EPAS1 haplotype carrying selective sweep signals.Adaptive evolution in humans has rarely been characterized for its whole set of components, i.e. selective pressure, adaptive phenotype, beneficial alleles and realized fitness differential. We combined approaches for detecting polygenic adaptations and for mapping the genetic bases of physiological and fertility phenotypes in approximately 1000 indigenous ethnically Tibetan women from Nepal, adapted to high altitude. The results of genome-wide association analyses and tests for polygenic adaptations showed evidence of positive selection for alleles associated with more pregnancies and live births and evidence of negative selection for those associated with higher offspring mortality. Lower hemoglobin level did not show clear evidence for polygenic adaptation, despite its strong association with an  EGLN1 and EPAS1, the genetic variants in which were swept to high frequency in Tibetans due to strong positive natural selection. However, it still remains unclear if and how these and other genetic variants are connected to adaptive phenotypes and ultimately to fitness advantage. In this study, we collected genotype and phenotype information of 1,000 ethnically Tibetan women from the high Himalayan valleys in Nepal. Using both genome-wide association analysis and test for polygenic adaptations, we show that natural selection systematically altered frequency of alleles associated with reproductive outcomes to the direction of increasing fitness. That is, alleles associated with more pregnancies and live births, as well as those associated with lower offspring mortality, were under positive selection. Omitting the EPAS1 haplotype under selective sweep, the other variants associated with lower hemoglobin did not collectively show a clear signal for polygenic adaptation. Our study highlights the polygenic nature of human adaptive traits.The adaptations to high altitude environments in Tibetan populations have long been highlighted as an important case study of adaptive evolution in our species. Recent genetic studies found two genes,  Decades of research have accumulated evidence for widespread adaptive phenotypic evolution in nature, including correlations between phenotypes and environmental factors –3, and hA complementary set of approaches aims at assessing directly the effects of genotype on reproductive fitness . These dEGLN1 (egl-9 family hypoxia inducible factor 1) and EPAS1  .–39.EGLN1EPAS1, and find no loci with strong signatures of selective sweep beyond EPAS1  and EGLN1   with 1KGp = 0.002). We also found that Hb correlated positively with the numbers of stillbirths or miscarriages , as well as their proportions among pregnancies .A previous analysis of this sample of Tibetan women found strong relationships between physiological traits and reproductive success in this Tibetan sample by using a large set of covariates, including physiological, sociocultural, and socioeconomic variables  . Becausep = 2.02×10−5 and 2.76×10−5, respectively; p = 0.005) after correcting for a woman’s age at her last pregnancy, even if weaker. The pulse and fertility traits were previously shown to be marginally correlated if a larger set of physiological and sociocultural covariates was included in the model  [Another interesting finding was the negative correlations between pulse and most of the fertility phenotypes, with the strongest correlations found with the numbers of pregnancies and livebirths (ctively) .These results suggest that both low Hb and low pulse are associated with better reproductive outcomes at high altitude and raise the possibility that genetic variants decreasing these traits were selected for in Tibetans.EPAS1 and EGLN1 loci harbored the highest PBS values  ascertained from our Tibetan Hb and oxyHb GWAS, respectively. Compared to control SNPs [p = 0.047 and 0.018, respectively; p = 0.102 and 0.046 for Tibetans and Sherpa, respectively; EPAS1 SNP rs372272284 was excluded, no difference between the Hb- or oxyHb-associated SNPs and control SNPs was observed  for oxyHb, or Hb (poverdispersion = 0.201 and poutlier = 0.846 with no multiple test correction) when the EPAS1 SNP was excluded . Therefore, these analyses do not provide evidence that alleles associated with lower Hb levels were selected for, except for the EPAS1 locus. Given that the EPAS1 SNPs explain a small fraction of the total variation in Hb levels (2.7% in our cohort), these results raise the question of whether unelevated Hb per se was the adaptive trait in Tibetans.GWAS SNP effect sizes have been shown to be correlated between European and East Asian populations , implyinulations . We founexcluded . Similarpoutlier = 0.023 and ppairwise = 0.002; r = 0.441 compared to that with oxyHb r = 0.874). The alleles associated with higher deoxyHb in Tibetans were on average less common in Tibetans than in 1KGP CHB and the genetic values of deoxyHb in Tibetans and the Sherpa tended to be lower than those in 1KGP East Asians. Maximizing oxygen delivery while minimizing blood viscosity is likely to be beneficial in high-altitude environments; therefore, this advantage may underlie our signal of polygenic adaptation for lower deoxyHb.In contrast to Hb and oxyHb, deoxyHb showed significant polygenic adaptation signals, with both the outlier and the pairwise difference tests . Interestingly, we do not see significant signals in either overdispersion or outlier test for Tibetans or Sherpa (p > 0.05); instead, we see a strong signal in the outlier test for lowland East Asians toward high pulse  and the fertility fitness component . Furthermore, consistent with expectations, alleles increasing offspring mortality were selected against whereas those increasing offspring survival were positively selected for. A variable known to be directly linked to reproductive fitness, i.e. a woman’s age at her first childbirth, is also under selection, with earlier ages being advantageous, as expected. Twinning appears to have been selected against in Tibetan women. Although twinning may increase fitness, it is also associated with increased risks to mother and offspring due to limits on women’s ability to support adequate weight gain for two babies during the third trimester and to the lower birth weight of twins relative to singletons [The GWAS of reproductive traits allowed us to identify candidate variants that are currently being selected for in the sampled Tibetan population. In our results, none of the most strongly associated variants with reproductive outcomes showed strong signals of selective sweeps. However, if these variants affected reproductive fitness in the past in addition to the current generation, we might expect signals of polygenic adaptation. Indeed, a number of reproductive traits showed strong signatures of polygenic adaptations based on the outlier test; the pairwise population difference test, which uses less information and hence is likely to be less powerful, gives broadly consistent results, although at lower levels of significance . We see ngletons , which iEPAS1 gene, even though we confirmed a correlation between low Hb and better reproductive outcomes. Because Hb concentration is a polygenic trait, these results raise the question of whether lower hemoglobin is causally related to higher reproductive fitness.We identified several genome-wide significant associations with key physiological and fertility phenotypes in Tibetans , by analEGLN1 and EPAS1 SNPs, was not significantly associated with reproductive success probably due to low power: we estimated that the lowest selection coefficients that we had 80% power to detect were 6.6% and 7.4% at the EGLN1 and EPAS1 SNPs, respectively  and live in a mostly traditional society, where modern medical care, including in some regions contraception, has been introduced only very recently . The repectively . These sectively . BecauseEPAS1 gene [EPAS1 haplotype and low oxyHb, which correlates highly with total Hb. Interestingly, the association was stronger for oxyHb than for total Hb (p = 0.883 for rs372272284). This observation raises the possibility that it is the oxygen-carrying portion of total Hb that drives the well-replicated association between EPAS1 SNPs and Hb. We also found that SNPs associated with Hb did not show polygenic adaptation signals in our Tibetan sample, if the EPAS1 SNP was excluded from the analysis (p = 0.019 without multiple test correction). Based on our estimate of 0.386 g/dL per allele, and a mean allele frequency difference of 0.743 between high and lowlanders, we calculated that the EPAS1 SNPs can explain 52% of the 1.1 g/dL difference reported in [EPAS1 SNP explains only 2.7% of inter-individual variation in Hb: therefore, almost all within-population (97.3%) as well as a substantial portion of between-population (48%) variation remains unexplained.An attenuated erythropoietin and Hb concentration response to hypobaric hypoxia is a hallmark phenotype of the “Tibetan pattern” of high-altitude adaptations, which is markedly different from that of Andean highlanders , 67, 68.AS1 gene , 34 haveAS1 gene ; this hyAS1 gene . Our GWAtotal Hb , while ianalysis . IntriguEPAS1 and with the significant evidence for polygenic adaptations toward lower deoxyHb. This finding raises the question of whether unelevated Hb was the true target of selection in Tibetans rather than a mere correlate of the true adaptive trait. This scenario would be consistent with the observed correlation between low Hb and better reproductive outcomes because pleiotropy can induce a non-causal association between phenotypes. A recent study showed that the same EPAS1 SNP that is associated with Hb and other hematological traits is also associated with uric acid levels [EPAS1, a transcription factor with dozens of target genes, may affect multiple, seemingly unrelated phenotypes. Interestingly, the peak of our association signal for oxyHb at EPAS1 spans active enhancer (H3K27Ac) marks in human umbilical endothelial cells, as detected by the ENCODE project [EPAS1 expression in the endothelium with effects on vascularization, vasoconstriction, vasodilation and possibly beneficial effects in oxygen delivery at high altitudes. These findings suggest that the WHO altitude-adjusted elevated hemoglobin cut-off for detecting iron-deficiency anemia [Several scenarios could account for these results. Incomplete power in the Tibetan GWAS and/or in the polygenic adaptation tests could underlie the lack of clear evidence for polygenic adaptation for lower Hb levels, although we had sufficient power to detect polygenic adaptation signals for several other traits in the same samples. One possibility is that post-reproductive Hb levels are a poor proxy for the levels while women are reproductively active. Some, but not all, studies of Tibetans find an increase in Hb concentration with age –75, but d levels , suggest project , pointiny anemia  may be iADH locus [OCA2 gene (CHB = 0.59 and JPT = 0.57 versus Tibetan = 0.06 and Sherpa = 0.16). Therefore, the observed shift towards higher genetic values for pulse at low altitude could be the result of a selective event that similarly affected only low altitude populations. However, the correlation between low pulse and better reproductive outcomes in Tibetans suggests that low pulse is adaptive  at high altitude and raises the possibility that lower pulse was selected for when ancestral low altitude populations moved to high altitude.The lower genetic values for pulse in Tibetans compared to low altitude East Asians, coupled with the correlation between lower pulse and better reproductive outcomes in Tibetans, suggest an important role for cardiac function in pregnancy at high altitude. Intriguingly, tests of polygenic adaptation that use data from worldwide populations are consistent with selection favoring higher pulse in low altitude East Asians, but not in the closely related populations at high altitude. There is some prior evidence for selective events that took place in low altitude, but not high altitude East Asians. For example, the well-known selective sweep signal at the DH locus  in low aCCDC141 gene (TTN (titin) gene, which codes for a major component of cardiac muscle and has been linked to idiopathic dilated and peripartum cardiomyopathy and cardiac remodeling [Our GWAS of fertility phenotypes discovered three genome-wide significant associations . Those s141 gene , which imodeling , 81. Genmodeling , 82. AltPAPOLA gene encoding a poly-A tail polymerase that affects mRNA stability and nuclear export. Intriguingly, the product of this gene is inhibited by cordycepin, an adenosine analog (3’ deoxyadenosine), found in a fungus, “Yartsa gunbu” or Cordyceps sinensis, which is native to the highlands of Nepal and Tibet. Cordycepin is known to interfere with important biochemical and molecular processes, such as purine biosynthesis, DNA/RNA synthesis and mTOR  signaling transduction . TherefOLA gene , or throThis study was designed to extend the genetic study of human local adaptation beyond selective sweeps and candidate gene associations, by collecting genotype and physiological phenotype and reproductive history data for a large group of indigenous high-altitude Tibetan women in Nepal. Using this data set, we successfully identified several new genome-wide associations and signatures of polygenic adaptations. Our sample size of 1,000 participants is remarkably large for the genetic study of populations living in remote locations in a traditional society, but we acknowledge that is rather small for a modern-day GWAS. The census population size of ethnic Tibetans of villages in this region set the ultimate constraint on our sample size, which was obtained by recruiting virtually all inhabitants fitting our inclusion criteria. Despite this constraint, this study shows the necessity to study phenotypes of locally adapted populations in their native environments to correctly identify the adaptive phenotypes. With ever increasing throughput to generate genetic and phenotypic variation data, in-depth phenotyping of potentially adaptive features will help better understand how Tibetans and other populations living in extreme environments have adapted to their habitats.The study protocol was approved by: the University Hospitals Institutional Review Board, University Hospitals of Cleveland (protocol no. 12-15-27), the Nepal Health Research Council, Kathmandu, Nepal (protocol no. 38/2011), the Oxford Tropical Research Ethics Committee, Oxford, UK (protocol no. 23–11), the Dartmouth College Committee for the Protection of Human Subjects (protocol no. 23374) and the Human Research Protection Office, Washington University in St. Louis (protocol no. 201202114). A written informed consent was signed by each participant.2), and pulse rate (pulse/minute) were measured altogether using a non-invasive device Masimo Pronto-7 ©  as described in Cho et al. [2 as follows: oxyHb = Hb × SaO2 / 100 and deoxyHb = Hb–oxyHb. For each participant, an interview session was held to retrieve detailed reproductive history as well as to collect other potential covariates. A summary of the Tibetan samples and their phenotype measurements are presented in A total of 1,008 ethnic Tibetan participants were recruited from high-altitude villages in Mustang and Ghorka districts in Nepal in the spring and summer of 2012. All participants were women of age 39 or older and lifelong residents above 3000 m of altitude. The study communities in Nepal lie on the southern aspects of the Tibetan Plateau. Although they are citizens of Nepal, local people speak Tibetan dialects, practice forms of religion and social organization akin to those across the Tibetan Plateau, and retain the characteristic agro-pastoral and trading mode of subsistence common among highland Tibetans . An addio et al. . Two addEPAS1, EGLN1, HIF1A and NOS2 genes. Then, a subset of 344 unrelated Tibetans from the present study and all 103 Sherpa individuals were genotyped on 716,503 markers using the Illumina OmniExpress-24 v1.0 array to obtain denser genome-wide variation data. For each array platform, genotypes were called using the genotyping module in the Illumina Genome Studio with default parameters . Previously defined clusters, downloadable from the Illumina website, were applied for genotype calling. For the 2,553 custom markers we added to the HumanCore array, we retrieved intensity data from the Illumina Genome Studio and performed genotype calling using the OptiCall v0.6.4 [We generated new genome-wide genotype data for a total of 1,104 individuals indigenous to the high-altitude regions in the Himalayas in Nepal, including 1,001 ethnic Tibetans from the present study and 103 Sherpa . Array gl v0.6.4 . For 344EGLN1 gene, rs12097901 and rs188966510, in the set of 344 unrelated Tibetans. We used Epicenter FailSafe PCR system with the manufacturer’s recommended condition in buffers G and H, instead of using standard TAQ polymerases. We generated a 1,025 bp PCR fragment in an 11 ul reaction volume using a previously published primer pair PHD2-X1F (CCCCTATCTCTCTCCCCG) and PHD2-X1R (CCTGTCCAGCACAAACCC) [We separately genotyped two non-synonymous SNPs in the CAAACCC) . These PWe generated novel whole genome sequence data for 18 Sherpa and 35 Tibetans from the present study, all from Nepal. Seventeen individuals were sampled with known familial relationships (four Tibetans mother-daughter duos and three Sherpa parents-offspring trios), and sequenced to high-coverage  to generate high quality phased genome sequences. The remaining 36 individuals were chosen to be unrelated and sequenced to low-coverage targeting 5x autosomal coverage.For Sherpa, we began with 172 individuals, including 103 newly genotyped in this study and 69 previously published , and choFor Tibetans, we ran ADMIXTURE with K = 3 in a supervised mode, with 103 1KGP CHB, 103 1KGP GIH  and the 51 unrelated Sherpa as three reference groups. Pairwise relatedness was then calculated with the ADMIXTURE output using the RelateAdmix v0.08, controlling for population structure due to admixture . Among ihttp://hgdownload.soe.ucsc.edu/goldenPath/hg19/chromosomes/, using BWA backtrack v0.7.4 with -q15 option [http://broadinstitute.github.io/picard/) and were excluded from further analysis. Local realignment around indels and base quality score recalibration were performed using the GenomeAnalysis ToolKit (GATK) v2.8–1, following the best practice pipeline [Single-barcoded libraries for Illumina sequencing were constructed using the TruSeq library preparation kit. Libraries were pooled into multiple batches and sequenced in the Illumina HiSeq 2500 and 4000 machines for paired-end (PE) 100 and 125 bp designs . Sequenc5 option . PCR andpipeline –93. Finapipeline  by filteLD-aware variant and genotype calling was performed using the GotCloud pipeline  with defp-value ≥ 0.00001 and per-individual missing rate ≤ 0.03. Strand-ambiguous (A/T and G/C) SNPs were removed and only SNPs in autosomes or X chromosome were retained for imputation. The filtering process was performed using PLINK v1.90 [https://mathgen.stats.ox.ac.uk/impute/1000GP_Phase3.html, as imputation references by merging them with “-merge_ref_panels” flag in IMPUTE2. For other parameters, we used default values set by the program. Following imputation, genotypes with posterior probability ≥ 0.9 were accepted. Genotypes were assumed to be missing if none of three possible genotypes reached posterior probability threshold of 0.9. Then, we conducted an additional round of quality control by removing SNPs with missing rate higher than 0.05 or HWE p-value smaller than 10−6.We performed genotype imputation of Tibetan and Sherpa samples, which were array-genotyped either in the present or in our previous study  S1 Tabl. For eacNK v1.90 . GenotypNK v1.90 . We usedAmong 1,001 successfully genotyped and imputed Tibetan women, 991 individuals were included in our genome-wide association analysis (GWAS). Four individuals were excluded from the analysis because they were born below 3,000 m. Another individual was excluded from the analysis was a genetic outlier who clustered with individuals from the Indian subcontinent. The other five were excluded either because they had inconsistent reproductive record or because they were nuns who became celibate during their reproductive years.p-value obtained from the “lrtest” function in the R “lmtest” library was bigger than 0.05. The final sets of chosen covariates for physiological covariates are listed in a priori chosen set of four covariates: age, subdistrict, use of contraception and “continuously married (CM)” status. Use of contraception was categorized into three classes: never used, previously used, and currently in use. “Continuously married” status is a binary variable defined as being in a marital relationship throughout the ages of 25 and 40. It includes two who had experienced less than two years of gap before re-marriage following divorce or death of the husband. For physiological phenotypes, we chose relevant covariates by performing a stepwise model selection, allowing removal of a single covariate each step if likelihood ratio test (LRT) p-values from GEMMA were used to assess significance of genetic association. P-values of the full and subsample sets were highly correlated for each fertility phenotype .GWAS was performed using GEMMA v0.94.1 . Univarip ≤ 10−4 and lumped them into peaks by allowing maximum inter-SNP distance of 200 kb. Finally, we chose one SNP with the smallest association p-value for each peak to retrieve a set of independently associated SNPs. We also retrieved a set of SNPs associated with blood hemoglobin level (Hb) using summary statistics from a published large-scale GWAS meta-analysis [p ≤ 10−5. Then, we removed SNPs in LD: for each pair of SNPs with r2 > 0.2 in 1KGP CEU, we removed one with larger association p-value.To detect signatures of polygenic adaptation, we investigated systematic changes in allele frequencies of SNPs associated with each phenotype. For all of Tibetan GWAS phenotypes, we first took all SNPs with analysis . To obtap-value was calculated as the proportion of random SNP sets with their mean allele frequency difference equal to or more extreme than the observed one.After retrieving phenotype-associated SNPs with their effect size, we first compared mean frequency difference of trait-increasing alleles between Tibetans and 1KGP CHB. Following , we sampWe also looked into comprehensive signatures of polygenic adaptation using a machinery introduced by . It requp, have the mean absolute fitness W0, W0 (1+s) and W0 (1+2s). Using the observed mean phenotype value, Wm, we can get the per-allele effect size sW0 as a function of s, Wm and p:s, the statistical power to detect association was calculated using the “pwr.r.test” function in the R package “pwr”.To estimate the strength of positive selection necessary to generate a significant association between the fertility count phenotypes and genotype in our sample of the unrelateds, we assumed a simple additive model. That is, genotypes with 0, 1 and 2 adaptive alleles, with population frequency S1 FigGWAS quantile-quantile (QQ) and Manhattan plots for fertility phenotypes with genome-wide significant associations:  the number of pregnancies,  the number of live births,  the number of stillbirths, (G-J) the proportion of children born alive but died < 15 yr.  show GWAS results using the continuously married (“CM”) subset of individuals.(TIF)Click here for additional data file.S2 Fig2 , Pulse , oxyHb  and deoxyHb .GWAS quantile-quantile (QQ) and Manhattan plots for five physiological phenotypes in Tibetans: Hb , SaO(TIF)Click here for additional data file.S3 FigEPAS1 gene and (A) Hb and (B) oxyHb, conditional on the genotypes of the top EPAS1 SNP rs372272284. No residual association was observed.Locuszoom plots of the conditional association between markers around the (TIF)Click here for additional data file.S4 Figp ≤ 10−4),  42 oxyHb-associated SNPs after excluding the EPAS1 SNP rs372272284, and  45 deoxyHb-associated SNPs (p ≤ 10−4).  The mean frequency difference of trait-increasing alleles was presented (solid red line) together with the empirical null distribution of 10,000 sets of matched random SNPs.  The genetic values of populations (filled dots) and of regions  were plotted. The size of dots and the width of lines are proportional to the significance of the corresponding outlier test.Tests of polygenic adaptation of oxyHb- and deoxyHb-associated SNPs in Tibetans:  all 43 oxyHb-associated SNPs ((TIF)Click here for additional data file.S5 Figp ≤ 10−4; n = 52) or  in the UK Biobank data .  The mean frequency difference of trait-increasing alleles was presented (solid red line) together with the empirical null distribution of 10,000 sets of matched random SNPs.  The genetic values of populations (filled dots) and of regions  were plotted. The size of dots and the width of lines are proportional to the significance of the corresponding outlier test.Tests of polygenic adaptation of pulse-associated SNPs  in Tibetans ((TIF)Click here for additional data file.S6 Figp < 0.05) for both the mean frequency difference and the outlier tests:  the number of children surviving at 1 yr,  the number of live births,  the number of children born alive but died < 1 yr,  the number of children born alive but died < 15 yr,  the number of miscarriages, and  the number of twin births. (C-L) show GWAS results using the continuously married (“CM”) subset, while  show GWAS results using all individuals.Tests of polygenic adaptation of six fertility phenotypes reaching nominal significance ((TIF)Click here for additional data file.S7 Figlsqproject: YES” option. Numbers in the parenthesis in the axis label show the percentage of total genetic variation explained by each PC.The first two principal components (PCs) calculated from 1,295 individuals belonging to 132 groups  are plot(TIF)Click here for additional data file.S8 Figlsqproject: YES” option. Numbers in the parenthesis in the axis label show the percentage of total genetic variation explained by each PC.The first two principal components (PCs) calculated from 357 individuals belonging to 31 groups  are plot(TIF)Click here for additional data file.S9 Figf3 signals, measuring shared genetic drift from a common outgroup Mbuti, are plotted for (A) Nubri, (B) Tsum, (C) Lower Mustang and (D) Upper Mustang. (E-F) The extra genetic affinity with South Asians  of the Himalayan Tibetans compared to (E) Tibetans from Lhasa and (F) Sherpas are measured by f4 statistics. Thick and thin horizontal bars represent ± 1 and 3 standard errors, respectively, estimated by 5 cM block jackknifing.(A-D) The top 15 outgroup-(TIF)Click here for additional data file.S10 FigThe distribution of (A) altitude of residence and (B) South Asian ancestry proportion across individuals are summarized into a violin plot, using R package “vioplot”. South Asian ancestry proportion is estimated by fitting a two-way admixture model of Sherpa+Pathan using the qpAdm program. In panel (B), grey triangles show South Asian ancestry proportion estimated by group. Group-based estimates match well with the mean value of individual-based estimates.(TIF)Click here for additional data file.S11 Figβ = -1.835×10−5, p = 2.89×10−9).Each color-filled symbols represents a single individual. The red solid line shows a simple linear regression line. The observed negative correlation is highly significant even after controlling for the sub-district label (effect size (TIF)Click here for additional data file.S12 FigThe solid line curves show an exponential fit to the observed weighted admixture LD decay using ALDER. Point estimates ± one standard error estimates are shown in each panel. Standard errors are estimated by leave-one-chromosome-out approach, as implemented in ALDER.(TIF)Click here for additional data file.S1 Table(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file.S3 Table(PDF)Click here for additional data file.S4 Tableβ’s are calculated per alternative allele. SNPs with a derived allele shared between Tibetans and Denisovan are marked in bold face.POS column is for the genomic position in hg19. REF, ALT and DEN columns show reference, alternative and Denisovan alleles, respectively. TBN and CHB present alternative allele frequencies in our Tibetan data and 1KGP CHB, respectively. Effect size estimates (PDF)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Tablep ≤ 0.01 were marked with grey shades. Positive regression coefficients are marked in red color.Tests with (PDF)Click here for additional data file.S7 Tablep ≤ 0.01.Per-allele selection coefficient for 80% power to detect association in a single SNP test (α = 0.05) was estimated for fertility count phenotypes. No test showed (PDF)Click here for additional data file.S8 Table(PDF)Click here for additional data file.S9 Tablef3 and f4 statistics. For each group, we show in which studies samples belonging to it were published in the “Study” column.This list includes 182 present-day and 58 ancient groups. “N” column shows the total number of individuals in each group. Four sub-district groups of the Himalayan Tibetans reported in this study are marked by yellow color. For each group, we assigned a unique three-letter code (“Symbol”) and used it across figures. “Eurasian” and “East Asian” PCA columns mark populations used for calculating PCs for each set. “F-statistics” column marks populations used for calculating world-wide outgroup-(XLSX)Click here for additional data file.S10 TableP2way ≥ 0.05). Coef1, Coef2 and SE columns represent estimated ancestry proportions from Ref1 (Sherpa) and Ref2 (South Asian), as well as their associated standard errors. Although the South Asian ancestry proportion is small (2.5–6.2%), it is necessary to explain the Himalayan Tibetans, as shown by the insufficiency of the Sherpa-only model (P1way << 0.05).Sherpas from the Khumbu region and a South Asian population are used as sources. All four sub-district groups are adequately approximated by the two-way model ((PDF)Click here for additional data file.S11 TableWe used effect size estimates from multiple studies, ranging from 0.386 to 1.676 g/dL per allele. Power was calculated using the observed allele frequency (maf = 0.336), sample size (n = 649) and standard deviation of Hb residuals after regressing out covariates (1.330 g/dL), assuming a single test (α = 0.05).(PDF)Click here for additional data file.S12 Tableind), the number of unrelated individuals (nunrelated), and Pearson’s correlation coefficient across overlapping SNPs (r). For fertility phenotypes, we present results both for all-sample set and for the continuously married subset.For each phenotype, we present the number of individuals included in the main GWAS (n(PDF)Click here for additional data file.S1 Text(PDF)Click here for additional data file.S2 Text(PDF)Click here for additional data file.S3 Text(PDF)Click here for additional data file.


There are a wealth of tools for fitting linear models at each location in the brain in neuroimaging analysis, and a wealth of genetic tools for estimating heritability for a small number of phenotypes. But there remains a need for computationally efficient neuroimaging genetic tools that can conduct analyses at the brain‐wide scale. Here we present a simple method for heritability estimation on twins that replaces a variance component model‐which requires iterative optimisation‐with a (noniterative) linear regression model, by transforming data to squared twin‐pair differences. We demonstrate that the method has comparable bias, mean squared error, false positive risk, and power to best practice maximum‐likelihood‐based methods, while requiring a small fraction of the computation time. Combined with permutation, we call this approach “Accelerated Permutation Inference for the ACE Model (APACE)” where ACE refers to the additive genetic (A) effects, and common (C), and unique (E) environmental influences on the trait. We show how the use of spatial statistics like cluster size can dramatically improve power, and illustrate the method on a heritability analysis of an fMRI working memory dataset. The additive genetic effect arises from the linear addition of independent genes, or more technically, allelic contributions at different gene loci, while the nonadditive genetic effect refers to, for example, dominance or the interactive influence among alleles within or between gene loci . The additive genetic variation is generally of more interest since it is the summed effects of a particular allele or alleles at a given locus or at multiple trait‐related loci. Thus, the narrow‐sense heritability is defined as the proportion of phenotypic variation accounted for by the additive genetic effect (σA2) with an expression ofThe heritability in the broad sense (2.12.1.1σP2) within the population is assumed to be the same and can be divided into additive genetic (A), common environmental (C), and unique environmental (E) components, written asNormally twins are categorized as identical or monozygotic (MZ) and fraternal or dizygotic (DZ) twins. MZ twins have identical genotypes and DZ twins share, on average, 50% of their gene variants, which leads to the assumption of differential levels of sharing of additive genetic effects. Even in the absence of genetic influences on a phenotype, it is likely that twins are phenotypically more similar than unrelated individuals since they have been raised in the same family environment. This gives rise to the common environmental factor, which contributes to the covariance within twin pairs regardless of MZ or DZ type. Finally, there is an independent unique error, corresponding to the usual independent and identically distributed (i.i.d.) noise corrupting the measurements plus actual unique environmental influences, for example, trauma and illness. The phenotypic variance . For voxel v, the data from all subjects can be written as a column vector In this section, we will outline the notation used in this article. Assume the experiment consists of v. Thus, the general linear model (GLM) in a matrix form for each voxel can be constructed asX is an n × p design matrix including p − 1 covariates, and ɛ is the error vector, assumed to be normally distributed, written as V is defined below. Typical covariates include age, sex, or other between‐subject effects.Some types of brain imaging data are directly measured, for example, grey matter density, producing one image per subject. However, fMRI requires hundreds of scans per subject to estimate blood flow change. A within‐subject model is often fitted to the imaging data for each subject, producing an image of BOLD effect magnitude for each subject . To identify twins, let j(i) be the index of the twin pair of subject i. The MZ twin covariance can then be written, for i with Ti=Tji=MZ, asTo simplify the description of variance/covariance decomposition, we introduce a subject type indicator function i with Ti=Tji=DZ, isThe DZ twin covariance, for i, j) with Ti=S or Tj=S, or pairs of unrelated twins,  with j ≠ j(i), we have unrelated covariance ofFor subject pairs involving one or more singletons from different families without twins, ′, a concise notation of the error variance‐covariance matrix V isTo facilitate a general implementation, we re‐write the pair‐wise covariance matrices for MZ twins , DZ twinℂovMZ=A+C1+E1001,ℂovDZ=A+C1+E1001,ℂovUN=A+Cariances .2.2For each voxel, we fit the GLM model to the voxel‐wise data from twins and singletons, then estimate the model parameters—variance components, and finally obtain the estimate of heritability. We will first describe our proposed method in detail, and then briefly review other methods/tools that are widely used for heritability estimation.2.2.1n subjects, there are (n2 − n)/2 distinct SqD's. Note that the expectation of a SqD depends on the covariance, that is, EA−B2=VarA−B=VarA+VarB−2CovA,B for random variables A and B with EA=EB. This allows SqD's to be related to variance parameters in a linear fashion, in particular construction of a linear regression where coefficients correspond to the variance components A, C, E  of each subject pair was proposed by Grimes and Harvey /2 different observations of SqD's, our modification of this method simplifies the computation such that only While Grimes and Harvey's method specifies a linear regression with the use of ), Ti=MZ, we havei, j(i)), Ti=DZ, we havei, j),Consider the case when the original GLM  is a simmatrices , 5), an, an(10)Ymatrices  and the n2 − n)/2 SqD's and specify the mean structure of a linear regression model:D is an (n2 − n)/2 × 1 SqD vector of observations, Z is an (n2 − n)/2 × 3 design matrix, and ρ is the unknown variance parameter vector.The relationships , 12), a, a12), an‐vectors p − 1 covariates, and β1, …, βp − 1 are the corresponding regression coefficients. The parameters β = ′ are not of interest and we treat them as nuisance parameters in variance component analysis. If we estimate β using OLS with an expression of β^OLS=X′X−1X′Y, where Now suppose that the GLM  is a mulEe=0 and variance R projects the unobservable error vector ɛ to its estimate e that is orthogonal to the space spanned by the columns of the design matrix X. When the sample size n is large enough, the error vector ɛ can be well approximated by the residual vector e. We assume that the correlation induced by removing covariates and mean centering is negligible when compared with variance components, that is, n.Denote the residual projection matrix by Here the variance components are derived in terms of nuisance‐free errors:n, the (n2 − n)/2 rows of the SqD data and design matrix is unwieldy. Hence we modify how we compute estimates ρ^=Z′Z−1Z′D. First, D, SSD=∑l=1n2−n/2Dl is the sum of all squared differences, s2Y=∑inYi−Y¯2/n−1. With the nuisance variables, we approximate this sum with the residual variance from the GLM  satisfying the inequality constraint ρ ≥ 0, then the following conditions hold:Z, D, and ρ found by OLS, the first two conditions are trivially satisfied, and hence, only the third condition needs to be checked. The NNLS algorithm proceeds by using OLS to estimate ρ and checking for negative elements. If a negative element is found, it is set to zero, effectively dropping that column from the Z, and OLS is re‐fit.Our APACE method proceeds by applying the NNLS algorithm to the linear regression model with SqD's  or 15)  15) for  Karush, . As Z′, the best fitting model is selected; as valid AE and CE models will always explain more variability than an E model, these are next selected when available. If both AE and CE models have valid estimates, we have two methods to assess the model fit. The model with the smallest residual sum of squares, that is, D−Zρ^′D−Zρ^, can be selected, which is our default APACE setting. Alternatively, we can return to the original GLM model  comparing the fitted model  ∞ Wilks, . In partp‐value can be easily calculated. Obtaining a p‐value less than a given significance level α, which is typically a small number , suggests that there is significant evidence against the null hypothesis and the null hypothesis should be rejected at level α. We note that when data is non‐Gaussian, the LRT computed under the normality assumption can be inaccurate and the use of Wilk's theorem in approximating its null distribution might lead to invalid results, which will be investigated in our simulation studies. We therefore compute both the asymptotic theoretical p‐value and the permutation‐based p‐value based on the empirical distribution of the LRT statistic (see below).Given the asymptotic null distribution of the LRT statistic, the theoretical 2.2.2Several approaches have been proposed for the analysis of heritability, and we briefly introduce these existing approaches in this section.The heritability method due to Falconer and Mackay  is basedSolving for narrow‐sense heritability , these eThis method has been widely used and is the simplest way to estimate heritability  and a half normal distribution.The null hypothesis of zero heritability can be tested by comparing the MZ and DZ correlation coefficients after Fisher's variance‐stabilising transformation. For MZ, Fisher's transformation isSakaori, . Considehttp://www.fil.ion.ucl.ac.uk/spm) provides a general framework for variance component model estimation in a Bayesian setting, and, as a special case, can implement the ACE model. Based on preliminary studies  software (http://openmx.psyc.virginia.edu) offers a structural equation SEM framework to allow flexible model definition and parameter estimation for variance components, both of which are commonly used in analysing genetic data for heritability inference. The SEM ACE model for univariate twin data can be displayed as a path diagram, shown in Figure a, c, and e can be described by the path coefficients A,C and E, respectively ..http://omatrices . Howevermatrices , but we matrices . For neuA, C, E. To test the null hypothesis of zero heritability, the LRT test statistic, which is asymptotically distributed as a mixture of chi‐square distributions, can be calculated  can read and write neuroimaging data.The sequential oligogenic linkage analysis routines (SOLAR) software is designed for the investigation of genetic effects in imaging genetics studies . Crucially, twin pairs stay linked, preserving any common environment effects. As even moderate sample sizes can yield Np too large to allow computing all permutations, in this case, an approximate or Monte Carlo permutation test is conducted for a smaller number of permutations, say Np = 1,000, based on a random subsample of all permutations  for voxel‐wise inference, and cluster size (number of voxels involved in a cluster after thresholding) and cluster mass  for cluster‐level inference. Hence, this permutation approach can be further partitioned into two parts: voxel‐wise single threshold test and cluster‐wise supra‐threshold tests.In order to resolve the multiple comparisons problem and strictly control false positives over the whole volume of regions of interest (ROI's) or voxels simultaneously, a permutation test can also be used to compute inferences corrected for the family‐wise error (FWE). FWE‐corrected 2.3.1π = 1, …, Np be the permutations considered including correctly labeled data. At a single ROI/voxel, the permutation test produces a level α threshold by finding the p‐values are computed as the proportion of null distribution values as large as or larger than the observed test statistic.Let α FWE threshold TαFWE is the p‐value, denoted by pTFWE, for any given test statistic T0 is likewise the proportion of permutation maximum distribution values equaling or exceeding that value . The associated FWE‐corrected p‐values areKπmax (or Mπmax) is element π of the maximum cluster size (or mass) distribution.Computation of FWE‐corrected inferences proceeds as with the single‐threshold test. The 3In this section, univariate simulation analysis is conducted to compare our newly proposed voxel‐wise heritability estimation methods with existing methods in terms of prediction accuracy, validity, sensitivity, and the overall computation time for different variance component settings. The ROC‐based simulation studies generate 2D image data for power evaluation and comparison between the voxel‐ and cluster‐wise heritability inference approaches for various settings.3.1p‐value based on 1,000 permutations), LR‐SqD  and LR‐SqD ReML, and existing methods including Falconer's method, Bayesian ReML in SPM, SEM in OpenMx, and SOLAR.We use Monte Carlo simulations to evaluate our proposed linear regression methods, LR‐SqD Perm  usually holds in practice, we choose 15 possible sets of A, C, E from the upper part of this parameter space satisfying E ≥ 1/3. Note that we assign values of A, C, E such that A + C + E = 1, meaning A is directly interpretable as h2. That is, the value of A is exactly h2. However, we still useThe parameter settings shown in Table n = 100, 300, 1,000. For instance, the sample of 100 subjects is comprised of 25 MZ twin pairs (50 subjects) and 25 DZ twin pairs (50 subjects). For the unbalanced design, the sample size is fixed as n = 300, and we consider the MZ:DZ ratios being 1:4 and 4:1, that is, n = 60 + 240 and n = 240 + 60.For balanced design with an equal number of subjects for each group (MZ and DZ twins), three samples are considered with the size of n = 300, that is, the number of MZ and DZ twin pairs is identical.Apart from the Gaussian random error, we also take into account the case where the error term is not normally distributed. Here we consider a log‐normally distributed unique environmental random noise. The sample considered is balanced with the size of A, C, E) parameter settings, lead to totally 90 simulation settings. For each setting, we consider both the one sample model  is calculated to compare 6 estimation methods including LR‐SqD, LR‐SqD ReML, Falconer's method, Bayesian ReML in SPM, SEM in OpenMx, and SOLAR. For each of all seven testing (inference) methods considered , we compute false positive rate (FPR), statistical power, and overall running time. As the one sample model and multiple linear regression model have qualitatively similar results, we will only report the results obtained from multiple linear regression.3.1.2The MSE comparison of six methods is shown in Figure α = 0.05 (under the null hypothesis of no heritability). With Gaussian noise (Rows 1–5), when the common environment effect C is also zero, all methods are highly conservative except LR‐SqD Perm and Falconer's, both of which are close to exact for sufficient sample sizes. In the presence of C > 0, the methods are generally valid but SOLAR struggles, having inflated FPR. We believe this is due to convergence problems for small samples. For the non‐Gaussian case (Row 6), we note that all methods are invalid with inflated FPR except LR‐SqD Perm, which does not rely on the assumption of normality.Figure p‐value and OpenMx have comparable power. LR‐SqD Perm using permutation‐based empirical p‐values has the largest power in almost all settings, particularly for small values of heritability and zero C effect. SPM's ReML method is generally less powerful. Falconer's method is around the linear regression methods using asymptotic p‐value and OpenMx, sometimes more, sometimes less powerful. In the case of log‐normally distributed random error (Row 6), we only consider LR‐SqD Perm with controlled FPR. As expected, the power is generally lower for all settings when compared with the Gaussian case with n = 150 + 150 (Row 2).Figure p‐values  always outperform other iterative methods including Bayesian ReML in SPM, SEM in OpenMx, and SOLAR. For each simulation setting, the overall computation time of all simulations for those noniterative methods is far smaller than the other iterative methods. The LR‐SqD Perm, based on 1,000 permutations, has running time comparable to, or even longer than, those iterative methods. Nonetheless, applying parallelization by running multiple jobs in parallel can help reduce the overall computation time.We evaluated the relative running time  for completion of 1,000 simulated datasets ; see Figure 3.2.2y‐axis) against FPR with varying threshold levels. A standard ROC analysis is suitable for only a single outcome, while we have 1282 outcomes. Hence we use an alternative, free‐response ROC approach , with a larger value for better performance. Since we are mostly concerned about FPR values between 0 and 0.05, corresponding to a family‐wise error rate of 5%, the normalised AUC is A, C, E) = , and the corresponding smoothed heritability signal images, where the signal were generated with  as per one configuration in Table Generate For each image, estimate heritability pixel‐by‐pixel and create the LRT test statistic image.Voxel‐wise inference. Apply a large number of predefined grids of thresholds to the LRT test statistic image, obtain the supra‐threshold pixels, and then calculate family‐wise FPR and TPR for each of these threshold levels, obtaining FPR from noise‐only image and TPR from the A > 0 pixels in signal images.Cluster‐wise inference. Threshold the LRT statistic images with a predetermined cluster‐forming threshold  and form clusters. Use a predefined grid of cluster size thresholds to define each cluster as detected or not.Compute the family‐wise FPR and TPR:FPR. Using the smoothed random noise images, for each threshold, the family‐wise FPR is the proportion of realizations having any  detections.TPR. Using the heritability images, for each threshold, compute the proportion of true positive pixels (detected and A > 0) out of all possible (number of the A > 0 pixels). This is computed for each realization and averaged over realizations.Plot the ROC curves and calculate the corresponding normalized AUC values.For clarity, the exact steps in this ROC calculation are as follows.3.2.3As described above, a range of simulation settings are investigated for both voxel‐ and cluster‐wise inference approaches using APACE. For different extents of smoothness, the returned ROC curves have fairly similar shape, so we will only illustrate the ROC curves created by medium degree of smoothing with FWHM of three pixels, which are shown in Figures For both focal and distributed signal, ROC curves of the cluster‐wise method are always above those of the voxel‐wise method, reflecting higher statistical power obtained for cluster‐ than voxel‐wise inference approaches. In general, for a particular family‐wise FPR level, the TPR value of both inference methods becomes larger when the sample size or the heritability is increased.The normalized AUC values Figure  show tha4Here we report the heritability analysis of a working memory fMRI task. We illustrate the above‐mentioned heritability inference approaches including univariate LR‐SqD and permutations.4.1n = 319 young and healthy participants from Queensland, Australia , consisting of t‐contrast images using a one‐sample t‐test, was extracted. Only areas of expected activation in the frontal and parietal regions are included in the mask, comprised of 14,627 voxels in total. Age, sex, and 2‐back performance accuracy (the percentage of correct responses) are included as the covariates in the statistical analysis , makes these spatially informed statistics more accessible. For equivalent FWERs, the cluster‐wise approach was found to have higher sensitivity, and thus more powerful in ROC‐based power simulations, which demonstrates the importance of such spatial statistics over voxel‐wise statistics and the need for permutation inference to take advantage of these cluster statistics. With few weak assumptions, permutation inference is a feasible alternative to the parametric approaches, which is even preferable in studies having small sample sizes or when the stronger assumptions of the parametric approaches cannot be met  for detecting heritability, but at least we found all methods are valid with normally distributed errors except SOLAR, which is specially designed for family studies with large sample sizes of various degrees of relatedness. For Gaussian noise, although Falconer's method has poor estimation accuracy, it seems to work well with the power comparable to that of LR‐SqD Perm. However, it relies on the normality assumption to test for the equivalence of MZ and DZ correlations. For non‐Gaussian noise, the null distribution of LRT computed under the misspecified normality assumption can be inaccurate and the corresponding asymptotic null distribution of LRT based on Wilk's theorem is problematic, which results in inflated FPR as shown in our simulations. LR‐SqD Perm, which relaxes the assumption of normality, is the only applicable method that maintains valid FPR control in the case of non‐Gaussian error, and thus we suggest sticking to LR‐SqD Perm. During univariate evaluations, we found adding singletons can improve neither estimation accuracy nor statistical power. However, we still suggest including singletons in the statistical analysis since a better estimate of the phenotypic variance can be obtained with more data taken into account. Averaging across all the simulation settings, we found LR‐SqD is roughly 2.5 times faster than LR‐SqD ReML, and around 45.5, 84.8, and 995.7 times faster than SPM, OpenMx and SOLAR, respectively.A = 0 is not asymptotically pivotal and its distribution varies discontinuously across the parameter space depending on the true value of variance component C. The configurations of C on the parameter space can be partitioned into two cases: (1) C > 0, (2) C = 0. For standard Case (1), the reference distribution for the LRT involving one parameter on the boundary of the parameter space has been proven to be a half‐half mixture of χ02 and χ12 , the asymptotic null distribution of the LRT statistic for a finite sample can be more similar to that for Case (2) when C is close enough to the boundary  to be applied in computing the p‐values, and enabling parallel execution further accelerates the implementation. The current version of APACE can be adopted for the family design including twins, siblings and singletons, and the generalization of APACE for any family designs is possible with the use of the pedigree information.We have developed a Matlab‐based tool “Accelerated Permutation Inference for the ACE Model (APACE)”, which provides different analysis approaches specialized for heritability inference based on LR‐SqD and is freely available at


Hanwoo, an important indigenous and popular breed of beef cattle in Korea, shows rapid growth and has high meat quality. Its yearling weight (YW) and carcass traits  are economically important for selection of young and proven bulls. However, measuring carcass traits is difficult and expensive, and can only be performed postmortem. Genomic selection has become an appealing procedure for genetic evaluation of these traits (by inclusion of the genomic data) along with the possibility of multi-trait analysis. The aim of this study was to compare conventional best linear unbiased prediction (BLUP) and single-step genomic BLUP (ssGBLUP) methods, using both single-trait  and multi-trait  models to investigate the improvement of breeding-value accuracy for carcass traits and YW. The data comprised of 15,279 phenotypic records for YW and 5,824 records for carcass traits, and 1,541 genotyped animals for 34,479 single-nucleotide polymorphisms. Accuracy for each trait and model was estimated only for genotyped animals by five-fold cross-validation. ssGBLUP models (ST-ssGBLUP and MT-ssGBLUP) showed ~19% and ~36% greater accuracy than conventional BLUP models (ST-BLUP and MT-BLUP) for YW and carcass traits, respectively. Within ssGBLUP models, the accuracy of the genomically estimated breeding value for CW increased (19%) when ST-ssGBLUP was replaced with the MT-ssGBLUP model, as the inclusion of YW in the analysis led to a strong genetic correlation with CW (0.76). For backfat thickness, eye muscle area, and marbling score, ST- and MT-ssGBLUP models yielded similar accuracy. Thus, combining pedigree and genomic data via the ssGBLUP model may be a promising way to ensure acceptable accuracy of predictions, especially among young animals, for ongoing Hanwoo cattle breeding programs. MT-ssGBLUP is highly recommended when phenotypic records are limited for one of the two highly correlated genetic traits. Hanwoo is a breed of beef cattle indigenous to Korea, very popular due to its high meat quality. The excessive marbling found in this breed has become an important factor influencing the quality of meat products in commercial beef markets , 2. MarbThe Hanwoo beef industry mainly aims to increase both the quantity  and quality (marbling score—MS) of meat. At present, Hanwoo cattle are selected by conventional methods involving two tests: a performance test for young bulls followed by a progeny test for selected young bulls. The estimated breeding values (EBVs) for MS and YW obtained from the classical animal model are used for selecting young bulls, while the EBVs for BT, CW, EMA, and MS are used for selecting proven bulls . HoweverA) and relationship matrix based on genomic information (G) are combined into a single matrix, H [H has a simple form and can substitute for the inverse of A in existing equations [Advances in genome-wide single-nucleotide polymorphism (SNP) panels have overcome disadvantages of conventional breeding methods. SNP panels enable accurate and cost- and time-effective prediction of genomically estimated breeding values (GEBVs), even in young animals. Studies on beef cattle have shown that several quantitative traits are polygenic –8. The aatrix, H , 14. Thequations . This mequations . In addiquations .Numerous genomic selection studies have demonstrated the advantages of ssGBLUP in various domesticated species, including beef cattle –20, dairThis study was aimed at evaluating the accuracy of breeding values for economically important carcass traits and YW in Hanwoo beef cattle, obtained using four models: conventional single-trait BLUP (ST-BLUP), multi-trait BLUP (MT-BLUP), single-trait single-step genomic BLUP (ST-ssGBLUP), and multi-trait single-step genomic BLUP (MT-ssGBLUP). We found that combining pedigree and genomic data in the ssGBLUP model may be a promising way to ensure acceptable accuracy of predictions, especially among young animals, for ongoing Hanwoo cattle breeding programs.http://www.aiak.or.kr), data for growth traits were obtained from the Hanwoo Improvement Center (http://www.limc.co.kr), and data for carcass traits were recorded by special inspectors, from the Institute of Korean Animal Products Evaluation (http://www.ekape.or.kr), at the slaughterhouse. Pedigree and phenotypic data related to growth and carcass traits were generated following the protocol for progeny test program, as notified by the Ministry of Agriculture, Food and Rural Affairs based on livestock law in Korea. HIC, as an enforcement institution for the testing program for selecting proven Hanwoo bulls, is obligated to maintain data and ownership of enrolled animals under notice.DNA samples were obtained from semen and/or blood samples collected by veterinarians. Ethics committee approval was not required for semen and blood collection, as they were collected specifically for this study from the Hanwoo Improvement Center(HIC) of the National Agricultural Cooperative Federation, which was involved as a partner in this research project that was supported by a grant from the IPET Program (No. 20093068), Ministry of Agriculture, Food and Rural Affairs, Republic of Korea. Pedigree data were recorded by the Korean Animal Registration Association  and carcass traits of 5,824 steers .t) and pervious weight at time (t -1) before termination , according to Park et al. [The animals analyzed in this study were born between 1989 and 2015. Pedigree data of 50,115 animals, obtained on tracing the pedigree file back up to 11 generations, were used in the animal model. YW for each animal was estimated from weight at termination (t) of the test  to the highest score of nine (abundant marbling). The records on MS collected before 2005 were excluded as they were not consistent with the newly adopted 9-point MS system. Carcass traits were measured in ~24-month-old steers by ribbing between the 13A total of 1,679 animals were genotyped using Illumina BovineSNP50K (n = 959) and HD 777K (n = 720) BeadChip . The SNPs common to the 50K and 777K SNP chips were matched to increase the sample size, resulting in 45,304 SNPs. Animals with more than 10% of missing genotype data (73 heads of cattle) and without a phenotype for five traits of interest (n = 15) as well as animals with parent−progeny conflicts (n = 11) or deviation errors between the pedigree and genomic relations (n = 39) were excluded from the final analyses. SNPs with unknown positions (302 SNPs) and those located on sex chromosomes  were removed from the analyses after quality control. Furthermore, SNPs with call rates lower than 0.98 , minor allele frequencies lower than 0.01 , and a Mendelian error (12 SNPs) were also excluded. The missing genotypes were imputed in the BEAGLE software . Finallyy is the vector of observations for the trait of interest; b is the vector of fixed effects, including batch-test place-sex (163 levels) and birth place (108 levels) for YW, batch-test place-slaughter date , birth place , and slaughter age (days from birth to slaughter) was considered as covariates for carcass traits ; u is the vector of random genetic additive effects; e is the vector of random residual effects; X and Z are incidence matrices related to fixed and random genetic additive effects, respectively. Var (u) = G⊗A and Var(e) = R⊗I were assumed, where A is the numerator relationship matrix, I is the identity matrix, and G and R are additive genetic and residual covariance, respectively, for the five traits. Priors for fixed effects (b) were uniform, and Gaussian distribution was assumed for random genetic additive effects (u), and inverse Wishart distribution was employed for variance components (G and R).The variance components for YW and carcass traits were estimated based on the classical Bayesian multi-trait animal model (with pedigree and phenotype data), similar to Choi et al.  and ParkThe model was in the gibbs2F90 software , and theFurthermore, a single-trait animal model was used for comparison with the multi-trait model, assuming zero genetic and residual covariance among the traits.yc) was calculated as the sum of the EBVs, and the residual  were performed using the following animal model:Furthermore, genetic and residual covariances for the five traits were assumed to be zero for the single-trait pedigree-based model (ST-BLUP).A−1, which was replaced by matrix H−1 [A is the numerator relationship matrix; G is the genomic relationship matrix; α (0.95) and β (0.05) are mixing parameters used to combine matrices G and A22  to avoid singularity problems [In the ssGBLUP method, the statistical model was the same as that for the traditional evaluation  except for the inverse of numerator relationship matrix trix H−1 , 14. Thitrix H−1 , 29:H−1problems .Variance components used in models MT-BLUP (ST-BLUP) and MT-ssGBLUP (ST-ssGBLUP) were estimated using the pedigree-based  multitraGenotyped animals  were allocated to five mutually exclusive subsets for cross-validation by K-means clustering  based onEstimates of variance components and heritability for YW and carcass traits, except CW, were almost similar in the single- and multi-trait analyses. For CW, slight difference in environmental variances was noted between two models, but genetic variance was significantly increased (~45%) in the multi-trait model, further increasing heritability (~26%), when compared with the single-trait model. Regardless of the model chosen, the lowest and highest heritability corresponded to YW and MS, respectively .Genetic and phenotypic correlations among traits are presented in The mean realized accuracy of EBVs (ST-BLUP and MT-BLUP) was 0.25 for BT, 0.38 for CW, 0.31 for EMA, 0.28 for MS, and 0.51 for YW . The accFor all traits, the regression coefficients ranged from 0.72 to 1.14 for single-trait BLUP, 0.68 to 1.18 for multi-trait BLUP, 0.81 to 1.32 for single-trait ssGBLUP, and 0.77 to 1.20 for multi-trait ssGBLUP methods .In general, no obvious changes in regression of the adjusted phenotype on EBVs / GEBVs were observed between single- and multi-trait analyses for either BLUP or ssGBLUP models, regarding BT, EMA, MS, and YW. However, the bias was decreased when the MT-ssGBLUP model was used for CW instead of the ST-ssGBLUP model. The absolute deviation of regression coefficients from 1.0 was 0.32 and 0.19 for ST-ssGBLUP and MT-ssGBLUP, respectively. In terms of bias, the range of variations for carcass traits was in agreement with that reported by Lee et al. .The phenotypic data on YW were considerably more abundant than those for carcass traits. Thus, the accuracy of carcass traits could be affected by additional phenotypic records because of the genetic correlation between YW and carcass traits obtained using multi-trait models. Therefore, we performed the analysis after reducing the YW data of the training population to the same size as CW data. No significant changes were revealed in mean realized accuracy of EBVs / GEBVs for BT, MS, and EMA, when compared with those obtained using the complete data. However, accuracy decreased for YW in all models, and for CW in MT-BLUP and MT-ssGBLUP . The smaDuring the national genetic evaluation of Hanwoo, YW is one of the traits used at the performance test stage for selecting young bulls. Thus, YW is recorded for all candidate young bulls, but carcass traits are measured only for the offspring of selected young bulls as steers . Hence, A with the H matrix can improve the accuracy of carcass traits  by approximately 17% in young Nellore males. The improved accuracies obtained in this study are greater than those reported by Lee et al. [The results showed a noticeable increase in the accuracy of GEBVs when models combining pedigree and genomic information were applied to the single-step analysis . Moreovee et al.  for Hanwe et al. , who anaThe use of multivariate models is known to provide more accurate breeding values than those obtained by single-trait models, as the information from genetically correlating traits can be utilized , 41–46. Moreover, tThe genetic correlation existing between traits underlies the advantage of multi-trait models. In our study, the superiority of the multi-trait model (in terms of accuracy) over the single-trait model was more obvious for CW. The genetic correlation between CW and YW (0.76) was twice as strong as that between EMA and YW (0.34). These results also support the findings of Calus and Veerkamp , who poiIn the present study, analysis of a reduced dataset decreased the accuracy of YW breeding values in all models, compared with those obtained using the complete YW phenotypic data . When adOur findings emphasize the importance of exploiting the high genetic correlation between traits by means of genomic multi-trait models. This approach is particularly relevant in practical breeding programs for traits such as CW, which are often not available for all animals under study.The results of this study indicate that the estimates of breeding values the single-step genomic methods are more accurate than those obtained using pedigree-based information for genetic evaluation of carcass traits and YW. Moreover, the multi-trait ssGBLUP model considerably increases the accuracy of breeding values for CW, a trait manifesting a high genetic correlation with YW, which is the most recorded trait. In general, the inclusion of genomic information in multi-trait methods may be a promising way to achieve acceptable accuracy of predictions. This approach is particularly relevant when phenotypic records are limited or missing for one of the two highly correlated traits. Furthermore, this approach could be suitable for evaluating genomic predictions, especially for young animals in the ongoing breeding programs on Hanwoo cattle.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


Expression quantitative trait loci (eQTLs) are important for understanding the genetic basis of cellular activities and complex phenotypes. Genome-wide eQTL analyses can be effectively conducted by employing a mixed model. The mixed model includes random polygenic effects with variability, which can be estimated by the covariance structure of pairwise genomic similarity among individuals based on genotype information for nucleotide sequence variants. This increases the accuracy of identifying eQTLs by avoiding population stratification. Its extensive use will accelerate our understanding of the genetics of gene expression and complex phenotypes. An overview of genome-wide eQTL analyses using mixed model methodology is provided, including discussions of both theoretical and practical issues. The advantages of employing mixed models are also discussed in this review. Gene expression is the frontier process linking genotypes to phenotypes, and thus the genetics of gene expression is critical for dissecting the genetic basis of complex phenotypes. Currently, the genetics of gene expression largely depends on identifying an expression quantitative trait locus (eQTL), i.e., an association between gene expression and the genotype at a locus. Genome-wide eQTL studies have shown that the eQTLs explain a substantial proportion of variation in gene expression ; about 9Mixed model methodology is an emerging method for genome-wide association studies (GWASs); it was originally applied to the genome-wide identification of loci associated with a phenotypic trait but can be extended to analyses of associations between loci and intermediate molecular traits, such as RNA and protein expression levels. The mixed model methodology has been employed for nearly a half century for genetic analyses because it can explain polygenic effects while this is the intractable problem using fixed models. The polygenic effects can be assessed as random effects which are the special feature of mixed models, using pedigree-based genetic relationships. Currently, GWAS data are evaluated by mixed models with genomic similarity among unrelated individuals modified from pedigree information to nucleotide variant information. The direct approach of the genetic difference among individuals is an efficient way of avoiding population stratification that is one of the critical problems producing spurious genetic associations in GWAS. An overview of eQTL analyses by the mixed model methodology is provided, with an emphasis on important issues. Only essential mathematical notation for analytical models and relevant estimation methods are concisely presented in this review to ensure a clear presentation of mixed models and to avoid the intricacies of specific conditions.Table 1). An example of distribution-free quadratic estimation is the minimum variance quadratic unbiased estimation (MIVQUE), in which a local best unbiased estimate is obtained with minimum variance of the quadratic form of a random variable , fn is the number of the fixed effects, and X is the n × fn design matrix for the fixed effects. The fixed effects include the minor allele effect of the candidate nucleotide variant, and the corresponding column of X includes elements of 0, 1, and 2 for the homozygous major allele, heterozygous genotype, and homozygous minor allele under the assumption of an additive model with a biallelic nucleotide variant. g is the n × 1 vector of random polygenic effects G is the n × n genomic similarity matrix with elements of pairwise genomic similarity coefficients based on genotypes of nucleotide variants, and j and k can be calculated as follows:where vn is the number of nucleotide variants that contribute to the genomic similarity, τij and τik represent the number  of minor alleles for the nucleotide variant i, and if is the frequency of the minor allele. ε is the n × 1 vector of random environmental effects n × n identity matrix, and where To avoid underestimating the association of gene expression with the candidate nucleotide variant by proximal contamination, genomic similarity coefficients can be estimated by excluding nucleotide variants that are in linkage disequilibrium with the candidate. One strategy is to exclude all variants located on the same chromosome as the candidate variant . Theoretr2 < 0.8. The selection process should be conducted for every gene and thus requires an expensive computing cost. Thus, it might be convenient to select variants (r2 < 0.8) with an arbitrary significance threshold (P < 0.05).Considering only independent variants with more than a certain effect size is another efficient way to substantially reduce the cost. Only representative variants based on linkage disequilibrium can be used to explain polygenic effects . The excThe variance components for polygenic and environmental effects are usually estimated by employing REML prior to estimating fixed and random effects. For example, variance components can be estimated by maximizing the log restricted likelihood  as folloWhere ion MME; :Any closed form solutions for variance components are unavailable because the likelihood is non-linear, and various computing algorithms for obtaining REML estimates of variance components have been suggested as a non-trivial task. The log likelihood function presented above is efficient for obtaining REML estimates as one of the simplified forms, especially for the derivative-free algorithm incorporating the Choleski decomposition and simplex method . For detThe fixed and random effects are then solved with the estimated variance components under the MME. The heavy computational burden on inverse matrices for solving MME can be avoided by Choleski decomposition or by iteration methods, such as the Jacobi and Gauss–Seidel algorithms .t-test with 1 degree of freedom for candidate variant effects. Since a large number of tests for associations with genome-wide nucleotide variants are usually conducted, adjustments for multiple testing are employed to avoid spurious eQTLs. The most common method is the Bonferroni correction under the assumption of independence among individual tests. Researchers often use a less conservative method , especially for a huge number of tests. Regardless of the number of tests, significance threshold value of P = 5 × 10-8 is acceptable for GWAS  genetic relationship  based on genotype information, unlike for the identical-by-descent genetic relationship based on pedigree information. That is, the IBS genetic relationship matrix can be flexibly constructed using genotype information for a customized set of selected nucleotide variants. This is useful for eQTL mapping where the cell-specific genomic similarity matrix should be constructed with different loci. Gene expression is regulated by the cell environment, and the cell environment is produced by gene expression regulation. Thus, trans-regulators as well as Using mixed models, it is feasible to extend the additive genetic analysis presented in this review to non-additive genetic analyses. For example, an analytical model may include random dominance polygenic effects with corresponding variances, e.g., a dominance genomic similarity matrix multiplied by dominance genetic variance . SimilarG2σg×g2 . HoweverG2σg×g2 . Filtericis- and trans- eQTLs, respectively. These cis- and trans- eQTLs might be interpreted further as potential global and cell-specific regulators  obtained by GWAS differs from the gene identified by the eQTL analysis. Paired ate gene .Sex effects might be simply treated as a covariate in the analytical model. However, heterogeneous effects of sex are also important as an interaction between eQTLs and sex, especially for genes with hormone-dependent functions. Heterogeneous eQTLs by sex can be explained by separate analyses with partitioned data or by sex-stratified bivariate mixed models . A straiJoint modeling in the mixed model framework can be extended to analyze various kinds of expression simultaneously. For example, expression data for multiple tissues can be treated as different phenotypes, and these analyses provide genetic covariance components and genetic correlations between tissues. A mixed model meta-analysis can be applied to the identification of eQTLs with heterogeneous effects across multiple tissues .Spurious eQTLs easily result from microarray expression data because confounding effects are induced by various measurement errors . Mixed mThe mixed model is usually applied with the statistical property of best linear unbiased estimator  and best linear unbiased predictor  derived from Henderson’s mixed model equations. The BLUE and BLUP are, however, only valid under the assumption of known variance components. In reality, variance components are unknown for specific data, and should be estimated with the data used for BLUE and BLUP. This contradictory assumption has not limited its practical application. This might be because employing REML works well for the practical estimation of variance components. In order to actively address with the problem, BLUE can be estimated simultaneously with the variance and covariance components by a Bayesian approach implemented with MCMC methods, such as Gibbs sampling and the Metropolis and Hastings algorithm . AnotherTable 2. In particular, GEMMA and TASSEL employed the Newton–Raphson algorithm using observed Fisher information matrix  as the second derivative of likelihood for REML . Of course, the specified analyses can be extended to the identification of any other potential heterogeneity in eQTLs. An example is age-dependent eQTLs, which may explain the heterogeneous heritability of complex phenotypes by age . Understanding the genetic architecture of complex phenotypes will be accelerated by genome-wide eQTL analyses using mixed models with a profile of transcriptome-wide gene expression for the activity of a single cell and further with multiple profiles across cells with different functions.Theauthor confirms being the sole contributor of this work and approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


To estimate effect of single nucleotide polymorphisms on the intramuscular fat content (IMF) of Hungarian Simmental bulls.longissimus dorsi muscle. A multi-locus mixed-model was applied for statistical analyses.Genotypes were determined on high-density Illumina Bovine DNA Chip. After slaughtering of animals, chemical percentage of intramuscular fat was determined from 10P>12) with IMF located on chromosome 1, 6, 13, and 17, respectively. The frequency of their minor alleles was 0.426, 0.221, 0.162, and 0.106.Analyses revealed four loci  to be highly associated (−logThe loci above can be useful in selection programs and gives the possibility to assist selection by molecular tools. The main aim of modern livestock agriculture is to satisfy the growing demands of consumers for high-quality, safe and delicious animal products. This trend is evident for the beef industry as well. The proper breeding scheme in the past was very successful in increasing of lean meat content, but resulted in reduced intramuscular fat content (IMF) and changed muscle fibre types as well . NowadayA total of 146 Hungarian Simmental muscle samples from eleven farms were collected and were stored in liquid nitrogen at −196°C until DNA extraction. Animals were kept in identical conditions, fed the same diet and slaughtered at approximately similar live weight (530.6±44.7 kg), under commercial conditions using Hungarian standard procedure.longissimus dorsi muscle (LD) cut between the 11th to 13th rib. Chemical percentage IMF was determined from LD. After removing surface fat, lipid content of LD was determined gravimetrically by Soxhlet method, using petroleum ether as solvent [During slaughtering, rib samples have been taken from  solvent . Lipid cFor isolation of genomic DNA from muscle, samples were incubated in 5% Chelex suspension and 0.6 μg/μL Proteinase-K solution at 56°C, overnight. Final treatment of the mixture was an incubating step at 98°C for ten minutes. After DNA extraction from LD, SNP typing was performed with high-resolution SNP chips developed for cattle . Illumina Final Report file was imported into SVS software . Samples were excluded from analysis if call rate was below 95%. Only SNPs having consistently high call rate (>95%) were included in this study. Duplicated samples (IBD >0.95) were excluded from dataset. After excluding monomorphic loci and loci with minor allele frequency <0.05, dataset included 129 animals and 120,774 SNPs. Statistical analyses were performed by SVS software . For visualising results, high resolution image has been produced by R using qqman library .For correction of population structure, genomic kinship matrix has been used in multi-locus mixed-model . PhenotyThe used model wasWhere y is the IMF, X is the matrix of fixed effects composed of SNPs and covariates (age and sex), Z is the matrix of random animal effects. The e means the residual effects. The β and u are vectors representing coefficients of fixed and random effects, respectively.The Ensemble cow UMD3.1 and gene ontology (GO)  database10P>12) seem to be useful in selection programs and are located on chromosome 1, 6, 13, and 17, their minor allele frequencies are 0.426, 0.221, 0.162, and 0.106, respectively , diphthamide biosynthesis 3 (DPH3), and serine/threonine-protein phosphatase 6 regulatory ankyrin repeat subunit A (ANKRD28).On chromosome 1 there are several protein coding sequences in near vicinity of the locus rs43284251, including polypeptide N-acetylgalactosaminyltransferase 15 —also known as GALNTL2, pp-GalNAc-T15, or GALNT7—is part of glycoproteome playing role in cell interactions with environment [GALNTs are localised in Golgi and endoplasmatic reticulum (ER). Their traffic from Golgi to ER often activated in human malignant tumors. In human, nonhuman primates and rodents, loss of function of GALNT2 has been shown to lower high-density lipoproteins and species specific glycosylation targets has been identified [ironment . GALNTs entified ,18 may aDPH3  is essential in the synthesis of diphtamide post-translationally modificate histidine elongation factor 2 [factor 2 . Down-rehttp://pathcards.genecards.org/) like Vesicle-mediated transport and Transport to the Golgi and subsequent modification.ANKRD28 is related to pathways (LAP3), mediator of RNA polymerase II transcription subunit 28 (MED28), family with sequence similarity 184 member B (FAM184B), DDB1 and CUL4 associated factor 16 (DCAF16), non-SMC condensin I complex subunit G (NCAPG), ligand-dependent nuclear receptor corepressor-like protein (LCORL). Haplotypes of LAP3  gene is reported [MED28  has negative regulation effect on smooth muscle cell differentiation. In vivo fate mapping showed, that a set of adipocytes arose from smooth muscle-like origin [DCAF16  is associated with average daily gain in cattle [On chromosome 6 there are several protein coding sequences in near vicinity of the locus rs109210955, including leucine aminopeptidase  is a major player in cellular maintenance processes and a major contributor to genetic variability in bovine feed efficiency [NCAPG together with LCORL  measured in adipose and muscle tissue are associated with cattle feed intake and weight gain [NCAPG affects arginine metabolism having influence on body-mass gain and lipid deposition.ficiency . Expressght gain . NCAPG aARFRP1), TNF receptor superfamily member 6b (TNFRSF6B ENSBTAG00000027407). ARFRP1  is required for the lipidation of chylomicrons in the intestine and required for very low density lipoprotein (VLDL) lipidation in the liver [TNFRSF6B might have role in response to lipopolysaccharide according to one of the GO annotations (GO:0032496). Its expression has been detected in bovine ovarian follicles [ENSBTAT00000045108. 3  and ENSBTAT00000052120.2. . GO annotation number 0006139 suggests this transcript is involved in nucleobase-containing compound metabolic process.Locus rs41630030 on Chr 13 is located close to ADP-ribosylation factor-related protein 1 (PRAME) and splicesomal RNA (U1) loci are located. PRAME  were shown that lipopolysaccharide together with type 2 interferon has increased its expression [Nearby locus rs41642251 on Chr 17 preferentially expressed antigen in melanoma (pression . Literatpression .FABP4) alleles in Japanese Black [DGAT1), FABP4, fatty acid synthase (FASN) and peroxisome proliferator activated receptor gamma coactivator 1 alpha (PPARGC1A) genes on chromosome 14, 14, 19, and 6, respectively. In our study, none of them was significantly associated with IMF content. However in previous studies we demonstrated the effect of leptin (Chr 4), DGAT1 (Chr 14) and thyroglobulin (Chr 14) gene polymorphisms on the IMF of Angus cattle [Fatty acid binding protein 4 (se Black  and in Hse Black  have effse Black  it affecse Black  looked fs cattle .The IMF or marbling represents a valuable beef quality trait and is important determinant of palatability due to its contribution to juiciness and flavour. Meat with low IMF may be dry and flavourless. Higher levels of IMF have been associated with increased tenderness, juiciness and flavour of beef ,36. Mole


Generativity—showing concern to establish and guide future generations—has been argued to be a biological adaptation central to cumulative culture and survival, but also, in turn, to be a cultural adaptation dependent on norms. From the perspective of human agency, concern for the future has played a key role in raising agency for generations that follow by creating infrastructure and cultural inheritance. Here, in a population-representative sample of 756 twin-pairs, we present the first test of the genetic and environmental structure of generativity using the Loyola Generativity Scale (short). Genetic analysis of scale sum-scores revealed that shared environmental effects were comparable in magnitude or exceeded effects estimated for genetic differences . At the item level, a well-fitting genetically-informed model suggested 3 factors influencing generativity via a common-pathway structure. The first was tentatively characterized as reflecting a heritable general concern for the future. The second reflected being a valued source of advice and assistance. The third factor showed only unique environment effects and had as its strongest indicator having had a good influence on the lives of others. Replicability of this structure should be tested in the full version of the scale. Work is needed also to validate influences of generativity on vocations such as teaching and on philanthropic activity improving life for subsequent generations. The research topics are broad in scope: from novel models of moral agency  as an environmental moderator  and “Mental cognitive artifacts” such as logic and formal systems of finance. Such are the benefits of such physical and mental cultural infrastructure, that cognitive adaptations specifically to support their creation have been argued to be a key element of human genetic adaptation  has examined the heritability of generativity. In review, we were asked why is a twin study still important? There are several reasons. Generativity theory claims a relatively strong influence of shared environment on generativity Erikson . This woA widely accepted reason to document the magnitude of variance attributable to genetic, family-environment, and unshared environmental influences, not just in a given sample , but in many samples. This impetuous flows from the finding that variance attributable to genes and environment can not only take on different values depending factors such as age or birth cohort  have not been collected. It is of value, then, to collect data on generativity, and to establish whether it has high, relatively modest, or even low levels of heritability, not only to add to the rather sparse database of heritabilities in the domain of attitudes and motives, but to begin to document variation in these traits across cultures and times.A further reason to examine generativity in a genetically informative sample is that in this, as in all areas of social science, concrete estimates of genetic influence not only to test theory that includes such influences, but also motivate other research to include controls for genetics. As was noted in a recent commentary, even longitudinal relationships of parent and offspring behavior are not evidence for effects of parental behavior  of generativity items has not been examined. While the phenotypic null hypothesis , shared or common environmental influences (C) shared by both twins, e.g. place of residence or neighborhood factors, and unique environment (E): environment influences which are not shared, e.g. their unique peer-group , while the scale is designed to be unifactorial, we were open minded as to the factor structure that would be revealed in a genetic analysis. In particular, the multiple components and influences on generativity identified in modern generativity theory  the choice of a baseline model is more complex. While it is common practice to evaluate such models against a multivariate Cholesky ACE model, algebraically, this model is not unbiased Carey . For thiThe data for this study originate from Wave II of the MacArthur Foundation Survey for Midlife Development in the US .We used an abbreviated and modified version of the 20-item Loyala Generativity scale, developed for MIDUS (see Appendix I have done nothing of worth to contribute to others”). The long scale is explicitly focused of effort and success at passing along knowledge (e.g. “I have made a difference to many people”) where the short scale focusses on possessing such knowledge or skills. The long scale also measures the enjoyment of a vocation (such as being a teacher), as opposed to “liking to teach things to people” in the short scale. Some behaviors are absent, for instance volunteering for charity, creative effort, commitment, productivity, neighborhood responsibility. The full version also emphasizes the creation of a legacy that will be remembered beyond a person’s own lifetime.Despite considerable overlap, the long and short scales differ in a number of substantive ways. The items are written in the third-person, and all are positively worded, whereas in the full version, items are in the first-person tense and include negative items  to 4 .To test the hypothesis that familial clustering in generativity is explained by both additive genetic and family environment factors , we fitted univariate biometrical genetic models , we again used the OpenMx package . The remaining proportion of variance was explained by non-shared or stochastic environmental risk factors including measurement error.2 (3) = 1.61, p = 0.657) and an improvement of AIC compared to a model containing these paths (AIC = − 96.00 versus − 91.6 including moderation).In an exploratory modelling phase, we also ran a gene × environment interaction model Purcell  testing We next turned to the item-level data, to test our hypothesis that, under behavior genetic analysis, the items of the scale would be well explained by a single common factor model with significant genetic (A) and shared environment (C) influences . To this end, we computed a 1-factor CPM, and compared this to the direct variance–covariance baseline model (see Table 2 (37) = 136.77, p < 0.001). We then explored sequentially more-complex models. A 1-factor IPM also showed inadequate fit (p < 0.001). We then executed CPM and IPM models with 2 and 3 factors, finding that a 3-factor CPM model fit well (χ2 (21) = 9.85, p < 0.98, see Table 2 (9) = 13.99, p < 0.123) but was not preferred by AIC compared to the 3 common pathway model  was disconfirmed. Instead, the analyses revealed a complex factor structure best accounted for in terms of three psychometric factors in a common pathway model. We discuss these two findings in more detail below.A surprising result of genetic research has been that often Plomin , but notC effects, for all behavior genetic traits, may be premature, not only because of GE covariance in different forms , it would be valuable to repeat the analyses with the full scale, and, preferably, in a larger sample. We are undertaking this task as part of the project this year.It would be of value also to have measures for more of the 7 predicted components of generativity, work that would not require access to a twin sample. Given the importance attributable to education in modern society, it would seem useful to understand better the origins of motivation to teach. Based on low rates of systematic teaching  in pre-industrial society, Lancy  suggestsThe present sample was predominantly middle aged. It would be valuable to study generativity in younger subjects . Also of value would be to measure wider social effects of generativity on important prosocial activities such as institution founding and maintenance.With these limitations, this study is the first step to understanding the genetic and environmental structure of generativity. It demonstrated that, at a scale level, generativity reflects large influences of the environment, including shared environment, while revealing a more complex structure at the item level.