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Determining the stability of genome-wide factors in BMI between ages 40 to 69 years

  • Nathan A. Gillespie ,

    Roles Conceptualization, Formal analysis, Methodology, Writing – original draft, Writing – review & editing

    Affiliations Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America, QIMR Berghofer Medical Research Institute, Herston, Australia

  • Amanda Elswick Gentry,

    Roles Data curation, Writing – original draft, Writing – review & editing

    Affiliation Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America

  • Robert M. Kirkpatrick,

    Roles Formal analysis, Methodology, Writing – original draft, Writing – review & editing

    Affiliation Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America

  • Chandra A. Reynolds,

    Roles Conceptualization, Writing – original draft, Writing – review & editing

    Affiliation Department of Psychology, University of California, Riverside, California, United States of America

  • Ravi Mathur,

    Roles Writing – original draft, Writing – review & editing

    Affiliation GenOmics, Bioinformatics, and Translational Research Center, Biostatistics and Epidemiology Division, RTI International, Research Triangle Park, North Carolina, United States of America

  • Kenneth S. Kendler,

    Roles Conceptualization, Writing – original draft, Writing – review & editing

    Affiliation Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America

  • Hermine H. Maes,

    Roles Writing – original draft, Writing – review & editing

    Affiliation Virginia Institute for Psychiatric and Behavior Genetics, Departments of Human and Molecular Genetics, Psychiatry, & Massey Cancer Center, Virginia Commonwealth University, Richmond, Virginia, United States of America

  • Bradley T. Webb ,

    Roles Data curation, Writing – original draft, Writing – review & editing

    ‡ These authors shared senior authorship on this work.

    Affiliations Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America, GenOmics, Bioinformatics, and Translational Research Center, Biostatistics and Epidemiology Division, RTI International, Research Triangle Park, North Carolina, United States of America

  • Roseann E. Peterson

    Roles Writing – original draft, Writing – review & editing

    ‡ These authors shared senior authorship on this work.

    Affiliation Virginia Institute for Psychiatric and Behavior Genetics, Department of Psychiatry, Virginia Commonwealth University, Richmond, Virginia, United States of America


Genome-wide association studies (GWAS) have successfully identified common variants associated with BMI. However, the stability of aggregate genetic variation influencing BMI from midlife and beyond is unknown. By analysing 165,717 men and 193,073 women from the UKBiobank, we performed BMI GWAS on six independent five-year age intervals between 40 and 72 years. We then applied genomic structural equation modeling to test competing hypotheses regarding the stability of genetic effects for BMI. LDSR genetic correlations between BMI assessed between ages 40 to 73 were all very high and ranged 0.89 to 1.00. Genomic structural equation modeling revealed that molecular genetic variance in BMI at each age interval could not be explained by the accumulation of any age-specific genetic influences or autoregressive processes. Instead, a common set of stable genetic influences appears to underpin genome-wide variation in BMI from middle to early old age in men and women alike.

Author summary

We used a new method called genomic structural equation modeling to analyse data from 165,717 men and 193,073 women from the UKBiobank. Our results revealed that genetic influences on BMI were very stable between ages 40 and 73. In other words, there did not appear to be any age-dependent genetic influences on BMI during this period. The same results were seen in men and women.


The recent decade has witnessed significant advances in the detection of multiple loci underpinning variation in complex traits [1]. Among the most successful endeavors has been genome-wide association scan (GWAS) analyses of adult BMI [24]. Notwithstanding the predictive validity of common BMI variants [5], GWAS BMI loci are based on large, aggregated meta-analytic samples derived from varying geographic and economic regions, derived from different birth cohorts and age distributions. Here, we examine this last caveat for it remains to be empirically determined if the genome-wide variation associated with adult BMI is age-invariant or age-specific. This has public-health consequences. For example, given the positive association between increased age and BMI with COVID19-related hospitalization and mortality [6,7], determining if genetic variants in BMI at older ages are qualitatively distinct is important.

BMI heritability & longitudinal genetic correlations

Despite moderate stability across time [812], average adult BMI increases from age 20 to age 65 at which time it levels off until age 80 [12] before beginning to decline. Such changes might be attributed to variable contributions of genetic and environmental risks across the lifespan. Apart from birth cohort differences, Dahl et al. [12], found that factors such as an obesity genetic risk score, type-2 diabetes mellitus, cardiovascular disease, substance use, and educational attainment were all differentially predictive of both average BMI and changes in BMI before age 65. In contrast, many of these risks were no longer predictive after age 65. In terms of genetics, whereas the overall lifetime BMI heritability is 0.75 [13], heritability actually increases throughout infancy and adolescence [14] before decreasing during adulthood [13]. In terms of cross-temporal associations, genetic influences in BMI are correlated across time [811,1416], sometimes very highly [17], which indicates continuous expression of the same genetic influences [18]. However, longitudinal genetic correlations for BMI never reach unity. Indeed, there is considerable variability in longitudinal genetic correlations [13,15,16]. This is also consistent with age-specific genetic influences, which could be obscured in GWAS meta-analytic results based on data aggregated across age or GWAS analyses with age as a covariate.

Linkage Disequilibrium Score (LDSC) regression

Until recently, estimates of heritability (h2) and genetic correlations (rG), have typically relied on twins reared together or family studies within a structural equation modeling (SEM) framework. The development LDSC [19] has circumvented the need for twin studies by now making it possible to estimate h2 and rG using unrelated and independent samples that have GWAS summary test statistics. Briefly, LDSC regression works by leveraging external linkage disequilibrium (LD) reference panels, which summarize correlations between genetic markers across the human genome, to produce genetic covariance matrices from GWAS summary statistics. In addition to estimating rG, these matrices can then be used within a traditional SEM framework to test hypotheses about comorbidity, or the nature of change. In terms of BMI, this approach could be used to address the question of whether or not genetic risks in BMI are correlated across time.

Currently however, there is a paucity of molecular-based reports examining h2 and rG between BMI assessed at different ages, and they have relied on different approaches to produce mixed results. For instance, Trzaskowski et al. [20] used LDSR to report a genetic correlation (rg = 0.86) between BMI assessed at age 11 and 65. Winkler et. al. [21] estimated Spearman rank genetic correlations between BMI assessed in populations above and below age 50, which revealed much smaller correlations (rg = 0.05 to 0.12). Notwithstanding the need for greater precision regarding longitudinal genetic correlations, such correlations are descriptive and provide no insight regarding competing theories underlying developmental processes in BMI.

We argue that at least two theoretical mechanisms [22] can be invoked to explain observed continuity in genetic correlations. The first is a common factor process whereby common genetic or environmental factors determine the levels and rates of change in BMI over time. In this model, variances and covariances between longitudinal measures of BMI depend on individual genetic or environmental differences in growth patterns unfolding with age i.e., random growth curves [2327]. We are aware of three twin studies that have applied genetically informative growth models to longitudinal BMI data [2830]. Unfortunately, random growth curves do not determine the extent to which stability or changes in BMI are governed by time-invariant versus age-specific genetic influences. To address this question, the second mechanism predicts that variances and covariances are determined by random, time-specific genetic and environmental effects, which are more or less persistent over time i.e., autoregressive effects’ [3133]. Illustrated in Fig 1, this approach predicts a causal process of inertial effects, whereby BMI genetics at one time causally affect BMI at the next. We have applied this validated approach to personality [34], anxiety and depression [35,36], substance use [37] and brain aging [38]. We are aware of two reports that have tested autoregression models with respect to BMI data [9,18]. Cornes et al. [9] found evidence of distinct, age-specific genetic influences on BMI at ages 12, 14 and 16. To our knowledge, autoregressive effects have never been tested in adult BMI, especially across a wide window comprising narrow age intervals in adulthood. Fortunately, the recent, innovative application of structural equation modelling (SEM) [39,40] to LDSC regression genetic correlations [39] based on available GWAS results can now address the aforementioned gaps.

Fig 1. Autoregression model depicting genome-wide variation in BMI at each age interval.

This development model predicts that genetic variation at each time interval can be decomposed into time-specific variation or ‘innovations’ & the causal contribution of genome-wide genetic variation from previous age intervals. Innovations refer to novel or age-specific genetic influences that are uncorrelated with previous genetic influences. This model also includes residual genetic variation not otherwise explained by the autoregression process. Double-headed arrows denote variation associated with innovations & residuals at each age interval. Beta (β) denotes the causal contribution of genetic variance from one age interval to the next.

By applying genomic structural equation modeling or “genomicSEM” to BMI GWAS summary statistics from the UK Biobank [41], our aim was to determine if genetic influences across middle to early old age were best explained by age-dependent versus age-invariant processes. We also tested if alternative, more parsimonious theoretical explanations i.e., common factor models, whereby covariance between genetic influences across time could be better captured by a single latent factor [42], provided a better fit to the data. Given that standardized estimates of BMI heritability for men and women are statistically equal [13] and that there appear to be no sex differences in terms of the observed adulthood decline in heritability [43], we hypothesized that developmental processes governing changes in heritability over time likewise ought to be comparable across sex.


All BMI and GWAS summary statistics came from the UK Biobank, a major biomedical database. The UK Biobank is a large-scale biomedical database and research resource containing genetic, lifestyle and health information from half a million UK participants. UK Biobank’s database, which includes blood samples, heart and brain scans and genetic data of the 500,000 volunteer participants, is globally accessible to approved researchers who are undertaking health-related research that’s in the public interest [41].

BMI data

Described in detail elsewhere [44], weight was collected from subjects using a Tanita BC418MA body composition analyzer. Standing and sitting height measurements were collected from subjects using a Seca 240cm height measure. Body mass index (BMI) was calculated as weight divided by height squared (kg/m2). We divided the BMI data into six age intervals: 40–45; 46–50; 51–55; 56–60; 61–65; and 66–73 years. The range was based on available data whereas the number of age tranches was selected to maximize our power to choose between competing longitudinal and multivariate models without minimizing the statistical power of the GWAS analyses at each interval. The number of subjects with complete BMI and GWAS summary statistics are shown in S1 Table.

Genotypic data

Genotype data were filtered according to the Neale Lab pipeline, using filtration parameters and scripts publicly available from the lab GitHub [45]. Samples were filtered to retain only unrelated subjects of British ancestry (n = 359,980.) Imputed variants [46] were filtered for INFO scores > 0.8, MAF > 0.001, and HWE p-value > 1e-10.

GWAS analyses

This is proof-of-principle illustration of the application of structural equation modelling (SEM) to GWAS summary data to test competing longitudinal hypotheses. Since the number of UKB subjects with repeated BMI measures and GWAS summary statistics was insufficient to be divided into a minimum of three age tranches needed to test the autoregression hypothesis, we treated the GWAS summary statistics at each 5-year age interval as pseudo-longitudinal. This resulted in 6 separate and independent age tranches for GWAS. Three separate GWAS analyses were conducted for each age tranche (men, women and combined) using the BGENIE (version 1.3.) [46]. The first 20 ancestry principal components were included as covariates in all models. Sex was included as a covariate in the combined (men + women) model.

Genomic structural equation modelling

We then applied the GenomicSEM software package [39] in R (version 4.0.3) [47] to the BMI GWAS results to estimate separate genetic variance-covariance (S) and asymptotic sampling covariance ‘weight’ (V) matrices for the male, female and then the combined GWAS results.

Estimation of the S and V matrices is a 3-step process. In step 1, the raw GWAS summary statistics were manipulated using the GenomicSEM munge option to remove all SNPs with MAF < 1%, information scores < 0.9, and SNPs in the MHC region. In step 2, we used the GenomicSEM ldsc option to run multivariate LD score regression [39] to estimate the S and V matrices between the GWAS summary statistics. This method has been successfully applied to detect genetic correlations between bio-medical, psychiatric and behavioural phenotypes [4868], which are commensurate with previous biometrical genetic correlations [6976] while revealing extensive pleiotropy across a wide variety of phenotypes. In step 3, the S and V matrices were then read into the lavaan (version 0.6–7) [77] SEM software package in R (version 4.0.3) [47] to fit and compare competing longitudinal and multivariate models. All GenomicSEM and lavaan scripts used here are publicly available at

The autoregression model predicts that time-specific random genetic or environmental effects are more or less persistent over time (autoregressive effects) [31]. As described by Eaves and others [3133], autoregression models assume that the covariance structure arises because of random, age-specific genetic or environmental effects, which are, at least partially, carried forward. As illustrated in Fig 1, innovations at each assessment reflect novel, time- or age-specific genetic or environmental influences, which are uncorrelated with previous genetic influences. Genetic differences at each occasion are therefore a function of new random effects on the phenotype that arise as well as a (linear) function of individual genetic differences expressed at the preceding time. Here, we assume that cross-temporal correlations arise because the innovations have a more or less persistent effect over time and may, under some circumstances accumulate, potentially giving rise to developmental increases in genetic variance and increased correlations between adjacent measures. One consequence of the autoregressive model is the tendency of cross-temporal correlations to decay as a function of increasing lag-time. Depending on the magnitude of an innovation and its relative persistence, the observed variances and cross-temporal covariances may increase towards a stable asymptotic value. We began by fitting innovations at all six time-intervals, which were then successively dropped. We also specified an autoregression model that included a single innovation at BMI 40–44 accounting for all subsequent genetic variances. Technically, this first innovation includes all genetic variance accumulated up to this first age interval. Finally, we fitted a factor analysis comprising a single factor.

Model fit indices & comparisons

In GenomicSEM analyses there is no one sample size to speak of. This is because GWAS studies from which the summary statistics are derived can vary in size and subject overlap. Thus, potentially, a different (effective) sample size may apply to each element of S. We were therefore limited to fit indices that do not explicitly depend upon sample size: the pseudo Akaike Information Criterion (pseudoAIC); Comparative Fit Index (CFI); Tucker Lewis Index (TFI); and the Standardized Root Mean Square Residual (SRMR) to judge the best-fitting model. Both the CFI and TFI are incremental fit indices that penalize models with increasing complexity. The SRMR is an absolute measure of fit based on the difference between the observed and predicted correlations under each model, such that a value of zero indicates a perfect fit. The pseudoAIC is a comparative fit index, whereby the model with the lowest AIC values is interpreted as the best-fitting.


Combined male & female analyses

The LDSR-based genome-wide genetic correlations between the six GWAS summary statistics, including GWAS sample sizes and the SNP-based heritability for each age interval, are shown in Table 1. The correlations do not decline with increasing time intervals, which would be indicative of a simplex structure best explained by autoregression models. For example, the LDSR genetic correlation (rg) between BMI at ages 40–45 and 66–73 years was higher than the rg between BMI at ages 40–45 and 56–60 years (rg = 0.97 vs 0.93). Overall, the genetic correlations were very high and ranged from 0.93 to 1.00.

Table 1. Sample sizes, estimates of SNP-based heritability (including standard errors along diagonal) & linkage disequilibrium score regression genetic correlations between the six age intervals based on the combined male & female GWAS summary statistics.

Formal model fitting comparisons are shown in Table 2. We began with a fully saturated autoregression model comprising unique genetic influences or innovations at each age interval (Fig 1). This provided a reasonable fit to the data as judged by the non-significant chi-square, very high CFI and TLI values and very low SRMR. Autoregression sub-models in which the genetic innovations at ages 66 to 73, 61 to 65, and 51 to 55 years were each successively removed provided only marginal improvements in terms of their pseudoAIC values. In contrast, the factor analysis with a single factor provided the overall best fit in terms of the smallest chi-square, lowest pseudoAIC and lowest SRMR. In this model (see Fig 2), genetic variance at each five-year age interval was best explained by a single factor with a genome-wide SNP heritability of 24%.

Fig 2. Best fitting factor analytic model with a single common factor (CF) based on the combined male and female data.

The CF explains covariation between the six GWAS summary statistics each based on five-year intervals between ages 40–73 years. To identify this model, the first factor loading from the CF to BMI GWAS at 40–45 years was constrained to one. The double-headed arrow on the CF denotes the standardized variance, or SNP-based heritability, for BMI. Double-headed arrows on the residuals denote genetic variation at each age interval not otherwise explained by the CF.

Table 2. Multivariate modeling fitting comparisons based on the combined male & female GWAS summary statistics.

Sex specific analyses

An identical pattern emerged when the model fitting was repeated by sex. Male and female sample sizes at each age interval are shown in S1 Table. Table 3 shows the LDSR genetic correlations for men and women. Varying only slightly, the separate male and female correlations were again high and ranged from rg = 0.88 to rg = 1.00. S1 Table also shows the SNP-based heritability estimates by sex, which were very similar at each age interval.

Table 3. Linkage disequilibrium score regression genetic correlations based on the male (below diagonal) & female (above diagonal italics) GWAS summary statistics at six age intervals.

As shown in Table 4, the genetic innovations at ages 46 to 66+ years for men and women could each be dropped from the full autoregression model as judged by the non-significant chi-square value. Overall, for both sexes, the factor analysis with a single common factor again provided the best fit to the data in terms of the lowest chi-square, pseudoAIC and SRMR values (see Fig 3). This suggests that there is no evidence of age-specific genome-wide variation in BMI for either men or women.

Fig 3.

Best fitting factor analytic model with a single common factor (CF) for men (A) & women (B). To identify this model, the first factor loading from the CD to BMI GWAS at 40–45 years was constrained to one. The double-headed arrow on the CF denotes the standardized variance, or SNP-based heritability, for BMI. Double-headed arrows on the residuals denote genetic variation at each age interval not otherwise explained by the CF.

Table 4. Multivariate modeling fitting comparisons based on the combined MALE GWAS summary statistics at six age intervals.


This is the first study to test a developmental theory regarding BMI heritability using molecular data and structural equation modeling. Between ages 40 and 73, changes in BMI heritability could not be explained by detectable age-specific genome-wide variation or an accumulation of genetic variants over time. Instead, individual differences in the molecular genetics of BMI across this time span were best explained by a single or common set of stable, genetic influences that are observable in early midlife. This pattern was observed in men and women.

Our results are consistent with Silventoinen et al.’s meta-analysis of twin data that revealed only minor differences in BMI heritability estimates across cultural-geographic regions and measurement time [78,79]. Dahl et al.’s [12] analysis of Swedish twin data revealed that for men and women, BMI increases across midlife, before leveling off at 65 years and declining at approximately age 80. The extent to which Dahl et al.’s observed inflexion at age 65 years is indicative of age-specific, distinct genetic influences or variance components was inconsistent with our results. Instead, we found that the genetic correlations between BMI at ages 61–65 years and the remaining four age tranches were all equally high. Thus, the molecular genetic variance at age 65 does not appear to be linked to age-specific or distinct genetic processes occurring around this time.

An outstanding question is whether or not our results generalize to earlier stages in life. Here, a number of reports, relying on different methods, suggest that genetic risks spanning childhood, adolescence and early adulthood likely comprise a combination of age-specific and age-invariant influences. For example, several studies have shown that the PRS for childhood BMI predicts adult BMI, metabolic outcomes and other complex traits [8084]. Other studies relying on twin data have reported genetic correlations between BMI assessed at shorter age intervals spanning infancy, adolescence and teenage years that are much higher compared to genetic correlations based on wider age intervals [8,14,85,86]. This pattern is consistent with autoregressive features. Cornes et al.’s [9] application of autoregressive modelling found evidence of largely age-invariant genetic influences on BMI at 12, 14 and 16. The authors also reported smaller but significant age-specific genetic influences on BMI, depending on sex, at 14 and 16 years that were uncorrelated with BMI at age 12 [9]. The pattern of age-invariant influences is consistent with the study by Couto Alves et al. [87], which examined BMI spanning ages 2 to 18 years and reported a robust overlap between the genetics of child and adult BMI. The same study also identified a completely distinct genetic architecture in infancy [87]. The reports by Warrington et al. [88] and Felix et al. [89] have shown how numerous replicated adult BMI loci also reach genome-wide significance in childhood GWAS studies of BMI. In terms of other LDSR studies, Trzaskowski et al. [20] reported a genetic correlation between BMI at 11 and 65 years of 0.86. The same study also found that the adult PRS for BMI explained at most 10% of the phenotypic variance in childhood BMI. Combined, the findings based on twin and molecular studies suggest that variability in heritability estimates spanning childhood, adolescence and early adulthood is likely explained by combination of mostly age-invariant plus age-specific genetic influences, which could potentially be better captured by autoregressive modeling.


Our findings should be interpreted in the context of four limitations.

First, the BMI data used here were not repeated measures, but pseudo longitudinal. This approach assumes no year of birth or cohort-related genetic heterogeneity. Until now, GenomicSEM reports have typically leveraged LDSR-derived genetic covariances in the context of cross-sectional hypotheses. Our pseudo longitudinal modeling is not unlike standard cross-sectional GenomicSEM analyses. Both approaches depend upon the GWAS summary statistics being derived from a homogenous ancestral group. There is also no requirement for summary statistics to be based on the same subjects. It remains important to reduce the likelihood that our age-specific GWAS results comprised subjects from heterogenous populations. This is important because cohorts can have different BMI heritability, different environmental influences on BMI, or differences in the genetic control of sensitivity to the environment, which can bias the covariance estimates. Danish and Swedish twin studies have illustrated differential heritability by showing how increases in mean BMI in successively younger cohorts has been accompanied by increasing genetic variance [90,91]. Therefore, to determine if cohort effects existed, we inspected the LDSR genetic correlations between the youngest and oldest age tranches i.e., two maximally age-discrepant samples of unrelated individuals. Here, the rg was 0.97 (see Table 1), which suggests that the likelihood of any cohort-related genetic heterogeneity was minimal. Note, we also performed GWAS on a subset of men (N = 8,337) and women (N = 7,681) with repeated BMI measures at any time from 48 to 61 years and then from 62 to 72 years. Here, the test-rest LDSR correlations were rg = 0.99 (p = 1.04e-03) and rg = 0.95 (p = 1.68e-04) for men and women respectively. Thus, genetic correlations were very high between and within subjects.

In another attempt to reduce the possibility of systematic differences between putative subpopulations in terms of allele frequencies, we re-ran the GWAS analyses using 40 PCs as covariates. As shown in S1 Table, there were only very minor differences in genomic inflation and SNP heritability between the 20 versus 40 PC results. Therefore, not only did genomic inflation remain the same regardless of the number of PCs, it did not change across age intervals. These results further reduce the likelihood of birth or cohort-related genetic heterogeneity.

Second, the UKB recruitment process did not represent a random sample of the UK population [92]. Subjects were predominately European, more likely to be older, female, to live in less socioeconomically deprived areas than nonparticipants, and when compared with the general population, were also less likely to be obese, to smoke, and to drink alcohol daily while reporting fewer self-reported health conditions [93,94]. Although Silventoinen et al.’s meta-analysis of twin data reported only minor differences in BMI heritability across divergent cultural-geographic regions [78,79], the extent to which the molecular-based genetic covariance structure observed here generalizes to non-European populations remains to be determined.

Third, while our results illustrate the flexibility of SEM in terms of its application to GWAS summary statistics to test a theory of longitudinal change, our modeling was not exhaustive. For instance, we did not test the hypothesis that changes in heritability could be better explained by latent growth or latent growth mixture models [95,96]. We note that the current method is limited to the analysis of summary variance-covariance matrices derived from the analysis of common variants. GenomicSEM does not model observed phenotypic information. Consequently, there was no mean information to model latent growth or mixture distributions. We also did not test hypotheses regarding sex differences other than to report results by sex. Dubois’ meta-analysis of 23 twin birth-cohorts found evidence of sex-limitation in terms of greater genetic variance in boys in early infancy through to 19 years [97]. In contrast, Elks et al.’s meta-regression of 88 twin-bases estimates of BMI heritability found no evidence of sex effects [13]. It remains to be determined if the observed minor differences in the genetic covariances and the ultimate, best fitting single-factor structure are empirically equivalent across sex.

Finally, our genomic modelling was based on aggregated GWAS summary data and so was entirely independent of environmental risks, which are known to be significant in the etiology of psychiatric and behavioral traits [98]. Consequently, our current approach precludes modeling the contribution of environmental influences with increasing age [99] or making allowances for any genetic control of sensitivity to the environment i.e. G x E interaction [78]. In this regard, methods that can simultaneously model the joint effect of genes and environment are likely to prove more informative. For instance, innovative approaches capable of applying genomic-relatedness based restricted maximum-likelihood [100] to structural equation modeling in the OpenMx [40] software package have the potential to analyze individual GWAS and phenotypic data and hold promise.


Structural equation model of GWAS summary statistics between the ages of 40 and 73 revealed that molecular genetic variance in BMI at successive 5-year age intervals could not be explained by the accumulation of age-specific genetic influences or autoregressive processes. Instead, a common set of stable genetic influences appears to underpin all genome-wide variation in BMI from middle to early old age in men and women.

Supporting information

S1 Table. Number of men & women with complete BMI & GWAS summary statistics at each age interval, as well as genomic inflation (λ) & SNP-based heritability (h2) for the GWAS analyses comprising 20 versus 40 principal components (PCs).



  1. 1. MacArthur J, Bowler E, Cerezo M, Gil L, Hall P, Hastings E, et al. The new NHGRI-EBI Catalog of published genome-wide association studies (GWAS Catalog). Nucleic Acids Res. 2017;45(D1):D896–D901. pmid:27899670
  2. 2. Speliotes EK, Willer CJ, Berndt SI, Monda KL, Thorleifsson G, Jackson AU, et al. Association analyses of 249,796 individuals reveal 18 new loci associated with body mass index. Nat Genet. 2010;42(11):937–48. pmid:20935630
  3. 3. Lee SH, Wray NR, Goddard ME, Visscher PM. Estimating missing heritability for disease from genome-wide association studies. Am J Hum Genet. 2011;88(3):294–305. pmid:21376301
  4. 4. Kaur Y, Wang DX, Liu HY, Meyre D. s. Obesity reviews: an official journal of the International Association for the Study of Obesity. 2019;20(3):385–406.
  5. 5. Yang J, Bakshi A, Zhu Z, Hemani G, Vinkhuyzen AA, Lee SH, et al. Genetic variance estimation with imputed variants finds negligible missing heritability for human height and body mass index. Nat Genet. 2015;47(10):1114–20. pmid:26323059
  6. 6. Popkin BM, Du S, Green WD, Beck MA, Algaith T, Herbst CH, et al. Individuals with obesity and COVID-19: A global perspective on the epidemiology and biological relationships. Obesity reviews: an official journal of the International Association for the Study of Obesity. 2020;21(11):e13128. pmid:32845580
  7. 7. Parohan M, Yaghoubi S, Seraji A, Javanbakht MH, Sarraf P, Djalali M. Risk factors for mortality in patients with Coronavirus disease 2019 (COVID-19) infection: a systematic review and meta-analysis of observational studies. Aging Male. 2020:1–9. pmid:32508193
  8. 8. Silventoinen K, Pietilainen KH, Tynelius P, Sorensen TI, Kaprio J, Rasmussen F. Genetic and environmental factors in relative weight from birth to age 18: the Swedish young male twins study. International journal of obesity (2005). 2007;31(4):615–21. pmid:17384662
  9. 9. Cornes BK, Zhu G, Martin NG. Sex differences in genetic variation in weight: a longitudinal study of body mass index in adolescent twins. Behav Genet. 2007;37(5):648–60. pmid:17896175
  10. 10. Haberstick BC, Lessem JM, McQueen MB, Boardman JD, Hopfer CJ, Smolen A, et al. Stable genes and changing environments: body mass index across adolescence and young adulthood. Behav Genet. 2010;40(4):495–504. pmid:20087641
  11. 11. Stunkard AJ, Foch TT, Hrubec Z. A twin study of human obesity. JAMA. 1986;256(1):51–4. pmid:3712713
  12. 12. Dahl AK, Reynolds CA, Fall T, Magnusson PK, Pedersen NL. Multifactorial analysis of changes in body mass index across the adult life course: a study with 65 years of follow-up. International journal of obesity (2005). 2014;38(8):1133–41. pmid:24193660
  13. 13. Elks CE, den Hoed M, Zhao JH, Sharp SJ, Wareham NJ, Loos RJ, et al. Variability in the heritability of body mass index: a systematic review and meta-regression. Front Endocrinol (Lausanne). 2012;3:29. pmid:22645519
  14. 14. Llewellyn CH, Trzaskowski M, Plomin R, Wardle J. From modeling to measurement: developmental trends in genetic influence on adiposity in childhood. Obesity (Silver Spring, Md). 2014;22(7):1756–61. pmid:24760426
  15. 15. Franz CE, Grant MD, Jacobson KC, Kremen WS, Eisen SA, Xian H, et al. Genetics of body mass stability and risk for chronic disease: a 28-year longitudinal study. Twin Res Hum Genet. 2007;10(4):537–45. pmid:17708694
  16. 16. Schousboe K, Willemsen G, Kyvik KO, Mortensen J, Boomsma DI, Cornes BK, et al. Sex differences in heritability of BMI: a comparative study of results from twin studies in eight countries. Twin Res. 2003;6(5):409–21. pmid:14624725
  17. 17. Silventoinen K, Kaprio J. Genetics of tracking of body mass index from birth to late middle age: evidence from twin and family studies. Obes Facts. 2009;2(3):196–202. pmid:20054225
  18. 18. Cardon LR. Genetic influence on body mass index in early childhood. In: Turner JR, Cardon LR, editors. Behavior Genetic Approaches in Behavioral Medicine. New York: Plenum Press; 1995. p. 133–43.
  19. 19. Bulik-Sullivan BK, Loh P-R, Finucane HK, Ripke S, Yang J, Schizophrenia Working Group of the Psychiatric Genomics C, et al. LD Score regression distinguishes confounding from polygenicity in genome-wide association studies. Nat Genet. 2015;47(3):291–5. pmid:25642630
  20. 20. Trzaskowski M, Lichtenstein P, Magnusson PK, Pedersen NL, Plomin R. Application of linear mixed models to study genetic stability of height and body mass index across countries and time. Int J Epidemiol. 2016;45(2):417–23. pmid:26819444
  21. 21. Winkler TW, Justice AE, Graff M, Barata L, Feitosa MF, Chu S, et al. The Influence of Age and Sex on Genetic Associations with Adult Body Size and Shape: A Large-Scale Genome-Wide Interaction Study. PLoS genetics. 2015;11(10):e1005378. pmid:26426971
  22. 22. Hewitt JK, Eaves LJ, Neale MC, Meyer JM. Resolving causes of developmental continuity or "tracking." I. Longitudinal twin studies during growth. Behav Genet. 1988;18(2):133–51. pmid:3377729
  23. 23. Nesselroade JR, Baltes PB. Adolescent personality development and historical change: 1970–1972. Monogr Soc Res Child Dev. 1974;39(1):1–80. pmid:4602888
  24. 24. McArdle JJ. Latent variable growth within behavior genetic models. Behav Genet. 1986;16(1):163–200. pmid:3707483
  25. 25. McArdle JJ, Epstein D. Latent growth curves within developmental structural equation models. Child Dev. 1987;58(1):110–33. pmid:3816341
  26. 26. Duncan TE, Duncan SC. A latent growth curve approach to investigating developmental dynamics and correlates of change in children’s perceptions of physical competence. Res Q Exerc Sport. 1991;62(4):390–8. pmid:1780561
  27. 27. Duncan TE, Duncan SC, Hops H. The effects of family cohesiveness and peer encouragement on the development of adolescent alcohol use: a cohort-sequential approach to the analysis of longitudinal data. J Stud Alcohol. 1994;55(5):588–99. pmid:7990469
  28. 28. Hjelmborg J, Fagnani C, Silventoinen K, McGue M, Korkeila M, Christensen K, et al. Genetic influences on growth traits of BMI: a longitudinal study of adult twins. Obesity (Silver Spring, Md). 2008;16(4):847–52. pmid:18239571
  29. 29. Ortega-Alonso A, Sipila S, Kujala UM, Kaprio J, Rantanen T. Genetic influences on adult body mass index followed over 29 years and their effects on late-life mobility: a study of twin sisters. J Epidemiol Community Health. 2009;63(8):651–8. pmid:19304672
  30. 30. Ortega-Alonso A, Sipila S, Kujala UM, Kaprio J, Rantanen T. Genetic influences on change in BMI from middle to old age: a 29-year follow-up study of twin sisters. Behav Genet. 2009;39(2):154–64. pmid:19067155
  31. 31. Eaves LJ, Long J, Heath AC. A theory of developmental change in quantitative phenotypes applied to cognitive development. Behav Genet. 1986;16(1):143–62. pmid:3707482
  32. 32. Boomsma DI, Molenaar PC. The genetic analysis of repeated measures. I. Simplex models. Behav Genet. 1987;17(2):111–23. pmid:3606535
  33. 33. Boomsma DI, Martin NG, Molenaar PC. Factor and simplex models for repeated measures: application to two psychomotor measures of alcohol sensitivity in twins. Behav Genet. 1989;19(1):79–96. pmid:2712815
  34. 34. Gillespie NA, Evans DE, Wright MM, Martin NG. Genetic simplex modeling of Eysenck’s dimensions of personality in a sample of young Australian twins. Twin Res. 2004;7(6):637–48. pmid:15607015
  35. 35. Gillespie NA, Kirk KM, Evans DM, Heath AC, Hickie IB, Martin NG. Do the genetic or environmental determinants of anxiety and depression change with age? A longitudinal study of Australian twins. Twin Res. 2004;7(1):39–53. pmid:15053853
  36. 36. Gillespie NA, Eaves LJ, Maes H, Silberg JL. Testing Models for the Contributions of Genes and Environment to Developmental Change in Adolescent Depression. Behav Genet. 2015;45(4):382–93. pmid:25894924
  37. 37. Long EC, Verhulst B, Aggen SH, Kendler KS, Gillespie NA. Contributions of Genes and Environment to Developmental Change in Alcohol Use. Behav Genet. 2017;47(5):498–506. pmid:28714051
  38. 38. Gillespie NA, Hatton SN, Hagler DJ Jr., Dale AM, Elman JA, McEvoy LK, et al. The Impact of Genes and Environment on Brain Ageing in Males Aged 51 to 72 Years. Frontiers in aging neuroscience. 2022;14:831002. pmid:35493948
  39. 39. Grotzinger AD, Rhemtulla M, de Vlaming R, Ritchie SJ, Mallard TT, Hill WD, et al. Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits. Nat Hum Behav. 2019;3(5):513–25. pmid:30962613
  40. 40. Neale MC, Hunter MD, Pritikin JN, Zahery M, Brick TR, Kirkpatrick RM, et al. OpenMx 2.0: Extended Structural Equation and Statistical Modeling. Psychometrika. 2016;81(2):535–49. pmid:25622929
  41. 41. Sudlow C, Gallacher J, Allen N, Beral V, Burton P, Danesh J, et al. UK biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age. PLoS Med. 2015;12(3):e1001779. pmid:25826379
  42. 42. Neale MC, Cardon LR. Methodology for Genetic Studies of Twins and Families. 1st ed. Dordrecht: Kluwer Academic Publishers; 1992.
  43. 43. Korkeila M, Kaprio J, Rissanen A, Koskenvuo M. Effects of gender and age on the heritability of body mass index. Int J Obes. 1991;15(10):647–54. pmid:1752725
  44. 44. UK Biobank Anthropometry [updated Version 1.0. Available from: [
  45. 45. Neale B. [Available from:
  46. 46. Bycroft C, Freeman C, Petkova D, Band G, Elliott LT, Sharp K, et al. The UK Biobank resource with deep phenotyping and genomic data. Nature. 2018;562(7726):203–9. pmid:30305743
  47. 47. R Core Team. R: A language and environment for statistical computing. Vienna, Austria 2020 [Available from:
  48. 48. Clarke TK, Obsteter J, Hall LS, Hayward C, Thomson PA, Smith BH, et al. Investigating shared aetiology between type 2 diabetes and major depressive disorder in a population based cohort. Am J Med Genet B Neuropsychiatr Genet. 2017;174(3):227–34. pmid:27480393
  49. 49. Day F, Karaderi T, Jones MR, Meun C, He C, Drong A, et al. Large-scale genome-wide meta-analysis of polycystic ovary syndrome suggests shared genetic architecture for different diagnosis criteria. PLoS genetics. 2018;14(12):e1007813. pmid:30566500
  50. 50. Deary V, Hagenaars SP, Harris SE, Hill WD, Davies G, Liewald DCM, et al. Genetic contributions to self-reported tiredness. Mol Psychiatry. 2018;23(3):609–20. pmid:28194004
  51. 51. Direk N, Williams S, Smith JA, Ripke S, Air T, Amare AT, et al. An Analysis of Two Genome-wide Association Meta-analyses Identifies a New Locus for Broad Depression Phenotype. Biol Psychiatry. 2017;82(5):322–9. pmid:28049566
  52. 52. Gibson J, Russ TC, Adams MJ, Clarke TK, Howard DM, Hall LS, et al. Assessing the presence of shared genetic architecture between Alzheimer’s disease and major depressive disorder using genome-wide association data. Translational psychiatry. 2017;7(4):e1094. pmid:28418403
  53. 53. Hagenaars SP, Harris SE, Davies G, Hill WD, Liewald DC, Ritchie SJ, et al. Shared genetic aetiology between cognitive functions and physical and mental health in UK Biobank (N = 112 151) and 24 GWAS consortia. Mol Psychiatry. 2016;21(11):1624–32. pmid:26809841
  54. 54. Haljas K, Amare AT, Alizadeh BZ, Hsu YH, Mosley T, Newman A, et al. Bivariate Genome-Wide Association Study of Depressive Symptoms With Type 2 Diabetes and Quantitative Glycemic Traits. Psychosom Med. 2018;80(3):242–51. pmid:29280852
  55. 55. Lehto K, Pedersen NL, Almqvist C, Lu Y, Brew BK. Asthma and affective traits in adults: a genetically informative study. Eur Respir J. 2019;53(5). pmid:30956207
  56. 56. Mills NT, Maier R, Whitfield JB, Wright MJ, Colodro-Conde L, Byrne EM, et al. Investigating the relationship between iron and depression. J Psychiatr Res. 2017;94:148–55. pmid:28715705
  57. 57. Ohi K, Otowa T, Shimada M, Sasaki T, Tanii H. Shared genetic etiology between anxiety disorders and psychiatric and related intermediate phenotypes. Psychol Med. 2019:1–13. pmid:30919790
  58. 58. Pain O, Dudbridge F, Cardno AG, Freeman D, Lu Y, Lundstrom S, et al. Genome-wide analysis of adolescent psychotic-like experiences shows genetic overlap with psychiatric disorders. Am J Med Genet B Neuropsychiatr Genet. 2018;177(4):416–25. pmid:29603866
  59. 59. Polimanti R, Peterson RE, Ong JS, MacGregor S, Edwards AC, Clarke TK, et al. Evidence of causal effect of major depression on alcohol dependence: findings from the psychiatric genomics consortium. Psychol Med. 2019;49(7):1218–26. pmid:30929657
  60. 60. Tylee DS, Sun J, Hess JL, Tahir MA, Sharma E, Malik R, et al. Genetic correlations among psychiatric and immune-related phenotypes based on genome-wide association data. Am J Med Genet B Neuropsychiatr Genet. 2018;177(7):641–57. pmid:30325587
  61. 61. van der Merwe C, Jahanshad N, Cheung JW, Mufford M, Groenewold NA, Koen N, et al. Concordance of genetic variation that increases risk for anxiety disorders and posttraumatic stress disorders and that influences their underlying neurocircuitry. J Affect Disord. 2019;245:885–96. pmid:30699873
  62. 62. Ward J, Tunbridge EM, Sandor C, Lyall LM, Ferguson A, Strawbridge RJ, et al. The genomic basis of mood instability: identification of 46 loci in 363,705 UK Biobank participants, genetic correlation with psychiatric disorders, and association with gene expression and function. Mol Psychiatry. 2019.
  63. 63. Wen Y, Zhang F, Ma X, Fan Q, Wang W, Xu J, et al. eQTLs Weighted Genetic Correlation Analysis Detected Brain Region Differences in Genetic Correlations for Complex Psychiatric Disorders. Schizophr Bull. 2018.
  64. 64. Wigmore EM, Clarke TK, Howard DM, Adams MJ, Hall LS, Zeng Y, et al. Do regional brain volumes and major depressive disorder share genetic architecture? A study of Generation Scotland (n = 19 762), UK Biobank (n = 24 048) and the English Longitudinal Study of Ageing (n = 5766). Translational psychiatry. 2017;7(8):e1205.
  65. 65. Witt SH, Streit F, Jungkunz M, Frank J, Awasthi S, Reinbold CS, et al. Genome-wide association study of borderline personality disorder reveals genetic overlap with bipolar disorder, major depression and schizophrenia. Translational psychiatry. 2017;7(6):e1155. pmid:28632202
  66. 66. Wong BC, Chau CK, Ao FK, Mo CH, Wong SY, Wong YH, et al. Differential associations of depression-related phenotypes with cardiometabolic risks: Polygenic analyses and exploring shared genetic variants and pathways. Depress Anxiety. 2019;36(4):330–44. pmid:30521077
  67. 67. Yang Y, Zhao H, Boomsma DI, Ligthart L, Belin AC, Smith GD, et al. Molecular genetic overlap between migraine and major depressive disorder. Eur J Hum Genet. 2018;26(8):1202–16. pmid:29995844
  68. 68. Ronald A, Pain O. A systematic review of genome-wide research on psychotic experiences and negative symptom traits: new revelations and implications for psychiatry. Hum Mol Genet. 2018;27(R2):R136–R52. pmid:29741616
  69. 69. Bulik CM, Sullivan PF, Wade TD, Kendler KS. Twin studies of eating disorders: a review. Int J Eat Disord. 2000;27(1):1–20. pmid:10590444
  70. 70. Fanous AH, Kendler KS. The genetic relationship of personality to major depression and schizophrenia. Neurotox Res. 2004;6(1):43–50. pmid:15184104
  71. 71. Fanous AH, Kendler KS. Genetic heterogeneity, modifier genes, and quantitative phenotypes in psychiatric illness: searching for a framework. Mol Psychiatry. 2005;10(1):6–13. pmid:15618952
  72. 72. Kendler KS. Twin studies of psychiatric illness. Current status and future directions. Arch Gen Psychiatry. 1993;50(11):905–15. pmid:8215816
  73. 73. Kendler KS. The genetic epidemiology of psychiatric disorders: a current perspective. Soc Psychiatry Psychiatr Epidemiol. 1997;32(1):5–11. pmid:9029981
  74. 74. Kendler KS, Diehl SR. The genetics of schizophrenia: a current, genetic-epidemiologic perspective. Schizophr Bull. 1993;19(2):261–85. pmid:8322035
  75. 75. Sullivan PF, Kendler KS. The genetic epidemiology of smoking. Nicotine & tobacco research: official journal of the Society for Research on Nicotine and Tobacco. 1999;1 Suppl 2:S51–7; discussion S69-70. pmid:11768187
  76. 76. Kendler KS, Chen X, Dick D, Maes H, Gillespie N, Neale MC, et al. Recent advances in the genetic epidemiology and molecular genetics of substance use disorders. Nat Neurosci. 2012;15(2):181–9. pmid:22281715
  77. 77. Rosseel Y. Lavaan: an R package for structural equation modeling. Journal of Statistical Software. 2012;48(2):1–36.
  78. 78. Silventoinen K, Jelenkovic A, Yokoyama Y, Sund R, Sugawara M, Tanaka M, et al. The CODATwins Project: The Current Status and Recent Findings of COllaborative Project of Development of Anthropometrical Measures in Twins. Twin Res Hum Genet. 2019;22(6):800–8. pmid:31364586
  79. 79. Silventoinen K, Jelenkovic A, Sund R, Honda C, Aaltonen S, Yokoyama Y, et al. The CODATwins Project: The Cohort Description of Collaborative Project of Development of Anthropometrical Measures in Twins to Study Macro-Environmental Variation in Genetic and Environmental Effects on Anthropometric Traits. Twin Res Hum Genet. 2015;18(4):348–60. pmid:26014041
  80. 80. Richardson TG, Sanderson E, Elsworth B, Tilling K, Davey Smith G. Use of genetic variation to separate the effects of early and later life adiposity on disease risk: mendelian randomisation study. BMJ. 2020;369:m1203. pmid:32376654
  81. 81. Brandkvist M, Bjørngaard JH, Ødegård RA, Åsvold BO, Smith GD, Brumpton B, et al. Separating the genetics of childhood and adult obesity: a validation study of genetic scores for body mass index in adolescence and adulthood in the HUNT Study. Hum Mol Genet. 2021;29(24):3966–73. pmid:33276378
  82. 82. Richardson TG, Crouch DJM, Power GM, Berstein FM, Hazelwood E, Fang S, et al. Disentangling the direct and indirect effects of childhood adiposity on type 1 diabetes and immune-associated diseases: a multivariable Mendelian randomization study. medRxiv. 2021.
  83. 83. Hone L, Jacobs BM, Marshall C, Giovannoni G, Noyce A, Dobson R. Age-specific effects of childhood BMI on multiple sclerosis risk: a Mendelian Randomisation study. medRxiv. 2021.
  84. 84. Helgeland O, Vaudel M, Juliusson PB, Lingaas Holmen O, Juodakis J, Bacelis J, et al. Genome-wide association study reveals dynamic role of genetic variation in infant and early childhood growth. Nature communications. 2019;10(1):4448. pmid:31575865
  85. 85. Silventoinen K, Bartels M, Posthuma D, Estourgie-van Burk GF, Willemsen G, van Beijsterveldt TC, et al. Genetic regulation of growth in height and weight from 3 to 12 years of age: a longitudinal study of Dutch twin children. Twin Res Hum Genet. 2007;10(2):354–63. pmid:17564525
  86. 86. Lajunen HR, Kaprio J, Keski-Rahkonen A, Rose RJ, Pulkkinen L, Rissanen A, et al. Genetic and environmental effects on body mass index during adolescence: a prospective study among Finnish twins. International journal of obesity (2005). 2009;33(5):559–67. pmid:19337205
  87. 87. Couto Alves A, De Silva NMG, Karhunen V, Sovio U, Das S, Taal HR, et al. GWAS on longitudinal growth traits reveals different genetic factors influencing infant, child, and adult BMI. Sci Adv. 2019;5(9):eaaw3095. pmid:31840077
  88. 88. Warrington NM, Howe LD, Paternoster L, Kaakinen M, Herrala S, Huikari V, et al. A genome-wide association study of body mass index across early life and childhood. Int J Epidemiol. 2015;44(2):700–12. pmid:25953783
  89. 89. Felix JF, Bradfield JP, Monnereau C, van der Valk RJ, Stergiakouli E, Chesi A, et al. Genome-wide association analysis identifies three new susceptibility loci for childhood body mass index. Hum Mol Genet. 2016;25(2):389–403. pmid:26604143
  90. 90. Rokholm B, Silventoinen K, Tynelius P, Gamborg M, Sorensen TI, Rasmussen F. Increasing genetic variance of body mass index during the Swedish obesity epidemic. PloS one. 2011;6(11):e27135. pmid:22087252
  91. 91. Rokholm B, Silventoinen K, Angquist L, Skytthe A, Kyvik KO, Sorensen TI. Increased genetic variance of BMI with a higher prevalence of obesity. PloS one. 2011;6(6):e20816. pmid:21738588
  92. 92. Keyes KM, Westreich D. UK Biobank, big data, and the consequences of non-representativeness. Lancet. 2019;393(10178):1297.
  93. 93. Fry A, Littlejohns TJ, Sudlow C, Doherty N, Adamska L, Sprosen T, et al. Comparison of Sociodemographic and Health-Related Characteristics of UK Biobank Participants With Those of the General Population. Am J Epidemiol. 2017;186(9):1026–34. pmid:28641372
  94. 94. Tyrrell J, Zheng J, Beaumont R, Hinton K, Richardson TG, Wood AR, et al. Genetic predictors of participation in optional components of UK Biobank. bioRxiv. 2020.
  95. 95. Hamer M, Bell JA, Sabia S, Batty GD, Kivimaki M. Stability of metabolically healthy obesity over 8 years: the English Longitudinal Study of Ageing. Eur J Endocrinol. 2015;173(5):703–8. pmid:26286585
  96. 96. Buscot MJ, Thomson RJ, Juonala M, Sabin MA, Burgner DP, Lehtimaki T, et al. Distinct child-to-adult body mass index trajectories are associated with different levels of adult cardiometabolic risk. Eur Heart J. 2018;39(24):2263–70. pmid:29635282
  97. 97. Dubois L, Ohm Kyvik K, Girard M, Tatone-Tokuda F, Perusse D, Hjelmborg J, et al. Genetic and environmental contributions to weight, height, and BMI from birth to 19 years of age: an international study of over 12,000 twin pairs. PloS one. 2012;7(2):e30153. pmid:22347368
  98. 98. Eaves L, Eysenck HJ, Martin NG. Genes, Culture, and Personality: An Empirical Approach. London: Academic Press; 1989.
  99. 99. Silventoinen K, Jelenkovic A, Sund R, Yokoyama Y, Hur YM, Cozen W, et al. Differences in genetic and environmental variation in adult BMI by sex, age, time period, and region: an individual-based pooled analysis of 40 twin cohorts. Am J Clin Nutr. 2017;106(2):457–66. pmid:28679550
  100. 100. Kirkpatrick RM, Pritikin JN, Hunter MD, Neale MC. Combining Structural-Equation Modeling with Genomic-Relatedness-Matrix Restricted Maximum Likelihood in OpenMx. Behav Genet. 2021. pmid:33439421