The current obesity “epidemic”: segregation of familial genetic risk in NHANES cohort supports a major role for large genetic effects ========================================================================================================================================= * Arthur B. Jenkins * Marijka Batterham * Lesley V. Campbell ## Abstract **Background/Objectives** The continuing increase in many countries in adult body mass index (BMI kg/m2) and its dispersion is contributed to by interactions between genetic susceptibilities and an increasingly obesogenic environment. Whether population susceptibility to obesogenic environments is mainly determined by a subgroup with high genetic susceptibility or susceptibility is more evenly distributed throughout the population is unresolved, due to uncertainties around relevant genetic and environmental architecture. We aimed to test the predictions of a Mendelian genetic architecture based on collectively common but individually rare large-effect variants and its ability to account for current trends in a large population-based sample. **Subjects/Methods** We studied publicly available adult BMI data (n = 9102) from 3 cycles of NHANES (1999, 2005, 2013) adjusted for age, gender and race/ethnicity. A first degree family history of diabetes (FH) served as a binary marker (FH/FH1) of genetic obesity susceptibility. We tested for multi-modality in BMI non-parametrically using a runs tests in conditional quantile regression (CQR) models of FH effects, obtained parametric fits to a Mendelian model in FH1, and estimated FH-environment interactions in CQR models and in ANCOVA models incorporating secular time. **Results** A unimodal FH effect on BMI was excluded (p≤0.0001) in CQR models and parametric fits to a Mendelian model in FH1 identified 3 modes at 25.8±1.0 (SEM), 32.1±1.8 and 40.6±2.5 kg/m2. Mode separation accounted for ~40% of BMI variance in FH1 providing a lower bound for the contribution of large effects. CQR analysis identified strong interactions between FH and environmental factors (p≤0.01) and FH1 accounted for ~60% of the secular trends in BMI and its SD in ANCOVA models. **Conclusions** Multimodality in the FH effect is inconsistent with a predominantly polygenic small effect architecture. We conclude that large genetic effects interacting with obesogenic environment provide a better, quantitative explanation for current trends in BMI. ## Introduction The recent and continuing increase in the global mean adult BMI, first seen in high income countries, is now apparent in most countries across a wide range of ethnic composition and socio-economic conditions (1) and is accompanied by increases in measures of dispersion (2, 3). Although BMI is known from family-based studies to be under strong genetic influences (4) population genetic backgrounds have been effectively constant over this time, implying that BMI trends are driven by change in environmental factors (obesogenic environment, OE). Evidence from twin studies, which demonstrate increased genetic variance over time, supports an important role for interactions between OE and genetic susceptibility (G × OE) on both mean and dispersion of BMI (3, 5), but how large a role is not yet clear. Defining the role of G × OE in “epidemic” obesity, and hence of genetic susceptibility itself, is hindered by problems of measurement and modeling of interactions (6) and by uncertainty around both the genetic architecture (4) and the exact nature of the environmental drivers (7). Whether a population’s susceptibility to OE is predominantly determined by a subgroup with high genetic susceptibility or is more evenly spread within populations is unresolved despite important implications for the management of obesity and related disorders at population and individual levels (2, 8–10). The genetic variants responsible for obesity susceptibility remain largely unknown. Genome-wide association studies (GWAS) have identified significant associations with >200 markers with small effects on BMI (polygenes), together explaining only approximately 3-4 % of total variance compared to family-based heritabilities (h2) of 50-75% (11). Few causative mechanisms responsible for these phenotypically weak associations are known (4). The sources of the h2 unaccounted for by GWAS are uncertain; proposals include overestimation of h2, large numbers of common genetic variants with small, statistically insignificant effects on phenotypes (12, 13) and importantly, candidates not tested in most GWAS. Among the latter are rare genetic variants with large phenotypic effects and G × OE interactions (4). Recently significant G × OE interactions have been detected in individual GWAS loci and in composite genetic risk scores, which explain little of the missing component of h2 (14, 15). A family history of diabetes (FH) is a potent, predominantly genetic (16, 17) risk factor for diabetes diagnosis (DM) and for obesity-related phenotypes (18–21) consistent with the strong association between type 2 DM and overweight/obesity. Familial effects on obesity-related phenotypes in adults are also predominantly genetic (3, 22), so to the extent that the DM generating FH is of type 2 (approximately 94% of DM in the US population (23)), FH is a prevalent and readily obtained marker of genetic susceptibility both to diabetes and to the obesity commonly preceding it. We have reported evidence from a small sample of a multi-modal effect of FH on a composite adiposity index consistent with segregation in families of discrete obesity risk (21). Polygenic risk scores (PRS) based on large numbers of small effects are expected to be, and appear to be, normally-distributed (24, 25) and cannot account for familial segregation of risk. The present work is based on the alternative hypothesis that individually rare, but collectively common, genetic variants with large phenotypic effects are the source of most of the missing h2 and of most of G × OE, and that their effects can be detected through analyses of phenotypic segregation in high-risk families (26). The Continuous National Health and Nutrition Examination Survey (NHANES) is a continuing (1999-) large-scale population-based survey incorporating an index of adiposity (Body Mass Index, BMI) and first-degree FH (FH/FH1) together with potential covariates and confounders. Although BMI has recognized limitations as an adiposity phenotype (26, 27) it is the basis for most large-scale genetic studies and like other authors, we assume that a large enough scale and appropriate modeling of covariates will reduce effects of imprecision and bias (11). We aimed to test in a large multi-cycle NHANES sample for the presence of familial segregation of genetic risk and to estimate the contribution of FH, and by extension all discrete genetic risk, to recent secular trends in adult BMI. Our results support a predominant role for large genetic effects interacting with OE in the obesity “epidemic”. ## Data and Methods ### Data We used data from the 1999-2000, 2005-2006 and 2013-2014 cycles of NHANES ([https://www.cdc.gov/nchs/nhanes/index.htm](https://www.cdc.gov/nchs/nhanes/index.htm) accessed 25 Aug 2017). We extracted records for participants age 20-65 years with non-missing gender, race/ethnicity, BMI, diabetes family history (FH) and diabetes diagnosis data, and current smoking status if available. The definitions of two fields changed over the sampling period: 1) Diabetes family history was defined in terms of 1° and 2° relatives in 1999-2000 but by 1° relatives only in subsequent cycles. We recoded the 1999-2000 diabetes family history data to conform to the later definition using the separately collected data for affected parents and siblings. 2) The self-identified race/ethnicity field (RIDRETH1) code was used excluding other races (OR) to maintain consistency across cycles (Supplementary Methods). We excluded from the primary analyses subjects diagnosed with diabetes because of possible confounding by effects of either diabetes or diabetes therapies on BMI. The resulting data set is summarized in Table 1. View this table: [Table 1:](http://biorxiv.org/content/early/2019/08/29/749606/T1) Table 1: Participants by diabetes status (DM/DM1) ### Statistical analyses #### Approach We treat the data as a convenience sample and took no account of the sampling weights provided by NHANES to permit nationally representative estimates. Our results are not intended to be representative of the US population. Our primary analyses are based on non-parametric visualization (kernel-smoothing) and analyses (conditional quantile regression, CQR) of distributions requiring no prior distributional assumptions. Parametric fits to multimodal distributions were then used to quantify the contributions of the predicted large genetic effects model. FH(0/1) is treated as a binary genetic risk marker and calendar time as a continuous surrogate of OE. Effects of OE interacting with FH were assessed in CQR models, and also in least-squares ANCOVA models using bootstrap resampling to minimize distributional assumptions in the calculation of effect size estimates and errors. All analyses were performed using R 3.3.1 (28). #### Summary statistics Heterogeneity of the samples across cycles was assessed by Chi square test for categorical variables and by one-way ANOVA for age. Effects on BMI were assessed by ANCOVA against continuous time (yr = calendar start year - 1999). Effects on phenotype SD’s were assessed by Bartlett’s test in one-way ANOVA models. #### Adjustment Prior to analysis BMI was adjusted for effects of age, gender and race/ethnicity in a linear model (age + age2 + race × gender). The adjustment model accounted for 4 % of the total variance in BMI (Supplementary Table S1). #### Distributions ##### Visualization The effect of FH on the distribution of adjusted BMI was visualized using kernel-smoothed density estimates by FH status (R base function density). The degree of smoothing is controlled by the bandwidth parameter (bw) which was obtained in the full non-diabetic data set (bw = 0.99) from a measure of the dispersion of the data (29). This produces a continuous distribution function and is widely used to visualise features of potential interest which may be obscured in histograms. The credibility of apparent effects of FH on the shape of the distribution was assessed by post-hoc analysis of density differences (FH1 – FH) by quantiles (n=20) of the full sample. Mean density differences with SE were obtained by quantile by bootstrap resampling with replacement (1000 draws, stratified by FH status with resample sizes = strata sizes) and tested against zero using a Z-test. ##### Conditional Quantile Regression (CQR) Conditional quantile regression is a powerful tool for analyzing the effect of covariates on distributions without assumptions of distributional shape. In contrast to ordinary least-squares (OLS) regression which characterizes effects on global features of a distribution, CQR analyses local effects of covariates independently at any specified quantiles and can detect and test variations in covariate effects across quantiles. Originating in econometrics (30) it is now used in other areas including genetics (31). In the CQR framework developed by Abadi et al (14) for analysis of genomic markers, trends in effect sizes across quantiles represent interactions between genetic effects and unobserved environmental and/or genetic factors. We treat FH as a binary genetic risk marker (FH/FH1) and a linear trend in quantile regression coefficients (ß1i) across quantiles (**T**i) represents summed linear interactions of FH with unobserved factors. We analysed the effects of FH on adjusted BMI by CQR using the R package quantreg. The effect of all interactions on the FH effect was tested in in a 2 parameter linear model: for each quantile **T**i in y, ![Formula][1] where y(**T**i | FH=fh) = the ith quantile of adjusted BMI conditional on the value of FH (0,1), the intercept ß0i is the ith quantile value in FH and ß1i is the FH effect size in quantile i. The interaction between FH and continuous calendar time was estimated in the ANCOVA model: ![Formula][2] where yr = cycle start year – 1999, ß0i is the ith quantile value in FH at yr =0 and ß2i and ß3i are CQR coefficients for time and time*FH interaction effects in quantile i. Equality of CQR parameter effect sizes across quantiles was tested using a Khmaladze test (32) (R package quantreg). The shape of the interaction relationship on the BMI scale was assessed in an OLS relationship between quantile coefficients ß1 and ß, which represents a linear model of a transformed quantile-quantile plot between FH1 and FH after adjustment for covariates, and models a unimodal effect. Residuals from the relationship were tested against randomness using a Wald-Wolfowitz runs test (R package randtests), a simple, general non-parametric test of randomness in ordered binary observations. The number of runs is compared to expectations under a normal approximation to the random sampling distribution. Randomness is rejected in a two-sided test if the number of observed runs is too high indicating high frequency oscillations, or too low indicating longer structures. We applied a left-sided runs test to residuals from regression relationships testing for large structures and interpret significance as excluding a unimodal effect and therefore as evidence of multiple modes in the effect. ##### Parametric fits We obtained fits to a 3-component normal mixture distribution representing a simple Mendelian model of fixed genetic effect using an expectation-maximization algorithm (normalmixEM function in the R package mixtools). The models are characterised by the fitted means (μi), standard deviations (σi) and mixing proportions (λi) of the three component distributions. Full model fits were obtained in FH1 but were not obtainable in FH or DM1 groups and we constrained μi in those groups to values estimated in FH1 in order to obtain comparable estimates of σi and λi. Risk allele frequencies (q) under an additive Mendelian model of large genetic effects were calculated from the fitted λi: ![Formula][3] where λ2 and λ3 represent the proportions of carriers of 1 and 2 risk alleles respectively.Within-sample consistency of calculated q across the three groups analysed was assessed by comparing fitted qFH1 with the prediction from random mating of DM1 into the full sample: ![Formula][4] #### Secular trends Effects of diabetes family history status (FH, FH1) and continuous time (yr = calendar start year - 1999) on adjusted BMI and its standard deviation (SD) were assessed in ANCOVA models of the form: ![Formula][5] where y = adjusted BMI mean or SD by FH status (0/1) and cycle, and yr = cycle start year – 1999. Each OLS fit estimated 4 parameters from the 6 data points. Mean parameter estimates with 95% CI were obtained by bootstrap resampling with replacement (1000 draws stratified by FH status and cycle with resample sizes = strata sizes). #### Comparison of cross-sectional and secular trend effects Effects of FH on BMI distribution and on secular trends in BMI were compared by calculating the contribution (%) of FH1 to the effect in the full non-diabetic sample for calculated risk allele frequency (q%) and to the slope (ß%) of the relationships between time and BMI in ANCOVA model described above. Mean (± SE where possible) q% and ß% were calculated in the relevant bootstrap samples. ## Results ### Participant characteristics Data from 9102 non-diabetic subjects met the inclusion criteria, approximately equally distributed across the 3 cycles. Gender balance varied little but there was a cycle effect in race/ethnicity, most obvious in the reduced representation of MA in the two later cycles. Average age varied across cycles but not its SD, while adjusted BMI and its SD showed linear trends with cycle time. FH1 prevalence was higher in the two later cycles compared to 1999-2000 as was DM1 prevalence. Current smoking status was predominantly missing in the data (55%) and was not included in the BMI adjustment model. However smoking status was not related to FH whether analysed in the full data (χ2 = 2.80, 2 df, p = 0.25) or in those with non-missing smoking status (χ2 = 0.43, 1 df, p = 0.51), hence is unlikely to confound analyses of FH effects. The mean age at diagnosis of DM (43.6 yr) is consistent with predominantly type 2 DM in the sample. ### Distributions #### Visualization Adjusted BMI in the non-diabetic sample showed an apparently unimodal distribution, right-skewed compared to a normal model and closer to a log-normal model (Fig 1A). When visualized by FH status (Fig 1B) the predicted multimodality in FH1 was indicated with modes in the normal weight, overweight and obese regions of the BMI distribution. In contrast FH showed an apparently unimodal distribution and a difference in shape between the two groups was supported by the pattern of formal significance in the post-hoc analysis of density differences between groups (Fig 1B). BMI distribution in the diabetic sample appeared to be depleted in the lower mode and enriched in the upper modes compared to FH1 (Fig 1C). ![Fig 1:](http://biorxiv.org/https://www.biorxiv.org/content/biorxiv/early/2019/08/29/749606/F1.medium.gif) [Fig 1:](http://biorxiv.org/content/early/2019/08/29/749606/F1) Fig 1: Distribution of adjusted BMI in non-diabetic (DM) and diabetic (DM1) participants in combined NHANES 1999-2000, 2005-2006 and 2013-2014 cycles. A) Full non-diabetic sample (n=9102) binned by quantiles (n=20) with superimposed kernel-smoothed and fitted densities in normal and log-normal models. B) Kernel-smoothed adjusted BMI density by FH status. * significant (p<0.05) difference in empirical density (FH1 – FH) by quantiles of the full sample shown in panel A. C) Kernel-smoothed adjusted BMI density in non-diabetic FH1 (n=3297) compared to diabetic participants (n=793). #### CQR Analysis of the effect of FH status on the shape of the BMI distribution using CQR demonstrated increasing FH effect size at higher levels of BMI (p ≤ 0.01, Fig 2A, main panel), indicating strong interactions between FH1 and other variables not included in the model. FH1 effect size ranged from < 1 kg/m2 in the lower quantiles to ~3 kg/m2 in the upper quantiles, substantially different in both regions to the OLS estimate (1.7 kg/m2). The approximate linearity of FH1 effects by quantile seen in main panel of Fig 2A supports simple 1st order interactions, with that linearity emphasised by an OLS analysis on the BMI scale between quantile coefficients ß1 (FH1) and ß (FH) (slope = 0.148 ± 0.003 (SE), R2 = 0.98). Adjustment for main and interaction effects of calendar time in the model (Supplementary Fig S2) weakened the trend in ß1 across quantiles (p > 0.1, Fig 2B main panel) and the OLS relationship between ß1 and ß (slope = 0.103 ± 0.006, R2 = 0.86), supporting the conclusion that calendar time is a strong surrogate of obesogenic environmental influences interacting with genetic factors as represented by FH status. ![Fig 2:](http://biorxiv.org/https://www.biorxiv.org/content/biorxiv/early/2019/08/29/749606/F2.medium.gif) [Fig 2:](http://biorxiv.org/content/early/2019/08/29/749606/F2) Fig 2: Conditional quantile regression effects of FH on adjusted BMI in non-diabetic participants in models consisting of FH alone (A) and in interaction with calendar time (B). The main panels show the FH main effect size (ß1) by quantile with 95% CI (grey-shaded area), the OLS estimate of the average effect (solid black line) with 95% CI (dotted black lines) and p-values associated with Khmaladze tests for equality of ß1 across quantiles. The insets show the patterns of residuals (Δß1) from linear regressions of ß1 against conditional quantiles in FH (ß), with 95% CI on the fits (dotted lines) around the lines Δß1 = 0 representing perfect fits. While the overall OLS relationship between ß1 and ß was linear there was strong evidence for additional non-linear structure in an analysis of residuals from the relationship (Fig 2A inset) which found significant non-randomness (runs test, p = 7.4 × 10−5) attributable to a small number of broad excursions. Adjustment for time effects accentuated the pattern (Fig 2B inset, runs test p = 2.2 × 10−5). While these patterns in the conditional quantiles do not map directly onto the unconditional quantile plots in Fig 1B, by rejecting the unimodal effect hypothesis they add strong support to the conclusion that FH1 has multimodal discrete effects on BMI. The pattern of residuals after adjustment for time effects (Fig 2B inset) exhibits 3 broad peaks, with suggestions of finer structure particularly in the central peak. The lower peak in the low-normal weight range may derive from the presence of type 1 diabetes family history in the sample, while the upper two are consistent with the predicted discrete effects of FH1 derived from type 2 diabetes. #### Parametric analysis The distribution of BMI in FH1 appears consistent with a simple Mendelian model and fitting a 3-component normal distribution model to the FH1 data resulted in robust estimates of component means and separations (Fig 3A), as well as mixing coefficients and SDs (Table 2). Approximately 50% of FH1 occupied the upper two modes and separation between modes accounted for approximately 40% of the total variance in adjusted BMI with the remainder assigned to dispersion within modes (Fig 2B). Under a Mendelian model the variance due to mode separation represents a lower bound on the contribution of large effects as some of the dispersion within modes represents variance in effect sizes of individual contributing causal loci (see Discussion) which will contribute to the ~60% of variance assigned to within-modes. Estimates of component SDs and mixing proportions with component means, constrained for FH and DM1 to those identified in the FH1 data, support enrichment in the two upper components in FH1 compared to FH (48% vs. 33%) and more strongly in DM1 (72%). Predicted risk allele frequencies in FH1 (q - Table 2) express these distributional properties in Mendelian terms and show within-sample consistency in that qFH1 predicted from random mating of DM1 (0.37) is not different to the fitted estimate (0.30 ± 10). View this table: [Table 2:](http://biorxiv.org/content/early/2019/08/29/749606/T2) Table 2: Three-component normal mixture distribution fits to adjusted BMI by FH and DM status¥ ![Fig 3:](http://biorxiv.org/https://www.biorxiv.org/content/biorxiv/early/2019/08/29/749606/F3.medium.gif) [Fig 3:](http://biorxiv.org/content/early/2019/08/29/749606/F3) Fig 3: A) Adjusted BMI density in FH1 by quantile (grey bars) and kernel-smoothed (black line) with fits to a three component normal mixture distribution. B) Estimated contributions in FH1 of the components of the mixture distribution to the prevalence (mixture coefficients, λ) and variance of adjusted BMI. ![Fig 4:](http://biorxiv.org/https://www.biorxiv.org/content/biorxiv/early/2019/08/29/749606/F4.medium.gif) [Fig 4:](http://biorxiv.org/content/early/2019/08/29/749606/F4) Fig 4: Effects of diabetes family history (FH0/1) on linear secular trends in age-, gender- and race/ethnicity-adjusted BMI mean ± se (A) and standard deviation ± se (B). Parameter estimates with 95% CI were obtained in ANCOVA models by stratified bootstrap resampling of all non-diabetic individuals (see Methods). Dotted lines enclose 95% CI on fitted values at each point; ß = regression slope vs. time (kg/m2 per year); Δß = ßFH1 – ßFH0 (95%CI). ### Secular trends Adjusted BMI mean (Fig 2A) and SD (Fig 2B) increased over the sampling period significantly faster in FH1 compared to FH in the bootstrapped ANCOVA model, and estimates of ß and Δß in the mean data were indistinguishable from the OLS estimates provided by the CQR analysis (Supplementary Fig S2). Similar results were obtained with log-transformed BMI (Supplementary Fig S3). FH1 accounted for 62% of the BMI mean trend and 60% of the BMI SD trend in this sample over the period 1999-2014, effects similar in magnitude to the estimated FH1 contribution to the sample risk allele frequency (50%, Supplementary Table S2). ## Discussion ### Summary We tested the prediction of segregation of discrete effects of FH on adult BMI (21), modeled as modes of distribution, and estimated the contribution of FH1 to recent trends in BMI mean and dispersion in a large population-based sample. The results support a predominant role in the recent obesity “epidemic” for rare genetic variants with large effects interacting with OE. ### Segregation of genetic susceptibility The non-parametric analysis provided evidence for a multi-modal distribution in the FH1 group consistent with the prediction of segregation of large genetic effects in families (21). Multi-modality was supported by the analysis of density differences between FH1 and FH by unconditional quantiles (Fig 1B) and by evidence of shape in the relationship between CQR coefficients on the BMI scale (Fig 2A&B insets). Polygenic risk scores (PRS) in population-based samples are expected to be normally-distributed, and appear to be so (24, 25). Any elevated polygenic obesity risk in DM1 will dilute into the mating population resulting in a right-shifted distribution in FH1 compared to FH, not multi-modality. Alternative explanations for multi-modality might be discrete stratification of OE which seems unlikely, or un-modeled interactions between FH and other covariates. Un-modeled interactions between FH and stratified residual confounders may exist and contribute but we found no evidence for this in plots of distributions by gender and race/ethnicity (Supplementary Fig S1) or in an analysis of smoking status against FH. Discrete inheritance of genetic variants with large effects remains the most likely explanation for multi-modality in the BMI distribution. Approximately 40% of the adjusted BMI variance in FH1 was accounted for by between-modes variance (Fig 3B) but this represents a lower bound since the identified modes are likely to be synthetic ie composed of a range of effect sizes due to rare variants at different loci. Indications of fine structure within the broad peaks (Fig 2B inset) are suggestive. Examples of rare variants with large effects on BMI in adults (ß) are known from studies of candidate genes and monogenic obesity loci (26) while more recently a common variant in Samoans (EAF = 0.26, ß ≈ 1.4 kg/m2), very rare in other populations (33), and an African-specific rare variant (EAF = 0.008, ß =4.6 kg/m2) undetected in Europeans and Asians (34) have been identified by GWAS. Overall, ß in these nine examples ranges from 1.4-9 kg/m2 and a similar range in effect sizes in the NHANES sample would contribute substantially to the within-mode variance estimated here. A combination of within-subject variance (~5% (35)) with polygenic variance (~ 5% (4)) sets a lower bound for within-modes variance and hence the upper bound for between modes, implying that between 40% and 90% of total variance in FH1 may be attributed to large genetic effects. ### G × OE FH1 is a prevalent (36%) and powerful determinant of the rate of change of mean BMI and its dispersion over time, accounting for 62% of the BMI trend and 60% of the BMI SD trend in this sample over 1999-2014. Under a polygenic model the familial risk would be distributed normally over FH1 which would then be a marker of a large fraction of the at-risk population. However under the Mendelian model supported here genetic risk would segregate in families and only approximately 50% of FH1 would acquire the excess familial risk and only ~18% of the sample would then account for ~60% of the trends. Individuals with DM1 must represent a fraction of individuals with elevated genetic obesity risk and it is likely that the remainder, particularly those with a family history of obesity without DM, would substantially increase the genetic component of the trends consequent to the high heritability of BMI (22). This Mendelian model is internally consistent in estimates of risk allele frequencies (q) in FH1, FH and DM1 (Table 2) and in comparisons of FH1 effect sizes in cross section (q, ~50%) and over time (ß, ~60%) (Supplementary Table S2). Our results support the proposition that the largest part and perhaps all of recent trends in mean and dispersion of BMI are due to a minor subset of individuals with elevated genetic susceptibility to OE. ### Limitations The design and interpretation of fits to parametric mixture distribution models involves choices concerning the number of components, parameter starting values and algorithms, and fit to a specific model cannot be taken in isolation as support for its structural validity. We base our choice and structural interpretation of 3-component normal mixture model fits and parameters on the *a priori* hypothesis of Mendelian segregation of obesity risk in families (21) supported by the non-parametric distributional plots (Fig 1B,C) and CQR analysis (Fig 2A,B insets). Like Abadi et al (14) we interpret interactions in the CQR analysis as predominantly G × OE although a contribution from G × G interactions cannot be excluded. Our interpretation is supported by the effects on the interaction of including calendar time in the CQR model (Fig 2B). Other limitations discussed above include our inability to exclude discreet stratification of OE and the possible influence of unmeasured/unknown confounders of FH. ## Conclusions We conclude that a Mendelian model of individually rare but collectively common genetic risk variants with large effects interacting with OE provides a plausible quantitative explanation for recent trends in obesity and should be favored over a predominantly polygenic model which does not. The evidence for a predominant role for polygenes (13) can appear to be strong (eg “Polygenic obesity is the most common form of obesity in modern societies…” (36)) but recent interpretations seek to explain the still missing heritability in obesity in terms of unidentified large genetic effects and G × OE (4, 37) and recommend a renewed focus on family-based designs and on specific populations in which large effect variants may be enriched (33, 34). Our results strengthen that view by showing that a model based on unidentified segregating variants with large effects interacting with OE can account for the largest part of the secular trend in obesity and its dispersion in a large population-based sample. We can’t predict what positive clinical or public health changes might follow from these findings but they should help refocus research away from the under-performing but entrenched big idea (38) that is polygenic obesity. ## Supporting information Supplemental Methods Figures Tables [[supplements/749606_file02.pdf]](pending:yes) Supplementary information is available at The International Journal of Obesity’s website. **Supplementary Methods:** Race/Ethnicity coding **Supplementary Table S1**: BMI-adjustment model parameters **Supplementary Table S2:** Comparison of effects of diabetes family history on secular trends in adjusted BMI and its SD and on calculated risk allele frequencies (q) in non-diabetic participants. **Supplementary Fig S1:** Kernel-smoothed adjusted BMI densities by FH, gender and race/ethnicity **Supplementary Fig S2:** time and time × FH interaction effects in a Conditional quantile regression of adjusted BMI in an ANCOVA model. **Supplementary Fig S3:** Secular trends in log-transformed adjusted BMI mean and SD ## Competing Interests The authors declare no competing financial or non-financial interests. * Received August 27, 2019. * Revision received August 27, 2019. * Accepted August 29, 2019. * © 2019, Posted by Cold Spring Harbor Laboratory This pre-print is available under a Creative Commons License (Attribution-NonCommercial-NoDerivs 4.0 International), CC BY-NC-ND 4.0, as described at [http://creativecommons.org/licenses/by-nc-nd/4.0/](http://creativecommons.org/licenses/by-nc-nd/4.0/) ## References 1. 1.Di Cesare M, Bentham J, Stevens GAA et al. 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