Genome Partitioning of Genetic Variation for Height from 11,214 Sibling Pairs
2007; Elsevier BV; Volume: 81; Issue: 5 Linguagem: Inglês
10.1086/522934
ISSN1537-6605
AutoresPeter M. Visscher, Stuart MacGregor, Beben Benyamin, Gu Zhu, Scott D. Gordon, Sarah E. Medland, William G. Hill, Jouke‐Jan Hottenga, Gonneke Willemsen, Dorret I. Boomsma, Yaozhong Liu, Hong‐Wen Deng, Grant W. Montgomery, Nicholas G. Martin,
Tópico(s)Genetic Associations and Epidemiology
ResumoHeight has been used for more than a century as a model by which to understand quantitative genetic variation in humans. We report that the entire genome appears to contribute to its additive genetic variance. We used genotypes and phenotypes of 11,214 sibling pairs from three countries to partition additive genetic variance across the genome. Using genome scans to estimate the proportion of the genomes of each chromosome from siblings that were identical by descent, we estimated the heritability of height contributed by each of the 22 autosomes and the X chromosome. We show that additive genetic variance is spread across multiple chromosomes and that at least six chromosomes (i.e., 3, 4, 8, 15, 17, and 18) are responsible for the observed variation. Indeed, the data are not inconsistent with a uniform spread of trait loci throughout the genome. Our estimate of the variance explained by a chromosome is correlated with the number of times suggestive or significant linkage with height has been reported for that chromosome. Variance due to dominance was not significant but was difficult to assess because of the high sampling correlation between additive and dominance components. Results were consistent with the absence of any large between-chromosome epistatic effects. Notwithstanding the proposed architecture of complex traits that involves widespread gene-gene and gene-environment interactions, our results suggest that variation in height in humans can be explained by many loci distributed over all autosomes, with an additive mode of gene action. Height has been used for more than a century as a model by which to understand quantitative genetic variation in humans. We report that the entire genome appears to contribute to its additive genetic variance. We used genotypes and phenotypes of 11,214 sibling pairs from three countries to partition additive genetic variance across the genome. Using genome scans to estimate the proportion of the genomes of each chromosome from siblings that were identical by descent, we estimated the heritability of height contributed by each of the 22 autosomes and the X chromosome. We show that additive genetic variance is spread across multiple chromosomes and that at least six chromosomes (i.e., 3, 4, 8, 15, 17, and 18) are responsible for the observed variation. Indeed, the data are not inconsistent with a uniform spread of trait loci throughout the genome. Our estimate of the variance explained by a chromosome is correlated with the number of times suggestive or significant linkage with height has been reported for that chromosome. Variance due to dominance was not significant but was difficult to assess because of the high sampling correlation between additive and dominance components. Results were consistent with the absence of any large between-chromosome epistatic effects. Notwithstanding the proposed architecture of complex traits that involves widespread gene-gene and gene-environment interactions, our results suggest that variation in height in humans can be explained by many loci distributed over all autosomes, with an additive mode of gene action. Research into the genetics of complex traits has moved from the estimation of genetic variance in populations to the detection and identification of variants that are associated with or directly cause variation. The standard paradigm has been to perform linkage studies in pedigrees, followed by fine-mapping or candidate-gene studies with the use of association. Recently, genomewide association (GWA) studies, which rely on linkage disequilibrium between observed and causal variants, have become a reality—in particular, for the study of common disease in human populations.1The Wellcome Trust Case Control Consortium Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls.Nature. 2007; 447: 661-678Crossref PubMed Scopus (7335) Google Scholar, 2Duerr RH Taylor KD Brant SR Rioux JD Silverberg MS Daly MJ Steinhart AH Abraham C Regueiro M Griffiths A et al.A genome-wide association study identifies IL23R as an inflammatory bowel disease gene.Science. 2006; 314: 1461-1463Crossref PubMed Scopus (2315) Google Scholar, 3Hampe J Franke A Rosenstiel P Till A Teuber M Huse K Albrecht M Mayr G De La Vega FM Briggs J et al.A genome-wide association scan of nonsynonymous SNPs identifies a susceptibility variant for Crohn disease in ATG16L1.Nat Genet. 2007; 39: 207-211Crossref PubMed Scopus (1444) Google Scholar, 4Smyth DJ Cooper JD Bailey R Field S Burren O Smink LJ Guja C Ionescu-Tirgoviste C Widmer B Dunger DB et al.A genome-wide association study of nonsynonymous SNPs identifies a type 1 diabetes locus in the interferon-induced helicase (IFIH1) region.Nat Genet. 2006; 38: 617-619Crossref PubMed Scopus (511) Google Scholar The success of both linkage and association studies depends on the frequency and distribution of individual gene effects in the population. Rare variants with large effects can most readily be mapped in pedigrees, whereas common variants with moderate effects can be mapped using an association study. Multiple rare variants in the same gene, each with a moderate effect on the phenotype, can be detected using linkage studies but would be hard to find in an association study. Despite the large research effort in the past decade or so, the nature of complex-trait variation—in terms of the number of causal variants, their frequency in the population, and the size of their effects—is still largely unknown.5Barton NH Keightley PD Understanding quantitative genetic variation.Nat Rev Genet. 2002; 3: 11-21Crossref PubMed Scopus (492) Google Scholar Emerging evidence suggests that there are common variants with effects large enough to be detected for a range of phenotypes across a number of species, but the number of identified causal variants remains small.6Glazier AM Nadeau JH Aitman TJ Finding genes that underlie complex traits.Science. 2002; 298: 2345-2349Crossref PubMed Scopus (667) Google Scholar, 7Korstanje R Paigen B From QTL to gene: the harvest begins.Nat Genet. 2002; 31: 235-236Crossref PubMed Scopus (190) Google Scholar Other evidence suggests that multiple rare variants in the same gene may segregate in the population, each with an effect large enough to increase susceptibility to disease.8Cohen JC Kiss RS Pertsemlidis A Marcel YL McPherson R Hobbs HH Multiple rare alleles contribute to low plasma levels of HDL cholesterol.Science. 2004; 305: 869-872Crossref PubMed Scopus (874) Google Scholar In human populations, there has frequently been inconsistency of linkage to disease and quantitative phenotypes across multiple samples and populations, with few examples of clear-cut replication. One possible explanation is that, for most phenotypes, the effects of causal variants are too small to be detected by linkage—that is, that most studies have been underpowered. Association analyses are much more powerful for detecting small effects but, again, are dependent on the actual distribution of effect sizes. Recent reports of associated and replicated SNPs from GWA studies show that the effect sizes of individual common variants are typically small.1The Wellcome Trust Case Control Consortium Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls.Nature. 2007; 447: 661-678Crossref PubMed Scopus (7335) Google Scholar, 2Duerr RH Taylor KD Brant SR Rioux JD Silverberg MS Daly MJ Steinhart AH Abraham C Regueiro M Griffiths A et al.A genome-wide association study identifies IL23R as an inflammatory bowel disease gene.Science. 2006; 314: 1461-1463Crossref PubMed Scopus (2315) Google Scholar, 3Hampe J Franke A Rosenstiel P Till A Teuber M Huse K Albrecht M Mayr G De La Vega FM Briggs J et al.A genome-wide association scan of nonsynonymous SNPs identifies a susceptibility variant for Crohn disease in ATG16L1.Nat Genet. 2007; 39: 207-211Crossref PubMed Scopus (1444) Google Scholar, 4Smyth DJ Cooper JD Bailey R Field S Burren O Smink LJ Guja C Ionescu-Tirgoviste C Widmer B Dunger DB et al.A genome-wide association study of nonsynonymous SNPs identifies a type 1 diabetes locus in the interferon-induced helicase (IFIH1) region.Nat Genet. 2006; 38: 617-619Crossref PubMed Scopus (511) Google Scholar Both linkage and association studies suffer from a multiple-testing problem, because they are generally hypothesis generating. There is also a conceptual problem with the null hypothesis in nearly all gene-mapping studies. The null hypothesis for a test at a given location in the genome is that there is no genetic variation associated with that location, despite the fact that we know that there is heritability, often considerable, for the phenotype in question. Hence, a priori, the null hypothesis cannot be true for all test locations. This assumption is particularly worrisome for linkage studies because of the strong linkage disequilibrium within families, such that many linked genes of small effects would result in false evidence of a major gene of large effect.9Visscher PM Haley CS Detection of putative quantitative trait loci in line crosses under infinitesimal genetic models.Theor Appl Genet. 1996; 93: 691-702Crossref PubMed Scopus (44) Google Scholar We recently showed that a number of these problems disappear if the emphasis is on estimation of variance rather than on hypothesis testing.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar The actual genomewide relationship between pairs of relatives varies because of segregation and can be estimated using dense genetic markers for each pair. For full siblings, for example, the average proportion of the genome shared identical by descent (IBD) is 50%, with a range of ∼38% to ∼62%.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar By calculating the covariance between the proportion of the genome shared and the similarity of siblings for the phenotype, we were able to estimate the genetic variance free from assumptions about nongenetic sources of resemblance between relatives.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar In this study, we apply the principle of chromosome- and genomewide-realized relationships10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar, 11Schork NJ Genome partitioning and whole-genome analysis.Adv Genet. 2001; 42: 299-322Crossref PubMed Google Scholar to partition genetic variance across the genome. We use a very large sample of sibling pairs with genomewide marker genotypes, a well-studied12Galton F Hereditary stature.Nature. 1886; 33: 295-298Crossref Scopus (3) Google Scholar quantitative phenotype in humans (i.e., height), and the independent segregation of chromosomes, to partition genetic variation across chromosomes. We show that at least six chromosomes are responsible for genetic variation but that the hypothesis that all chromosomes contribute variation cannot be rejected. We find no evidence of dominance or epistatic variation. Thus, our data are consistent with a large number of underlying variants acting additively across all chromosomes to affect height in humans. The data comprised quasi-independent sibling pairs (QISPs) from three studies in Australia (AU), the United States (US), and the Netherlands (NL). All individuals were of European descent. Pairs of MZ twins were excluded, but QISPs, including a single MZ individual, were maintained. Descriptions of the pedigrees, phenotypes, and genotypes have all been given elsewhere.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar, 13Liu YZ Xiao P Guo YF Xiong DH Zhao LJ Shen H Liu YJ Dvornyk V Long JR Deng HY et al.Genetic linkage of human height is confirmed to 9q22 and Xq24.Hum Genet. 2006; 119: 295-304Crossref PubMed Scopus (25) Google Scholar, 14Willemsen G Boomsma DI Beem AL Vink JM Slagboom PE Posthuma D QTLs for height: results of a full genome scan in Dutch sibling pairs.Eur J Hum Genet. 2004; 12: 820-828Crossref PubMed Scopus (25) Google Scholar, 15Zhu G Evans DM Duffy DL Montgomery GW Medland SE Gillespie NA Ewen KR Jewell M Liew YW Hayward NK et al.A genome scan for eye color in 502 twin families: most variation is due to a QTL on chromosome 15q.Twin Res. 2004; 7: 197-210Crossref PubMed Scopus (104) Google Scholar In brief, for each of the three samples, QISPs were created from pairs of siblings within a nuclear family. Pairs were included if they had both phenotypic and genomewide genotypic information, with a minimum of 210 microsatellite markers per individual and an average of >400 markers for each of the studies.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar, 13Liu YZ Xiao P Guo YF Xiong DH Zhao LJ Shen H Liu YJ Dvornyk V Long JR Deng HY et al.Genetic linkage of human height is confirmed to 9q22 and Xq24.Hum Genet. 2006; 119: 295-304Crossref PubMed Scopus (25) Google Scholar, 14Willemsen G Boomsma DI Beem AL Vink JM Slagboom PE Posthuma D QTLs for height: results of a full genome scan in Dutch sibling pairs.Eur J Hum Genet. 2004; 12: 820-828Crossref PubMed Scopus (25) Google Scholar, 15Zhu G Evans DM Duffy DL Montgomery GW Medland SE Gillespie NA Ewen KR Jewell M Liew YW Hayward NK et al.A genome scan for eye color in 502 twin families: most variation is due to a QTL on chromosome 15q.Twin Res. 2004; 7: 197-210Crossref PubMed Scopus (104) Google Scholar Height measurements were adjusted for sex and for age at measurement, and standardized residuals (Z scores) were calculated for each individual for each sample separately, to avoid the influence of heterogeneous variances across populations. There were 5,952, 3,996, and 1,266 QISPs for the AU, US, and NL samples, respectively, with a total sample size of 11,214. There were 1,936 brother-brother pairs, 4,011 sister-sister pairs, and 5,267 brother-sister pairs. After adjustment for sex and age, the sibling correlations for the AU, US, and NL samples were 0.432, 0.502, and 0.451, respectively, and the sibling correlation in the entire sample was 0.461. The brother-brother, sister-sister, and brother-sister correlations in the entire sample, after adjustments for age (and for the mean difference in sex in the brother-sister pairs), were 0.494, 0.479, and 0.435, respectively. Additive coefficients of relationship were calculated using Merlin16Abecasis GR Cherny SS Cookson WO Cardon LR Merlin—rapid analysis of dense genetic maps using sparse gene flow trees.Nat Genet. 2002; 30: 97-101Crossref PubMed Scopus (2696) Google Scholar for each chromosome and genomewide for all three samples, as described elsewhere.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar For the X chromosome, IBD probabilities were estimated using MINX. The genetic length of the chromosomes was taken from independent pedigree data.17Kong X Murphy K Raj T He C White PS Matise TC A combined linkage-physical map of the human genome.Am J Hum Genet. 2004; 75: 1143-1148Abstract Full Text Full Text PDF PubMed Scopus (193) Google Scholar We estimated from the marker data the proportions of individual chromosomes and of the genome as a whole that are shared IBD between all 11,214 pairs of siblings.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar, 13Liu YZ Xiao P Guo YF Xiong DH Zhao LJ Shen H Liu YJ Dvornyk V Long JR Deng HY et al.Genetic linkage of human height is confirmed to 9q22 and Xq24.Hum Genet. 2006; 119: 295-304Crossref PubMed Scopus (25) Google Scholar, 14Willemsen G Boomsma DI Beem AL Vink JM Slagboom PE Posthuma D QTLs for height: results of a full genome scan in Dutch sibling pairs.Eur J Hum Genet. 2004; 12: 820-828Crossref PubMed Scopus (25) Google Scholar These proportions are coefficients of additive relationship, which are, on average, 0.5 for full siblings but which vary considerably around their expectation, both between chromosomes for the same full-sib pair and between full-sib pairs for the same chromosome.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar, 18Gagnon A Beise J Vaupel JW Genome-wide identity-by-descent sharing among CEPH siblings.Genet Epidemiol. 2005; 29: 215-224Crossref PubMed Scopus (16) Google Scholar The mean±SD of genomewide additive relationships in our sample of 11,214 sibling pairs was 0.4994±0.036 and the range was 0.309 to 0.644, consistent with previous results and with theory.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar Variance components were estimated by maximum likelihood, as implemented in the statistical package Mx19Neale MC Boker SM Xie G Maes HH Mx: statistical modeling. Virginia Institute for Psychiatric and Behavioral Genetics, Richmond2003Google Scholar and described elsewhere.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar Mixed linear models were fitted, including nongenetic family effects, chromosome and genomewide additive genetic effects, and residual effects. We first estimated genetic variance associated with the entire genome, by fitting a model that estimated the covariation between phenotypic similarity and the coefficient of additive relationship. For this whole-genome analysis, we confirmed our previous results,10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar which were based on a smaller data set of 4,919 pairs from only one source of data. The estimate of heritability for stature from genomewide IBD from the sample of 11,214 sibling pairs was 0.86 (95% CI 0.49–0.95; P<.00001). The estimate of the proportion of phenotypic variation due to nongenetic family effects was 0.03 (P=.38), which is statistically nonsignificant. In addition to the genomewide additive effect, we fitted a genomewide dominance effect, using the probability of sharing two alleles IBD, averaged across the genome.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar The estimated proportions of variance due to additive and dominance effects were 0.699 and 0.160, respectively, but the dominance component was not significantly different from zero (P=.35). However, statistical power to separate these effects is low in our sibling-pair design, since the genomewide additive and dominance coefficients are highly correlated (r=0.911; n=11,214), as predicted by theory.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar After the genomewide analyses, we estimated genetic variance associated with individual chromosomes, using chromosomewide coefficients of additive relationship. The proportion of additive genetic variance explained by a particular chromosome was estimated in two ways—first, by fitting a full model that included effects due to a single chromosome and a reduced model in which no chromosomal effects were fitted, and, second, by fitting a full model containing effects for all 22 autosomes and a reduced model that fitted 21 autosomes only. Table 1 shows that, for the individual-chromosome analyses, 6 of 22 estimates of chromosomal heritability were significantly different from zero at P<.05 and of these 3 at P<.01. The six most significant chromosomes were, in order of the size of the test statistic, 17, 4, 3, 18, 15, and 8. This order is not the same as that of estimated chromosomal heritability, because SEs of estimates are larger for longer chromosomes.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar The estimate of the proportion of variance due to nongenetic family effects (f2) in the single-chromosome analyses captures the variation due to the other autosomes not fitted—for all 22 estimates, the sum of the estimates of f2 and (1/2)h2 was ∼0.459, the observed overall sibling correlation. Very similar estimates and test statistics were obtained from a full model with 22 additive genetic-variance components, from which chromosomal heritabilities were dropped one by one (table 1), consistent with the absence of any large between-chromosome epistatic effects.Table 1Estimates of Variance Proportions from Single-Chromosome Analyses and a Joint Analysis of All 22 AutosomesSingle-Chromosome AnalysesCombined-Chromosome AnalysisChromosomef2aProportion of variance due to sibling resemblance not accounted for by single-chromosomal genetic effects.h2ibProportion of variance due to additive genetic effects on the chromosome.e2cProportion of variance due to individual environmental effects.LRTdThe likelihood-ratio test (LRT) statistic from comparing a full model fitting three variance components with a reduced model fitting two variance components. The P value was calculated assuming that the LRT statistic is distributed as 0 or χ21, each with a probability of 1/2.Ph2iLRTeThe LRT statistic from comparing a full model fitting 24 variance components (22 additive genetic, 1 common environmental, and 1 residual) with a reduced model fitting 23 variance components, by dropping the ith additive genetic-variance component. The P value was calculated in the same way as that in the single-chromosome analyses.P1.4285.0607.51081.201.137.06331.418.1172.4525.0131.5344.065.399.0097.037.4243.4023.1134.48435.704.008.11606.269.0064.4036.1124.48405.938.007.10825.705.0085.4458.0264.5278.319.286.0196.191.5006.4336.0506.51581.294.128.05081.370.5007.4284.0616.51002.019.078.06302.230.0688.4234.0708.50582.778.048.08564.172.0219.4482.0216.5302.277.299.0325.663.50010.4590.0000.5410.000.500.0000.000.50011.4590.0000.5410.000.500.0000.000.50012.4365.0451.51841.121.145.04891.434.50013.4545.0089.5366.056.406.0006.000.50014.4427.0323.5250.728.197.0185.246.50015.4241.0703.50563.353.034.07604.028.02216.4556.0069.5375.035.426.0180.251.30817.4023.1142.48349.019.001.11248.967.00118.4237.0703.50603.753.026.06223.013.04119.4437.0309.5253.759.192.0317.840.50020.4575.0031.5395.008.464.0037.012.45621.4590.0000.5410.000.500.0000.000.50022.4590.0000.5410.000.500.0000.000.500 Total….9126…38.427….920540.846…a Proportion of variance due to sibling resemblance not accounted for by single-chromosomal genetic effects.b Proportion of variance due to additive genetic effects on the chromosome.c Proportion of variance due to individual environmental effects.d The likelihood-ratio test (LRT) statistic from comparing a full model fitting three variance components with a reduced model fitting two variance components. The P value was calculated assuming that the LRT statistic is distributed as 0 or χ21, each with a probability of 1/2.e The LRT statistic from comparing a full model fitting 24 variance components (22 additive genetic, 1 common environmental, and 1 residual) with a reduced model fitting 23 variance components, by dropping the ith additive genetic-variance component. The P value was calculated in the same way as that in the single-chromosome analyses. Open table in a new tab We estimated variance on the X chromosome separately from the autosomes and separately for brother-brother, sister-sister, and brother-sister pairs, because the expected additive genetic covariance between siblings depends on their sex and on assumptions regarding dosage compensation.20Kent Jr, JW Dyer TD Blangero J Estimating the additive genetic effect of the X chromosome.Genet Epidemiol. 2005; 29: 377-388Crossref PubMed Scopus (14) Google Scholar There was no evidence of additive genetic variance for height on the X chromosome for all three groups. The estimates of the proportion of variance due to additive effects on the X chromosome was 0.007 in brother-brother pairs (P=.47), 0.081 in sister-sister pairs (P=.39), and 0.00 in brother-sister pairs (P=.50). Figure 1 shows the relationship between the genetic length of the chromosome and the estimate of the proportion of additive genetic variance attributed to it in the single-chromosome analyses. In general, the longer the chromosome, the more variation it explains. A weighted least-squares regression was performed, with use of the empirical variance of chromosomal additive coefficients as weights, because this variance is inversely proportional to the sampling variance of the estimate of heritability.10Visscher PM Medland SE Ferreira MA Morley KI Zhu G Cornes BK Montgomery GW Martin NG Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings.PLoS Genet. 2006; 2: e41Crossref PubMed Scopus (357) Google Scholar The relationship was highly statistically significant in a no-intercept model (F test, P<.0001), and adding an intercept after the regression was not statistically significant (P=.683). The slope of the regression line (0.03 heritability per 100 cM) is consistent with what would be expected if variance were apportioned according to genetic length, with the assumption of 0.86 for the overall heritability and a total sex-averaged map length of 2,864 cM for the autosomes.17Kong X Murphy K Raj T He C White PS Matise TC A combined linkage-physical map of the human genome.Am J Hum Genet. 2004; 75: 1143-1148Abstract Full Text Full Text PDF PubMed Scopus (193) Google Scholar The correlation (r=0.23) between our estimates of chromosomal heritability and the number of genes per chromosome, obtained from Ensembl build 36, was smaller than the correlation with chromosomal length. The estimates and log-likelihoods of models in which all 22 additive genetic components were fitted were compared with those for the model in which a single genomewide additive genetic component was fitted. The drop in the log-likelihood of the data was 19.2 (P=.57, χ2 test with 21 df), which means that the more parsimonious model of variance contributed by chromosomes proportional to their length was not rejected. What is the minimum number of chromosomes needed to explain genetic variance for height? To address this question, we ordered chromosomes according to the amount of genetic variance they explained from the joint analysis (table 1) and, in a stepwise procedure, added one chromosome at a time. We compared the log-likelihoods, stopping when the addition of an extra chromosome did not improve the fit after accounting for the number of parameters in the model. To compare models, we used Akaike’s information criterion (AIC), calculated as −2(difference in log-likelihood) + 2(number of additive genetic-variance components), between the model and the null model of no additive genetic-variance components. In all models, a nongenetic family effect (f2) was fitted. The best and most parsimonious model, based on AIC, includes six chromosomes: 17, 4, 3, 18, 15, and 8, in order of statistical significance. The scaled AIC values for fitting 1–8 chromosomes were −7.02, −10.41, −13.73, −15.35, −16.36, −19.09, −19.03, and −18.51, with a minimum of six fitted genetic-variance components. Hence, our data indicate that at least 6 but as many as 22 chromosomes may contribute to additive genetic variation for height. For internal validation, we estimated the proportion of additive genetic variance attributable to each chromosome separately for the two lar
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