Genotype–covariate interaction effects and the heritability of adult body mass index

Journal name:
Nature Genetics
Volume:
49,
Pages:
1174–1181
Year published:
DOI:
doi:10.1038/ng.3912
Received
Accepted
Published online

Abstract

Obesity is a worldwide epidemic, with major health and economic costs. Here we estimate heritability for body mass index (BMI) in 172,000 sibling pairs and 150,832 unrelated individuals and explore the contribution of genotype–covariate interaction effects at common SNP loci. We find evidence for genotype–age interaction (likelihood ratio test (LRT) = 73.58, degrees of freedom (df) = 1, P = 4.83 × 10−18), which contributed 8.1% (1.4% s.e.) to BMI variation. Across eight self-reported lifestyle factors, including diet and exercise, we find genotype–environment interaction only for smoking behavior (LRT = 19.70, P = 5.03 × 10−5 and LRT = 30.80, P = 1.42 × 10−8), which contributed 4.0% (0.8% s.e.) to BMI variation. Bayesian association analysis suggests that BMI is highly polygenic, with 75% of the SNP heritability attributable to loci that each explain <0.01% of the phenotypic variance. Our findings imply that substantially larger sample sizes across ages and lifestyles are required to understand the full genetic architecture of BMI.

At a glance

Figures

  1. Systematic inflation of BMI heritability estimates in close relatives that share developmental environments.
    Figure 1: Systematic inflation of BMI heritability estimates in close relatives that share developmental environments.

    (a,b) Phenotypic correlations (a) and heritability estimates (b) from behavioral genetic models (see Online Methods) among different male sibling pairs taken from Swedish army conscription BMI (blue) and height (green) records from 1950 to 1969. In b, estimates are presented assuming assortative mating for both traits (see Online Methods), with transparent points giving the estimate when trait assortment is ignored or assumed absent. Error bars, s.e.

  2. Genotype-covariate interactions described through estimation of genetic variance and genetic correlations across a gradient.
    Figure 2: Genotype–covariate interactions described through estimation of genetic variance and genetic correlations across a gradient.

    (ad) Different scenarios of genotype–covariate interaction with shaded lines giving expected phenotypic values for five genotypes across five measurement points. (a) When there is no genotype–covariate interaction, differences among genotypes are constant across the covariate and the correlation of SNP marker effects (genetic correlation) = 1 across measurements. (b) Changing differences among genotypes with a constant ordering results in increased genetic variance along the covariate but a genetic correlation of 1 among measurements. (c) Changing ordering of genotypes, with a genetic correlation of 0 across all pairs of measurement points but constant genetic variance. (d) Changing ordering of genotypes, with a genetic correlation of 0 across all pairs of measurement points, and differences in genetic variance.

  3. Genotype-age interactions for BMI and height in 43,407 individuals in the composite AHTHEL sample.
    Figure 3: Genotype–age interactions for BMI and height in 43,407 individuals in the composite AHTHEL sample.

    (a,b) MV-GREML and RR-GREML estimates of the proportion of phenotypic variation attributable to common HapMap3 SNP markers (left) and of the correlation of SNP effects (right) across five age groups for BMI (a) and height (b). Akaike information criterion (AIC) values are also shown. Zero-order RR-GREML estimates are shown in a and b. Dashed lines and numbers in parentheses indicate s.e. (Online Methods). Age groups (in years) and numbers of individuals (n) in each were as follows: 18–39 (n = 5,136) 40–53 (n = 11,573); 54–59 (n = 7,829) 60–66 (n = 9,843), and ≥67 (n = 9,025).

  4. Genotype-environment interactions for BMI in 97,510 participants of the UK Biobank study across a range of lifestyle factors.
    Figure 4: Genotype–environment interactions for BMI in 97,510 participants of the UK Biobank study across a range of lifestyle factors.

    (ah) Estimates of the phenotypic variance captured by common HapMap3 SNP loci (SNP heritability) from MV-GREML models (error bars, s.e.) and RR-GREML models (dashed lines show s.e.) for each lifestyle factor. For the RR-GREML model estimates, we present the model of best fit to the data, as assessed by LRT (Table 2). Also shown are estimates of the correlation of SNP marker effects (genetic correlation) across groups for each lifestyle factor (s.e. given in parentheses).

  5. A Bayesian mixture model of common HapMap3 SNP markers for BMI and height in 107,488 participants of the UK Biobank study.
    Figure 5: A Bayesian mixture model of common HapMap3 SNP markers for BMI and height in 107,488 participants of the UK Biobank study.

    BayesR model estimates of the proportion of genetic variance contributed by SNPs with different mixture distributions of effect sizes for BMI (blue) and height (green) are shown; error bars, 95% credible intervals of the posterior distribution.

  6. Simulation study of genotype-covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study.
    Supplementary Fig. 1: Simulation study of genotype–covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study.

    (a) Estimates of the variance tagged by common SNP markers from multivariate REML (MV-GREML) and random regression REML (RR-GREML) models across five different simulation scenarios (see Online Methods). For each simulation scenario, there were five measurement points, representing different points along a continuous gradient. The estimates of the RR-GREML models come from a model fitting the highest order of Legendre polynomial function that gave a significant improvement in model fit based on a log-likelihood ratio test (LRT). Estimates are the mean value obtained over 10 simulation replicates and error bars give the s.d. across replicates. The solid lines give the pattern of variance change predicted from the polynomial function of the RR-GREML models and dotted lines give the approximate s.d. across replicates (see Online Methods). (b) The analysis of a is repeated but the phenotype is standardized with an inverse normal transformation within each measurement point. (c) Simulated and estimated correlation in common SNP marker effects from MV-GREML models (green circles) and RR-GREML models of first order polynomial (blue circles). (d) P-value of a LRT with two degrees of freedom of a first order polynomial RR-GREML model versus a zero order RR-GREML model for simulation scenarios with and without genotype-covariate interaction and with and without-standardization. Points give the mean, and error bars show the full distribution of the LRT statistic P-values across all 10 replicates. (e) P-value of a LRT of increasing orders of polynomial (k = 1, 2, 3, 4) RR-GREML models across different simulation scenarios.

  7. Simulation study of genotype-covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study.
    Supplementary Fig. 2: Simulation study of genotype–covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study.

    (a) Estimates of SNP coheritability, V(G), and variance attributable to genotype-covariate interaction effects, V(GCI), from genotype-covariate interaction (GCI-GREML) models across five simulation scenarios described in Supplementary Figure 1, for both rank inverse normal transformed phenotypes and unstandardized ones. For each simulation scenario, there were five measurement points, representing different points along a continuous gradient, and the estimates are the mean value obtained over 10 simulation replicates with error bars giving the s.d. across replicates. (b) We repeat the GCI-GREML models but we only use the extreme measurement points. Expectations for V(G) and V(GCI) were derived from our theory (see Supplementary Note). (c) The significance of the likelihood ratio tests comparing the fit to the data of a GCI-GREML model (fitting a genetic variance component and a genetic interaction variance component) and a null GREML model (fitting a single genetic variance component) across the simulation scenarios.

  8. Phenotypic variance and variance tagged by common HapMap3 SNP loci for body mass index (BMI) and height in the AHTHEL sample.
    Supplementary Fig. 3: Phenotypic variance and variance tagged by common HapMap3 SNP loci for body mass index (BMI) and height in the AHTHEL sample.

    (a,b) The phenotypic variance of BMI (a) and height (b) were unstandardized within age groups allowing testing for variance heterogeneity for both traits. The phenotypic variance is shown in grey circles. The variance captured by common HapMap3 SNP loci from both an MV-GREML model is shown in blue circles for BMI, and green circles for height. The estimates from a zero order RR-GREML model are shown by a solid blue line for BMI, and a solid green line for height, with dashed lines giving the approximate s.e. LRT values give the likelihood ratio test statistic values for a RR-GREML model with a first order polynomial as compared to a RR-GREML model of zero order, to test for the presence of changes in variance tagged by SNP markers.

  9. No evidence for genotype-age interaction for BMI in 107,488 individuals from the UK Biobank study.
    Supplementary Fig. 4: No evidence for genotype–age interaction for BMI in 107,488 individuals from the UK Biobank study.

    (a,b) The UK Biobank sample contained individuals measured between the ages of 46 and 73 and we divided the age distribution into deciles of approximately equal sample size. The age ranges were: (1) 9,655 individuals aged 40 to 44; (2) 10,379 individuals aged 45 to 48; (3) 9,205 individuals aged 49 to 51; (4) 13,669 individuals aged 52 to 55; (5) 7,689 individuals aged 56 and 57; (6) 8,590 individuals aged 58 and 59; (7) 11,211 individuals aged 60 and 61; (8) 11,019 individuals aged 62 and 63; (9) 14,559 individuals aged 64 to 66; and (10) 11,612 individuals aged 67 and above. We corrected for sex effects and standardized BMI measures within each decile with a rank inverse normal transformation to remove differences in phenotypic mean and variance across age. We used a full MV-GREML model to estimate the proportion of variance attributable to common HapMap3 SNPs for each age groups as shown in blue dots with s.e. bars (a), and the covariance in genome-wide SNP effects across age groups (b), with s.e. of the genetic correlations among age groups given in brackets. We used a RR-GREML model with a first order polynomial and compared the model fit to the data to a RR-GREML model of zero order, to test for the presence of genotype-age interaction effects using a likelihood-ratio test (LRT). We find no evidence for genotype-age interaction effects (LRT = 1.02, P = 0.601) and thus the estimates of the RR-GREML model of zero order are presented in a with dashed lines giving the approximate s.e.

  10. Correlations among the self-reported lifestyle factors found to influence BMI of 97,510 individuals of the UK Biobank study.
    Supplementary Fig. 5: Correlations among the self-reported lifestyle factors found to influence BMI of 97,510 individuals of the UK Biobank study.

    A description of the variables and the data fields can be found in Supplementary Table 5 and the Supplementary Note.

  11. Phenotypic variance and variance tagged by common HapMap3 SNP loci for BMI of 97,510 individuals within the UK Biobank study across self-reported lifestyle factors.
    Supplementary Fig. 6: Phenotypic variance and variance tagged by common HapMap3 SNP loci for BMI of 97,510 individuals within the UK Biobank study across self-reported lifestyle factors.

    A series of self-report lifestyle factors shown to significantly influence mean BMI within the UK Biobank were used to group individuals. We corrected BMI for sex, age and the effects of all lifestyle factors and then converted BMI values to a z-score across but not within groups. This means that the phenotypic variance of BMI was unstandardized within groups allowing testing for variance heterogeneity and these values are shown in grey circles. Estimates of the variance captured by common HapMap3 SNP loci from a MV-GREML model are shown in blue circles, and those from a first order RR-GREML model are given by a solid blue line, with dashed line giving the approximate s.e. For the RR-GREML model estimates, we present the model of best fit to the data, as assessed by likelihood-ratio test statistics (LRT), which are given in Supplementary Table 6.

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Author information

Affiliations

  1. Institute for Molecular Bioscience, The University of Queensland, Brisbane, Australia.

    • Matthew R Robinson,
    • Geoffrey English,
    • Gerhard Moser,
    • Luke R Lloyd-Jones,
    • Zhihong Zhu,
    • Jian Yang &
    • Peter M Visscher
  2. Department of Computational Biology, University of Lausanne, Lausanne, Switzerland.

    • Matthew R Robinson
  3. Queensland Brain Institute, The University of Queensland, Brisbane, Australia.

    • Marcus A Triplett
  4. Department of Epidemiology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands.

    • Ilja M Nolte &
    • Harold Snieder
  5. Department of Endocrinology, University of Groningen, University Medical Center Groningen, Groningen, the Netherlands.

    • Jana V van Vliet-Ostaptchouk
  6. Estonian Genome Center, University of Tartu, Tartu, Estonia.

    • Tonu Esko,
    • Lili Milani,
    • Reedik Mägi &
    • Andres Metspalu
  7. Division of Endocrinology, Boston Children's Hospital, Cambridge, Massachusetts, USA.

    • Tonu Esko
  8. Program in Medical and Population Genetics, Broad Institute, Cambridge, Massachusetts, USA.

    • Tonu Esko
  9. Department of Genetics, Harvard Medical School, Boston, Massachusetts, USA.

    • Tonu Esko
  10. Institute of Molecular and Cell Biology, University of Tartu, Tartu, Estonia.

    • Andres Metspalu
  11. Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden.

    • Patrik K E Magnusson &
    • Nancy L Pedersen
  12. Department of Medical Sciences, Molecular Epidemiology and Science for Life Laboratory, Uppsala University, Uppsala, Sweden.

    • Erik Ingelsson
  13. Division of Cardiovascular Medicine, Department of Medicine, Stanford University School of Medicine, Stanford, California, USA.

    • Erik Ingelsson
  14. Stockholm School of Economics, Stockholm, Sweden.

    • Magnus Johannesson
  15. Center for Experimental Social Science, Department of Economics, New York University, New York, New York, USA.

    • David Cesarini

Consortia

  1. The LifeLines Cohort Study

  2. A full list of members and affiliations appears in the Supplementary Note.

Contributions

M.R.R. and P.M.V. conceived and designed the study. M.R.R. conducted all analysis, with contributions from G.E., G.M., L.R.L.-J., D.C., and M.A.T. G.M. developed the BayesR software, and J.Y. developed the GCTA software. The LifeLines Cohort Study, Z.Z., I.M.N., J.V.v.V.-O., H.S., T.E., L.M., R.M., A.M., P.K.E.M., N.L.P., E.I., M.J., J.Y., and D.C. provided study oversight, sample collection, and management. M.R.R. and P.M.V. wrote the manuscript. All authors reviewed and approved the final manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

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Author details

Supplementary information

Supplementary Figures

  1. Supplementary Figure 1: Simulation study of genotype–covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study. (339 KB)

    (a) Estimates of the variance tagged by common SNP markers from multivariate REML (MV-GREML) and random regression REML (RR-GREML) models across five different simulation scenarios (see Online Methods). For each simulation scenario, there were five measurement points, representing different points along a continuous gradient. The estimates of the RR-GREML models come from a model fitting the highest order of Legendre polynomial function that gave a significant improvement in model fit based on a log-likelihood ratio test (LRT). Estimates are the mean value obtained over 10 simulation replicates and error bars give the s.d. across replicates. The solid lines give the pattern of variance change predicted from the polynomial function of the RR-GREML models and dotted lines give the approximate s.d. across replicates (see Online Methods). (b) The analysis of a is repeated but the phenotype is standardized with an inverse normal transformation within each measurement point. (c) Simulated and estimated correlation in common SNP marker effects from MV-GREML models (green circles) and RR-GREML models of first order polynomial (blue circles). (d) P-value of a LRT with two degrees of freedom of a first order polynomial RR-GREML model versus a zero order RR-GREML model for simulation scenarios with and without genotype-covariate interaction and with and without-standardization. Points give the mean, and error bars show the full distribution of the LRT statistic P-values across all 10 replicates. (e) P-value of a LRT of increasing orders of polynomial (k = 1, 2, 3, 4) RR-GREML models across different simulation scenarios.

  2. Supplementary Figure 2: Simulation study of genotype–covariate interaction using observed genotype data from 25,000 randomly selected unrelated individuals in the UK Biobank study. (227 KB)

    (a) Estimates of SNP coheritability, V(G), and variance attributable to genotype-covariate interaction effects, V(GCI), from genotype-covariate interaction (GCI-GREML) models across five simulation scenarios described in Supplementary Figure 1, for both rank inverse normal transformed phenotypes and unstandardized ones. For each simulation scenario, there were five measurement points, representing different points along a continuous gradient, and the estimates are the mean value obtained over 10 simulation replicates with error bars giving the s.d. across replicates. (b) We repeat the GCI-GREML models but we only use the extreme measurement points. Expectations for V(G) and V(GCI) were derived from our theory (see Supplementary Note). (c) The significance of the likelihood ratio tests comparing the fit to the data of a GCI-GREML model (fitting a genetic variance component and a genetic interaction variance component) and a null GREML model (fitting a single genetic variance component) across the simulation scenarios.

  3. Supplementary Figure 3: Phenotypic variance and variance tagged by common HapMap3 SNP loci for body mass index (BMI) and height in the AHTHEL sample. (161 KB)

    (a,b) The phenotypic variance of BMI (a) and height (b) were unstandardized within age groups allowing testing for variance heterogeneity for both traits. The phenotypic variance is shown in grey circles. The variance captured by common HapMap3 SNP loci from both an MV-GREML model is shown in blue circles for BMI, and green circles for height. The estimates from a zero order RR-GREML model are shown by a solid blue line for BMI, and a solid green line for height, with dashed lines giving the approximate s.e. LRT values give the likelihood ratio test statistic values for a RR-GREML model with a first order polynomial as compared to a RR-GREML model of zero order, to test for the presence of changes in variance tagged by SNP markers.

  4. Supplementary Figure 4: No evidence for genotype–age interaction for BMI in 107,488 individuals from the UK Biobank study. (203 KB)

    (a,b) The UK Biobank sample contained individuals measured between the ages of 46 and 73 and we divided the age distribution into deciles of approximately equal sample size. The age ranges were: (1) 9,655 individuals aged 40 to 44; (2) 10,379 individuals aged 45 to 48; (3) 9,205 individuals aged 49 to 51; (4) 13,669 individuals aged 52 to 55; (5) 7,689 individuals aged 56 and 57; (6) 8,590 individuals aged 58 and 59; (7) 11,211 individuals aged 60 and 61; (8) 11,019 individuals aged 62 and 63; (9) 14,559 individuals aged 64 to 66; and (10) 11,612 individuals aged 67 and above. We corrected for sex effects and standardized BMI measures within each decile with a rank inverse normal transformation to remove differences in phenotypic mean and variance across age. We used a full MV-GREML model to estimate the proportion of variance attributable to common HapMap3 SNPs for each age groups as shown in blue dots with s.e. bars (a), and the covariance in genome-wide SNP effects across age groups (b), with s.e. of the genetic correlations among age groups given in brackets. We used a RR-GREML model with a first order polynomial and compared the model fit to the data to a RR-GREML model of zero order, to test for the presence of genotype-age interaction effects using a likelihood-ratio test (LRT). We find no evidence for genotype-age interaction effects (LRT = 1.02, P = 0.601) and thus the estimates of the RR-GREML model of zero order are presented in a with dashed lines giving the approximate s.e.

  5. Supplementary Figure 5: Correlations among the self-reported lifestyle factors found to influence BMI of 97,510 individuals of the UK Biobank study. (172 KB)

    A description of the variables and the data fields can be found in Supplementary Table 5 and the Supplementary Note.

  6. Supplementary Figure 6: Phenotypic variance and variance tagged by common HapMap3 SNP loci for BMI of 97,510 individuals within the UK Biobank study across self-reported lifestyle factors. (172 KB)

    A series of self-report lifestyle factors shown to significantly influence mean BMI within the UK Biobank were used to group individuals. We corrected BMI for sex, age and the effects of all lifestyle factors and then converted BMI values to a z-score across but not within groups. This means that the phenotypic variance of BMI was unstandardized within groups allowing testing for variance heterogeneity and these values are shown in grey circles. Estimates of the variance captured by common HapMap3 SNP loci from a MV-GREML model are shown in blue circles, and those from a first order RR-GREML model are given by a solid blue line, with dashed line giving the approximate s.e. For the RR-GREML model estimates, we present the model of best fit to the data, as assessed by likelihood-ratio test statistics (LRT), which are given in Supplementary Table 6.

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    Supplementary Figures 1–6, Supplementary Tables 1–6 and Supplementary Note.

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