To this end, we conducted a genome-wide association study of gc of adult leaves in a maize inbred association panel that was evaluated in four environments . Five genomic regions significantly associated with gc were resolved to seven plausible candidate genes . These candidates are potentially involved in cuticle biosynthesis, trafficking and deposition of cuticle lipids, cutin polymerization, and cell wall modification. Laser microdissection RNA sequencing revealed that all these candidate genes, with the exception of the CER7 homolog, were expressed in the zone of the expanding adult maize leaf where cuticle maturation occurs. With direct application to genetic improvement, moderately high average predictive abilities were observed for whole-genome prediction of gc in locations (0.46 and 0.45) and across all environments (0.52). The findings of this study provide novel insights into the genetic control of gc and have the potential to help breeders more effectively develop drought-tolerant maize for target environments.The cuticle, a hydrophobic layer of cutin and waxes synthesized by plant epidermal cells, is the major barrier to water loss when stomata are closed at night and under water-limited conditions. Elucidating the genetic architecture of natural variation for leaf cuticular conductance ( The cuticle is a hydrophobic layer covering the surface of the shoot, which limits transpiration, in addition to protecting shoot tissues from UV radiation, heat, and pathogen attack . The majCuticle composition and structure varies widely among species and tissue types . RelatioIn addition to modulation of its composition by drought stress, a variety of other observations support a role for the cuticle in drought tolerance. Most mutations and other genetic modifications affecting cuticle composition or wax load increase its permeability to water, and this has often been associated with decreased drought tolerance . Maize is most sensitive to drought stress at flowering  enhance selection of candidate genes impacting this trait through an LM-RNAseq analysis of the expanding maize adult leaf; and (iii) evaluate whole-genome prediction models to facilitate genomic selection on this trait, providing tools for potential improvement of drought-tolerance in maize for target environments.In this study, we utilized GWAS combined with laser microdissection RNA sequencing (LM-RNAseq) of epidermal tissue samples, from zones of the expanding maize leaf where the cuticle develops, to implicate candidate genes controlling the water barrier function of the maize leaf cuticle. Methods directly measuring permeability of the cuticle to water . While slowering , we utilgc). The inbred lines were planted at the Maricopa Agricultural Center, Maricopa, AZ, and University of California San Diego, San Diego, CA, in 2016 and 2017. The layout of the experiment in each of the four environments (location × year combination) was arranged as an augmented incomplete block design. Within each of the 26 incomplete blocks, the incomplete block of 18 experimental lines was augmented by the addition of two checks  in random positions, for a total of 20 entries. The entire experiment of 468 unique inbred lines and 52 repeated checks was grown as a single replicate in each environment. Edge effects were reduced by planting a locally adapted maize inbred line around the perimeter of the experiment. Experimental units were one-row plots of 3.05 m (Maricopa) and 4.88 m (San Diego) in length with 1.016 m inter-row spacing. There was a 0.91 m alley at the end of each plot. In each plot, 12 kernels were planted, followed by thinning the stand as needed to limit plant-to-plant competition. We obtained and summarized meteorological data (Table S1) from automated weather stations located at a distance of ∼200 m or less from the experimental field sites in Maricopa, AZ  and San Diego, CA (Scripps Hydroclimate Weather Station).A set of 468 maize inbred lines from the Wisconsin Diversity panel , and transferred to a dark room where they were kept with cut leaf bases immersed in water throughout the analysis. Diffusion conductance was measured at a series of timepoints for a selection of lines that had previously been demonstrated to have high gc, and B73 as a reference standard harvested each sampling day. As shown in Figure S1, most lines reached minimum conductance values, indicating stomatal closure, within 30 min, and all lines reached minimum values within 90 min. Based on these findings, we concluded that 2 h in the dark was sufficient to achieve stomatal closure, even for lines with high gc.Initially, a porometer  was used to measure diffusion conductance for adult leaves collected from the field in the morning  was recorded as the number of days from planting to initiation of pollen shed for 50% of the plants in a plot. For each plot, gc phenotyping process was flattened, imaged, and then oven-dried as earlier described and weighed. Each image contained 4 to 7 leaves, depending on their sizes. Next, images were individually analyzed with a custom ImageJ (2) of each leaf. Even though every attempt was made to flatten the leaves, there were frequent occurrences of where wavy leaves could not be completely flattened. Very strong Pearson’s correlations were observed between the plot-level averages of leaf dry weight and surface area in MA (r = 0.93) and SD (r = 0.92) in 2017 . Given these strong correlations and challenges in measuring surface area, leaf dry weight was considered to be a reasonable approximation of leaf surface area, and was used in the calculation of cuticular conductance as described below.To investigate the degree to which dry weight approximates surface area, we constructed an imaging table that consisted of a digital camera (Canon PowerShot S110) mounted at a fixed distance and folding table top to help flatten the adult maize leaves. In 2017, each experimental leaf that had completed the gc) from unit surface area was calculated as follows:-1) is the coefficient of the linear regression of leaf wet weight (g) on time (h), and dry weight (g) is an approximation of leaf surface area.Adult leaf cuticular conductance (gc) for significant outliers, univariate mixed linear models that enabled the estimation of genetic effects independent of field design effects were fitted as follows: (1) each single environment; (2) the two environments in each location; and (3) all four environments. The model terms included grand mean and check as fixed effects and environment, genotype, genotype-by-environment (G×E) interaction (only for Models 2 and 3), incomplete block within environment, and column within environment as random effects. The Studentized deleted residuals (gc and DTA for each line (Table S4).To screen the phenotypic data  was tested using the function “cor.test” in R version 3.5.1 (Variance component estimates from the fitted full models (Table S5) were used to estimate heritability on a line-mean basis . The constructed 192-plex GBS libraries were sequenced on a NextSeq 500 .For each inbred line, total genomic DNA was isolated from a leaf tissue sample consisting of bulked young leaves from a single plant. The leaf tissue samples were lyophilized and ground using a GenoGrinder , followed by isolation of total genomic DNA using the DNeasy 96 Plant Kit . The genotyping-by-sequencing (GBS) procedure was conducted on the DNA samples following panzea.org). Given that missing genotype data still remained following partial imputation, the imputed genotype data set was further filtered to retain SNPs with a minimum call rate of 0.6, a minimum inbreeding coefficient of 0.8, and a minimum minor allele frequency of 5%. The final complete set contained 235,004 high-quality SNP markers scored on 451 lines that had a BLUP value for gc in one or more environments. The genome coordinates of the SNP loci were uplifted by aligning 101 bp context sequences containing target SNPs (± 50 bp) to the B73 RefGen_AGPv4 reference genome with Vmatch  loci in B73 RefGen_v2 coordinates following the method of h Vmatch .We estimated population structure from the 451 line × 235,004 SNP genotype matrix in fastSTRUCTURE version 1.0 . Next, rgc from the 451 inbreds, a GWAS was conducted with a univariate mixed linear model that employed population parameters previously determined (P3D) approximation (2r ≤ 0.2) of the complete marker data set in PLINK version 1.09_beta5 (R2 statistic (R2LR)  .r2) method (2r < 0.10) and assess the pattern of LD surrounding GWAS-detected SNPs.The squared allele-frequency correlation  method  was usedgc. Gene functional annotations (B73_RefGen_v4) of identified candidate genes were obtained from Gramene (http://www.gramene.org/). Additionally, the Gramene Mart tool was used to identify homologs of candidate genes in Arabidopsis thaliana (L.) Heynh. (Columbia-0 ecotype) and rice (Oryza sativa L. ssp. Japonica cv. ‘Nipponbare’). Gene functional annotations for the Arabidopsis and rice homologs were obtained from TAIR (https://www.arabidopsis.org/) and RAP-DB (https://rapdb.dna.affrc.go.jp/), respectively.We searched for candidate genes within ±200 kb of the most significant SNP (peak SNP) for each detected genomic region associated with gc of maize leaves, we analyzed the LM-RNAseq dataset of rd replicate were removed as outliers . With the remaining epidermis samples, a gene was declared expressed in the epidermis if its cpm was greater than one for at least three out of the 20 samples.To investigate the patterns of transcript abundance for candidate genes potentially regulating gc was conducted using a maximum likelihood approach to ridge regression in the ‘rrBLUP’ R package , SD (two environments), or AllEnv (four environments), then each of the three models were separately used to predict gc for MA, SD, and AllEnv. Collectively, this resulted in a total of nine prediction scenarios. Fivefold cross-validation as described in gc in each of the nine scenarios by calculating the Pearson’s correlation between observed BLUP values and genomic estimated breeding values. We used a stratified sampling approach to account for the presence of population structure, enabling each fold to have the proportion of subpopulations (1 to 6 and admixed) observed for the whole panel (Table S6). The procedure was conducted 50 times for each scenario, and the predictive ability was calculated as a mean of the correlations.WGP of  package . The finhttp://datacommons.cyverse.org/browse/iplant/home/shared/GoreLab/dataFromPubs/Lin_LeafCuticle_2019). The ImageJ macro for image analysis is available at Github (https://github.com/GoreLab/Maize_leaf_cuticle/blob/master/GWAS_CE/cliveMacro_2.4.txt). RNAseq reads of epidermal cells along the developmental gradient of the expanding leaf 8 of maize inbred B73 were deposited in the NCBI SRA under accession number SRP116320 and in BioProject under accession PRJNA400334, as described in https://doi.org/10.25387/g3.10262951.The raw GBS sequence data were deposited in the National Center of Biotechnology Information (NCBI) Sequence Read Archive (SRA) under accession number SRP160407 and in BioProject under accession PRJNA489924. The BLUP values of the phenotypes are provided in Table S4. The FILLIN partially imputed SNP genotype data for the 235,004 loci scored on the 451 inbred lines, weather data from Maricopa and San Diego in 2016 and 2017, and leaf image data from Maricopa and San Diego in 2017 are available at CyVerse  in 2016 and 2017. The climatically contrasting environments of the SD and MA locations (Table S1) had the lowest and highest average gc estimates, respectively (gc between years in a location (r = 0.52 and 0.54), whereas correlations were slightly weaker (r = 0.36 to 0.48) between locations in and across years . With respect to flowering time, gc tended to have a moderately weak negative correlation with days to anthesis (DTA) in each environment (r = -0.14 to -0.50), with the exception of a negative correlation of moderate strength (-0.50) in the MA17 environment . Comparatively, the first two principal components (PCs) but not the third PC calculated from the SNP genotype matrix , which infers population structure from genetic data, showed comparable correlations with gc across all four environments (|r| = 0.14 to 0.31). Heritability on a line-mean basis across (AllEnv) locations was 0.71, with a range of 0.63 to 0.67 in locations  and across locations (AllEnv) using a mixed linear model that controls for population structure (PCs) and unequal relatedness (kinship). In addition, flowering time, which was found to have high heritability (0.88 to 0.93) for MA, SD, and AllEnv (Table S7) and mostly moderate weak correlations with gc , was retained as a covariate for GWAS of gc from MA and AllEnv based on the BIC values, thus attenuating the confounding effect of maturity when estimating allelic effects. A total of nine unique SNPs localized to five different genomic regions were significantly associated with gc from MA and/or AllEnv at a genome-wide FDR of 10% .The genetic basis of natural variation for R of 10%  and S6. ciations . No signr2 < 0.1) by 213 kb at the 90% percentile of the 2r distribution . This percentile cutoff of the distribution was used to sample the large variance in LD structure presumably caused by rare variants  and AllEnv , respectively. The peak SNP S4_30201599 resides within a microRNA locus (zma-MIR2275a) and is located 1,146 bp from a gene (Zm00001d049479) encoding an INCREASED SALT TOLERANCE1-LIKE1 (ISTL1) protein  (Zm00001d033835), but this gene encodes an uncharacterized protein. Two genes adjacent to this one encode closely related SEC14 homologs, separated by about 50 kb  . SEC14 proteins in plants and other eukaryotes function in the transfer of phosphoinositides between different cellular membranes (gc because of their function in stimulating vesicle formation from the trans Golgi network in yeast (Zm00001d033842) and a CYCLASE-ASSOCIATED PROTEIN (CAP) (Zm00001d033830) located (+) 179,198 bp and (-) 152,746 bp from the peak SNP, respectively . CER7, a 3′-to-5′ exoribonuclease family protein, is a core subunit of the RNA degrading exosome that positively regulates the expression of CER3/WAX2/YRE, a key wax biosynthesis gene in Arabidopsis (The genomic region associated with  × 10−7) . The peain yeast , given tbidopsis .gc was detected in MA on chromosome 8, defined by S8_152967952 as the peak SNP  along with two neighboring SNPs (S8_152967929 and S8_152967966). The closest gene (Zm00001d011655) is located 4,067 bp from the peak SNP, and it encodes a MITOGEN-ACTIVATED PROTEIN KINASE KINASE KINASE18. A gene encoding a GLY-ASP-SER-LEU ESTERASE/LIPASE (GDSL lipase) (Zm00001d011661) was identified 170,643 bp from the peak SNP , and it was identified as the most plausible candidate in this region based on the known functions of GDSL lipases in lipid biosynthesis  and S10_144686998 , respectively. The peak SNP on chromosome 7 is located within a gene encoding CYTOKININ-N-GLUCOSYLTRANSFERASE1 (Zm00001d019250) . The peak SNP on chromosome 10 is located within a gene that encodes β-D-XYLOSIDASE 4 (Zm00001d026415), a xylan-degrading enzyme . The latter is a plausible candidate given that the outer epidermal cell wall and cuticle are closely connected and polysaccharides, for example, pectins and hemicelluloses like xylan or xyloglucans, can be found embedded in some parts of the cuticle  and SD (0.49).Whole-genome prediction (WGP) was performed with the complete marker data set of 235,004 SNPs to assess the feasibility of implementing genomic selection for the genetic improvement of gc), a trait of potential agronomic value related to drought tolerance. To that end, we evaluated the phenotypic variation of gc using detached adult leaves in a maize diversity panel in two climatically contrasting field locations (Table S1) and conducted a GWAS and WGP to explore the genetic architecture and the potential genetic gains that could be expected under selection in a breeding program for gc.The cuticle, a crucial barrier to plant water loss . Howevergc in and across locations, as well as how gc related to flowering time (DTA). Moderately strong correlations (r) of gc measurements were observed between years in a location, while relatively weaker correlations existed between locations . Given the lower relative humidity and higher solar radiation and air temperature of MA compared to SD during maize growing seasons (Table S1), the weaker correlative patterns between locations imply that gc is moderately responsive to environmental conditions. Noticeably, weak to moderately strong negative correlations  existed between gc and flowering time collected from the same year in each location. These findings suggest low to moderate levels of confounding between gc and maturity depending on the environment, with the prolonged exposure of the developing cuticle of plants to more extreme weather variables possibly explaining the stronger correlations in the MA field location. Even though these results implicated the need to assess for the confounding effect of flowering time when conducting GWAS, the ∼twofold range in gc variation, calculated as the ratio between the maximum and minimum BLUP values, in (MA and SD) and across (AllEnv) locations, and the moderately high heritabilities of gc , two in AllEnv (chromosomes 7 and 10), and one (chromosome 4) was detected in both MA and AllEnv . This is also further supported by comparing the ratio of genetic variance to G×E variance, which was 3.95, 2.57, and 1.81 for SD, MA, and AllEnv, respectively (Table S5). All together, these observations are consistent with those of previous studies showing that both the content and composition of cuticular waxes can be influenced by environmental factors such as ultraviolet (UV) radiation, temperature, humidity, and drought stress  might be inducing compositional features that affect water loss relative to plants in SD.We conducted a GWAS that resulted in the identification of five genomic regions associated with d AllEnv ; Table 2t stress , but a dgc. The candidate genes we propose for gc via GWAS encode proteins with functions that can be related to cuticle formation.As the major barrier of water vapor diffusion from the intercellular air space to the atmosphere when stomata are closed, the composition and structure of the cuticle can affect water evaporation resistance, thus causing variation in gc encode proteins with likely functions in membrane trafficking, a process needed for deposition of cuticle lipids at the cell surface as well as for delivery of lipid transport proteins to the plasma membrane . GDSL lipases catalyze the hydrolysis of mono-, di- and triglycerols and release free fatty acids and alcohols . Sometimes the cuticle is described as a specialized lipidic modification of the cell wall, and polysaccharides are known to be deposited in some regions of the cuticle  of the variation in the panel  with unscored causal variants that are potentially rare in frequency , the prediction abilities were lowest when the MA and SD training sets predicted gc each other (gc across locations, it is highly recommended that phenotyping and selection occur in the specific target breeding environments, especially if the focus is on hot, arid environments such as MA. Furthermore, if gc does ultimately have a polygenic genetic basis, genomic selection would be the optimal breeding strategy for gc in maize breeding populations rather than a marker-assisted selection approach designed for only a few loci with large-effects (Genomics-assisted breeding approaches for improving plant water-use efficiency and drought tolerance include the use of genetic markers to select for increased water uptake through roots and diminished water loss through stomata and cuticles (


FST outlier test and two genotype–environment association methods, latent factor mixed models (LFMMs) and redundancy analysis (RDA), to detect complex signatures of local adaptation. Results indicate 79 genomic regions of potential adaptive importance, with limited overlap between the detection methods. Of the 58 loci detected by LFMM, 51 showed strong correlations to a precipitation‐driven composite variable and seven to a temperature‐related variable. RDA revealed 24 outlier loci with association to climate variables, all of which showed strongest relationship to summer precipitation. Nine candidate loci were indicated by two methods. After correcting for geographic distance, RDA models using climate predictors accounted for 49% of the explained variance and showed significant correlations between SNPs and climatic factors. Here, we present evidence of local adaptation in giant sequoia along gradients of precipitation and provide a first step toward identifying genomic regions of adaptive significance. The results of this study will provide information to guide management strategies that seek to maximize adaptive potential in the face of climate change.Uncovering the genetic basis of local adaptation is a major goal of evolutionary biology and conservation science alike. In an era of climate change, an understanding of how environmental factors shape adaptive diversity is crucial to predicting species response and directing management. Here, we investigate patterns of genomic variation in giant sequoia, an iconic and ecologically important tree species, using 1,364 bi‐allelic single nucleotide polymorphisms (SNPs). We use an  FST outlier tests, we identify 79 genomic regions of potential adaptive importance, with limited overlap between the detection methods. The majority of the outlier loci show strong correlations to moisture‐related variables indicating local adaptation of giant sequoia populations along gradients of precipitation.We investigate patterns of genomic variation in giant sequoia, an iconic and ecologically important tree species, using 1,364 bi‐allelic single nucleotide polymorphisms (SNPs). Using genotype–environment association and  Given the rapid rate of climate change, new beneficial mutations are expected to play a limited role for species with low mutation rates and long generation times. Therefore, adaptive evolution under climate change for many species will depend on standing genetic variation  provides evidence for abundant heritable variation for quantitative traits that are organized along environmental clines  that occur in a highly disjunct range consisting of ~70 groves spanning approximately 400 km north to south , to find signatures of local adaptation among giant sequoia populations and locate potential genomic regions under selection.This elevational range includes the extant groves of the iconic, long‐lived conifer, giant sequoia . We constructed three sequencing libraries using a double‐digest restriction enzyme‐associated genotyping‐by‐sequencing (GBS) protocol outlined in Peterson, Dong, Horback, and Yong‐Bi . Genomic2.22. Nineteen climate variables were obtained from the WorldClim database , the inbreeding coefficient (FIS), and the pairwise fixation index (G′ST). Since the removal of rare alleles  can bias genetic diversity estimation, we also calculated genetic diversity statistics without this filtering step for comparison. To further investigate the partitioning of genetic variation, we used AMOVA with 10,000 permutations to estimate FST across all populations as well as between northern and southern regions which previous evidence suggested were divergent  that correct for the neutral genetic structure of our data. First, we ran a principal component analysis on the individual allele frequencies. We then determined the number of components that explain the genetic variance, based on the Tracy–Widom test on the eigenvalues, as an estimate of K  without prior information about geographic origin  using ten independent replications at 50,000 iterations after a burnin period of 25,000 with the number of latent factors (K) ranging from 8 to 12, as the methods outlined above suggested r| < 0.7), and subsequently by using the “ordistep” function for backwards model selection to remove variables lacking explanatory power. The above process resulted in climate being represented by “isothermality” (ISO), a measure diurnal and annual temperature fluctuation, “precipitation of driest quarter” (PDQ), a measure of summer precipitation in Mediterranean climates, and “climate water deficit” (CWD), a measure of aridity, in all RDA models, and space represented by two dbMEM vectors, MEM3 and MEM5. All variables were centered and standardized before use in each model.We also utilized RDA, a multivariate GEA method, to test for more subtle polygenic signatures of adaptation and detect outlier loci as candidates of functional importance. Redundancy analysis (RDA) is an extension of multiple regression to multivariate response variables  varied from 0.09 to 0.32 and was lowest for GFOR and highest for PLAC . Diversity analysis of SNPs without minor allele count (MAC) filtering yielded significantly different results: Ho and uHe were lower and ranged from 0.08 to 0.15 and 0.06 to 0.18, respectively  and a larger portion of genomic variation distributed among populations  with little admixture . Since our focus here is on patterns of spatially varying selection, no further discussion is presented for locus 1,114. A BLAST search found one of these loci exhibited functional significance  indicated a total of 58 loci with strong correlations to composite environmental variables  provided additional support for K = 9  Figure  and S8. 3.4FST outlier) and LFMM at one locus . Annotation through BLAST identified two of these loci as having a putative function . The first two canonical axes from the full RDA model were significant  and together accounted for 77% of the explained variation  and constrained 49% of the variance explained by the full model. The first partial RDA axis was significant at the 0.1 level (p = .098) and accounted for 45% of the variation. The partial RDA model with space conditioned on climate accounted for 24% of the explained variation and was nonsignificant (p = .207). The remaining 27% of the explained variation was confounded between climate and geography.The full RDA model explained 45% of the total variation in allele frequency and supported an influence of climate and/or space in shaping allelic variation , which was close to our earlier estimate of FST = 0.14 from microsatellite variation , we found evidence for adaptive differentiation across giant sequoia populations in response to gradients in precipitation and a more limited signal of local adaptation to temperature. LFMM analyses demonstrated seven times as many outliers correlated with precipitation‐related PC2 than to temperature‐related PC1 Figure . Althoug4.4It is important to note that GEA methods can suffer from low power or high false‐positive rate under some demographic scenarios. Although LFMM has been shown to be robust to various demographic scenarios, including those that create high levels of population structure, this method can have elevated false discovery rates (FDR) under scenarios that create IBD . More comprehensive sampling of the genome as well as an incorporation of phenotypic information will greatly improve our understanding of local adaptation in this species. In addition, future annotation of the giant sequoia genome will provide opportunities to better understand the genetic underpinnings of many phenotypic traits.A trend toward increased aridity along midelevation Sierra Nevada forests could undermine the long‐term persistence of giant sequoia. With end‐of‐century predictions for this region that include decreasing snowfall and earlier snowmelt, forests of the Sierra Nevada mountains will likely experience an accentuation of the summer drought that is typical of Mediterranean climates ; Data curation (lead); Formal analysis (lead); Methodology (lead); Writing‐original draft (lead); Writing‐review & editing . Richard S. Dodd: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (lead); Methodology (supporting); Supervision (lead); Writing‐original draft (supporting); Writing‐review & editing .Appendix S1Click here for additional data file.Appendix S2Click here for additional data file.Appendix S3Click here for additional data file.Appendix S4Click here for additional data file.Appendix S5Click here for additional data file.Appendix S6Click here for additional data file.Appendix S7Click here for additional data file.Appendix S8Click here for additional data file.Appendix S9Click here for additional data file.


There is a robust observational relationship between lower birthweight and higher risk of cardiometabolic disease in later life. The Developmental Origins of Health and Disease (DOHaD) hypothesis posits that adverse environmental factors in utero increase future risk of cardiometabolic disease. Here, we explore if a genetic risk score (GRS) of maternal SNPs associated with offspring birthweight is also associated with offspring cardiometabolic risk factors, after controlling for offspring GRS, in up to 26,057 mother–offspring pairs  from the Nord-Trøndelag Health (HUNT) Study. We find little evidence for a maternal  genetic effect of birthweight associated variants on offspring cardiometabolic risk factors after adjusting for offspring GRS. In contrast, offspring GRS is strongly related to many cardiometabolic risk factors, even after conditioning on maternal GRS. Our results suggest that the maternal intrauterine environment, as proxied by maternal SNPs that influence offspring birthweight, is unlikely to be a major determinant of adverse cardiometabolic outcomes in population based samples of individuals. Observationally, lower birthweight is a risk factor for cardiometabolic disease. Using Mendelian Randomization, the authors investigate whether maternal genetic factors that lower offspring birthweight also increase offspring cardiometabolic risk and show that the observational correlation is unlikely to be due to the intrauterine environment. Evidence in favor of DOHaD has primarily come from observational8 and animal studies9; however, definitive causal evidence from human studies is lacking.There is a robust and well-documented observational relationship between lower birthweight and higher risk of cardiometabolic diseases in later life, including cardiovascular disease (CVD) and type 2 diabetes (T2D). The Developmental Origins of Health and Disease (DOHaD) hypothesis posits that adverse environmental factors in utero or in the early years of life result in increased future risk of cardiometabolic disease10. Several studies have recently attempted to use MR to investigate the relationship between lower birthweight and cardiometabolic disease to inform on the validity of DOHaD13. However, these MR studies have used sub-optimal methodologies in which only offspring genotypes are considered as genetic instruments to proxy offspring birthweight14. This limitation contrasts strikingly with the argument that many DOHaD proponents would make, i.e. that an adverse maternal environment during pregnancy, results in low birthweight and increased risk of future cardiometabolic disease6. This hypothesis is entirely distinct from postulating that birthweight itself has a direct causal effect on risk of cardiometabolic disease14. Thus, these early MR studies have ignored the potential contribution of the maternal genome (correlated 0.5 with the offspring genome16), meaning that any association between offspring SNPs and offspring cardiometabolic risk may in fact be due to maternal genotypes, violating core assumptions underlying MR17, and complicating interpretation of the results. Indeed, Smith and Ebrahim10 in their initial description of the MR methodology, noted that the appropriate way of using MR to investigate the effects of the intrauterine environment on offspring outcomes , was to use maternal genotypes to proxy the intrauterine environment10.Mendelian randomization (MR) is an epidemiological method used to investigate whether an observational association between an exposure and an outcome represents a causal relationship20. For example, one possibility is to test whether SNPs in the mother that are directly related to offspring birthweight are also associated with offspring cardiometabolic risk factors, after conditioning on offspring genotypes at the same loci. To understand why this analysis would be informative, consider Fig. MR principles can be harnessed to test aspects of DOHaD using maternal SNPs that are related to offspring birthweight and/or adverse maternal environmental exposures during pregnancyIn other words, the presence of correlation between maternal genotypes and offspring cardiometabolic risk factors, after conditioning on offspring genotypes at the same loci, is highly suggestive of DOHaD mechanisms related to lower birthweight . We emphasize that the paradigm illustrated in Fig. 18. Interestingly, this showed that maternal SNPs related to low offspring birthweight were actually associated with lower offspring systolic blood pressure after conditioning on offspring genotype at the same loci . However, the number of mother–offspring pairs used in this previous study was small  and systolic blood pressure was the only cardiometabolic risk factor investigated. Therefore, the results from this preliminary study need to be replicated and further cardiometabolic risk factors examined. The Norwegian based HUNT Study21, which contains approximately 70,000 genotyped individuals, including 45,849 parent–offspring pairs, is one of the few cohorts where such analyses can be conducted. The average age of the HUNT offspring is approximately 40 years, rendering this cohort not only one of the largest cohorts in the world with genotyped mother–offspring pairs (and father–offspring pairs) with birthweight information, but also one of the few with offspring old enough to have developed adverse cardiometabolic profiles.We have previously used this paradigm to examine the association between maternal birthweight related SNPs and offspring blood pressure in the UK Biobank study as a preliminary test of the validity of this possible DOHaD mechanismIn this work, we perform genetic association analyses in up to 26,057 genotyped mother–offspring pairs from the Norwegian HUNT Study in order to investigate whether there is evidence for a causal effect of the intrauterine environment  on offspring cardiometabolic risk factors. We investigate whether maternal genotypes associated with lower offspring birthweight are also associated with later life offspring cardiometabolic risk factors such as blood pressure, non-fasting glucose levels, body mass index (BMI), and lipid levels, after conditioning on offspring genotype at the same loci. We also perform similar analyses in up to 19,792 father–offspring pairs to investigate whether there is evidence for a postnatal environmental effect (genetic nurture or dynastic effects), rather than an intrauterine environmental effect. In the course of executing these analyses, we implement a computationally efficient genetic linear mixed model that not only enables the investigation of causal questions relevant to the specific DOHaD mechanism that is the focus of this paper, but also simultaneously accounts for the non-independence between siblings and the considerable cryptic relatedness within the HUNT Study. We show no evidence for a causal effect of the intrauterine environment  on offspring cardiometabolic risk factors. We do, however, find evidence that offspring SNPs pleiotropically influence both birthweight and future cardiometabolic risk factors, which helps explain the robust observational relationships between the variables.25, linear regression yielded negative point estimates of the observational relationship between birthweight and blood pressure, LDL, total cholesterol, and BMI. We also found evidence for positive quadratic terms in the model between birthweight and both BMI and glucose, suggesting U-shaped/J-shaped relationships between these variables. Finally, we found evidence for a positive linear relationship between HDL cholesterol and birthweight with additional evidence for a convex quadratic term indicating small and large babies are likely to have slightly reduced HDL levels in later life.HUNT offspring with recorded values for birthweight were on average 30.1 years old, with a minimum age of 19, and a maximum age of 41 at the time of measurement used in this study. Descriptive statistics on the mother–offspring and father–offspring pairs are presented in Table 18 were also related to offspring birthweight in HUNT. The full results are presented in Supplementary Table 18 birthweight GWAS, offspring GRS was not strongly related to offspring birthweight after controlling for maternal GRS. As expected, paternal GRS was not associated with offspring birthweight after conditioning on offspring GRS. The effect size of the offspring GRS was similar in mother–offspring and father–offspring pairs, and did not attenuate after adjusting for paternal GRS.We first checked whether the GRSs of birthweight associated SNPs from the latest GWAS of birthweightN = 26,057) (two tailed α = 0.05) and slightly lower power (>68%)  to detect a paternal genetic effect responsible for a similar proportion of the offspring phenotypic variance. Due to some missing data in the offspring’s cardiometabolic risk factors, the number of mother–offspring and father–offspring pairs differed slightly across the outcomes  GRS and any of the offspring cardiometabolic risk factors in later life, after adjusting for offspring GRS Tables . These tRS Table . SpecifiN = 12,037 and N = 11,849) (α = 0.05) and slightly lower power (>66%)  to detect a paternal genetic effect responsible for a similar proportion of the offspring phenotypic variance. Table 18. Whereas Warrington and colleagues found a significant positive effect of maternal GRS on offspring SBP when adjusting for offspring GRS, we find no effect in the stratified analyses.Cardiometabolic pathology becomes more apparent with increasing age. Indeed, it is possible that younger individuals within the HUNT Study do not show observable compensatory changes in cardiometabolic risk factors, reducing the power of our analyses to detect evidence for the observational associations between birthweight and cardiometabolic risk factors to be causal. We therefore divided our dataset into two strata based on age of the offspring (i.e. offspring under 40 years of age and offspring between 40 and 60 years of age). Our asymptotic power calculations indicated that we had (≥80%) power to detect a maternal genetic effect that explained as little as 0.09% of the variance in offspring SBP  hypothesis posits that adverse environmental factors in utero or in the early years of life result in increased future risk of cardiometabolic diseaseα = 0.05). In contrast, our previous study in the UK Biobank18 (where we first used this MR paradigm to investigate DOHaD), involved only 3886 mother–offspring pairs, and was likely underpowered. Interestingly, Warrington and colleagues found evidence for a positive relationship between maternal birthweight lowering SNPs and reduced offspring SBP (i.e. the opposite of what DOHaD would predict); however, this result did not replicate in our sample. Possible reasons for the discrepancy include the differences in sample ascertainment across the studies, or that the younger offspring in HUNT did not manifest a large enough effect18. When stratifying our analysis by age, we did find effects in the same direction as our original study for the 40-60 years age group; however, the statistical support for the effect was weak. Taken together, the UK BioBank and HUNT results provide converging evidence that maternal genetic effects that predispose to low offspring birthweight are not associated with increased systolic blood pressure in later life.Our study is, to the best of our knowledge, the largest parent–offspring MR study of DOHaD performed to date. The HUNT Study contains over 25,000 genotyped mother–offspring pairs where the majority of the offspring are middle-aged adults, and are therefore old enough to have begun developing observable signs of cardiometabolic disease. Our asymptotic calculations indicated that we had strong (≥80%) power to detect a maternal genetic effect that explained as little as 0.04% of the variance in offspring outcome  compared to the maternal effects. Also important to take into account is the fact that the lipid and glucose measurements were performed in non-fasting samples, which could influence these results, particularly as it is known that mean blood glucose levels and triglycerides are higher in the first three hours after calorie intake31. Nevertheless, our results show clearly that maternal SNPs that influence offspring birthweight have pleiotropic effects on offspring cardiometabolic traits when these same SNPs are transmitted to their offspring.In contrast, we did find evidence for association between offspring GRS and a number of offspring cardiometabolic risk factors, even after conditioning on maternal GRS. These results are broadly consistent with the Fetal Insulin hypothesisN. In contrast, our implementation permits complicated tests of association to be performed in the fixed effects part of the model, whilst simultaneously modeling cryptic relatedness in the random effects part of the model in a computationally efficient manner32. We hope that our implementation will prove useful in complicated genetic analyses of other large scale population-based cohorts where cryptic relatedness/population stratification is likely to be an issue. We have included an example R script in Supplementary Note 1 of the manuscript that can be used as a template by interested researchers. We caution users, however, that specification of the covariance part of the model is more rigid using our speed up in that only two variance components can be fitted simultaneously, one being a residual variance component that is uncorrelated across individuals.Another novel facet of our study was the use of the OpenMx software package to model the complicated data structure within the HUNT Study. Using traditional formulations of FIML to model the relatedness structure using a genetic relationship matrix would be computationally prohibitive within the HUNT sample, as maximizing the likelihood would involve an inversion of a matrix of order Our approach has a number of limitations which we discuss in the remaining paragraphs. First, we assume that the maternal SNPs that affect offspring birthweight do so via fetal growth (as reflected in birthweight). This is important, because as many others have noted, it may not be fetal growth/birthweight itself that is relevant for the validity of DOHaD. Rather it could be poor development of different key organs, in key stages of the pregnancy or a particular adverse maternal environment due to famine, disease or a range of other factors. Indeed, it would likely be profitable to use the same framework to investigate the association between offspring cardiometabolic disease and other adverse maternal exposures, such as maternal BMI, maternal alcohol consumption, preeclampsia, and gestational diabetes. Their effect may be qualitatively and quantitatively different from the maternal effect on birthweight within healthy subjects delivering babies within the normal range. However, even though the mechanisms through which our maternal SNPs influence offspring birthweight are largely unknown (and therefore our genetic risk score is largely unspecific), we know that they play an important part in fetal growth of the offspring. Further MR studies on different maternal exposures are warranted including on those that do not necessarily exert observable effects on offspring birthweight, but proxy other more specific maternal environments. Moreover, we used unweighted GRS of birthweight associated SNPs in our MR framework. Using a weighted maternal GRS and conditioning on a weighted offspring GRS does not completely block the path through the offspring’s genome, increasing type 1 error rate for the maternal effect on offspring cardiometabolic phenotype. To avoid the inflation in type 1 error, we use an unweighted maternal GRS and condition on offspring unweighted GRS, which is sufficient to block this path. However, the main reason for using an unweighted GRS is that weighting SNPs by the strength of association between maternal genotype and offspring birthweight would only be appropriate if the effect of the maternal SNP on the offspring’s cardiometabolic phenotype was mediated through offspring birthweight  at the extreme ends of the spectrum. These effects may be qualitatively different from small perturbations in the environment that produce relatively subtle variations in the normal healthy population. If DOHaD is only relevant in the case of extreme environmental effects, then MR approaches applied to population data may not be well suited to testing the hypothesis.Third, although our methods rely on MR principles to inform on the validity of DOHaD , we did not perform formal instrumental variables analyses in this manuscript. The reason is that we do not have appropriate estimates of the effect of maternal genotypes on the intrauterine environment. We only have estimates of the relationship between SNPs and offspring birthweight, which is an imperfect proxy of fetal growth restriction. Therefore, it does not make sense to estimate causal effect sizes in our study as in typical MR analyses. However, we note that it may be possible to estimate the effect of a putative latent variable indexing growth restriction using, for example, latent variable models; this is an area of future research for our group.α = 0.05) to detect an association between maternal genetic risk score and offspring cardiometabolic risk factors responsible for as little as 0.04% of the phenotypic variance. However, whilst our study, to the best of our knowledge, is the largest and most powerful genetic investigation into DOHaD to date, the actual variance in the offspring cardiometabolic risk factor explained by the maternal GRS, depends critically upon the underlying genetic model, and could be even smaller than 0.04%. In an attempt to make this clear, Fig. λ1 and λ2). The second is the residual covariance between birthweight and the cardiometabolic risk factors. This latter pathway includes both environmental factors other than fetal growth restriction that affect both phenotypes and the effect of polygenes that are not modeled in the experiment whose joint effects are quantified by the parameter Θ. These correlations could be positive or negative individually, but when combined produce a very small (|r | <= 0.05) negative phenotypic correlation between birthweight and most of the cardiometabolic risk factors. The point is that, unless the residual covariance between birthweight and the cardiometabolic risk factor is positive, the values for path coefficients λ1 and λ2 are likely to be very small in order to be consistent with the observed phenotypic correlations.Fourth, our power calculations show that we were well powered (>80% at γ), and the effect of the intrauterine environment on birthweight (the path coefficient λ1—the precise formula being: γ2λ12). The variance explained in the cardiometabolic risk factor by the maternal GRS is equal to the product of the SNPs’ direct effect on the intrauterine environment . In order for the underlying model to also be consistent with the maternal GRS explaining a small percentage of the variance in birthweight (say 0.5% of the variance), then the path coefficient between the maternal GRS and the latent intrauterine variable γ would equal 2 × 0.12 = 0.02%, which is a small proportion of the variance, and one that we are only moderately well powered to detect (>50%) in our study. Our point, however, is that the proportion of variance in the outcome explained by the maternal GRS may be very small, and so power may only be moderate despite the very large sample size of HUNT. The corollary to this though is that we are very well powered to detect larger effects of the intrauterine environment influencing offspring birthweight on cardiometabolic risk factors, and the fact that we do not detect these suggests that if such an effect is present, it is likely to be small.The variance in birthweight explained by the maternal GRS is a function of the direct association between the SNPs and the intrauterine environment  correlation between maternal GRS and paternal GRS due to conditioning on a collider variable, potentially biasing the results of our maternal GRS analyses. However, any such bias is likely to be small in magnitude as it relies on the existence of  direct paternal genetic effects from the same SNPs on the offspring phenotype. As sizeable paternal genetic effects on offspring cardiometabolic risk are unlikely at these loci, we doubt that collider bias is a serious impediment to the validity of our studyIn conclusion, we did not find evidence for a causal effect of the intrauterine environment  on offspring cardiometabolic risk factors in a population-based sample of individuals. We did, however, find evidence of genetic pleiotropy between offspring birthweight and offspring cardiometabolic risk factors which helps explain the robust observational relationships between the variables.21. Approximately every 10 years the entire adult population of Nord-Trøndelag  is invited to attend a health survey which includes comprehensive questionnaires, an interview, clinical examination, and detailed phenotypic measurements (HUNT1 (1984 to 1986); HUNT2 (1995 to 1997); HUNT3 (2006 to 2008) and HUNT4 (2017 to 2019)). These surveys have high participation, with 89%, 69%, 54%, and 54% of invited adults participating in HUNT1, 2, 3, and 4, respectively34. Additional phenotypic information is collected by integrating national registers. Approximately 90% of participants from HUNT2 and HUNT3 were genotyped in 201535, and the genotype and phenotype data used in the subsequent analysis are exclusively from these two surveys.The Nord-Trøndelag Health Study (HUNT) is a large population-based health study of the inhabitants of Nord-Trøndelag County in central Norway that commenced in 1984. A comprehensive description of the study population has been previously reportedThe HUNT Study was approved by the Regional Committee for Medical and Health Research Ethics, Norway and all participants gave informed written consent .35. Genomic position, strand orientation, and the reference allele of genotyped variants were determined by aligning their probe sequences against the human genome  using BLAT36. Ancestry of all samples was inferred by projecting all genotyped samples into the space of the principal components of the Human Genome Diversity Project (HGDP) reference panel 38, using PLINK v1.9039. The resulting genotype data were phased using Eagle2 v2.340. Imputation was performed on the 69,716 samples of recent European ancestry using Minimac3 41 with default settings (2.5 Mb reference based chunking with 500 kb windows) and a customized Haplotype Reference consortium release 1.1 (HRC v1.1) for autosomal variants and HRC v1.1 for chromosome X variants42.DNA from 71,860 HUNT samples was genotyped using one of three different Illumina HumanCoreExome arrays N = 348) as well as individuals showing high or low heterozygosity (±5 SD from the mean) (N = 412) were removed . In addition, variants with minor allele frequency <0.005 or more than 5% missing rate were removed. Parent–offspring pairs were identified by kinship analysis using the KING software version 2.2.443. Only genotyped SNPs shared across the arrays on autosomal chromosomes were used for the analysis – a total of 257,488 SNPs.Before the kinship analysis, the plink files with genotyped SNPs underwent a second stage of cleaning. Any individuals whose inferred sex contradicted their reported gender  results previously published18. Unweighted genetic risk scores (GRS) were constructed by simply adding the expected number of increasing birthweight alleles together for each individual. We used unweighted scores because we do not know the extent to which each allele influences growth restriction, and so weighting the scores by e.g. their observed effect on birthweight would be less appropriate. Three GRS were constructed—one using all autosomal SNPs shown to have an effect on birthweight (N = 204) from the recent EGG Consortium GWAS paper of birthweight18 that found 205 autosomal SNPs, but rs9267812 was not available in the HUNT data), one using SNPs shown to have a maternal effect , and one using SNPs that only had a significant maternal effect (N = 31) (Supplementary Data SNPs previously associated with own or offspring birthweight at genome-wide levels of significance in the Early Growth Genetics (EGG) Consortium paper21 clinical examination, and detailed phenotypic measurements were performed on all participants, data from HUNT3 or HUNT2 were used in the subsequent work. For all cardiometabolic risk factors in the offspring , diastolic blood pressure (DBP), non-fasting glucose (Glucose), total cholesterol, high density lipoprotein (HDL) cholesterol, low density lipoprotein (LDL) cholesterol, and triglycerides), the most recent value  was used if available. If the individuals were not a part of HUNT3, measurements from HUNT2 were used. Age at participation was calculated to correspond with the health survey chosen. Blood pressure was taken three times during the clinical examination, and SBP and DBP measurements were calculated as the average of the second and third measurement. For individuals who only had two blood pressure measurements taken (12% of offspring in the mother–offspring pairs and 9% of offspring in the father–offspring pairs), the second measurement was used.During the health surveys (HUNT1-4)For the blood measurements, samples were taken from non-fasting participants. In HUNT3, participants’ total cholesterol was measured by enzymatic cholesterol esterase methodology; HDL cholesterol was measured by accelerator selective detergent methodology; triglycerides were measured by glycerol phosphate oxidase methodology; and glucose was measured by Hexokinase/G-6-PDH methodology . In HUNT2, participants’ total and HDL cholesterol and triglycerides were measured by applying enzymatic colorimetric cholesterol esterase methods  and glucose was measured by an enzymatic hexokinase method. The measurements are shown in millimole per liter. Weight and height were measured in light clothes and BMI was calculated as weight (kilograms) divided by the squared value of height (in meters).44. Non-fasting LDL cholesterol was calculated using the Friedewald formula45. All values more than 4 standard deviations from the mean were removed. If the variable was not normally distributed  the values were natural log transformed before removing outlying values.We adjusted the blood pressure measurements of individuals who self-reported using blood pressure lowering medication by adding 15 mmHg to their SBP and 10 mmHg to their DBP. We chose this procedure over including medication use as a covariate to avoid introduction of possible collider biases into the analyses46 using the unique 11-digit identification numbers assigned to all Norwegian residents. This was performed by a third party and the researchers only had access to de-identified data. The registry commenced in 1967, when health authorities began reporting pregnancy-related data; therefore, birthweight measurements were only available for HUNT participants born in 1967 or later. The validity of information on birthweight in the MBRN has previously been reported as very good47. Individuals in HUNT with own birthweight who were part of a multiple birth (210 twins and 4 triplets) were excluded from the analysis. Additionally, we excluded individuals with a known congenital malformation (N = 317), if their birth was induced or performed via a cesarean section , if their birthweight was under 1000 g (N = 1), or if they were born before 258 days of gestation (N = 451). To investigate if we could replicate the previously reported phenotypic associations between birthweight and cardiometabolic risk factors, we fitted a linear mixed model to N = 7,825 mother–offspring pairs and then N = 6,875 father–offspring pairs using the software package OpenMx48 using the procedure described below. We modeled offspring cardiometabolic risk factor as the outcome and included offspring birthweight, offspring birthweight squared, offspring age, offspring sex and measurement occasion (HUNT2 or HUNT3) as fixed effects. Offspring birthweight squared was included as a fixed effect to capture a possible non-linear relationship between birthweight and cardiometabiolic risk factors, as has been observed in some studies previously51. The other covariates were included to reduce error variance in the cardiometabolic risk factor and consequently increase the power of the analyses. The non-independence between siblings and the cryptic relatedness between offspring was modeled using a genetic relatedness matrix in the random effects part of the model as described below.Own birthweight was available for individuals in HUNT after linking with the Medical Birth Registry of Norway (MBRN)Cryptic relatedness is a problem for genetic studies of large population-based cohorts like HUNT. Whilst point estimates from genetic association analyses will often be unbiased in the presence of cryptic relatedness, standard errors can be too small, meaning that statistical tests of association may have inflated Type 1 error rates. Dropping one person from each pair of putatively related individuals is inefficient and requires an arbitrary threshold to be specified in order to declare a pair of individuals related (e.g. first-order relatives). Thus, dropping individuals is unlikely to remove the non-independence of the error terms completely. In the case of single SNPs, this problem can be solved by using custom-written software packages. These software packages allow users to fit linear mixed models where a dataset is analyzed as one large set of related individuals and the similarity between individuals is parameterized by a genome-wide genetic relationship matrix. However, these software packages are designed for GWAS analysis and may not have the flexibility to enable users to fit more complicated statistical models such as those involving genetic risk scores and conditional association analyses, as we wish to do here.48 in the R statistics software. OpenMx allows users to model multivariate normal data flexibly in terms of fixed and random effects, and to estimate parameters simultaneously using full information maximum likelihood (FIML). We used the fixed effects part of the model to test for genetic association between the maternal GRS and offspring phenotype, and modeled the similarity between individuals in the random effects part of the model. The model for the fixed effects included terms for the genetic risk score of the mother (father), the genetic risk score of the offspring, age, sex and the measurement occasion (HUNT2 or HUNT3). Again, the inclusion of age, sex and measurement occasion in the fixed effects part of the model was to reduce error variance in the cardiometabolic risk factor of interest and hence increase power. In the random effects part of the model we modeled the similarity between individuals in terms of a genetic relationship matrix (GRM) and an identity matrix for residual effects:Σ is the expected N x N phenotypic covariance matrix, A is an N x N genetic relationship matrix calculated using the GCTA software version 1.9352, I is an N x N identity matrix, N is the number of individuals in the analysis. When creating the GRM it was important to exclude the SNPs (and the SNPs in linkage disequilibrium around them) used in the genetic risk scores. Otherwise we would risk some of our association signal in the fixed effects part of the model being attenuated because they would also be modeled in the random effects part of the model. The GRM was therefore calculated after excluding the known birthweight SNPs and any SNPs 1 Mb away from them.We therefore parameterized our statistical model using the OpenMx packageN x N matrix, to one involving a 1 ×1 matrix (see Supplementary Note 2 for details). Our implementation involved first performing a spectral decomposition of the genetic relationship matrix (A), and then pre-multiplying the matrices of outcomes and fixed effects respectively by the matrix of eigenvectors32. This pre-multiplication has the effect of “rotating away” the dependence between outcome trait values, leaving the random effects uncorrelated. The problem then reduces from N correlated observations (modeled by an N x N matrix), to N independent observations, greatly facilitating computation. An R script with code illustrating our method is included in the Supplementary Note 1.Estimating these parameters using FIML in OpenMx is computationally intensive in that it involves inverting a matrix of order N. Indeed, our initial attempts to do this suggested that fitting the model to the HUNT data this way may not be possible given the limitations of our computing hardware. We therefore reparametrized the statistical model using a factor rotation which converted the problem from one involving an N = 7,825 mother–offspring pairs and N = 6,875 father–offspring pairs to confirm that our GRS explained some of the variance in offspring birthweight. We then performed our primary analyses testing the relationship between maternal GRS and each of the offspring cardiovascular risk factors, whilst conditioning on offspring GRS. We performed the same analyses in father–offspring pairs to assess whether there was evidence for a postnatal effect from either parent  to calculate power to detect association53. We assumed N = 26,057 complete mother–offspring pairs, the absence of offspring genetic effects, and a Type 1 error rate of α = 0.05 .We were interested in the statistical power of our approach to detect maternal genetic effects on offspring cardiometabolic risk factors. We therefore used the Maternal and Offspring Genetic Effects Power Calculator (Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Reporting Summary


P = 0.18 (T1D) and P = 0.26 (RA) imprinting variances were not significant. Explaining up to 19.00% (± 2.00%) and 15.00% (± 6.00%) of the phenotypic variance, the maternal environmental variance was significant for T1D (P = 1.60 × 10−24) and for RA (P = 0.02). For the first time, the existence of maternal genetic effects on RA was indicated, contributing up to 16.00% (± 3.00%) of the total variance. Environmental factors such as the social economic index, the number of offspring, birth year as well as their interactions with sex showed large effects.Imprinted genes, giving rise to parent-of-origin effects (POEs), have been hypothesised to affect type 1 diabetes (T1D) and rheumatoid arthritis (RA). However, maternal effects may also play a role. By using a mixed model that is able to simultaneously consider all kinds of POEs, the importance of POEs for the development of T1D and RA was investigated in a variance components analysis. The analysis was based on Swedish population-scale pedigree data. With  Type I diabetes (T1D) is an AI that causes chronic destruction of pancreatic islet ß-cells and hyperglycemia due to reduced insulin production2. With the incidence said to be increasing by 3–4% yearly, more than 20 million individuals are estimated to have T1D worldwide3. Rheumatoid arthritis (RA) is associated with autoantigen presentation with antigen specific T and B cell activation and aberrant inflammatory cytokine production. Consequences thereof include synovitis, proliferation of synovia and cartilage, and subchondral bone destruction4. The occurrence of RA is relatively constant and ranges between 0.5 and 1.0% in European and North-American populations5. The exact etiology of T1D and RA remains largely unknown1, however, a complex interplay of genetic, environmental, and epigenetic factors is assumed7.The failure of the immune system to distinguish self from non-self antigens is the basis for autoimmune disorders (AIs)HLA, PTPN22, CTLA4, and TAGAP8. Causal loci explain over 80% of T1D heritability which reportedly ranges between 40 and 92%3. For RA, associated variants outside and inside of the major histocompatibility complex region explain about 5% and 60% of the heritability10. Heritability estimates range between 12 and 60%13.With regard to genetic factors, the strongest effects have been found within the major histocompatibility complex or human leukocyte antigen system. T1D and RA show genetic overlap in terms of associations within 16. Perhaps the best-known example for all epigenetic phenomena is imprinting, in which the expression of genes is either maternally or paternally inactivated. Inactivation can either be full or partial17. Partial imprinting occurs when the inactivation of alleles is not complete. For example, loci may be imprinted in a tissue-specific manner18, or the imprinting status varies over time during the developmental stages19. As they appear as phenotypic differences between heterozygotes depending on their parental allele origin, imprinting effects belong to the class of parent-of-origin effects (POEs)20. Imprinting has been identified in mammals, insects, and plants21. It is nevertheless assumed that less than 1% of all genes in mammals are imprinted22, however, they have important functions in stem cells, neuronal differentiation, development, and growth23. In humans, imprinted genes are associated with diseases such as Prader–Willi syndrome24, Angelman syndrome25, and cancer27. They are also assumed to affect susceptibility to diabetes. This assumption originates from observations that T1D is preferentially expressed by children of T1D-affected fathers30. Whether this observation is due to imprinting or other factors is not clear since findings are contradictory31. With regard to RA, the existence of imprinting has been discussed since its incidence is considerably higher in women than in men32. However, imprinting studies are rare and results have been inconclusive; the role of imprinting in RA susceptibility is therefore not yet understood34. Imprinted genes are difficult to detect in conventional association studies as their effects depend on the parental origin of the risk allele35. The incorporation of knowledge on whether imprinting affects susceptibility to T1D and RA could increase the power to find causal genes34. Moreover, the development of therapeutic approaches targeting these genes or their regulators could be improved33. Therefore, the first goal of this study was to investigate the impact of imprinting on the susceptibility to T1D and RA in a variance components analysis by applying a unique mixed model (imprinting model). The model allows for the simultaneous consideration of all kinds of imprinting patterns . As it has never been applied to human population data before, it opens up new opportunities for understanding the etiology of T1D and RA40.As disorder concordance rates in monozygotic twins have been observed to be less than 100%, AIs are assumed to be subject to epigenetic modifications41. The second research goal was therefore to incorporate maternal effects into the statistical model; not only to prevent biases in the imprinting variances, but also to investigate the maternal contribution to T1D and RA susceptibility. Like imprinting effects, maternal effects contribute to the broader class of POEs. However, their variation is assigned to the environmental contribution to the phenotypic variance. According to Falconer42, they are defined as prenatal and postnatal effects on offspring and can have two main components. The first component is the maternal genotypic effect on, for example, the birthweight of her children 43. The second component is the maternal environmental effect on the birthweight of her offspring42. This component refers to the permanent environmental effects of the mother on all of her offspring and can therefore also be considered a shared household effect42. Although T1D and RA differ in their average age of onset, attention must be given to the maternal contribution in the development of both diseases since early environmental factors can permanently modify the development of the immune system44. The imprinting model is able to separate maternal effects from maternal imprinting effects, allowing the first imprinting variance components analysis to be performed in human population genetics.In an imprinting variance components analysis, maternal effects must be accounted for in the model to avoid inflated estimatesThe third goal of this study was to gain knowledge on the importance of sex and environmental triggers such as birth year, social economic index, and the number of offspring on the susceptibility to T1D and RA. Overall, this study brought to light the complex interplay between genetic, epigenetic and environmental factors in the development of autoimmunity.45. The advantage this model confers is that it is able to simultaneously consider all kinds of imprinting  in its analyses17, ultimately separating maternal imprinting effects from maternal “non-imprinting” effects . This was not possible with previous population-scale imprinting analyses models, for example, that of Engellandt and Tier46. Our imprinting model estimates two parental gametic variances and one covariance simultaneously. It is written as:Y is a vector of the response variable; b is a vector of fixed effects; gs is the vector of random gametic effects under a paternal expression pattern; gd is the vector of random gametic effects under a maternal expression pattern; X, Zs, and Zd are the corresponding incidence matrices; and e is the vector of random residuals. The variance–covariance structure is:G is the gametic relationship matrix reflecting the relationships between the gametes of all individuals in a pedigree. It is therefore twice the size of the number of individuals included in the analysis48. The symbol ⊗ denotes the Kronecker product. The imprinting effect is defined as the vector of differences (gs − gd) and the corresponding variance of differences is A unique mixed model, previously used on animal data, was applied to investigate the existence of imprintingimprinting model to the REML log-likelihood outcome of a corresponding linear Mendelian model . At a 5% significance level, the analysis revealed that imprinted genes did not significantly contribute to the total genetic variance in T1D susceptibility in the Swedish population data (P = 0.18).Using a REML log-likelihood ratio test (RLRT), the significance of the imprinting variance was tested by comparing the logarithmic value of the restricted maximum likelihood (REML log-likelihood) of the linear Mendelian model 1). This led to a T1D heritability estimate (h2) of 0.19 (± 0.1 × 10−1), i.e. 19% of the phenotypic variation in T1D is due to the variation in genetic factors in the analysed population  revealed significant maternal environmental variance with P = 1.60 × 10−24. The relative maternal T1D environmental variance was 0.19 (± 0.2 × 10−1), i.e. 19% of the phenotypic variance in T1D is due to the variation in maternal environmental effects . Augmentation of Mendelian model 2 by the maternal genetic effect (Mendelian model 3) did not change the REML log-likelihood or variance component ratios  with only the maternal environmental effect in addition to the two parental gametic effects, and (b) with only the maternal genetic effect in addition to the two parental gametic effects. The RLRT of model version (a) did not indicate significant imprinting variance (P = 0.26). Model version (b) led to a REML log-likelihood of 8,408.70, which was slightly smaller than the REML log-likelihood obtained from the corresponding null model containing a gametic effect and a maternal genetic effect . Because the addition of a parameter to a model should result in an REML log-likelihood value either being equal to or larger than that found here, these results could indicate a flat likelihood surface or numerical inaccuracies.As maternally derived environmental and genetic effects could not be unambiguously disentangled, the Mendelian model 1), which resulted in an h2 value of 0.10 , the h2 value was reduced to 0.85 × 10−1 (± 0.3 × 10−1). The corresponding maternal variance component was significant at a 5% significance level (P = 0.02). The relative maternal environmental variance was 0.15 , the relative maternal RA genetic variance estimate was 0.14  to 0.49 × 10−1 (± 0.7 × 10−1). To investigate the importance of maternal genetic effects in more detail, a linear model that corresponded to the Mendelian model 2 but substituted the maternal environmental effect with maternal genetic effect was applied. The application of this model resulted in a relative maternal genetic variance of 0.16 (± 0.3 × 10−1) and an h2 estimate of zero . Comparing the results to those associated with Mendelian model 3, the REML log-likelihood was not significantly different (P = 0.53). Detailed information on RA variance component estimates and REML log-likelihoods of the models is provided in Supplementary Table Maternal effects were initially ignored (Mendelian model 1 resulted in an h2 of 0.26 × 10−1 (± 0.2 × 10−1). As an equal additive genetic variance, and thus the same h2, was found using the threshold version of Mendelian model 2, maternally derived environmental factors appeared not to play a role (Table Mendelian model 3) the h2 value was 0.65 × 10−2 (± 0.1), while the maternal environmental variance remained zero and the relative maternal genetic variance was 0.20 × 10−1 , the effects of the year of birth (ranging from 1944 to 2012) were shown to differ significantly  was found for the intermediate group of non-manual employees (code 4). The lowest effect  was found for professionals as well as higher civil servants and executives (code 5).When considering the social economic index (SEI), analyses revealed that the effects of the mother’s SEI differed significantly for T1D with ls Table . AlthougP values ranging from 2.12 × 10−156 to 4.60 × 10−104 , with significantly different effects seen across all models for sex. 20 Table . The ana11 Table . Minimal11 Table .P values ranging from 3.34 × 10−265 to 2.64 × 10−24  was observed for foremen in industrial production and assistant non-manual employees.The SEIs of individuals significantly differed for RA with an average ls Table . Effect P values ranged from 0.01 to 0.02 .Maternal SEIs had a small but significant effect on RA susceptibility in offspring under both the linear and threshold models. 02 Table . Effectssd = 1.25), while men had an average number of 2.04 children . The number of offspring affected RA development significantly across all models (P < 1.00 × 10−3). An inverse and almost linear relationship between RA susceptibility and the number of children is depicted in Fig. In the dataset, women had an average number of 1.94 children , while an effect of − 0.15 (± 0.06) was observed under the threshold models.We found that being a single child or having siblings made a significant difference regarding RA susceptibility with ls Table . For theP values ranging from 6.86 × 10−149 to 6.61 × 10−101 across models . No clear trend was visible for interaction effects amongst male patients  as well as between sex and the number of offspring were observed . The latter interaction was not significant using threshold models  stated that the male preponderance in T1D prevalence, fecundity differences, misclassification of T1D and birth order effects could have led to a higher T1D-prevalence in children of T1D-affected fathers30. In contrast, a genome-wide association study of European T1D patients showed that an imprinted T1D-associated locus was located within the maternally expressed MEG3 gene31.Our finding that imprinting did not seem to affect T1D susceptibility supported previous findings by McCarthy et al. (1991), who analysed the importance of imprinting in an epidemiological study of clinical data from the Children’s Hospital of Pittsburgh IDDM Registry in Pennsylvania, USA. (2007), who found that imprinting is unlikely to affect the susceptibility to RA34. In most tissues, the IGF2 (insulin-like growth factor 2) gene is only paternally expressed, i.e. the maternal allele is imprinted. Martin-Trujillo et al. (2010) found an increased expression of IGF2 in a subset of RA fibroblast-like synoviocytes33. This cell type forms the synovial intimal lining and contributes to cartilage destruction and synovial inflammation49. The authors reported that IGF2-linked “loss of imprinting” was responsible for the increased expression that contributed to the autonomous growth of RA fibroblast-like synoviocytes33. These findings demonstrated the effects of partially imprinted loci on RA susceptibility.With regard to RA our findings are consistent with observations made by Zhou et alimprinting model considers all kinds of imprinting37, our study may have been underpowered and therefore unable to obtain statistical significance. Power to detect significant imprinting variances depends on both the h2 value of a trait and relative imprinting variance. In this study, heritability estimates for T1D and RA were comparatively small at 19.00% and 10.00%, respectively. However, h2 estimates vary widely in literature; T1D estimates range between 40 and 92%3 while RA estimates range between 12 and 60%13. Estimates also depend on the underlying data or the method used in the analysis. For example, twin studies result in broad sense heritability estimates where epigenetics are not taken into account. This increases the risk of inflated estimates50. Furthermore, sample size and pedigree information affect the ability to estimate genetic parameters and thus the power to detect significance. The depth of the pedigrees was theoretically sufficient to derive imprinting variances, but coancestry information between the maternal and paternal gametes of individuals with RA phenotypes would be a requirement for imprinting variance components analyses. In this context, the availability of genealogy databases in combination with genotypic data would increase the traceability of coancestries. Examples of such databases include the Utah Population database and a number of reliable Icelandic databases52. The availability of population-scale family trees53 would further allow the determination of the parental origin of alleles54 and generally enable large scale human population studies on epidemiological history55. Overall, the reliability of data and its impact on T1D and RA diagnoses must be discussed. According to Ludvigsson et al. (2011) the ratio of correct diagnoses for RA in the Swedish Hospital Discharge Register is 93.5% and 87.1% with and without lymphoma, respectively. In this study, no distinction was made between T1D and T2D from ICD-7 through ICD-9. T1D was therefore defined according the age at first hospitalisation as being not older than 20 years. For T1D and T2D 79% of cases were correctly diagnosed. The Swedish Hospital Discharge Register has provided complete national coverage since 1987 with more than 99% of all somatic hospital discharges currently registered56.In our study, the hypothesis that imprinted loci were the major cause influencing T1D and RA susceptibility was rejected. However, where a small number of fully or partially imprinted genes with small or moderate effect sizes does exist, the relative imprinting variance  is expected to be small. Although the The replicability of the results of this study depends on the available data basis. Our results are based on data collected until 2007 (RA) and 2012 (T1D). The constant upgrade of the Swedish Hospital Discharge Register, supported by an increasing digitization of data collections, will further improve the size of good quality data and increase the pedigree depth so that higher power to detect significance can be expected when fitting our methods. Furthermore, while disease incidences in the data may not reflect the population incidences, the extension of data will lead to an accumulation of information on family affiliations as well as on the occurrence of the disorders across generations. This will improve the efficiency of estimating heritability in general and the separation of variance components in particular.7, while Nisticò et al. (2012) found significant effects of the shared environment on T1D susceptibility in an Italian twin cohort study57. Maternal environmental effects are expected to especially affect an individual in utero, perinatally, or during early childhood 58. Factors such as early exposure to cow milk and cereals or a shortened duration of breastfeeding have been mentioned in this context58. In addition, we found the mother’s SEI to have a significant effect on T1D susceptibility in her offspring. It should however be considered that the SEI of a mother is in itself influenced by her environment. Examples include her husband’s SEI or other life circumstances. Apart from indications for the importance of maternal environmental effects, corresponding variance component analyses in full-sib populations could indicate the existence of an autosomal dominant inheritance pattern. However, based on findings from studies in Finland and the University of Southern California, Jerram and Leslie (2017) concluded that T1D susceptibility is unlikely to be affected by autosomal dominant genes59.With regard to the impact of the mother, we found highly significant maternally derived environmental effects on T1D susceptibility. This finding is supported by Hirschhorn (2003) who stated that there are convincing data that non-genetic factors, such as environmental factors in early childhood, play a role in T1D susceptibility61. In addition, the existence of maternal environmental effects on RA susceptibility cannot be excluded. In utero effects, which include maternal smoking62 or protective effects of maternal non-inherited HLA-antigens63, breast-feeding in perinatal life64, or hygiene standards during postnatal development44 have been reported. This study found that RA development was affected by the mother’s SEI. To conclude, while their relative importance could not clearly be quantified, both maternal genetic and environmental effects are indicated in RA susceptibility. Furthermore, while the ability to estimate covariances depends on the population structure65, the existence of covariances between additive and maternal genetic effects is nevertheless possible given that the h2 value was reduced to zero when a maternal genetic effect was added to the various models.With regard to RA, the maternal genetic variance was found to be significant when maternal environmental effects were not part of the model. Moreover, results indicated an inflation of both, the additive genetic and the maternal environmental variance by maternal genetic effects if ignored in the models. The threshold model results underline these findings. Maternal genetic effects on RA susceptibility have not been reported before. However, as sex-linked effects such as X-chromosomal and mitochondrial effects were not considered in the analysis, an inflation of the maternal genetic variance cannot be excluded. The role of the X-chromosome for the development of RA has previously been discussed; however, these studies have focused on the impact of skewed X-chromosomal inactivation in the context of sex differences in RA susceptibility66.Regardless, our study clearly indicated the significance of maternal effects on the development of T1D and RA. This was important as some of the contributory factors could be modified, possibly leading to the prevention of disease or treatment interventions67. Hence, birth year effects could be attributed to environmental factors which have changed during the last century. There is a reason to suspect that these factors are linked to adjustments in living conditions which are, among others, affected by the economic state of a country. The Swedish economy has been characterised by a steady acceleration in economic growth with decelerations observed during the 1970s and early 1980s68. Increased disposable incomes are usually associated with improved living conditions. That living conditions can have an effect on T1D susceptibility is supported by our finding that the SEI of the mother, and thus the environment she provides for her children, significantly affects their likelihood of being diagnosed with T1D. In earlier studies, the susceptibility to T1D has also been shown to be associated with increased, lifestyle-associated linear growth and obesity69. While T1D susceptibility varied between regions, medical and the presumed corresponding residential regions were found to significantly affect the likelihood of being diagnosed with this condition. This finding is supported by Tzaneva et al. (2001), who reported that the onset of T1D is strongly dependent on the area of residence70. Nevertheless, as observed in Fig. 56.The development of T1D and RA were found to be significantly different over the last century when considering the effects of the year of birth. With regard to T1D, Gale (2002) stated that an increase in the incidence thereof over the second half of the twentieth century within a genetically relatively stable population would imply that environmental factors play a role in its etiology44. This was supported by our novel finding that the SEI of the mother significantly affected RA susceptibility in children and that the SEI of the individual affected RA susceptibility later in life. The latter effect is also influenced by environmental factors such as the intake of oral contraceptives71. In addition, an inverse relationship between the total number of children and RA susceptibility was found. Pregnancy has been reported to typically ameliorate symptoms of RA72 and breast feeding is known to decrease RA susceptibility64. With regard to men, causal effects remain to be discussed. It should be noted that while the effect of the number of children on RA susceptibility was not investigated separately in women and men, significant interactions between sex and the number of children underline existing sex-associated differences. The difficulty in determining when environmental triggers occurred in individual life times may be reflected in the challenging endeavor of estimating the effects of medical regions on disease susceptibility. No information was available for how long individuals have resided in the analysed regions, potentially explaining the small effects and large standard errors. However, as for T1D, the periodic and regional variation in the data collection might also be a reason for this56. Nevertheless, geographical variation in RA incidence has previously been reported. Indications were found for the lower incidence rates in South European countries compared to North American and north European countries74.As rheumatoid arthritis usually occurs later in life, it cannot accurately be determined which environmental factors have operated during a lifetime. There is evidence that an immune system can be permanently modified by environmental factors at an early age, with growth, nutrition and infectious exposure already having activated the immune system before disease onset76. Our study confirmed that there was a significant sex effect in the development of both disorders. Moreover, especially for T1D, significant interactions between sex and birth year were found. This raises the question whether environmental effects preferentially interact with either sex. Based on the hypothesis that the prevalence of T1D amongst males increases proportionally in relation to disease incidence when the underlying environmental causes preferentially affect males, Gale and Gillespie (2001) reviewed sex ratios in T1D-incidence in multiple populations. They found that, although disease incidence increased, the sex ratio does not change and the trend towards male cases is specific for some populations75. They concluded that environmental effects do not interact with males over females. In our study, the effect of sex on T1D was only visible from 1960 to the mid-1980s.In the context of sex differences in T1D and RA susceptibility, effects of the X-chromosome, sex hormones, sex-specific behavior, and sex-specific differences in body composition and structure have been discussed77. There are currently no alternatives to the ASReml-package for our specific imprinting analysis as it is the only package that allows setting an appropriate correlation between the two parental gametic effects. This function ensures equivalence between the Mendelian and imprinting models. Equivalence is needed to perform an RLRT. Regarding the utilisation of linear and threshold models, both models generated similar results in uncovering the underlying genetic variation for T1D and RA. High correlations between the estimated genetic values indicated a fairly good fit of both models to the data.One difficulty in this study was that the affection status was measured as a categorical trait with binomial distributions. Therefore, the linear models are not appropriate to analyze this data type. Nevertheless, statistical significance of genetic parameters could only be tested using the REML log-likelihood of linear models via RLRT. When a threshold model is used, the ASReml-package employs an approximate likelihood  that cannot be used to test differencesNot only was new knowledge gained on the environmental effects on T1D and RA development, the separate contributions of each POE was able to delineate the genetic and phenotypic variation in T1D and RA susceptibility for the first time. Results supported findings that imprinting was of minor importance, but confirmed the role maternal factors played in the occurrence of both diseases. The prospects of fitting complex genetic variance–covariance structures can be expected to further improve given the size of good quality epidemiological data and pedigree depth.78) and from the Outpatient Register since 2001. For further information see Hemminki (2001) and Hemminki et al. (2009)80.This study was based on Swedish population-based registries with national coverage. Registry entries were linked using each person’s unique identification number. To ensure participant confidentiality, this identification number was replaced by a serial number. The project registry was linked to the Multigeneration Register and Population Registers providing information on family relations, and SEI , medical region and birth year, respectively. Individuals diagnosed with AIs were identified from the Swedish Hospital Discharge Register  to unambiguously delineate T1D from type 2 diabetes81. Furthermore, as AIs were recorded from 1964, it was assumed that the health status of individuals born prior to 1944 cannot be unambiguously defined. Therefore, only individuals born after 1943 were assigned a case/control status  classification systemsd = 16.65; Supplementary Fig. S4). Ancestral data was extracted from the Multigeneration Register for all patients. The generated dataset included 60,684 individuals , with birth years ranging between 1875 and 2007. The dataset contained five generations with 37,142 founders and 15,314 families. The smallest family contained two individuals, and the largest 21 individuals. The average number of cases per family was 1.04 .To not erroneously assign an individual with RA to the control status, health status was only declared for individuals born after 1938, i.e. for individuals not older than 25 years in 1964 when AIs registration was initiated . It can be written as:Y is a vector of the response variable; b is a vector of fixed effects; g is the vector of random gametic effects; X and Zg are incidence matrices; and e is the vector of random residuals. They are assumed to be normally distributed with a mean of 0 and variances GTo test the significance of the imprinting variance, a nested, equivalent version of the 41. To be able to distinguish maternal effects due to imprinting from other POEs as well as to investigate the importance of the latter, the following versions of Mendelian model 1 were applied:c and m are vectors of random maternal environmental and maternal genetic effects, respectively. They are assumed to be normally distributed with a mean of 0 and variances IcAIc is an identity matrix and A is the additive genetic relationship matrix; the incidence matrices Zc, and Zm relate observations and random effects. The significance of the additional random maternal environmental effect in Mendelian model 2 was tested by comparing the REML log-likelihood values of Mendelian model 1 and Mendelian model 2 using a one-sided RLRT. The RLRT is assumed to be χ2-distributed with a degree of freedom (DF) of one. The significance of the maternal genetic effect in Mendelian model 3 was tested by comparing the REML log-likelihood values of Mendelian model 2 and Mendelian model 3 using a one-sided RLRT (χ2-distributed with DF = 1).Other POEs such as maternal genetic or maternal environmental effects have been reported to be potential nuisance factors, i.e. erroneously assumed to be maternal effects due to imprinting, if not considered within the model definitionsimprinting model was used to investigate the significance of the imprinting variance in T1D:As described for T1D, the maternal environmental variance turned out to be significant. Therefore, the following Mendelian model 2 but assumes different contributions of maternal and paternal gametes to the susceptibility to T1D.This model is equivalent to imprinting model was applied with an additional maternal environmental effect (see above) but also with an additional maternal genetic effect:With regard to RA, the existence of maternal environmental and maternal genetic effects could not be excluded. Hence, the imprinting model with the REML log-likelihood outcome of the corresponding Mendelian models using a one-sided RLRT. The test statistic was assumed to be asymptotically distributed as a mixture of two χ2 distributions with DF = 1 and DF = 282.In general, the significance of the imprinting variance was determined by comparing the REML log-likelihood value of the Mendelian models the direct heritabilities were calculated as Mendelian model 1, Mendelian model 2, and Mendelian model 3. The latter two expressions of Mendelian model 2 and Mendelian model 3, respectively. To calculate Mendelian model 3, For the imprinting models the direct heritabilities were calculated as For the 77. The probability that an observation with index k belongs to class zero is:Mendelian model 2 as an example—the linear predictor is:xk, zg,k, and zc,k are the kth rows of the aforementioned incidence matrices X, Zg, and Zc and the vectors ß, g and c are defined as described for Mendelian model 2.As the case/control-status is denoted 1/0, the trait can be assumed binomially distributed. Hence, apart from the linear mixed models, which were needed for hypotheses testing, generalised linear mixed models (threshold models) were applied using a logit link and the pseudo-likelihood approach of Gilmour et al. (2015)1 = unskilled/ semi-skilled workers2 = skilled workers3 = foremen in industrial production and assistant non-manual employees4 = intermediate non-manual employees5 = employed and self-employed professionals and higher civil servants and executives6 = unknownFixed effects included sex , birth year , medical region , and the SEI of the mother (6 levels) for which the following codes were used:Note that coding differed across the various versions of the population database. Therefore, they were adjusted and equalised according to the 2012 version. The time an individual was under observation was considered by including the Legendre polynomials from the years under observation up to order three . Additional effects included in the RA model were the SEI of the individual (6 levels), whether an individual was a single child or had any siblings , and the number of offspring . Furthermore, interactions between sex and birth years were fitted for both disorders. Interactions between sex and SEIs, as well as sex and the number of offspring were considered for RA.Note that due to the underrepresentation of individuals in birth year levels, individuals were shifted to the next birth year level so that at least five individuals were obtained for each level.F test implemented within the statistical software package ASReml version 4.277. Note that ASReml caters for linear dependencies in the model by setting singular effects to zero83. Variance–covariance components were also estimated via ASReml. The R-packages “kinship2” version 1.6.484 and “pedigree” version 1.485 in R version 3.5.286 were used to prepare the data.The significance of all fixed effects was tested using an incremental Wald https://www.scb.se/hitta-statistik/regional-statistik-och-kartor/regionala-indelningar/digitala-granser/ (accessed in November 2019) in the ArcView-shape format. Data were edited using the “readOGR” function implemented in the R-package “rgdal” version 1.4–887 which was used in R version 3.6.188.Coordinates of Sweden used for Fig. Supplementary Information 1.Supplementary Information 2.