure 1), keeping rX=(2/3)rfX. Thus, the authors' expression essentially double-corrects for unequal male-female population sizes. The correct expression (rX=(2/3)rfX) has been previously derived (reviewed in 4Hedrick P.W. Sex: differences in mutation, recombination, selection, gene flow, and genetic drift.Evolution. 2007; 61: 2750-2771Crossref PubMed Scopus (109) Google Scholar) and has also been used to interpret differences in patterns of genetic variation on the X chromosome and autosomes in Drosophila.5Andolfatto P. Przeworski M. A genome-wide departure from the standard neutral model in natural populations of Drosophila.Genetics. 2000; 156: 257-268PubMed Google Scholar, 6Przeworski M. Wall J.D. Andolfatto P. Recombination and the frequency spectrum in Drosophila melanogaster and Drosophila simulans.Mol. Biol. Evol. 2001; 18: 291-298Crossref PubMed Scopus (42) Google Scholar The expression for the sex-averaged recombination rate on the X chromosome is the same for humans and Drosophila because, in both species, it does not recombine in males. Using the correct equation for rX, Equation 4 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar should readρX=83NeXrfx. Then, it follows that the X chromosome-to-autosome ratio of population recombination rates (Equation 7) should beρXρA=rfXrA2NeX3NeA=rfXrA3(β+1)4(β+2),in which rA is the sex-averaged recombination rate on the autosomes. The ratio of the normalized X chromosome recombination rate to the normalized autosomal recombination rate (R) defined in Equation 8 then becomesR=ρXρArArfX=2NeX3NeA=3(β+1)4(β+2). The breeding ratio as a function of R (captured in Equation 9) isβ=8R−33−4R. Figure 2 shows the population recombination rate ratio (solid blue curve) along with the ratio computed from Equation 8 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar (dotted blue curve). Equation 8 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar underpredicts R when β is low (an excess of breeding males) and overpredicts R when β is high (an excess of breeding females). Given that it appears that the error in the derivations of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar has a substantial impact on R (Figure 2), we reanalyzed the data presented in Table 1 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar from the three HapMap populations. We calculated β from the estimates of R from Labuda et al.,1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar using the corrected version of Equation 9. The corrected Equation 9 results in larger estimates of β than those reported in Table 1 of the original paper1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar (see Table 1 in this paper). For example, in YRI, β=2.63, as compared to 1.42 before correction. In terms of NeX/NeA, the corrected equation gives a ratio of 0.882 in YRI instead of 0.796 reported by Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar These larger estimates of β and NeX/NeA from the HapMap CEU and YRI populations are consistent with the estimates reported in Hammer et al.2Hammer M.F. Mendez F.L. Cox M.P. Woerner A.E. Wall J.D. Sex-biased evolutionary forces shape genomic patterns of human diversity.PLoS Genet. 2008; 4: e1000202Crossref PubMed Scopus (100) Google Scholar and support the claim of an excess of breeding females in human history. Incidentally, although we follow Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar in reporting results in terms of β, we note that NeX/NeA is a more robust statistic and that deriving β from NeX/NeA introduces the restrictive assumptions of discrete nonoverlapping generations and a Poisson distribution of offspring.7Caballero A. On the effective size of populations with separate sexes, with particular reference to sex-linked genes.Genetics. 1995; 139: 1007-1011PubMed Google Scholar, 8Charlesworth B. The effect of life-history and mode of inheritance on neutral genetic variability.Genet. Res. 2001; 77: 153-166Crossref PubMed Scopus (114) Google Scholar, 9Laporte V. Charlesworth B. Effective population size and population subdivision in demographically structured populations.Genetics. 2002; 162: 501-519PubMed Google ScholarTable 1Original and Corrected Estimates of β and NeX/NeA from Table 1 of Labuda et al.ρXaReproduced from Table 1 of Labuda et al.1ρAaReproduced from Table 1 of Labuda et al.1RaReproduced from Table 1 of Labuda et al.1Original βaReproduced from Table 1 of Labuda et al.1Corrected βOriginal NeX/NeAaReproduced from Table 1 of Labuda et al.1Corrected NeX/NeAYRI0.2640.4490.5881.422.630.7960.882CEU0.1360.2370.5741.342.270.7880.861CHB, JPT0.1580.3010.5251.101.330.7630.787a Reproduced from Table 1 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar Open table in a new tab Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar then used their estimates of β from the LD patterns in the HapMap data combined with diversity and divergence levels on the X chromosome and autosomes to estimate the ratio of male germline mutations to female germline mutations (α). The expression that the authors derived for the sex-averaged X chromosome mutation rate (μX) depends on β. For the same reasons described above with regard to rX, μX is independent of β as well. Corrected expressions for Equations A2–A6 of Labuda et al. are presented in Appendix S1, available online. Importantly, when the correct expressions are used, the ratio of X chromosome-to-autosome diversity (ΘX/ΘA) follows a monotonically increasing function of β for all values of α (Figure S1), rather than the complex pattern shown in Figure 2 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar The corrected expressions, corrected estimates of β (Table 1), and the estimates of ΘX/ΘA from Table S2 of Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar provide estimates of α between 4.95 and 22.43. These estimates are higher than those obtained by Labuda et al.,1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar though estimates of α equal to 5 have been previously noted in humans.4Hedrick P.W. Sex: differences in mutation, recombination, selection, gene flow, and genetic drift.Evolution. 2007; 61: 2750-2771Crossref PubMed Scopus (109) Google Scholar, 10Ellegren H. Characteristics, causes and evolutionary consequences of male-biased mutation.Proc. Biol. Sci. 2007; 274: 1-10Crossref PubMed Scopus (121) Google Scholar, 11Makova K.D. Li W.H. Strong male-driven evolution of DNA sequences in humans and apes.Nature. 2002; 416: 624-626Crossref PubMed Scopus (183) Google Scholar The highest estimate of α is from the YRI population, which has the largest estimate of β. The reliability of this estimate is unclear, because ΘX/ΘA may differ across populations3Keinan A. Mullikin J.C. Patterson N. Reich D. Accelerated genetic drift on chromosome X during the human dispersal out of Africa.Nat. Genet. 2009; 41: 66-70Crossref PubMed Scopus (102) Google Scholar and the data used by Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar do not account for this. Furthermore, it is not clear that estimates of β from LD-based summary statistics can be used to obtain reliable estimates of mutational parameters, given that Labuda et al.'s work1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar and previous work12Lohmueller K.E. Bustamante C.D. Clark A.G. Methods for human demographic inference using haplotype patterns from genomewide single-nucleotide polymorphism data.Genetics. 2009; 182: 217-231Crossref PubMed Scopus (44) Google Scholar have shown that complex demography can affect SNP diversity and frequency patterns differently than it affects LD patterns. Labuda et al.1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar also suggested that estimates of α from X chromosome and autosome divergence depend on the sex ratios of the populations involved. However, this is at odds with previous work showing that when ignoring ancestral polymorphism, α can be estimated solely from the X chromosome versus autosome divergence without regard to β.4Hedrick P.W. Sex: differences in mutation, recombination, selection, gene flow, and genetic drift.Evolution. 2007; 61: 2750-2771Crossref PubMed Scopus (109) Google Scholar, 13Graur D. Li W.H. Fundamentals of Molecular Evolution. Sinauer, Sunderland, MA2000Google Scholar, 14Miyata T. Hayashida H. Kuma K. Mitsuyasu K. Yasunaga T. Male-driven molecular evolution: a model and nucleotide sequence analysis.Cold Spring Harb. Symp. Quant. Biol. 1987; 52: 863-867Crossref PubMed Scopus (230) Google Scholar In conclusion, we applaud Labuda et al.'s1Labuda D. Lefebvre J.F. Nadeau P. Roy-Gagnon M.H. Female-to-male breeding ratio in modern humans-an analysis based on historical recombinations.Am. J. Hum. Genet. 2010; 86: 353-363Abstract Full Text Full Text PDF PubMed Scopus (28) Google Scholar use of LD-based summary statistics to distinguish between competing complex demographic models. However, errors in their analytical derivations undermine their conclusion that there is little evidence for larger female than male effective population sizes throughout human history. Instead, when the corrected equations presented here are used, their results from some populations are consistent with a female effective population size roughly twice that of males. We thank Andrew Clark and Rasmus Nielsen for helpful discussions and comments on previous versions of the manuscript. We also thank other members of the Nielsen laboratory for helpful discussions and two anonymous reviewers for helpful comments on the manuscript. K.E.L. was supported by a Ruth Kirschstein National Research Service Award from the National Human Genome Research Institute (F32HG005308). Download .pdf (.07 MB) Help with pdf files Document S1. Supplemental Appendix and One Figure Female-to-Male Breeding Ratio in Modern Humans—an Analysis Based on Historical RecombinationsLabuda et al.The American Journal of Human GeneticsFebruary 25, 2010In BriefWas the past genetic contribution of women and men to the current human population equal? Was polygyny (excess of breeding women) present among hominid lineages? We addressed these questions by measuring the ratio of population recombination rates between the X chromosome and the autosomes, ρX/ρA. The X chromosome recombines only in female meiosis, whereas autosomes undergo crossovers in both sexes; thus, ρX/ρA reflects the female-to-male breeding ratio, β. We estimated β from ρX/ρA inferred from genomic diversity data and calibrated with recombination rates derived from pedigree data. Full-Text PDF Open Archive
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