Thus, there is a need to find selection criteria for IMF independent from lean growth. In pigs, the proportion of linoleic (C18:2) and arachidonic (C20:4) acids decline with fat deposition and therefore they can be considered as indicators of fatness. The aim of this research was to estimate the genetic variation for C18:2 and C20:4 in IMF and their genetic correlations with IMF and lean growth traits, with the objective to assess their potential as specific biomarkers of IMF. The analysis was conducted using a full-pedigreed Duroc resource line with 91,448 records of body weight and backfat thickness (BT) at 180 days of age and 1371 records of fatty acid composition in the muscle The heritability estimates for C18:2 and C20:4 in IMF, whether expressed in absolute (mg/g of muscle) or in relative (mg/g of fatty acid) terms, as well as for their ratio (C20:4/C18:2), were high (> 0.40), revealing that the C18:2 to C20:4 pathway is subjected to substantial genetic influence. Litter effects were not negligible, with values ranging from 8% to 15% of the phenotypic variance. The genetic correlations of C18:2 and C20:4 with IMF and BT were negative , if expressed in relative values, but almost null (− 0.04 to 0.07), if expressed in absolute values, except for C18:2 with IMF, which was highly positive (0.88). The ratio of C20:4 to C18:2 also displayed a stronger genetic correlation with IMF (− 0.59) than with BT (− 0.10).The amount of C18:2 in muscle can be used as an IMF-specific biomarker. Selection for the absolute amount of C18:2 is expected to deliver a similar response outcome as selection for IMF at restrained BT. Further genetic analysis of the C18:2 metabolic pathway may provide new insights into differential fat deposition among adipose tissues and on candidate genes for molecular markers targeting specifically for one of them. Linoleic acid C18:2) is a major ingredient of feeds and the most abundant PUFA in pig adipose tissue and muscle 8:2 is a . Thus, aIntramuscular fat (IMF) content and fatty acid composition are relevant traits for high-quality Mediterranean meat products such as dry-cured ham. Increasing IMF has the undesirable correlated effect of decreasing lean growth, so that, in this scenario, a common commercial target is to find selection criteria for IMF independent from lean growth . Althouggluteus medius muscle. These barrows were raised in 23 batches to slaughter at around 215 days of age. From 160 days of age they were fed a finishing diet  including around 6.0% fat . All barrows were slaughtered in a slaughterhouse equipped with a carbon dioxide stunning system . After chilling for about 24 h at 2 °C, a sample of at least 50 g of the gluteus medius muscle was taken from the left side ham. Muscle samples were immediately vacuum packaged and stored at − 20 °C until required for IMF and fatty acid determinations. The number of records, sires, dams, and litters used for each analyzed trait is given in Table Data from a purebred Duroc line  were used for the analyses , 10. Then-9, C18:0, C18:1n-7, C18:1n-9, C18:2n-6, C18:3n-3, C20:0; C20:1n-7, C20:2n-6 and C20:4n-6. Intramuscular fat content was calculated as the sum of each individual fatty acid expressed as triglyceride equivalents  ~ N , where R was the (co) variance matrix. Sorting records by trait, and pig within trait, R could be written as R0 ⊗ I, with R0 being the 6 × 6 residual (co) variance matrix between the six traits analyzed and I an identity matrix of appropriate order. Flat priors were used for bi and residual (co) variance components. Additive genetic and litter values, conditionally on the associated (co) variance components, were both assumed to be multivariate normally distributed with mean zero and with (co) variance G ⊗ A and C ⊗ I, respectively, where A was the numerator relationship matrix, G was the 6 × 6 genetic relationship matrix between the six traits, and C was the 6 × 6 (co) variance matrix between litter effects. The matrix A was calculated using all the pedigree information summarised in Table Z-criterion of Geweke and visual inspection of convergence plots. The genetic parameters for C20:2/C18:2 and C20:4/C18:2 were estimated separately using the same procedure but with a 4-trait multivariate animal model including BW, BT and IMF.Genetic parameters were estimated in a Bayesian setting, in line with the methodology described in Ros-Freixedes et al. , and usiExpected genetic responses in BW, BT and IMF were predicted after selecting for IMF, BT, IMF at constant BT and C18:2. A population with discrete generations was simulated in which 40 boars were randomly mated to 400 sows with a mating ratio of 1 boar to 10 sows. The breeding scheme consisted of one selection stage resulting in the top 25% males and 50% females. It was assumed that two males and two females from the offspring of each sow were performance-tested for BW and BT and three paternal half-sibs of different dams were used for IMF and C18:2 determinations. Pigs were assumed to be selected for one trait at a time, but using the records taken only on the traits included in the selection criterion or in all traits. Selection response was predicted by deterministic simulation of a one-stage selection scheme with discrete generations using the program SelAction . The proThe content of C18:2, C20:2 and C20:4 in IMF is influenced by the pig’s genetic background  with IMF  and BT  was in line with the observed in gluteus medius. Alternatively, the fatty acid composition in subcutaneous fat could also work as a BT-specific biomarker. Current evidence indicates that the C18:2 content in subcutaneous fat is negatively correlated to BT [We have used the stantial . This haed to BT . If confFADS2), a rate-limiting enzyme in the conversion of C18:2 into C20:4. The activity of FADS2 can be indirectly measured by C20:4/C18:2 and C20:2/C18:2. These two ratios are expected to decrease and increase, respectively, with IMF rather than with BT, thereby suggesting that FADS2 could be a candidate gene to explore IMF-specific molecular markers. In this context, Gol et al. [FADS2 gene that modifies C20:4/C18:2 and C20:2/C18:2. The correlated effects on IMF and BT were in line with the expected, i.e., the allele showing a positive effect on C20:4/C18:2 had less absolute C18:2 and IMF, while it did not alter BT. All in all, the results obtained would confirm that quantitative biological analysis is a good approach to find new traits and candidate markers for an efficient selection for IMF and lean growth.Over the last decades molecular markers have also raised interest as a tool to improve genetic analysis and selection. Several markers have been described to be associated with IMF, BT and fatty acid composition, although only one of them has proved to be IMF-specific . The disl et al.  found a In conclusion, our work demonstrates that the C18:2 to C20:4 pathway is subjected to genetic variation. Also, we show that the genetic (co) variation structure of the fatty acids in this pathway with IMF and BT differs by fatty acid and on whether they are expressed in absolute (mg/g of muscle) or relative values (mg/g of fatty acid). In particular, the distinct genetic relationship of C18:2 and C20:2  in IMF with IMF (positive) and BT  allow us to propose them as candidate IMF-specific biomarkers. In addition, we have proved that selection for the absolute amount of C18:2 in IMF is expected to deliver a similar genetic response outcome that selection for IMF at restrained BT. The quantitative genetic analysis of the C18:2 metabolic pathway has provided new insight into the relationship between IMF and lean growth, pointing to relevant candidate genes to search for potential IMF-specific markers.


N = 86,335 and 88,005 respectively), with the mean corneal astigmatism or refractive astigmatism in fellow eyes analysed as a quantitative trait (dependent variable). Genetic correlation between the two traits was calculated using LD Score regression. Gene-based and gene-set tests were carried out using MAGMA. Single marker-based association tests for corneal astigmatism identified four genome-wide significant loci (P < 5 × 10−8) near the genes ZC3H11B (1q41), LINC00340 (6p22.3), HERC2/OCA2 (15q13.1) and NPLOC4/TSPAN10 (17q25.3). Three of these loci also demonstrated genome-wide significant association with refractive astigmatism: LINC00340, HERC2/OCA2 and NPLOC4/TSPAN10. The genetic correlation between corneal and refractive astigmatism was 0.85 . Here, we have undertaken the largest genome-wide association studies for corneal and refractive astigmatism to date and identified four novel loci for corneal astigmatism, two of which were also novel loci for refractive astigmatism. These loci have previously demonstrated association with axial length (ZC3H11B), myopia (NPLOC4), spherical equivalent refractive error (LINC00340) and eye colour (HERC2). The shared role of these novel candidate genes for astigmatism lends further support to the shared genetic susceptibility of myopia and astigmatism.Previous studies have suggested that naturally occurring genetic variation contributes to the risk of astigmatism. The purpose of this investigation was to identify genetic markers associated with corneal and refractive astigmatism in a large-scale European ancestry cohort (UK Biobank) who underwent keratometry and autorefraction at an assessment centre. Genome-wide association studies for corneal and refractive astigmatism were performed in individuals of European ancestry (The online version of this article (10.1007/s00439-018-1942-8) contains supplementary material, which is available to authorized users. Astigmatism occurs when the eye fails to bring light from a point source object to a single point focus on the retina, resulting in impaired vision. If uncorrected in childhood, astigmatism is a risk factor for amblyopia development  for corneal astigmatism  for refractive astigmatism  for refractive astigmatism have been identified near the genes VAX2, TOX and LINC00340  for the highly heritable refractive traits spherical equivalent and myopia in GWAS studies  estimated at 50–65%  of astigmatism occur across the lifespan . UK Biobank received ethical approval from the NHS Research Ethics Committee (Reference: 11/NW/0382). Baseline assessment was undertaken at 1 of 22 assessment centres distributed across the UK . Up to 6 measurements were taken for each eye using 6-mm diameter keratometry mires, from which corneal astigmatism was derived (see below). 130,521 participants had non-cycloplegic autorefraction performed for at least one eye using the same auto autorefractor-keratometer, with up to ten measurements taken for each eye. In all instances, participants were required to remove contact lenses, if worn. Refractive astigmatism was derived from the autorefraction cylindrical power. Spherical equivalent was recorded as the spherical power plus half of the cylindrical power from autorefraction. All keratometry/autorefractor measurements flagged with an error code “E” (indicating “Lower reliability data”) were recoded as missing before taking the mean trait values for each eye individually across assessment centre visits, then the mean of both eyes for each individual. The mean corneal astigmatism and mean refractive astigmatism for each individual were also categorised as dichotomous variables using a grid of thresholds to define case/control status, from 0.50 to 1.50 D, in 0.25 D steps. After the exclusion of unreliable readings, 119,799 participants had measures for corneal astigmatism, and 130,459 participants had measures for refractive astigmatism and spherical equivalent refractive error.http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id=157020. As detailed below, of these 152,725 genotyped participants, 141,751 were of European ancestry based on principal components analysis (PCA), and were non-outliers for heterozygosity. Data from this UK Biobank “Interim 150K” release were used for SNP-heritability estimation.Participant DNA samples were genotyped by UK Biobank researchers at approximately 800,000 genetic markers using one of two genotyping arrays, the UK BiLEVE Axiom array or the UK Biobank Axiom array. Genetic data were released in two waves. In the UK Biobank “Interim 150K” release, data were made available for 152,725 samples imputed at 72,355,689 markers using IMPUTE2  and/or known inversions . The remaining SNPs were intersected with those included on the two genotyping arrays used by UK Biobank  and LD-pruned  of genetic data released from the UK Biobank consisted of imputed genotype information for all 488,377 participants whose data passed quality control filters  a set of approximately 890,000 “high-confidence” markers in weak LD was generated using PLINK 2.0  estimates were obtained using the default additive effects model in GCTA . All individuals in the “Interim 150K” release dataset who, after exclusions, had information available for the respective phenotype were included in the initial GRMs, which were subsequently restricted to unrelated individuals based on a pairwise relatedness threshold of 0.025  . Both additive and dominance GRMs for each trait were included in a joint GCTA analysis to ascertain the partitioned contributions of additive and dominance effects to the respective phenotypic variances. All traits were coded as continuous variables for these GREMLd analyses.Additional SNP-heritability estimates were obtained in an attempt to partition SNP-heritability into separate additive and dominance components. GCTA-GREMLd  and for refractive astigmatism  using individuals with genetic data made available in the UK Biobank second data release (July 2017 release). Corneal and refractive astigmatism were considered as continuous traits using the standard “infinitesimal” mixed linear model approach implemented in BOLT-LMM v2.3. In BOLT-LMM, GRMs constructed using the “high-confidence” markers were used to account for residual population structure and cryptic relatedness  was determined by dividing the median observed χ2 test statistic by 0.456  were then compared between males and females, as described by Winkler et al. . The sexGene-based and gene-set tests were performed using the summary statistics results from GWAS in MAGMA v1.06  were combined to obtain a joint association statistic. This statistic was compared against that for all other genes not in that set whilst accounting for the number of SNPs within each gene, gene density and differential sample size  .Pearson correlation coefficients were calculated for all unrelated individuals included in the single marker GWAS analyses who had data available for all refractive error traits investigated  of White British/European ancestry, based on genetic principal components analysis. Approximately 54% of the sample were female, and the mean spherical equivalent refractive error was − 0.29 D . Approximately 4.0% of the participants had high myopia (defined as a refractive error averaged between the two eyes ≤ − 6.00 D) and 18.0% of the sample had anisometropia of at least 1.00 D. The level of corneal astigmatism was relatively constant across the age spectrum of the participants, while the level of refractive astigmatism increased with age (Online Resource 1). Full details of the refractive error and demographic characteristics of the participants have been reported by Cumberland et al. .Astigmatism has often been analysed as a dichotomous trait in genetic studies; however, the choice of the threshold used to define case/control status has varied from study to study  and negligible for a case threshold of 1.50 D : corneal astigmatism = 0.061 (0.021); refractive astigmatism = 0.046 (0.020); spherical equivalent = 0.387 (0.022)  for corneal astigmatism and refractive astigmatism, respectively (Online Resource 4). Specifically, for corneal astigmatism, genome-wide significant markers clustered in four regions , LINC00340 , HERC2  and TSPAN10/NPLOC4  . Conditional analyses carried out by conditioning on the top marker at each of the four novel genome-wide significant loci suggested that these four association signals were each driven by a single causal marker (Online Resource 5). However, the strength of the association signal at the HERC2 locus when conditioning on top marker rs1129038 did yield a suggestive association signal within the adjacent OCA2 gene .For corneal astigmatism, the nearest gene at each of the four genome-wide significant loci was LINC00340, , HERC2  and TSPAN10/NPLOC4 . Notably, all of these loci also demonstrated significant association with corneal astigmatism. Conditional analyses for these genome-wide significant loci also suggested these association signals were each driven by a single causal marker with the exception of the association signal at HERC2 which appeared to be driven by an additional independent causal marker within the OCA2 gene at rs1800407 (P = 9.03 × 10−15) (Online Resource 6). Conditioning on both rs1129038 and rs1800407 at the HERC2-OCA2 locus resulted in a suggestive association signal at rs7497044 (P = 1.90 × 10−6), an intronic variant within the nearby GABRG3 gene. In a previous meta-analysis of GWAS for corneal curvature in European ancestry cohorts from Australia . Pairwise LD between markers rs7497044, rs17137734, rs1129038 and rs1800407 varies from low to negligible in Europeans (r2 = 0.0–0.1).As mentioned above, for refractive astigmatism, markers achieving genome-wide significant association clustered in three regions Table : LINC003λGC) were 1.094 for corneal astigmatism and 1.045 for refractive astigmatism; however, when accounting for the polygenic nature of these respective traits using the intercepts from LD Score regression (λLDSC), inflation due to uncorrected population effects was estimated to be considerably lower for both traits .Genomic inflation factors . For corneal astigmatism, all four loci identified using the mixed linear model analysis also demonstrated genome-wide significant association using the linear regression model in PLINK, while only two of the three loci originally associated with refractive astigmatism (LINC00340 and HERC2) continued to demonstrate genome-wide significant association . Additional sensitivity analyses were performed using logistic regression for the same groups of individuals and covariates as analysed by linear regression, with cases defined as individuals with corneal or refractive astigmatism ≥ 1.00 D. Here, three of the four previously identified loci, near the genes ZC3H11B, HERC2 and TSPAN10/NPLOC4, demonstrated genome-wide significant association for corneal astigmatism, while only the LINC00340 locus continued to demonstrate genome-wide significant association for refractive astigmatism . In all instances, the association signals were reduced using linear and logistic regression compared to the mixed linear model analyses. This was likely due to the substantial drop in sample size necessitated by standard regression-based methods, which cannot account for relatedness between individuals. Tests for a difference in genetic effect size in male vs. female participants for the genome-wide significant loci for corneal astigmatism and refractive astigmatism did not identify any such differences after accounting for multiple testing (Online Resources 13 and 14), suggesting that the newly identified variants confer susceptibility to astigmatism in both sexes.As validation for the use of mixed linear models to conduct the association tests, analyses were repeated using linear regression (implemented in PLINK 2.0) and an identical set of covariates  < 0.05. These genes included a cluster of nine genes at the TSPAN10/NPLOC4 locus  along with the genes HERC2 , PDGFRA , and B3GNT7  (Online Resource 15). For refractive astigmatism, gene-based analysis identified 35 genes with FDR < 0.05. Of these genes, seven were clustered at the gene-dense TSPAN10/NPLOC4 locus . Additional genes identified included TMEM211 , PROX1 , HERC2 , and PLAUR  (Online Resource 16). Gene-set analyses in MAGMA yielded non-significant findings after correction for multiple testing.To identify potential candidate genes and biological mechanisms enriched with markers attaining low but not necessarily genome-wide significant P = 4.34 × 10−10) and 0.034 , respectively . In contrast, genetic correlations between the astigmatism traits and spherical equivalent were weaker at −0.108 for corneal astigmatism and spherical equivalent; and − 0.104 for refractive astigmatism and spherical equivalent  were all significantly different from the null hypothesis of zero Table . The genThe GWAS analyses undertaken here for corneal and refractive astigmatism are the largest performed to date, and led to the discovery of four novel genome-wide significant loci associated with corneal astigmatism, and two novel genome-wide significant loci associated with refractive astigmatism.h2SNP = 0.387; P < 1 × 10−10) was similar to a previously published estimate, which suggested a SNP-heritability of 0.35 , with a negligible contribution of dominance effects. The SNP-heritability estimates for spherical equivalent calculated here were approximately 50% of those obtained from twin studies . Therefore, the common variants that confer susceptibility to astigmatism appear to comprise only a subset of the wider collection of common genetic variants contributing to susceptibility to spherical equivalent refractive error.It could be argued that astigmatism and spherical equivalent refractive error share little genetic susceptibility since the genetic correlations between these respective pairs of traits were not significantly different from zero. Possible explanations for these relatively weak genetic correlations are the differences in their respective SNP-heritabilities, the number of genome-wide significant associations identified for each trait, and the fact that spherical equivalent was included as a covariate in our GWAS analyses for astigmatism. Few commonly occurring markers have demonstrated association with astigmatism, yet it is notable that the novel loci for corneal and refractive astigmatism identified in our GWAS analyses have previously shown association with other ocular traits. Table Comparison of the genotypic correlations calculated here for UK Biobank participants against those reported previously by the CREAM consortium  on chromosome 1 (1q41) have previously demonstrated association with pathological (high) myopia in Asian ancestry cohorts and with axial length in both European and Asian ancestry individuals , is a long, non-coding RNA transcript located on chromosome 6 (6p22.3). In a previous meta-analysis of GWAS from European and Asian ancestry cohorts, this locus demonstrated genome-wide significant association with spherical equivalent refractive error  with refractive astigmatism  and its neighbouring gene OCA2  on chromosome 15 (15q13.1) have both previously demonstrated association with eye, skin and hair pigmentation , also known as Oculospanin, is a protein-coding gene located within a gene-dense region on chromosome 17 (17q25.3). This gene regulates the transmembrane metalloprotease ADAM10 as part of the Notch signalling pathway  associated with eye colour and astigmatism implies that certain eye colour(s) may confer susceptibility to astigmatism or that these eye colour-related genes have distinct, pleiotropic actions that lead to astigmatism. . It is notable that Pan et al.


Mendelian randomization (MR) is an epidemiological technique that uses genetic variants to distinguish correlation from causation in observational data. The reliability of a MR investigation depends on the validity of the genetic variants as instrumental variables (IVs). We develop the contamination mixture method, a method for MR with two modalities. First, it identifies groups of genetic variants with similar causal estimates, which may represent distinct mechanisms by which the risk factor influences the outcome. Second, it performs MR robustly and efficiently in the presence of invalid IVs. Compared to other robust methods, it has the lowest mean squared error across a range of realistic scenarios. The method identifies 11 variants associated with increased high-density lipoprotein-cholesterol, decreased triglyceride levels, and decreased coronary heart disease risk that have the same directions of associations with various blood cell traits, suggesting a shared mechanism linking lipids and coronary heart disease risk mediated via platelet aggregation. Mendelian randomization (MR) is a method for inferring causal relationships between risk factors and outcomes via associated genetic variants. Here, Burgess et al. develop the contamination mixture method which yields robust MR results in the presence of invalid instrumental variables and groups variants by their effect estimates. The approach treats genetic variants as proxy measures for clinical interventions on risk factors, using the variants analogously to random assignment in a randomised controlled trial3. As an example, genetic variants in the HMGCR gene region predispose individuals to lower lifelong levels of low-density lipoprotein (LDL) cholesterol, and are also associated with lower risk of coronary heart disease (CHD)4. HMGCR is the target of statins, a class of LDL-cholesterol lowering drugs that are an effective treatment for reducing CHD risk.Distinguishing between correlation and causation is a fundamentally important problem when trying to understand disease mechanisms. Mendelian randomisation is an epidemiological approach to assess whether a risk factor has a causal effect on an outcome based on observational data5. A valid IV must be associated with the risk factor of interest in a specific way, such that it is not associated with confounders of the risk factor–outcome association, nor does it affect the outcome directly . An IV can be used to estimate the average causal effect of the risk factor on the outcome6. If we assume that the effect of the risk factor on the outcome is linear and homogeneous in the population, and similarly for the associations of the IVs with the risk factor and outcome, the estimates from different valid IVs should be similar to each other7. If estimates differ substantially, then it is likely that not all the IVs are valid.Mendelian randomisation relies on genetic variants satisfying the assumptions of an instrumental variable (IV)8. Genetic variants are fixed at conception, providing some immunity to reverse causation  and confounding (as the genetic code cannot be influenced by confounding factors that act after conception). However, there are also several reasons why genetic variants may not be valid IVs: such as pleiotropy , linkage disequilibrium with a variant that influences another causal pathway, and population stratification11.Genetic variants represent a fertile source of candidate IVs, particularly for genes that have well-understood functions and specific effects on risk factors14, and those that assume a plurality of the candidate instruments are valid IVs16. The plurality assumption means that out of all groups of candidate instruments having the same asymptotic causal estimate, the largest group is the group of valid IVs. A similar assumption is made in outlier-removal methods, such as MR-PRESSO, which sequentially removes candidate instruments from the analysis based on a heterogeneity measure until all the remaining variants have similar estimates17. Other assumptions have also been made: for example, the MR-Egger method assumes that the distribution of direct effects of candidate instruments on the outcome is independent from the distribution of associations with the risk factor (referred to as the Instrument Strength Independent of Direct Effect – InSIDE – assumption)18.For many complex risk factors, Mendelian randomisation analyses may require multiple genetic variants to have enough power to detect a causal effect. Several approaches for making causal inferences with some invalid instruments have previously been proposed. These include methods that assume that a majority of the candidate instruments are valid IVs20. These summarised data, comprising beta-coefficients and standard errors from regression of the trait of interest (either risk factor or outcome) on each genetic variant in turn, have been made publicly available by several large consortia21. Several of the above methods use summarised data as inputs, and do not require access to individual-level data.Mendelian randomisation can exploit summarised data on genetic associations obtained from genome-wide association studies to link modifiable risk factors to disease outcomesWe here introduce the contamination mixture method as a method for obtaining valid causal inferences with some invalid IVs. Compared to other approaches for robust instrumental variable analysis, we believe our proposal has a number of advantages in giving asymptotically consistent estimates under the ‘plurality of valid instruments’ assumption, being fully likelihood-based, being computationally scalable to large numbers of candidate instruments, and being implemented using summarised genetic data.In this paper, we examine the performance of the proposed contamination mixture method in an extensive simulation study with realistic parameters. We show that our method performs well compared to previously proposed methods in terms of bias, Type 1 error rate, and efficiency. We then illustrate the use of the method in an example considering the causal effect of high-density lipoprotein (HDL) cholesterol on CHD risk, demonstrating a bimodal distribution of the variant-specific estimates, as well as to consider the effect of LDL-cholesterol on CHD risk , and of body mass index (BMI) on risk of Type 2 diabetes (T2D). We investigate factors that identify a group of genetic variants associated with HDL-cholesterol and triglyceride levels having a strong protective effect on CHD risk, showing that several of these variants have the same directions of associations with various blood cell traits. We then discuss the implications for identifying causal risk factors and mechanisms.There are two broad contexts in which the contamination mixture method can be used. First, under the assumption that there is a single causal effect of the risk factor on the outcome, the method can estimate this effect robustly and efficiently even when some genetic variants are not valid IVs. Secondly, the method can identify distinct subgroups of genetic variants having mutually similar causal estimates. If multiple such groups are identified, this suggests that there may be several causal mechanisms associated with the same risk factor that affect the outcome to different degrees.The contamination mixture method is implemented by constructing a likelihood function based on the variant-specific causal estimates. For each genetic variant, an estimate of the causal effect can be obtained by dividing the genetic association with the outcome by the genetic association with the risk factor; thus the only inputs to the method are the genetic association estimates (beta-coefficients and standard errors). If a genetic variant is strongly associated with the risk factor, then its causal estimate will be approximately normally distributed. If a genetic variant is a valid instrument, then its causal estimate will be normally distributed about the true value of the causal effect. If a genetic variant is not a valid instrument, then its causal estimate will be normally distributed about some other value. We assume that the values estimated by invalid instruments are normally distributed about zero with a large standard deviation. This enables a likelihood function to be specified that is a product of two-component mixture distributions, with one mixture distribution for each variant. The computational time for maximising this likelihood directly is exponential in the number of genetic variants. We use a profile likelihood approach to reduce the computational complexity to be linear in the number of variants (Methods).χ2 distribution with one degree of freedom. We note that the confidence interval from this approach is not constrained to be symmetric or even a single range of values. A confidence interval consisting of multiple disjoint ranges would occur if there were multiple groups of genetic variants having estimates that are mutually consistent within the group, but different between the groups.Briefly, we consider different values of the causal effect in turn. For each value, we calculate the contribution to the likelihood for each genetic variant as a valid instrument and as an invalid instrument. If the contribution to the likelihood as a valid instrument is greater, then we take the variant’s contribution as a valid instrument; if less, then its contribution is taken as an invalid instrument. This gives us the configuration of valid and invalid instruments that maximises the likelihood for the given value of the causal effect. This is a profile likelihood, a one-dimensional function of the causal effect. The point estimate is then taken as the value of the causal effect that maximises the profile likelihood. A 95% confidence interval is constructed by taking the set of values of the causal effect for which twice the difference between the log-likelihood calculated at the value and at the maximum is less than the 95th percentile of a 22, a weighted median method that assumes that a majority of genetic variants are valid IVs14, the MR-Egger method18, a weighted mode-based estimation method that assumes a plurality of genetic variants are valid IVs16, MR-PRESSO17, and the proposed contamination mixture method. In all, 10,000 simulated datasets were analysed for each scenario (Methods).To compare the performance of the contamination mixture method against other robust methods for Mendelian randomisation, we performed a simulation study with a broad range of realistic scenarios. We consider the first context, in which there is a single causal effect of the risk factor on the outcome, to enable comparison with other methods. We simulated data in a two-sample setting  under 4 scenarios: (1) all genetic variants are valid IVs, (2) invalid IVs have balanced pleiotropic direct effects on the outcome, (3) invalid IVs have directional pleiotropic direct effects on the outcome, and (4) invalid IVs have directional pleiotropic effects on the outcome via a confounder. In the first three scenarios, the InSIDE assumption is satisfied, while in the fourth it is not. We took 100 genetic variants as candidate instruments, with the number of invalid IVs in Scenarios 2–4 being 20, 40, or 60. We performed several methods: the standard inverse-variance weighted (IVW) method that assumes all genetic variants are valid IVs23, but biased when one or more genetic variants are invalid IVs. The contamination mixture and weighted median methods are slightly less efficient, while the mode-based method and MR-Egger methods are considerably less efficient. Mean estimates are attenuated towards the null in all methods due to weak instrument bias24; attenuation was more severe in the MR-Egger and mode-based methods The contamination mixture method gives a likelihood function that is bimodal  has been previously evidenced in Mendelian randomisation analyses40. Similarly, evidence from famines such as the Dutch Hongerwinter has suggested that low birthweight and caloric restriction in early childhood is associated with increased risk of Type 2 diabetes41. Our analysis provides further evidence that birth weight is the key factor explaining the opposing effects of BMI on T2D risk: having high BMI from birth appears to be protective of T2D, whereas having high BMI later in life only increases risk of T2D.As a further illustration of the ability of this approach to identify biologically relevant pathways, we conducted a similar analysis with BMI as the risk factor and T2D as the outcome. We considered 97 genetic variants previously demonstrated to be associated with body mass index at a genome-wide level of significanceIn this paper, we have introduced a robust method for Mendelian randomisation analysis referred to as the contamination mixture method. Compared to other robust methods, the contamination mixture method had the best all-round performance in a simulation study – maintaining little bias and close to nominal Type 1 error rates under the null with up to 40% invalid genetic variants, having reasonable power to detect a causal effect in all scenarios, and having the lowest average mean squared error of all methods. In a Mendelian randomisation analysis for HDL-cholesterol on CHD risk, the method detected two separate groups of variants suggesting distinct protective effects on CHD risk. A hypothesis-free search of traits revealed that several variants in the group with the stronger protective effect were associated with platelet distribution width and two other blood cell traits, with consistent directions of association across 11 variants in 9 gene regions. This suggests that the apparent protective effect of these variants may be driven by a shared mechanism, potentially relating to platelet aggregation. This mechanism has some plausibility, as platelets are implicated in atherosclerosis and thrombus formation. The approach also prioritised birth weight as the primary predictor of whether genetic variants that are associated with increased BMI are associated with increased or decreased T2D risk. Overall, the proposed method is able to make reliable causal inferences in Mendelian randomisation investigations with some invalid instruments, as well as highlighting when there are multiple causal effects represented in the data that may be driven by different mechanisms.42, on which the contamination mixture method is based, would be prohibitively slow even with 30 genetic variants. A disadvantage of our proposed method is sensitivity to the standard deviation parameter. In the example of HDL-cholesterol and CHD risk, while the two distinct groups of genetic variants were detected at some values of the standard deviation parameter, at other values distinct groups were not detected.Rather than attempting to model the distribution of the estimates from invalid genetic variants, the contamination mixture method proposes that these estimates come from a normal distribution centred at the origin with a wide standard deviation that is pre-specified by the user. We experimented with alternative methods that estimate this distribution. However, as the identity of the invalid instruments is unknown, the performance of these methods was worse than the approach presented here. The runtime of our proposed method is low – on an Intel i7 2.70 GHz processor, the contamination mixture method took 0.08 seconds to analyse one of the simulated datasets with 100 variants. In comparison, the MR-PRESSO method took 120 seconds, and the mode-based estimation method 81 seconds. The complexity of the contamination mixture model is linear in the number of genetic variants, so the benefit in computational time over other methods would be even greater if more genetic variants were included in the analysis. The previously proposed heterogeneity-penalised methodAs genome-wide association studies become larger, the number of genetic variants associated with different traits increases, and it is increasingly unlikely that all these genetic variants are valid instruments for the risk factor of interest. For risk factors with dozens or even hundreds of associated variants, a paradigm shift is required away from approaches that assume the majority of genetic variants are valid instruments, and towards methods that attempt to find genetic variants with similar estimates that might represent a particular causal mechanism. Heterogeneity in variant-specific estimates is inevitable, but heterogeneity should be seen as an opportunity to find causal mechanisms, rather than a barrier to Mendelian randomisation investigations. In our example, we demonstrated how a group of genetic variants having similar causal effects for HDL-cholesterol on CHD risk are linked by their association with platelet distribution width, suggesting a possible mechanism linking lipids to CHD risk related to platelet aggregation. While further research is needed to establish this mechanism, the approach demonstrates the possibility of finding information on causal mechanisms amongst heterogeneous data.There are many reasons why multiple causal mechanisms may exist between a risk factor and an outcome. It may be that the risk factor is not a single entity, but a compound measurement incorporating multiple risk factors with different causal effects. It may be that the risk factor is a single entity, but there are different ways to intervene on it, leading to different magnitudes of causal effect. Alternatively, it may be that some variants do not affect the risk factor directly, but rather affect a precursor of the risk factor. When multiple causal effects are evidenced in the data, we would not want to label one subset of genetic variants as valid and others as invalid in an absolute sense. Validity of variants is relative to the proposed value of the causal effect – different subsets of variants will be valid for different values of the causal effect. Any cluster of variants may indicate a causal mechanism linking the risk factor to the outcome, even if it is not the largest cluster.Identifying variables that associate with a cluster of variants having similar causal estimates may help us identify mediators on a particular causal mechanism, or it may help us identify a precursor of the nominal risk factor that is the true causal factor. However, unless we have biological knowledge that a variable identified from such a procedure is on a causal pathway from the risk factor to the outcome, a formal mediation analysis would be speculative. A further possibility is that the link with the variable is coincidental. However, if multiple variants in the cluster are all associated with the same variable with the same direction of association, then a common mechanism is likely.In conclusion, we have introduced a robust method for Mendelian randomisation that outperforms other methods (including MR-PRESSO) in terms of all-round performance, and can identify groups of variants having similar causal estimates, enabling the identification of causal mechanisms.it is associated with the risk factor of interest,it is not associated with any confounder of the risk factor–outcome association, and8.it is not associated with the outcome except potentially indirectly via the risk factorA genetic variant is an instrumental variable if:We use the term ‘candidate instrumental variable’ to indicate a variable that is treated as an instrumental variable, without prejudicing whether it satisfies the instrumental variable assumptions or not.43. These assumptions are not necessary for the instrumental variable estimate to be a valid test of the causal null hypothesis, but they ensure that all valid instrumental variables estimate the same causal effect.We assume that the associations between the instrumental variable and risk factor, and the instrumental variable and outcome are linear and homogeneous between individuals with no effect modification, and the causal effect of the risk factor on the outcome is linearj with the risk factor  estimate can be expressed as:ϕ, which is the residual standard error in the regression model. In a fixed-effect analysis, this parameter is fixed to be one, but in a random-effects analysis, we allow this term  to be estimated 49.If there are multiple instrumental variables, then a more precise estimate of the causal effect can be obtained using information on all the instrumental variables. If individual-level data are available, the two-stage least squares method is performed by regressing the risk factor on the instrumental variables, and then regressing the outcome on fitted values of the risk factor from the first stage regression. The same estimate can be obtained by taking a weighted mean of the variant-specific causal estimates using inverse variance weights, as in a meta-analysis23. However, it is only a consistent estimate of the causal effect if all the candidate instrumental variables are valid. We introduce the contamination mixture method as a robust method for instrumental variable analysis .The two-stage least squares method (and hence the fixed-effect IVW method) is the most efficient unbiased combination of the variant-specific estimatesJ genetic variants that are candidate instrumental variables. We assume that the genetic variant is strongly associated with the risk factor, so that its variant-specific estimate is normally distributed 50. If genetic variant j is a valid instrumental variable, then the variant-specific estimate from that variant θ with standard deviation equal to the standard error of the ratio estimate θF,j with standard deviation equal to the standard error of the ratio estimate θF,j are normally distributed about zero with standard deviation ψ, such that the distribution of θF,j (which is ψ2) plus the uncertainty in the estimate about its asymptotic value (which is the square of its standard error). Although it would be possible to estimate the distribution of the invalid estimands, their distribution is not the focus of the investigation. Our attempts to model their distribution resulted in greater uncertainty in which variants were valid and invalid instruments, and less reliable inferences overall.Suppose we have θ, then the likelihood corresponding to the genetic variant being a valid instrument will be larger; if the variant-specific estimate is not close to the proposed causal parameter θ, then the likelihood corresponding to the genetic variant being a invalid instrument will be larger.If the variant-specific estimate is close to the proposed causal parameter ζ, where ζj = 1 when genetic variant j is valid, and ζj = 0 otherwise. The likelihood function is then:LV,j if genetic variant j is valid and LF,j if genetic variant j is invalid. Making inferences using this likelihood is not simple, as the parameter space for ζ grows exponentially with the number of genetic variants, and there is no guarantee that the likelihood will be unimodal, making it difficult to apply stochastic approaches to explore the model space.We notate the model  as a vector θ is fixed, then the optimal model ζ to maximise the likelihood is clear: we should take ζj = 1 if LV,j >  LF,j and ζj = 0 otherwise. We denote this model choice as θ. We perform inferences on θ by calculating this profile likelihood at a range of values of θ. The causal estimate θ that maximises the profile likelihood, and the confidence interval as the values of θ such that:51. However, in practice the number of genetic variants is limited, and no issues with inference were reported in the simulation study. The profile likelihood is a continuous function of θ: it is clearly a continuous function for ranges of θ when ζj only change their value when the profile likelihood is the same for ζj = 0 and ζj = 1.We proceed using a profile likelihood approach. If the causal estimate ϕ from weighted regression of the genetic associations with the outcome on the genetic associations with the exposure using the genetic variants judged to be valid at the causal estimate 49. We then replace To allow for excess heterogeneity in estimates of the true causal parameter from variants judged to be valid IVs, we estimate an overdispersion parameter as the residual standard error ψ. We suggest taking the standard deviation of the ratio estimates based on all the genetic variants multiplied by 1.5 as an initial starting point in considering different values of this parameter. This value was taken in the applied example. This means that the standard deviation of invalid estimands θF,j is guided by the variability of the observed ratio estimates, but inflated as the valid instruments will have more similar causal estimates. However, a sensitivity analysis for this parameter is advised. In the applied example, the causal estimate, as well as whether the method detected two separate groups of variants or not, was sensitive to the choice of this parameter , and relatively less strong evidence for neighbouring values of the causal effect, leading to a distinct peak in the likelihood function. Subgroups could not easily be identified using a heterogeneity measure only, as such an approach would typically downweight or remove from the analysis variants having outlying causal estimates, without assessing whether the estimates from outlying variants were mutually similar.no pleiotropy – all genetic variants are valid instruments;balanced pleiotropy – some genetic variants have direct (pleiotropic) effects on the outcome, and these pleiotropic effects are equally likely to be positive as negative;directional pleiotropy – some genetic variants have direct (pleiotropic) effects on the outcome, and these pleiotropic effects are simulated to be positive;pleiotropy via a confounder – some genetic variants have pleiotropic effects on the outcome via a confounder. These pleiotropic effects are correlated with the instrument strength.To compare the contamination mixture method with previously developed methods for Mendelian randomisation, we perform a simulation study. We consider four scenarios:18 is satisfied; in Scenario 4, it is violated. This is the assumption required for the MR-Egger method to provide consistent estimates.In the first three scenarios, the Instrument Strength Independent of Direct Effect (InSIDE) assumptionX, outcome Y, confounder U (assumed unmeasured), and J genetic variants Gj, j = 1, …, J. Individuals are indexed by i. The data-generating model for the simulation study is as follows:θ is zero through the unmeasured confounder U. The genetic variants are modelled as single nucleotide polymorphisms (SNPs) with a minor allele frequency of 30%. A total of J = 100 genetic variants are used in each analysis. For each of Scenarios 2–4, we considered cases with 20, 40 and 60 invalid instruments. For valid instruments, the αj and ζj parameters were set to zero. For invalid instruments, the αj parameters were either drawn from a uniform distribution on the interval from  − 0.1 to 0.1 (Scenario 2), or from 0 to 0.1 (Scenario 3), or set to zero (Scenario 4). The ζj parameters were either set to zero (Scenarios 2 and 3), or drawn from a uniform distribution on the interval from  − 0.1 to 0.1 (Scenario 4). The causal effect θ was either set to 0  or +0.1 . The γj parameters were drawn from a uniform distribution on 0.03 to 0.1, meaning that the average value of the R2 statistic for the 100 variants across simulated datasets was 9.3% (from 10.5 to 12.7% in Scenario 4) corresponding to an average F statistic of 20.5 (from 23.3 to 28.9 in Scenario 4).We simulate data for a risk factor 18 (both using random-effects), the weighted median method14, MR-PRESSO17, and the mode-based estimation (MBE) method of Hartwig et al.16. To avoid extreme values in a minority of analyses, we set ψ = 1 in the contamination mixture method in all analyses. Each of the methods was implemented using summarised data only. Default values were used by the methods; in particular, the MBE method was implemented using the weighted option with bandwidth ϕ = 1 under the no measurement error (NOME) assumption (for similarity and thus comparability with other methods), and the MR-PRESSO method was performed trimming variants at a p-value threshold of 0.05 for the heterogeneity test.In total, 10,000 datasets were generated in each scenario. We considered a two-sample setting in which genetic associations with the risk factor and outcome were estimated on non-overlapping groups of 20,000 individuals. We compared estimates from the proposed contamination mixture method with those from a variety of methods: the standard IVW method, MR-EggerFor computational reasons (the methods took over 100 times longer to run than the other methods put together), the MR-PRESSO and MBE methods were performed on 1000 datasets per scenario only. Mean squared error was calculated in each scenario by averaging across the 10,000 datasets (1000 datasets for the MR-PRESSO and MBE methods).δX and δY in the equations below:δX = δY = 1. We first took δX = ±1 and δY = ±1 and considered a null causal effect θ = 0 and a positive causal effect θ =  0.1. To assess the validity of the method for providing appropriate inferences and appropriately-sized confidence intervals with small samples , we simulated datasets with 10 genetic variants that were valid instruments and a sample size of 5000 for the genetic associations with the risk factor, and 5000 for the genetic associations with the outcome. We also repeated the simulation study in Scenarios 1 to 4 with 40 invalid instruments out of 100. We considered several values for the parameters : ; ; ; ; and . All other parameters were the same as in the original simulation study. We performed 1000 simulations for each set of parameters in each scenario.To assess how the contamination mixture method performs with different degrees and directions of confounding, we repeated the simulation study in Scenario 1 with all valid instruments varying the parameters δY is smaller in magnitude). In Scenario 3, estimates are also less biased in this case, as the pleiotropic effects remain constant in magnitude, and so pleiotropic variants can be detected more easily. In Scenario 4, estimates are more biased in this case, as the pleiotropic effects act via the confounder. Additionally in Scenario 4, the direction of bias depends on the direction of confounding. Otherwise, results are no more different between simulations than would be expected by chance alone.Results are shown in Supplementary Tables γj drawn from a normal distribution with mean 0.065 and standard deviation 0.02. Again, we performed 1000 simulations for each set of parameters in each scenario. Results are shown in Supplementary Table We also repeated the simulation study in Scenarios 2–4 with the genetic effects on the risk factor πj0 is the prior probability of being a valid instrument. We take πj0 to be the absolute value of the association of variant j with HDL-cholesterol in standard deviation units. This ensures that variants having greater association with the risk factor receive a higher prior weight. If the prior weights for all variants were equal, then a variant having a weak association with the risk factor and an imprecise association with the outcome that is compatible with multiple values of the causal effect could receive the same posterior weight as a variant having a strong association with the risk factor and a precise association with the outcome that is compatible with a far narrow range of values of the causal effect.The posterior probability of a genetic variant being a valid instrumental variable can be calculated as:ζj parameters here, these are indicator variables and only take the value zero or one. In contrast, the posterior probabilities account for the value of the variant-specific causal estimate, its precision, and the association of the variant with the risk factor. The combination of these factors is useful in determining which variants have strong evidence for inclusion in a particular subgroup.Although we could have used the p < 10−5. We also exclude traits that are major lipid fractions, and filter out duplicates and highly-related traits. For each trait that remains, we calculate the mean posterior probability for variants associated with the trait at p < 10−5.We consider the subgroup of variants corresponding to the maximum of the likelihood function, and use external data on genetic associations with traits in PhenoScanner to find predictors of subgroup membership. As the external data were not used in determining the subgroups, this can provide validation that the subgroup of variants represents a real biological pathway. For each variant, we calculate the posterior probability of being a valid instrument at the causal estimate. To avoid spurious results, we filter the list of traits to include only traits having at least 6 variants associated at https://github.com/jrs95/hyprcoloc). This package performs multi-trait colocalization in a similar way to moloc, the multi-trait extension to coloc52, but in a computationally efficient way that allows colocalization of large numbers of traits to be performed. We investigated colocalization between six traits: HDL-cholesterol, triglycerides, CHD risk, mean corpuscular haemoglobin concentration, platelet distribution width, and red cell distribution width. These blood cell traits were selected as variants associated with these traits have the greatest mean posterior probability of belonging to the largest group of variants identified by the contamination mixture method , and with the uniform priors setting as the default setting can be overly conservative.Multi-trait colocalization was performed using the Hypothesis Prioritization Colocalization (HyPrColoc) package  at posterior probability 0.96. For the two gene regions that did not show evidence of colocalization between these traits, one possible explanation is the presence of multiple causal variants in the region; as the ATXN2 gene region reported colocalization between HDL-cholesterol and CHD risk, and separately between the blood cell traits. For COBLL1, there was colocalization between HDL-cholesterol and the blood cell traits, but not CHD risk.While the exact pattern of colocalization differed between the gene regions, colocalization between HDL-cholesterol, CHD risk, and at least one blood cell trait was observed for 3 of the gene regions using the conservative priors, and for 7 regions using uniform priors (Supplementary Table As this investigation only uses publicly available summarised data on genetic associations with traits and diseases, no specific ethical approval is required.Further information on research design is available in the Peer Review FileSupplementary Information NewDescription of Additional Supplementary FilesSupplementary SoftwareReporting Summary


Genetic parameters play an important role in designing a breeding program. Many software and methods are used to estimate genetic parameters in livestock population. Multi-trait models are efficiently used these days for productive traits, reproductive traits, milk traits, etc. These models are more useful in the case of low heritability trait and with missing phenotypes. In this study, Hanwoo cattle, an indigenous breed from South Korea, is studied for four carcass traits . Single-trait and multi-trait models are constructed using BLUPF90 software to estimate variance components. In addition, the effect of genetic correlations among traits is scrutinized in multi-trait models for these traits.Hanwoo breed is preferred in South Korea because of the high standards in marbling and the palatability of its meat. Numerous studies have been conducted and are ongoing to increase the meat production and quality in this beef population. The aim of this study was to estimate and compare genetic parameters for carcass traits using BLUPF90 software. Four models were constructed, single trait pedigree model (STPM), single-trait genomic model (STGM), multi-trait pedigree model (MTPM), and multi-trait genomic model (MTGM), using the pedigree, phenotype, and genomic information of 7991 Hanwoo cattle. Four carcass traits were evaluated: Back fat thickness (BFT), carcass weight (CWT), eye muscle area (EMA), and marbling score (MS). Heritability estimates of 0.40 and 0.41 for BFT, 0.33 and 0.34 for CWT, 0.36 and 0.37 for EMA, and 0.35 and 0.38 for MS were obtained for the single-trait pedigree model and the multi-trait pedigree model, respectively, in Hanwoo. Further, the genomic model showed more improved results compared to the pedigree model, with heritability of 0.39 (CWT), 0.39 (EMA), and 0.46 (MS), except for 0.39 (BFT), which may be due to random events. Utilization of genomic information in the form of single nucleotide polymorphisms (SNPs) has allowed more capturing of the variance from the traits improving the variance components. Korean beef cattle Hanwoo is one of the four aboriginal breeds among Hanwoo, Chikso, Heugu and Jeju Black. Its farming is streamlined due to high customer demand and competition with other types of meat. Therefore, emphasis is laid on the improvement of carcass traits such as back fat thickness (BFT), carcass weight (CWT), eye muscle area (EMA), and marbling score (MS) to enhance the selection of animals for breeding programs. . UtilizaMany traits are genetically correlated, such as reproductive traits, milk yielding traits, etc., and have different heritabilities when calculated in single-trait and multi-trait models. Multi-trait models can improve the estimations of traits with low-heritability trait or small population size ,8. Many 2). There were no missing phenotypes.Phenotypic data for carcass traits, i.e., back fat thickness (BFT), carcass weight (CWT), eye muscle area (EMA), and marbling score (MS), were collected from 7991 commercial Hanwoo cattle, which were slaughtered at the age of approximately 30 months . All proSingle nucleotide polymorphism (SNP) data comprised 53,866 SNPs from 7991 animals. Tissue samples were genotyped using Illumina Bovine SNP50k. Quality check for the SNP data was done by the PREGSF90 program of BLUPF90. In total, 143 SNPs were removed which had less than 0.90 call rate, 488 SNPs with allele frequency <0.01 were removed, and another 324 monomorphic SNPs were also eliminated. All animals had more than 0.90 call rate and there were no animals removed after using a Hardy–Weinberg equilibrium threshold of 0.15 . Finally, 48,984 SNPs and 7991 animals were left for further analysis.As our data comprised much information therefore, statistical significance of fixed effects needed to be analyzed. This was calculated through the ANOVA package present in R program . Significant effects were used as fixed effects in further analysis. HYM (herd birth year month), slaughter year month, slaughter place, and sex were taken as categorical values, whereas age was taken as a continuous value ,11. ThroBLUPF90, a software that comprises a family of program in Fortran 90/95 for mixed model computations in animal breeding . In this(i) Single-Trait Model.β is the vector of all fixed effects calculated above; α is the vector of random additive genetic effect for each animal in STPM and STGM; r is the vector of random residual; and X and Z are the incidence matrices for each corresponding effect. Variance components comprising additive genetic variance and residual variance can be found in log file generated by software. EBV  and GEBV , along with s.e (standard error), were also predicted.In the single-trait model (ST), genetic parameters were estimated for each single-trait . A comparative study was also done between pedigree and genomic models. Hence, two single-trait animal models were built—one with pedigree and phenotype data (STPM) and the other with pedigree, phenotype, and genomic information (STGM). A linear mixed model of BLUPF90 software was used for single-trait analysis as in Equation (1):(ii) Multi-Trait ModelA multi-trait model (MT) was built considering all the four carcass traits  through BLUPF90 software. A comparative study was done between multi-trait pedigree (MTPM) and multi-trait genomic (MTGM) models. Hence, two multi-trait animal models were built—one with pedigree and phenotype data and the other with pedigree, phenotype, and genomic information. The models and inferences were similar to the pedigree-based models described above, with the exception that this model uses a genomic relationship matrix (G) created from the SNP markers instead of the pedigree-based relationship (A). Following VanRaden , the G mEBVs  were predicted from phenotypic data by both STPM and MTPM. The GEBVs were predicted by the GM using genotype (SNPs) and phenotype data for STGM and MTGM. The variance component comprising genetic variance and residual variance was estimated.Heritability was calculated as in Equation (3):g is the genetic correlation, covg is genetic covariance between trait 1 and trait 2, Vg1 is the genetic variance of trait 1, and Vg2 is genetic variance of trait 2.In actual breeding, many traits that are correlated. Considering correlation among the traits might result in more accurate GEBV, the genetic correlations were calculated based on covariance as in Equation (4):2 for 7991 animals.The descriptive statistics for the carcass traits analyzed in this work are listed in Variance components, i.e., additive genetic variance and residual variance, were estimated for both STPM and STGM. Heritability was calculated from the variance components obtained through STPM. It was 0.40, 0.33, 0.36, and 0.35 for BFT, CWT, EMA, and MS, respectively . There wThe multi-trait (MT) models were constructed considering all four traits together for both PM and for GM. A comparative study was conducted between MTPM and MTGM . A slighThe genetic correlations were calculated by the multi-trait animal model using BLUPF90 software. As correlations always occur between two or more traits, the multi-trait model was used to compute genetic correlation among the four traits. Results obtained for both genetic and phenotypic correlation are shown in Genetic parameters play a significant role in designing a breeding program. Therefore, a study was conducted to evaluate single-trait and multi-trait models and to compare pedigree and genomic models to highlight the significance of using SNPs. Variance components were estimated through the above constructed model. Until now, many methods and software were used to estimate breeding value. One such software is WOMBAT , in whicIn this work, BLUPF90 software was used to construct various models using pedigree, phenotype, and genomic information. Four different models were created and compared for four traits. An increased heritability was estimated by the genomic model (GM) as compared to the pedigree model (PM), i.e., BFT (0.39), CWT (0.39), EMA (0.39), and MS (0.46), for both single-trait and multi-trait models.Genetic correlation is the proportion of variance that two traits share due to genetic causes. It can be positive or negative; a positive genetic correlation helps in improvement of the two traits, whereas a negative correlation implies that selection of one trait can cause deterioration of both traits . It alsoThere was no increase in heritability for any traits from STGM to MTGM. This may be because the heritabilities are not low for the traits, and all traits have full phenotype information available. An increased genetic parameter in the genomic model infers that genomic information, i.e., SNPs, plays a vital role in the prediction of breeding values and estimation of heritability in a population. It is because these SNPs can comprehend Mendelian sampling, i.e., heritability in populations, based on the expected proportion of genes shared between different types of relatives ,18, and Accurate estimation of genetic parameters plays an essential strategic step for breeding programs, which can help in selective breed improvement in a population. Increased heritabilities obtained by MTPM as compared to STPM highlights the significance of correlation. Whereas, increased heritability of the genomic model over the pedigree model infers a significant role of SNPs in breeding. This can be seen through noticeable increased values of heritability and breeding values for marbling score. Genetic parameters estimated through this work can be used for developing future breeding programs involving genomic prediction methods.


ZmPGP1, involved in the polar auxin transport, has been shown to be associated with plant height, leaf angle, yield traits, and root development in maize. To explore natural variation and domestication selection of ZmPGP1, we re-sequenced the ZmPGP1 gene in 349 inbred lines, 68 landraces, and 32 teosintes. Sequence polymorphisms, nucleotide diversity, and neutral tests revealed that ZmPGP1 might be selected during domestication and improvement processes. Marker–trait association analysis in inbred lines identified 11 variants significantly associated with 4 plant architecture and 5 ear traits. SNP1473 was the most significant variant for kernel length and ear grain weight. The frequency of an increased allele T was 40.6% in teosintes, and it was enriched to 60.3% and 89.1% during maize domestication and improvement. This result revealed that ZmPGP1 may be selected in the domestication and improvement process, and significant variants could be used to develop functional markers to improve plant architecture and ear traits in maize. Zea mays L.) is one of the most widely grown and important cereal crops, which plays a critical role in ensuring food security. Maize was domesticated from the wild grass teosinte more than 8700 years ago [Maize  is a complicated quantitative trait and is mainly determined by three yield components: effective ear number, kernel number, and kernel weight . Maize kfea2, fea3, the ramose genes and KRN4 for kernel row number, df3, df8, df9, and br2 for plant height, and td1, bif2, ba1, and tsh4 for tassel morphology [Tb1 has been shown to be associated with maize branching [gt1 confers multiple ears per branch [tga1 was associated with kernel structure [Most plant and ear traits are quantitative traits, which are controlled by a large number of small effect quantitative trait locus (QTLs). Many QTLs related to yield components and plant architecture traits have been identified in several maize linkage populations. A total of 163 QTLs were detected for four ear traits in 10 different RIL populations, accounting for 55.4–82% of phenotypic variation . In the rphology ,19,20,21ranching , the teor branch , and tgatructure . In addiZmPGP1 (ABCB1 or br2) was firstly cloned using a Mu element, the mutant was characterized by compact lower stalk internodes and the plants showed semi-dwarf stalks [ZmPGP1 was an adenosine triphosphate (ATP) binding cassette (ABC) transporter which belonged to the multidrug resistant (MDR) class of P-glycoproteins (PGPs), and functioned as an efflux carrier in polar auxin transport. The protein had two transmembrane domains that provide the translocation pathway of auxin and two cytoplasmic nucleotide-binding domains that hydrolyse ATP and drive the transport reaction [ZmPGP1 have been shown to be associated with plant height, ear height, leaf angle, ear length, yield traits, and root development under aluminum stress [ZmPGP1 have also been identified, the sequence polymorphism and natural variations of the gene have not been investigated. It is also unclear whether ZmPGP1 exists as a signal of selection during maize domestication and improvement. In the present study, we re-sequenced ZmPGP1 in 349 inbred lines, 68 landraces, and 32 teosintes, and aimed to: (1) examine the ZmPGP1 nucleotide diversity between maize inbred lines, landraces, and teosintes, (2) identify natural variations in candidate genes associated with grain yield and plant architecture traits, and (3) examine the significant associations for their involvement in maize domestication and improvement.Indole-3-acetic acid (IAA), an active form of auxin, is a key regulator of plant growth and development. f stalks . ZmPGP1 reaction ,26. Diffm stress ,29,30,31A total of 349 inbred lines, 68 landraces, and 32 wild relatives were selected in this study . After hZmPGP1 gene were sequenced by BGI (Beijing Genomics Institute) Life Tech Co. China using targeted sequence capture technology on the NimbleGen platform [ZmPGP1 (GRMZM2G315375) of the B73 inbred line was used as a reference for target sequence capture.A modified cetyl trimethylammonium bromide (CTAB) method was used to exact genomic DNA from young leaves of each line at the seedling stage. The sequences of the platform . The genZmPGP1 gene was performed using MAFFT software and was further edited manually [Multiple sequence alignment of the maize manually . Using Dmanually , we analmanually , Fu and manually  statistiZmPGP1-based markers with minor allele frequency (MAF) ≥0.05 were selected for association analysis in 349 inbred lines, and the p value threshold was set at 2.00 × 10−3 (0.5/499).Genotyping-by-sequencing (GBS) was used to identify the genotypes of 349 inbred lines . A totalZmPGP1 sequence alignment of 349 inbred lines, 68 landraces, and 32 teosintes spanned 9710 bp, which covered a 1762 bp upstream region, a 182 bp 5′UTR region, a 6821 bp coding region containing five exons and four introns, a 400 bp 3′UTR region, and a 545 bp downstream region  and 5′UTR (14 bp). The overall nucleotide diversity (π) of the ZmPGP1 locus was 0.007. Among five regions of the ZmPGP1, and when the coding regions were less diverse than other regions (0.006), the downstream and 3′UTR showed high nucleotide diversity .The m region . SequencZmPGP1 in inbred lines, landrace, and teosinte, the sequence conservation (C) and nucleotide diversity (π) were analyzed and compared. For all test lines, the values of C and π × 1000 were 0.793 and 7.110, respectively  and lower diversity . The highest divergence between inbred lines and teosintes was observed in the upstream and downstream regions  ≥0.05 in 349 inbred lines. Three mixed linear models (MLM), MLM + K, MLM + Q + K, and MLM + PCA + K, were employed to perform marker-traits association analysis. Comparing the Quantile-Quantile (QQ) plots generated for these models, we selected MLM + PCA + K to minimize both false positives and false negatives a.ZmPGP1-based markers, the P-value thresholds were set at 0.001 (0.5/499). A total of 24 significant marker–trait associations involved 15 variants (12 SNPs and 3 InDels) were identified for 9 traits using the MLM + PCA + K model (p = 9.34 × 10−7), explained the most phenotypic variation, up to 6.93%. In addition, 4 pleiotropic sites, including SNP1473, SNP1708, SNP7213, and InDel3387, were significantly associated with ED, EGW, KL, EGW, LA, and RDW  with each other in inbred lines. After the clumping of variants, 11 significant sites were identified. Six major haplotypes which contained more than 10 lines emerged from the 11 significant sites across inbred lines, and a significant phenotypic difference was observed between haplotypes in 8 traits, except for TMAL (p = 6 × 10−10) between haplotypes. Hap1, carrying all increased alleles, had the longest kernel length, followed by Hap2, which included the majority of tested inbred lines. Hap3, carrying all decreased alleles, had the shortest kernel length. SNP1473 was the most significant sites, the allele T group had a significantly longer KL than the allele C group . The SNP at site 1473 also had the most significant association with EGW. Three variants were identified for HKW that divided the inbred lines into four groups (p = 8.3 × 10−9). The most significant site was SNP-769, and the frequency of the increased allele, SNP-769T, increased from 8.3% in teosintes to 33.3% in inbred lines. Five SNPs with high LD (r2 > 0.95) were significantly associated with PH. The plant height in the inbred lines carrying allele SNP453G was higher than those containing the C allele (Linkage disequilibrium (LD) analysis found that SNP438, SNP453, SNP555, SNP628 and SNP706 showed strong LD . Plant hormones, such as auxins, play a key role in plant growth, development, defenses, and stress tolerance [ZmPGP1 with high sequencing depth (more than 100×), which could help us to identify the selection signals with larger effective and high accurate.The process of maize domestication and improvement has been studied with population genetics–genomics , QTL mapolerance . A previolerance . We founolerance ,43. Manyolerance ,45. In tZmPGP1 (ABCB1 or br2), involved in auxin polar transport, has been shown to be associated with plant height, stalk diameter, leaf length and leaf angle [ZmPGP1 [ZmPGP1 have also been identified [ZmPGP1 has good potential to reshape plant architecture without the loss of yield in maize breeding. Candidate gene association analysis can identify the elite variation and the best haplotype for target traits. The elite variations of more than 30 genes involved in flowering time, kernel composition, drought tolerance, and root development were detected by candidate gene association analysis [crtRB1 was proved to be associated with β carotene concentration and conversion in maize kernels, and the most favorable alleles were developed to inexpensive markers to use for crop provitamin A biofortification [ZmPGP1, 1070 variations were detected from 9710 bp re-sequenced genomic region of ZmPGP1. In total, 11 variants were identified for 5 yield-related traits and 4 plant architecture (KRN4, which is likely responsible for increased kernel row number in maize [ZmPGP1 gene in 349 inbred lines, 68 landraces, and 32 teosintes, sequence polymorphisms, nucleotide diversity and neutral tests revealed that ZmPGP1 might be selected during domestication and improvement processes. A total of 11 variants significantly associated with 4 plant architecture and 5 ear traits were identified by marker–trait association analysis in inbred lines. The significant variants could be used to develop new markers to improve plant architecture and ear traits in maize.Plant architecture and kernel and ear traits, the key factors affecting grain yield, were the main traits targeted of maize breeding. The identification of the natural variations in these traits could help to improve the efficiency of breeding selection. Although hundreds of QTLs related to these traits have been identified ,11, few af angle . Three M [ZmPGP1 . These m [ZmPGP1 . Naturalentified ,29,30,31entified . A new 2entified . The resanalysis . For exafication . In thisitecture ; Table 2itecture . The selin maize . In conc