ABCC9, VPS13B, MGST1, SCD, MKL1, CSN1S1 for production, CHEK2, GC, KALRN for reproduction, and TMTC2, ARRDC3, ZNF613, CCND2, FGF6 for conformation traits. Collectively, these results demonstrated the utility of BFMAP, identified candidate genes, and enhanced our understanding of the genetic basis of cattle complex traits.A hundred years of data collection in dairy cattle can facilitate powerful studies of complex traits. Cattle GWAS have identified many associated genomic regions. With increasing numbers of cattle sequenced, fine-mapping of causal variants is becoming possible. Here we imputed selected sequence variants to 27,214 Holstein bulls that have highly reliable phenotypes for 35 production, reproduction, and body conformation traits. We performed single-marker scans for the 35 traits and multi-trait tests of the three trait groups, revealing 282 candidate QTL for fine-mapping. We developed a Bayesian Fine-MAPping approach (BFMAP) to integrate fine-mapping with functional enrichment analysis. Our fine-mapping identified 69 promising candidate genes, including  Jicai Jiang et al. report the analysis of sequence variants from over 27,000 Holstein bulls associated with 35 traits for production, reproduction, and body conformation. They identify 282 candidate QTL regions for fine-mapping, ultimately finding 69 candidate genes involved in important agronomic traits. A comprehensive spectrum of phenotypes has been recorded in dairy cattle, including production, reproduction, health, and body type traits2. GWAS on these traits simultaneously in the same population can provide a better understanding of the effects of underlying QTLs. Because of the intensive use of artificial insemination and strong selection in dairy bulls, there are a much smaller number of males than females in the cattle population3, and chromosome segments can be quickly traced back to an ancestral bull. The high relatedness in the cattle population can facilitate accurate imputation4, especially with the availability of many important ancestor bulls sequenced by the 1000 Bull Genomes project8. These unique features of the cattle population make a large-scale GWAS with imputed sequence variants possible and valuable.Phenotypic records have been routinely collected in dairy cattle to facilitate selective breeding for more than one hundred years. The phenotype of a bull can be highly accurately calculated from thousands of phenotypic records of his daughters and other relatives10. Because of the high levels of linkage disequilibrium (LD) in the livestock population11, fine-mapping of GWAS signals is still difficult in cattle. Additionally, existing fine-mapping methods are not easily applicable to large-scale cattle GWAS and fine-mapping studies. Some methods, e.g., CAVIARBF12 and PAINTOR13, generally use a logistic model with a binary response and categorical functional annotations as covariates. Such a logistic model is then incorporated into a model search scheme that often limits the maximum number of causal variants  and is computationally impractical for a locus containing thousands of sequence variants. When multiple functional data sets are to be tested, model-searching needs to be conducted separately for each set of functional annotation data, further increasing the computational burden. In cattle, Bayes and BayesRC methods have been applied to incorporate sequence data into genomic selection models, but the large amount of computation from MCMC prohibits their direct application to large-scale fine-mapping studies15. Although GCTA-COJO is capable of fast conditional analysis for fine-mapping in cattle16, the use of summary statistics and LD data from a reference population can be suboptimal when direct genotype and phenotype data are available. To address these problems, we develop a fast Bayesian Fine-MAPping method (BFMAP) that can efficiently integrate functional annotations with fine-mapping. Specifically, BFMAP can re-use initial model search results for various functional annotations and can be employed for both fine-mapping and functional enrichment analyses. More importantly, the functional enrichment estimated from BFMAP is, by definition, the enrichment of causal effects, in contrast to the enrichment of heritability by the well-known stratified LD score regression17.Fine-mapping of complex traits to single-variant resolution has started in human studies, e.g., ref. 18.In our study, the large number of bulls with highly reliable phenotype and imputed sequence variants can facilitate powerful GWAS and fine-mapping of major GWAS signals. Although the high LD in the cattle genome makes fine-mapping and functional enrichment studies difficult, the large sample size and improved methods can help identify candidate genes of complex traits as well as biologically informative enrichment of candidate variants in functional annotation data. Specifically, we seek to use BFMAP to identify and incorporate functional annotation into the fine-mapping of 35 production, reproduction, and conformation traits in dairy cattle. The fine-mapped genes and variants can provide candidates readily testable in functional studies. The functional data enriched with variants associated with complex dairy traits will be useful for future cattle GWAS and genomic prediction studies. Additionally, the initial model search results can be reused for estimating enrichment of causal effects of dairy traits for additional functional annotations that are being generated by the FAANG and related projects in cattleWe imputed over 3 million selected sequence variants to 27,214 Holstein bulls after quality control edits, using the 1000 Bull Genomes data as reference. These bulls were selected to have highly reliable breeding values  for 35 production, reproduction, and body conformation traits, with an average reliability of 0.71 across traits  had been previously reported while 163 associations (57%) were newly discovered in this study. We identified 15 new association signals (out of 68) even for the five production traits that had been extensively studied previously, and 92 new associations (out of 125) for type traits that drew less attention in previous studies . This is likely due to the proportion of QTLs with pleiotropic effects on related traits is less than expected, and/or the limited benefit of including additional traits in cattle studies where individual traits are already highly accurate  that calculates a posterior probability of causality (PPC) for variants in candidate regions. We picked QTL regions for fine-mapping from both single- and multi-trait GWAS results. Initially, we fine-mapped 434 association signals for 282 QTLs using a significance threshold of 5E−7  on fine-mapping performance. First, incorporating variant impacts resulted in a substantial change of PPC for variants in the 308 fine-mapped association signals. Variants with moderate impact had a considerable increase in PPC when functional information was included in the calculation, while modifier variants generally had a decreased PPC Fig. . Second,23, and evolutionary constrain predicted by GERP24. Our enrichment analysis estimated the probability of a causal variant being in a functional category and the probability of a non-causal variant being in the category. The ratio of the two probabilities was used to measure the enrichment of causal variants for this functional category25, with a value larger than one indicating higher enrichment than the genome background. This enrichment analysis has also been implemented in BFMAP.To verify the quality of our fine-mapped variants and characterize their distribution on the cattle genome, we investigated the enrichment of fine-mapped variants with different functional annotation data available to cattle, including location in protein-coding gene, effect predicted by SnpEff26, we observed distinctive enrichment patterns across these five categories . Despite the strong LD levels in the cattle genomeies Fig. . Using b23. When modeling these four categories, we found severe depletion of variants with high impact . Low-impact variants also showed an enrichment (2.0×), though it was not statistically significant  predicted by SnpEffant Fig. . As expeP = 0.02). When further categorizing variants into six groups based on both constrained elements and variant impacts , we found the highest enrichment in moderate-impact variants inside constrained elements . For the other categories, we observed no enrichment of fine-mapped variants , as highly conserved DNA sequences may imply functional importance. As shown in Fig. nts Fig. .EC(Production)/EC(Reproduction+Type) and showed that the difference was statistically significant , milk production (milk and protein yields), and daughter pregnancy rate, with a PPC of almost 1 for all the associated traits. In addition, we found that there were no common variants among the credible variant sets for these traits , with PPC being ≥0.95 for all those traits. Abo-Ismail et al. reported CCND2 was associated with stature30. Our fine-mapping results determined its association with four type traits . It is worth noting that our fine-mapping study not only discovered association of a gene with a trait, but also provided the posterior probability of being causal for a gene.This short list had 69 unique genes including both previously reported genes and newly discovered ones for cattle traits Table . For exaABCG227 and Chr26:21144708 in SCD32. We also found other promising candidate variants, e.g., Chr7:93244933 in ARRDC3 with an average PPC of 0.608 on 9 traits, Chr8:83581466 in PTH1 with an average PPC of 0.68 on two type traits (body depth and strength), Chr1:69673871 in KALRN with an average PPC of 0.46 on two reproduction traits (cow conception rate and daughter pregnancy rate), Chr17:70276788 in CHEK2 with an average PPC of 0.39 on two calving traits .Because our stringent quality control filtering during and after imputation removed many variants , fine-mapping of the QTL regions to single-variant resolution could not always be achieved. Nevertheless, we obtained 95% credible variant set for each independent signal and merged them into one table. This resulted in a total of 1582 unique variants , we attempted to find causal effects in hundreds of loci each of which contained thousands of variants. We also investigated the functional enrichment patterns of several functional annotation data available in the cattle genome, and incorporated useful functional information into the final fine-mapping. In sum, we provided not only a credible candidate gene list for follow-up functional validation, but also a unique resource that can be easily employed by future functional enrichment studies.DGAT1 gene. Minor inflations were observed in GWAS for calving traits  and final score , we could still locate a few credible GWAS peaks where there were a cluster of significant variants.In the single-trait GWAS, we found many association signals that have not been discovered Fig. , clearlymeff) at the locus-by-trait level. We also noticed that there were more locus-by-trait association pairs with multiple signals than with only one signal. By examining those with multiple signals, we found the models often contained a strong signal and several much weaker ones. Those weak signals might result from imperfect model fitting of the lead variants in other signals, instead of being true positives. Nevertheless, filtering out these weak signals with genome-wide significance levels did little harm to the discovery of strong ones.Initially, our fine-mapping discovered as many as 19 signals in a candidate region for a trait, as we applied a variant inclusion threshold accounting for only the effective number of independent variants  algorithm that is computationally impractical for large studies37. CAVIARBF, PAINTOR, and FINEMAP38, use summary test statistics and are approximately equivalent to BIMBAM. In theory, these methods work for independent samples by using summary statistics from linear model analyses and genotype correlations between variants. Further studies are warrant to investigate how these summary-statistics methods perform for structured or related samples when using summary statistics from linear mixed models.It is widely acknowledged that population structure and relatedness need to be properly accounted for in GWAS via a linear mixed model18.Using BFMAP, we pinpointed some promising candidate genes for economically important traits in dairy cattle. It is promising to validate those genes with high posterior probability of causality Table  in futur5. Here we provide a brief summary. SNP and insertion-deletion (InDel) calls (sequence variants) from Run 5 of the 1000 Bull Genomes Project6 were released in July 2015. After stringent quality control edits and removal of intergenic and intronic SNPs, 3,148,506 sequence variants were retained for 444 Holstein bulls. The sequence variants and high-density SNP genotypes of 312K markers for 26,949 progeny-tested Holstein bulls (and 21 Holstein cows) were combined by imputation using the FindHap software (version 3)39. Finally, we had genotypes of 3,148,506 sequence variants for 27,214 Holstein bulls (179 bulls had both sequence and high-density genotypes) and 21 cows. Imputation quality from FindHap was assessed with 404 of the sequenced animals as the reference population and 40 randomly selected animals for validation. The sequence genotypes of the validation animals were reduced to high-density SNP genotypes and then imputed back to sequence variants. The average imputation accuracy was 96.7% for the 3,148,506 variants5. After excluding high-density SNPs, we found an average accuracy of 96.4% for the newly imputed sequence variants. Chromosome-specific imputation accuracy was >95% for all autosomes except Chromosome 12.Genotype data have been described in more details previously40. Deregressed PTAs were used as phenotype in all our analyses, which excludes parent information and reduces the dependence among animals41. Because each of the bulls had many phenotyped daughters, their PTAs were generally of high reliability, even for low-heritability traits  PTAs for 35 production, reproduction, and type traits . Basically, MMAP efficiently implements a mixed-model approach for association tests that is similar to GEMMA42 but different from EMMAX;43 that is, variance component is estimated uniquely for each marker. We used the following modely is deregressed PTAs, μ is global mean, X is genotype of a candidate variant  and b is its effect, g is a polygenic effect accounting for population structure, and e is residual. The genomic relationship matrix (G)44 was built using ~312K high-density SNP markers (filtered by MAF >1%). R is a diagonal matrix (Rii = 1/r2−1), which is used to model differential reliability among animals.The software MMAPp < 1E−6). After QC, there were ~2.7 million variants to be tested for association. We used a genome-wide significance level of P < 5E−8. QTLs were located by finding GWAS peaks where there were a cluster of significant variants. We used a custom Perl script to find all GWAS peaks and further examined each of the peaks based on the Manhattan plots to filter out suspicious ones . Subsequently, we determined a total of 286 QTLs  of flanking SNPs for each term from the Cattle QTLdb data, and then used the identifiers to find flanking SNPs’ positions on UMD 3.1 in the Ensembl genome variation database. These SNP positions were used as QTL positions. This procedure can rule out QTL terms whose physical positions are inaccurately converted from genetic maps. The Cattle QTLdb release 35 covers 599 different traits, in which we extracted those with the  same definition as the 35 traits in our study  that contains 113,256 QTLs/associations from 848 publications21, our multi-trait association tests were based on a chi-square statistic with multiple degrees of freedom. For each variant, the chi-square statistic for the multi-trait association test was calculated by:ti is a n × 1 vector of the signed t-values of variant i for n traits, and V is an n × n correlation matrix for the n traits which is calculated using signed t-values of genome-wide variants. In our analysis, the signed t-values were obtained from single-trait GWAS for 2,619,418 variants passing QC, and the correlations between traits were calculated using all the variants. To test the robustness of the estimated correlation using all sequence variants45, we also computed the correlation matrix using two variant subsets obtained by selecting every 10th and every 100th variant. The three variant sets produced similar correlation estimations  effects and X is corresponding design matrix, a is a vector of variant effects and Z is corresponding genotype coding matrix , g is a vector of polygenic effect for controlling population structure, G is a corresponding variance structure matrix , and e is the residual with variance structure R for modeling reliability or accuracy of phenotypic records as in model (1). The common variance component  are treated as known. Generally, we can set φ to a large value  to make a act like fixed effects. A genomic variant is usually considered to have a small but noticeable effect, so we can set γ at 0.01 or 0.0448. When Za only accounts for a tiny proportion of phenotypic variance , we can set η based on the heritability (h2) by η = h2/(1−h2). In practice, we can instead use heritability estimate (η.We developed the following Bayesian model for fine-mapping:P(D|M)  by integrating out 0: a = 0) in model (2) by an extension of the results by Zhou and Guan48  to each variant with fine-mapping. Following the method by Huang et alφ = γ = 1E8 in model (2) for fine-mapping, which enables easy calculation of p-value for a newly added variant conditional on variants already in model  < 2logmeff, where meff is the effective number of independent variants calculated using the method by Li and Ji50. Suppose that we select p independent signals in forward selection and determine a set of lead variants (Sl) for the p signals after repositioning. Then, for signal i with lead variant (li), we have a variant set (Si) containing variants that have substantial LD with li but weak LD with lead variants in other signals Sl /{ li }. Accordingly, we can compute PPC of variant j (vij) in Si conditioning on Sl /{ li }:Mi = vij denotes that the causal variant in signal i is variant j in Si (i.e. vij). Weöó can easily get a credible variant set passing a given confidence level  for a signal, by sorting variants in a descending order of PPC and including them in the set from top to bottom. We can also calculate PPC of a gene by summing up PPCs of all variants within the gene.We set 10, an equal prior for each variant was used; that is, P(Mi=vij)=1 ∀ vij ∈ Si. Here, we propose a method to apply differential prior probabilities by integrating functional annotation, following a previous study on adjusting significance threshold based on functional annotation in GWAS25. With our fine-mapping procedure, it is usually safe to assume one and only one causal variant in each independent signal. For a functional annotation with several categories, we denote the probability of a causal variant being in category C as pC and the probability of a non-causal variant being of category C as qC. We can accordingly obtain:cij denotes the category of variant j in Si (i.e. vij).In the study by Huang, et al.qC with the genome-wide frequencies of the categories25. To estimate pC, we can use all available independent signals (Mi):We estimate When the signals identified in fine-mapping are independent of each other, we can get:pC} and then get their maximum likelihood estimates (MLEs), pC, qC} and Eq. Taking Eqs. When setting an equal prior for each variant, we find:pC} by Eq. qC} with the genome-wide frequencies of the categories and estimating {pC} with these PPCs, and updating PPCs with {pC, qC}. These features make our approach easier to use compared with PAINTOR13 and CAVIARBF12.Thus, to estimate {r2 of >0.3 with the lead variants26.Genomic regions for find-mapping were determined by lead variants in single-trait and multi-trait GWAS results. We first determined a minimal region that covered each lead variants (either in single- or multi-trait QTLs), and then extended it 1 Mb upstream and downstream, resulting in a ≥ 2 Mb candidate region for fine-mapping. The 1-Mb extension allowed the region to cover most variants that have an LD 51, we used 5E−7  as the significance threshold. Subsequently, we found 434 association signals  with other traits. We also removed another six association signals, since these signals have a substantial LD with another signal (measured by LD r2 between lead variants >0.25). These edits reduced the number of association signals from 308 to 249. We estimated {pC, qC} for variant impact categories based on the 249 association signals, and updated PPCs for all 308 signals by integrating the estimated functional enrichment. Effect impact-incorporated PPCs were used for determining candidate variants or genes. When computing PPC of a gene, all variants within its 2-kb upstream and downstream ranges were included.Besides assuming an equal prior for each variant, we further applied differential prior probabilities based on SnpEff-inferred impactspC  and qC . The two probabilities can be estimated using the models described in BFMAP. The enrichment for category C is defined as EC = pC/qC25, for which a value larger than one indicates that candidate causal variants are more enriched in category C than across the whole genome. Functional annotations investigated included locations of variants regarding protein-coding genes, effect impact inferred by SnpEff23, and constrained elements predicted by GERP24. Confidence intervals of the enrichment estimates were derived by percentile bootstrap as in ref. 25. The association signals were resampled 1,000 times to calculate the confidence intervals. We removed very small categories (like HIGH in SnpEff-inferred effect impacts) in bootstrapping to avoid non-convergence of the maximum likelihood estimation.Our enrichment analysis was based on our 249 fine-mapped association signals to estimate Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesReporting SummarySupplementary Data 1-17


Complex genetic traits are often characterized by multiple quantitative phenotypes. Because values of such phenotypes vary over time, it is thought that analyses of longitudinal data on the phenotypes may lead to increased power in detecting genetic association. In this paper, we extend a transmission-based association test applying quasi-likelihood that has been developed by us to the longitudinal framework and to carry out a genome-wide association analysis of triglyceride levels based on the data provided in GAW20. We consider different phenotype definitions based on administration of fenofibrate and obtain significant association findings within genes involved in heart diseases. Most clinical end-point traits are governed by quantitative precursors and it may be a prudent strategy to analyze these precursor phenotypes for association mapping of a clinical end-point trait. The family-based design for detecting association as implemented in the classical transmission disequilibrium test  is a popFor our analyses, we use pedigree information on triglyceride levels at 4 different time points for 200 nuclear families, along with their genotypes at all the available 597,145 variant sites distributed over 22 autosomal chromosomes, as provided in the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) data set as part of GAW20. We exclude loci that are monomorphic or have minor allele frequency < 0.05. Because HDL is a potential confounder in the genetic association with triglyceride levels, we use HDL levels at the 4 time points as covariates. To adjust for the effect of fenofibrate, which was administered after the second time point, we perform our transmission disequilibrium analyses based on summarized values of triglyceride and HDL levels before and after the administration of the drug.Data on triglyceride levels and HDL levels are not available for all individuals at every time point. The assumption of multivariate normality provides a computationally elegant framework for the expectation-maximization (EM) algorithm  to estimN nuclear families with ni offspring in the ith family, Yj =  denotes a vector of k phenotypes for the jth offspring, Zj and Wj are indicator random variables (1 or 0), respectively denoting whether the heterozygous parent and the other parent (heterozygous or homozygous) at a SNP transmits the minor allele or not to the jth offspring. For the ith family, we model the conditional distribution of {Xj =  : j = 1, 2, …, ni} given Y =  using a quasi-likelihood function as follows:λj  is the vector of the conditional expectations of Zj and Wj given Yj, both of which are modeled as logistic link functions involving α and γ, while Vj is the conditional variance–covariance matrix of  given Yj. The test for association is equivalent to testing H0:γ = 0 versus H1:γ ≠ 0, and the usual Wald test statistic is distributed as chi-squares with k degrees of freedom in the absence of association.The phenotypes for our association analyses are unadjusted triglyceride levels and triglyceride levels adjusted for HDL levels using the algorithm described in the preceding section. We use a novel quasi-likelihood regression framework based on a resistance generalized estimating equation approach  to test Our association analyses comprise 3 different choices of phenotypes. As fenofibrate was administered after the second time point, we consider the first principal component of the log-transformed triglyceride levels of the first and the second time points along with the first principal component of the log-transformed triglyceride levels of the third and the fourth time points as a bivariate phenotype. We compare the association findings based on this phenotype with (a) the first principal component of the log-transformed triglyceride levels of the first and the second time points  and (b) the first principal component of the log-transformed triglyceride levels of the third and the fourth time points . To evaluate the effect of HDL on triglyceride levels, we perform each of the above analyses for unadjusted log-transformed triglyceride levels and log-transformed triglyceride levels adjusted for HDL levels. We denote the unadjusted bivariate phenotype analysis as MTBAT and the adjusted analysis as MTBATAdj. Similarly, the corresponding univariate analyses based on Kulkarni and Ghosh [The tests for association are based on 200 nuclear families comprising 990 offspring. As our proposed test procedure requires that at least 1 parent in the family is heterozygous at the marker locus, we selected only those SNPs that have more than 20 informative families. Hence, we performed our analyses on 552,556 SNPs. Of the 990 offspring, data on triglyceride levels were available for 719 offspring at the first time point, 988 offspring at the second time point, 554 offspring at the third time point, and 731 offspring at the fourth time point, and data on HDL levels were available for 719 offspring at the first time point, 989 offspring at the second time point, 709 offspring at the third time point, and 772 offspring at the fourth time point. To correct for multiple testing, we used the Benjamini-Hochberg procedure [MSRA, the SNP rs2466051 located on 8p12 within the gene NRG1, the SNP rs1281132 located on 4p16.1 within the gene SH3TC1, and multiple SNPs in the region 12q13.12 within the gene FMNL3 exhibited significant evidence of association with all phenotype definitions. Although the SNP rs1712316 within the gene SH3TC1 was found to be significantly associated with all phenotype definitions except TBATPreadj, multiple SNPs in the region 10q.24.1 within the gene ENTPD1 were significantly associated with all phenotype definitions except TBATPost. Among the SNPs mentioned above, rs6601447 and rs1986677 ranked among the top 10 significant findings in all our analyses. We note that although multiple SNPs within the gene FMNL3 showed significant evidence of association, the significances for the multivariate phenotype were more pronounced  for the unadjusted triglyceride phenotypes compared to those adjusted for HDL, whereas the opposite phenomenon was observed for the univariate phenotypes, although it seems intuitively difficult to explain the phenomenon. We observe that a higher number of SNPs exhibited significant evidence of association for the bivariate phenotype and that defined by the postdrug measurements compared to the phenotype defined by the predrug measurements. Interestingly, we observed that the analyses based on transmission only from heterozygous parents did not yield a single significant finding with any of the phenotype definitions after FDR correction This is consistent with the results of the simulations corresponding to the quasi-likelihood approach for univariate phenotypes [The number of SNPs found to be significantly associated with the different phenotype definitions were as follows: 718 based on MTBAT, 685 based on MTBATadj, 147 based on TBATPre, 657 based on TBATPreAdj, 121 based on TBATPost, and 622 based on TBATPostAdj. Among these SNPs, 28 were common for all 6 phenotype definitions, 448 were common between MTBAT and MTBATadj, 80 were common between TBATPre and TBATPreAdj, and 42 were common between TBATPost and TBATPostAdj. With respect to unadjusted triglyceride levels, 51 SNPs were common between MTBAT, TBATPre, and TBATPost, whereas for adjusted triglyceride levels, 390 SNPs were common between MTBATAdj, TBATPreAdj, and TBATPostAdj. The SNPs rs6601447 and rs1986677 located on 8p23.1 within the gene In this paper, we modified a transmission-based test for association that includes transmission information from noninformative parents using a quasi-likelihood approach  in the mMSRA (methionine sulfoxide reductase A) protects cardiac myocytes from oxidative stress and is an important therapeutic target for ischemic heart diseases [NRG1) activation improves cardiac function and survival in different forms of cardiomyopathy [FMNL3 (formin-like 3) is involved in cardiac myofibril development and repair [FMNL3 exhibited much higher significance with unadjusted triglyceride levels compared to those adjusted for HDL levels, it is likely that the gene modulates the effect of HDL levels rather than the effect of triglyceride levels. We also found that the number of SNPs associated with the bivariate phenotype or the phenotype defined by postdrug measurements was much higher than the phenotype defined by predrug measurements. One possible explanation for this phenomenon is that some of the SNPs modulate the interaction effect of fenofibrate and triglyceride levels. However, separate interaction analyses are necessary to validate this hypothesis.Many of our association findings are mappable to genes related to heart diseases. The SNP rs2510873, which exhibited significant evidence of association with the bivariate phenotype and was defined by the postdrug measurements, is located in the same genomic region 11q23.3) as the SNP rs964184, which was previously reported to be significantly associated with both triglyceride and HDL levels based on the same GOLDN data [q23.3 as d repair . BecauseLinear mixed models are a popular method of choice for genetic association analyses in a family-based framework primarily because such models have the flexibility of accounting for relatedness within families and to correct for population stratification between families . Our proIt has been argued that association tests based on imputed phenotypes may lead to biased inferences and it may be more prudent to perform an EM procedure based on the joint likelihood of genotype and phenotype data. However, such a strategy would substantially increase the computational load. Moreover, given that the quasi-likelihood approach is retrospective in nature, the test is less likely to be adversely affected by imputed phenotypes compared to a test based on prospective likelihood. We finally wish to highlight that while the inclusion of transmission information from noninformative parents in the proposed test procedure  results


Given the importance of linkage disequilibrium (LD) in gene mapping and evolutionary inferences, I characterize in this review the pattern of LD and discuss the influence of human intervention during domestication, breed establishment, and subsequent genetic improvement on shaping the genome of livestock species. To this end, I summarize data on the profile of LD based on array genotypes vs. sequencing data in cattle and chicken, two major livestock species, and compare to the human case. This comparison provides insights into the real dimension of the pairwise allelic correlation and haplo-block structuring. The dependency of LD on allelic frequency is pictured and a recently introduced metric for moderating it is outlined. In the context of the contact farm animals had with human, the impact of genetic forces including admixture, mutation, recombination rate, selection, and effective population size on LD is discussed. The review further highlights the interplay of LD with runs of homozygosity and concludes with the operational implications of the widely used association and selection mapping studies in relation to LD. Linkage disequilibrium (LD) is the non-random assortment of alleles at different loci. The terms linkage and LD are often confused. As highlighted by Ne) and past demography. Populations with smaller Ne experience more genetic drift than larger populations. This genetic drift causes LD between alleles at independently-segregating loci, at a rate inversely proportional to Ne  was developed by The concept of LD was first introduced in D is the differencebetween the observed and the expected gametic haplotype frequencies comprising two loci A and Bunder linkage equilibrium (AB-PAPB=PABPabD=P–AbPaBP). Besides D, several measures of LD  have been suggested  that takes advantage of the historic LD to connect phenotypes to genotypes. This approach detects inherited markers in the vicinity of the genetic causatives or loci controlling the complex quantitative traits. It is often performed by scanning the entire genome for significant associations between a panel of SNPs and a particular phenotype  an association with the trait of interest. Given the fact that SNPs are in LD with one another, if a common SNP affects a trait, one can probably genotype a SNP in LD with it (a “marker” SNP) and that marker will be correlated with the trait of interest.Quantifying the extent of LD is the essential first step to determine the number of markers required to cover the entire genome in an association study with succinct power and precision. Theoretically, extensive LD reduces the number of markers required to localize an association between marker and trait but in lower resolution. In contrast, when LD promptly decays within a short distance, many markers are needed to map a gene of interest.Although the LD-based association analysis is a powerful tool routinely applied for gene mapping, it has not been very successful for targeting genes of complex traits, especially where the causative variants are low in frequency. This is due to the fact that commercial genotyping arrays largely under-represent infrequent alleles  based on a metric proposed by Even if a frequency independent measure of LD may not exist, it would be desirable to develop one which is less affected by frequencies than nt study , we deveρ is easy to compute and much less dependent on allele frequency than 2r  for genomic selection to achieve an accuracy of 0.85 for genomic breeding values has to be 0.2  appears to have a larger population size present day in comparison to the commercial birds. A similar pattern of historical demography is observed in cattle  emerges in human and livestock genomes from sequence data see . The SFSAcross the genome, every chromosome behaves as a unique linkage group and may experience independent demography. This is similar to the inter-species or inter-population scenarios, where it generates different profiles of LD for each unit. LD levels are also higher for sex chromosomes than autosomes because recombination on the sex chromosomes only occurs in females. Previous studies of measuring LD revealed a substantial difference among chromosomes of farm animals e.g., . In humaLD persists for several hundreds of kilobases at least for a portion of marker pairs in the contemporary populations of chicken and cattle , which cThe unusually long ROH may also persist in outbred populations. These homozygosity islands may originate from the locally low mutation or recombination rates, or be a result of the positive selection for a favorable allele followed by the hitch-hiking of the polymorphism around the target locus (see section “Mapping selection”).LD in sequencing resolution decays more rapidly than previously reported using array data. This enables higher resolution mapping of a trait of interest in outbred populations employing either association or selection mapping strategies. This also implies that selection mapping using haplotype-based metrics demands a panel of denser SNPs arrays to efficiently reveal patterns generated by unusually long haplotypes than medium-density arrays. The low reproducibility of the results reported in some of the first genome-wide selection studies in farm animal populations e.g.,  based onThe extent of LD varies across the genomic regions, chromosomes, among populations and between species. In other words, genome-wide averaged estimates of the extent of LD may not adequately reflect LD patterns of specific regions or population groups. These observations have broader practical relevance in genomic studies of farm animals, as such the optimal number of samples and marker density in either genome-wide association or selection mapping studies may largely vary due to the extremely adverse pattern of LD within and among chromosomes. Finally, confounding population characteristics such as cryptic allelic correlations or stratification may have serious impact on pattern and structure of LD in livestock populations that need to be taken into consideration in conducting unbiased genome-wide association mapping  and the Federal Ministry of Education and Research . The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.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.


P < 1.1 × 10−4) and 128 (88%) at nominal significance (P < 0.05). LAMA2 variant rs12193446, for example, had an effect size varying from −0.20 diopters (95% CI −0.18 to −0.23) to −0.89 diopters (95% CI −0.71 to −1.07) in different individuals. SNP effects were strongest at the phenotype extremes and weaker in emmetropes. A parsimonious explanation for these findings is that gene-environment or gene-gene interactions in myopia are pervasive.A genetic contribution to refractive error has been confirmed by the discovery of more than 150 associated variants in genome-wide association studies (GWAS). Environmental factors such as education and time outdoors also demonstrate strong associations. Currently however, the extent of gene-environment or gene-gene interactions in myopia is unknown. We tested the hypothesis that refractive error-associated variants exhibit effect size heterogeneity, a hallmark feature of genetic interactions. Of 146 variants tested, evidence of non-uniform, non-linear effects were observed for 66 (45%) at Bonferroni-corrected significance ( Alfred Pozarickij et al. present an analysis of effect-size heterogeneity among myopia-associated variants in the UK Biobank dataset. They find evidence for non-uniform effects for 45% of variants using a conservative cutoff, suggesting that gene-environment and/or gene-gene interactions are pervasive in myopia. By 2050 it is predicted that 50% of the world population will be myopic (near-sighted), with 4.8 billion individuals affected4. Myopia is associated with axial elongation of the eye, which increases the risk of retinal detachment, myopic maculopathy, glaucoma, and other pathological complications, making it an increasingly common cause of visual impairment and blindness7. Susceptibility to myopia is determined both by genetic and environmental factors. Genome-wide association studies (GWAS) have identified ~150 genetic variants associated with refractive error11, including some overlap with monogenic disease gene loci12. The time children spend outdoors, time performing near-viewing tasks, and the number of years in education are also strongly associated with myopia development20.The prevalence of refractive error has doubled in several parts of the world in the past few decades24. A major advantage of this approach is that it does not require the identity of the environmental risk factor underlying a GxE effect to be pre-specified or measured, nor the identity of the second genetic variant to be known when detecting GxG interactions. Instead, the presence of GxG or GxE interaction can be inferred using only genotype information for a genetic marker and phenotype information for the trait of interest.In conventional GWAS analyses of quantitative traits, it is assumed that each copy of a genetic variant shifts the phenotype by the same amount in all individuals, i.e. genetic effect sizes are assumed to be uniform. This assumption feeds forward into metrics such as SNP-heritability, and polygenic risk scores (PRS) used for genetic prediction. However, loci with gene-gene (GxG) or gene-environment (GxE) interactions will violate this assumption: for these loci the  effect size of a variant varies from person to person, depending on their genotype at other loci or their environmental exposure profile . Accordingly, a number of elegant studies have used evidence of a non-uniform effect size across individuals as a ‘signature’ to identify GxG or GxE interaction loci28, and yet currently very few such interacting variants have been discovered, we aimed to comprehensively assess the known genetic variants associated with refractive error for involvement in interactions by testing for this ‘signature’ of non-uniform genetic effect sizes across individuals. We compared our results for refractive error with those for height, a highly polygenic trait with little or no evidence of gene-environment or gene-gene interactions.Since GxE effects are implicated in myopia susceptibilityIn the sample of 72,985 unrelated, European-ancestry participants whose genotype data passed quality control and had phenotype information available, the mean ± SD refractive error was −0.25 ± 2.67 diopters (D) and the average age was 57.8 ± 7.8 years.p < 5 × 10−8) with refractive error in a recent meta-analysis carried out by the CREAM Consortium and 23andMe and that showed evidence of independent replication in the UK Biobank sample11. We coded the risk allele as the allele associated with a more negative refractive error.We assessed 146 genetic variants that showed genome-wide significant association .A standard, ordinary least squares (OLS) linear regression analysis of SNP effects under the assumption of constant effect size across all individuals produced very similar results to those reported previously in UK Biobank participantsFigure The type I error rate and statistical power of CQR-MR were investigated (see Methods) and full results are presented in the LAMA2), which had the strongest effect in the conventional OLS analysis, the effect size varied from −0.20 D (95% CI from −0.18 to −0.23) for individuals near the centre of the trait distribution to −0.89 D (95% CI from −0.71 to −1.07) for the most highly myopic individuals  and rs9388766 (L3MBTL3), which displayed non-constant, yet nearly linear changes in effect size across quantiles of the refractive error distribution, along with SNPs such as rs9680365 (GRIK1) and rs7449443 (FLJ16171-DRD1), which had essentially flat effect size profiles similar to those obtained under the OLS assumption of a constant effect size in all individuals.CQR-MR was used to determine if effect sizes for the 146 refractive error-associated variants differed across individuals depending on their position (i.e. their quantile) in the refractive error distribution. Nearly all variants exhibited an inverse-U shaped effect size profile, with the strongest effect size in individuals at the extremes of the refractive error distribution and a minimum effect size in emmetropic participants near the center of the distribution. Representative results are presented in Fig. p-value threshold of 0.05/(3 × 146) = 1.1 × 10−4, a total of 66 (45%) of the variants showed significant non-uniform effects, i.e. p < 1.1 × 10−4 for the β1 (linear) or β2 (quadratic) model coefficients (Table LAMA2) variant, p = 2.12 × 10−36 for the β1 component, and p = 1.19 × 10−30 for the β2 component. Notably, only 18 (12%) of the variants failed to show at least nominal evidence of an interaction effect .We used a 3-parameter model to quantify the non-uniformity of effect sizes (see Methods). After correcting for multiple-testing by applying a Bonferroni adjusted 0.05/3 × 46 = 1.1 For comparison, an analogous set of analyses to those performed above were carried out for genome-wide significant variants associated with height. For height, only 6% of variants (nine out of 148) displayed at least nominal evidence of a non-uniform effect size . The largest change in PRS effect size due to such an interaction with education was 0.57 D (at quantile 0.2). The PRS effect size difference associated with educational attainment was smallest in emmetropes. For example, the PRS effect size was within a narrow range of −0.25 to −0.37 D for participants in quantile 0.6, irrespective of their level of education. For participants in the hyperopic tail of the refractive error distribution (quantiles > 0.8), the PRS effect size was smaller in those with greater educational attainment, opposite to the relationship seen in the myopic tail. Thus, for example, for hyperopic participants in quantile 0.9, a 1 SD reduction in PRS was associated with a +0.62 D (95% CI from +0.55 to +0.69) effect on refractive error in those in the lowest education stratum, yet only a +0.41 D (95% CI from +0.38 to +0.44) effect in those from the highest education stratum .We used the 146 refractive error-associated variants to create a polygenic risk score (PRS) and examined whether this too exhibited a non-uniform effect size in different individuals. As shown in Fig. Evidence of effect size heterogeneity—a signature of involvement in GxG or GxE interactions—was found for 88% of the refractive error-associated variants tested. Furthermore, the impact of this phenomenon was dramatic: genetic effect sizes were as much as four-fold higher in certain individuals compared to others. Previous studies of refractive error genetics have always assumed that genetic effect sizes are the same in every person in the sample, and thus this important source of inter-individual variation has remained hidden.29. We speculate that emmetropization may act as a buffer against the myopia- or hyperopia-predisposing effects of genetic risk variants. Thus, suppose that, during childhood, a myopia-predisposing risk allele led to a small increase in axial eye length. This might subsequently be countered by a slowing of the rate of axial elongation via visually-mediated feedback. Furthermore, suppose there exists a limit to the amount of axial elongation that the emmetropization system can compensate for  then in those individuals whose emmetropization limit is surpassed, genetic variants would have free reign to attain much higher effects than in those individuals whose emmetropization limit is not exceeded. Finding evidence to support a direct role for emmetropization in causing the observed genetic effect size heterogeneity of refractive error-associated variants would likely require studies in animal models; the recent discovery of a genetic locus for susceptibility to visually-induced myopia is a first step in this direction31.Refractive error-associated variants typically had inverse-U shaped effect size profiles, with the strongest effects observed at the phenotype extremes, and effects closer to zero in emmetropes. Very few SNPs had constant effects across all quantiles of the sample distribution that matched those assumed in conventional analyses. One potential explanation for these findings is the process of ‘emmetropization’, in which the rate of axial eye elongation during infancy is fine-tuned by a visual feedback loop in order to maintain a sharp retinal image28. The current work suggests that such interaction effects are likely to be widespread. Applying our same analysis methods to a different trait, height, yielded far fewer variants with signatures of a GxG or GxE interaction (6% for height vs. 88% for refractive error). Given that height and axial eye length share genetic determinants in common (genetic correlation 0.1–0.2)33, it would be interesting to examine genetic effect sizes across quantiles of the axial length distribution, for example in samples of emmetropes and myopes.Prior to this work, only a handful of specific GxE interactions, and no GxG interactions had been reported for refractive errorThe PRS findings confirmed the dramatic difference in phenotypic effect exerted by refractive error-associated genetic variants in different individuals, which contrasts starkly with the simple deterministic effects expected of high risk genotypes. Individuals who reached adulthood as emmetropes appeared to have been ‘buffered’ against their genetic risk burden, and thus genetic effect sizes in these individuals were correspondingly small. By contrast, genetic effect sizes were often several-fold larger in individuals who became highly myopic or highly hyperopic by the time they reached adulthood. Time spent in education appeared to further modify the phenotypic effects of risk SNPs.36, it is not the only cause. Parent-of-origin effects will give rise to increased variance heterogeneity in heterozygous individuals at loci in which the effect size varies dependent on which parent transmitted the risk allele34. Similarly, ‘genetic nurture’, whereby untransmitted alleles in parents  influence the phenotype37 may also lead to variance heterogeneity. For example, if the environment of the child is partly determined by the parents’ genotype, then risk alleles inherited by the child will potentially show interactions with untransmitted parental alleles, i.e. an inter-generational GxG interaction mediated via a GxE interaction for the child. Allelic heterogeneity, whereby multiple genotypes in linkage disequilibrium influence the same phenotype, can also give rise to variance heterogenity40. Finally, examples of genetic variants with striking inter-individual genetic effect heterogeneity exist for which mechanistic explanations are currently lacking or incomplete. For instance, rs3825942 in LOXL1 is associated with an increased risk of exfoliation syndrome in certain populations, but a reduced risk in others41 , and rs6817105 near PITX2 is associated with an ~1.6-fold increased risk of atrial fibrillation overall; however, the level of risk varies widely across populations42. Explanations based on simple GxG or GxE interactions have not been able to account for the observed effect size heterogeneity at these loci42.Our strategy for detecting inter-individual differences in genetic effect sizes was based on a statistical test for variance heterogeneity across genotypes. While variance heterogeneity is a signature of GxG and GxE interactionsTo conclude, our study provides evidence that most of the currently-known refractive error-associated variants have different effect sizes in different individuals. A parsimonious explanation is that the variants are involved in GxG or GxE interactions. The phenotypic effect imparted by risk alleles was found to vary as much as four-fold, with greater effects observed for individuals in the phenotype extremes compared to those in the center. This variation in inter-individual effects remains hidden when conventional analysis methods are used to detect genetic effects. Widespread GxG or GxE interactions will contribute to the ‘missing heritability’ for refractive error, and adversely impact the accuracy of genetic prediction of children at-risk of developing myopia.43. Ethical approval for the study was obtained from the National Health Service National Research Ethics Service (Ref 11/NW/0382) and all participants provided written informed consent. Participants provided a blood sample, from which DNA was extracted and genotyped using either the UK BiLEVE Axiom array or the UK Biobank Axiom Array44. We analysed data from the July 2016 data release for genetic variants in 488,377 individuals imputed to the HRC45 reference panel.The UK Biobank project is an ongoing cohort study of ~500,000 UK adults aged 40–70-years-old when recruited (2006–2010)avMSE). Individuals who self-reported any of the following eye disorders were excluded from the analyses: cataracts, “serious eye problems”, “eye trauma”, a history of cataract surgery, corneal graft surgery, laser eye surgery, or other eye surgery in the past 4 weeks. Individuals whose hospital records (ICD10 codes) indicated a history of the following were also excluded: cataract surgery, eye surgery, retinal surgery, or retinal detachment surgery. Of 488,377 individuals with genetic information, samples were excluded due to: ocular history , withdrawal of consent (n = 8), self-report of non-white British ethnicity or genetic principal components indicative of non-European ancestry , outlying level of genetic heterozygosity (n = 648), or refractive error not measured . The remaining 86,286 individuals were tested for relatedness using the --rel-cutoff command in PLINK v1.946. A genetic relationship matrix was created using a linkage disequilibrium (LD)-pruned set of well-imputed variants  > 0.005, missing rate ≤ 0.01, and ‘rs’ variant ID prefix). LD-pruning was accomplished by using the --indep-pairwise 50 5 0.1 command in PLINK v246. One member of each pair with genomic relatedness greater than 0.025 was excluded. This resulted in a final sample size of 72,985 unrelated individuals of European ancestry.Participants self-reported whether they had a university or college degree. An ophthalmic assessment was introduced towards the latter stages of UK Biobank recruitment, hence only about 25% of participants were examined. Refractive error was measured using non-cycloplegic autorefraction . The mean spherical equivalent (MSE) refractive error was calculated as the sphere power plus half the cylinder power, and averaged between the two eyes (p < 5 × 10−8) with refractive error in the CREAM Consortium and 23andMe meta-analysis and that replicated in a UK Biobank sample11. The risk allele was coded as the allele associated with a more negative refractive error. Of the 149 genetic variants tested, reliable results could be obtained for 146 .We originally assessed 149 genetic variants that showed genome-wide significant association . Reliable results could be obtained for 148 height SNPs  was the dependent variable and genotype, age, age-squared, sex, and a binary variable indicating genotyping array were fitted as covariates. Conditional quantile regression (CQR)47 was carried out using the quantreg package v5.36 in R version 3.5.1, using the same set of covariates as above. We used 10,000 Markov-chain-marginal-bootstrap replicates to calculate standard errors. As a sensitivity analysis, we also tested linear regression and quantile regression models with the first 10 principal components included as covariates. However, including principal components in the models did not change parameter estimates substantially, hence only the results of the original analyses are reported.A ‘conventional’ OLS regression analysis was carried out to quantify the effect size of each of the 146 variants under the assumption of a constant effect size across the full sample. Refractive error averaged between the two eyes (metafor package v2.0.0 in R48) with the estimated SNP effect at each quantile modelled as the dependent variable and the quantile at which these estimates were obtained as the independent variable. A term for quantile-squared was also included in the meta-regression model to test for non-linear genetic effects across quantiles, resulting in the model: y = β0 + β1q + β2q2 + e . Figure SNP effect estimates and their standard errors from quantile regression at 9 different quantiles  were meta-regressed using a mixed-effects model  SNP genotypes.Null phenotype: The avMSE phenotype of the 72,985 individuals in the analysis sample was permuted 100 times. For each permutation, the association between the null phenotype and the genotype of each of the 149 variants was assessed using CQR-MR. The type 1 error rate was calculated as the proportion of SNPs with P < 0.05 for each of the three meta-regression coefficients  from the total of (100 × 149) = 14,900 permutations. Null SNPs: The 72,985 individuals in our analysis sample were independently assigned genotypes for a biallelic SNP with MAF ranging from 0.05 to 0.45, simulated from a binomial distribution. Association between avMSE and the genotype of the null SNP was assessed using CQR-MR. The type 1 error rate was calculated as the proportion of SNPs with P < 0.05 for each of the three meta-regression coefficients  after simulating 10,000 null SNPs.avMSE phenotype in samples of varying size. Specifically, from the full sample of 72,985 individuals, we selected a random sample of 10,000–70,000 individuals, in steps of 10,000, and tested each of the 149 variants for association. This procedure was repeated 20 times. Power was computed as the proportion of replicates in which the null hypothesis was rejected at a nominal significance level of α = 0.05 . The total number of tests used for these power evaluations was 149 × 7 × 20 = 20,860. The same set of covariates as in original analysis was included in the CQR step when assessing power and type 1 error.To obtain a relative indication of statistical power, the 149 refractive error-associated variants were tested for association with the observed q = 0.1 to 0.9 in steps of 0.1) followed by meta-regression of the resulting genetic effect size estimates. In preliminary work, we explored the effect on type 1 error rate and power of selecting more or fewer than 9 quantiles, by testing: (a) 19 quantiles, q = 0.05–0.95 in steps of 0.05; (b) 10 quantiles, q = 0.05–0.95 in steps of 0.1; (c) 5 quantiles, q = 0.1–0.9 in steps of 0.2. For simplicity, we refer to these CQR-MR models by the number of quantiles included in the meta-regression, i.e. 5, 9, 10, or 19. CQR-MR analysis with 9 quantiles performed optimally  was selected as an exemplar environmental variable. UK Biobank participants with a university degree were not asked the age they completed full-time education, hence these individuals were assumed to have completed their education at the age of 21 years. Age completed education categories with low counts were merged with adjacent categories, resulting in four final EduYears categories: 13–15, 16, 17–20, and 21–26 years. We carried out a CQR-MR analysis stratified by EduYears category.To test for the presence of gene-environment interaction, we constructed a polygenic risk score (PRS) by counting the number of risk alleles  carried by each individual. We did not weight these by SNP effect sizes in order to avoid introducing bias by using weights obtained from, and applied in, the same sample (UK Biobank). ‘Age completed full-time education’ (Further information on experimental design is available in the Supplementary InformationDescription of additional supplementary itemsSupplementary DataReporting Summary


The selection objective for animal production is the highest income with the lowest production cost, while ensuring the highest animal welfare. A selection experiment for environmental variability of birth weight in mice showed a correlated response in the mean after 20 generations starting from a crossed panmictic population. The relationship between the birth weight and its environmental variability explained the correlated response. The scale effect represents a potential cause of this correlation. The relationship between the mean and the variability implies: the higher the mean, the higher the variability. The study was to quantify by simulation the genetic correlation between a trait and its environmental variability. This can be attributable to the scale effect in a range of coefficients of variation and heritabilities between 0.05 and 0.50. The resulting genetic correlation ranged from 0.1335 to 0.7021 being the highest for the highest heritability and the lowest CV. The scale effect for a trait with heritability between 0.25 and 0.35 and CV between 0.15 and 0.25 generated a genetic correlation between 0.43 and 0.57. The genetic coefficient of variation (GCV) affecting residual variability was modulated by the strength reducing the impact of the scale effect. GCV ranged from 0.0050 to 1.4984. The strength of the scale effect might be in the range between 0 and 1. The scale effect would explain many reported genetic correlation and the additive genetic variance for the variability. This is relevant when increasing the mean of a trait jointly with the reduction of its variability. Currently, interest is increasing in the genetic control of environmental variability for application in livestock breeds. Environmental variability refers to the variation in phenotypes that cannot be explained by genetic variation or identifiable genetic differences . The impUnderstanding the forces that underlie the importance of the non-genetic component of phenotypic variance is a broad question in evolutionary biology . ClassicGenetic correlation is explained by linkage, pleiotropy or a combination of these factors . On the The scale effect represents a potential cause for the observed correlation between a trait mean and its variance. The scale effect is caused by a direct relationship between the mean and variance, for instance when a trait has a constant coefficient of variation (CV) such that an increase in the mean also increases the variability. For most distributions the variance is directly connected to the mean, where the normal distribution is an important exception. In a Poisson distribution the variance is equal to the mean and in a Gamma distribution there is a direct relationship between the mean and CV .The scale effect is then a consequence of a manmade way to measure heterogeneity which is a difficult way to express the real natural determining process  and partThe presence of an additive genetic variance for a trait in a population would imply the possibility of changing the mean by selection of that trait which would automatically generate the appearance of an additive genetic variance for the variability originated by the scale effect.The CV is a statistical parameter defined as the ratio of the standard deviation (σ) to the mean (µ) to quantify the variability in a dimensionless manner. Thus, for a given CV, the higher mean, the higher standard deviation. Considering the CV to be fixed allows simplifying the scope of the study, as there is no natural direct relationship between mean and variability in a normally distributed variable. For a fixed CV, modifying the mean would automatically increase the standard deviation and vice versa. Since it is not common to have a CV constant across the whole range of a trait, a scenario in which the scale effect should be modulated was considered. The objective of this study was to quantify by simulation up to what extent the genetic correlation between a trait and its environmental variability could be attributed to the scale effect. The reduction of the scale effect due to an incomplete relationship between mean and variability, understood as the strength of the scale effect, were also assessed in the resulting additive genetic variance, thus affecting the residual variance.iv affecting the residual variability, which has a Gaussian distribution, i.e., iy is the record i, μ is the mean of the trait, iu the additive genetic effect, eη is the residual variance  proposed by k is in turn multiplied by k, with its CV unaltered. This relationship between the level of a trait and its variability was assumed here to be for the performance level of each animal. Two simulation analyses were performed to explore the influence the scale effect can have on the genetic correlation between a trait and its residual variability. The first analysis was performed to compute the genetic correlation between a trait and the variability that occurs as a consequence of the scale effect. The second analysis was performed to assess the strength of the scale effect originating from the incomplete determination that the CV would have on the modulation of the magnitude of the additive genetic variance generated for the variability based on the scale effect.The scale effect shows the relationship between the mean and the variability so that the higher the mean of a variable, the higher its variability. Thus, for instance, the standard deviation of a variable multiplied by a constant 2h ranging from 0.05 to 0.50 at 0.05 increments. Single records were simulated for a trait with a mean value (µ) of 100. The values for µ, CV and 2h were fixed, but all the other parameters were derived from them. But for the sake of simplicity, residual and additive genetic effects were assumed to be the only random effects in the model. Simulations were performed in such a manner that higher phenotypes would have higher variance keeping the CV constant as expected by the scale effect. Phenotypic variance :First, each record where ia is the additive genetic effect and ie the residual effect that were randomly obtained from the following Gaussian distributions with unique variances:iy described the level of the phenotype of the individual i, and the equivalent residual standard deviation in this individual , would proportionally modify the residual variance in model HO (i (iv) was then obtained from the following equation:Based on the HE model equation described above, the additive genetic value of individual To accommodate the additive genetic value affecting the trait, the ia simulated by the HO model was rescaled:u) and for the variability (v) were directly computed from the simulated values since they were available from the simulation. The mean genetic correlation of 10 independent replicates was computed within a scenario and 100,000 individuals were simulated for each scenario.A total of 100 scenarios were simulated for the values of CV and v from the scale effect by defining a new parameter r (0 < r ≤ 1). This new parameter r would weaken the scale effect if it is less than 1; as a consequence the scale effect strength reduces the absolute value of the environmental additive genetic effect of the individual i as follows:2h) nor the value of r will affect the genetic correlation between mean and residual variance, but the additive genetic variance of the variability 2r. In addition, this variance is dependent on the magnitude of the CV of the trait. This is a simple way to model the incomplete determination of the variability from the level of the trait, but many other models are possible.It is assumed that the simulation described above has the scale effect proportional to the value of the trait, but this assumption could be unrealistic. A direct determination of the variability from the level of the trait and the CV would then seem to be unrealistic, leading in addition to unreliable values for han 0.25 . This ser. Here, CV ranged from 0.05 to 0.50, and r ranged from 0.05 to 1. Both variables were altered in increments of 0.05. Genetic coefficient of variation for environmental variance (GCV) is a measure of evolvability . Different positive r values were employed to determine how GCV would be affected. For the sake of simplicity, a constant value for the entire range of the trait was assumed although the value of r can differ for different values of the interval  and CV values. The CV values ranged from 0.0050 (r = 0.05 and CV = 0.05), increasing with the value of the simulated parameters up to 1.4854 (r = 1.00 and CV = 0.50). Compared with the values reviewed by r = 0.60) and 0.2008 (r = 0.65) from To conclude, this simulation study demonstrates how the scale effect can justify the genetic correlation that often appears between the mean and the environmental variability of some traits in some populations, and the additive genetic variance for the variability that might simply be generated by this scale effect. Breeders should be well aware of this fact when their selection objective is to increase the mean of a trait jointly with the reduction of its variability to develop an adequate selection index for this trait or to find an adequate transformation of the trait to remove the scale effect. The issue is also important in the search of vQTL in which it would help to make the mean and variable independent . Further