The objectives of this study were to estimate genetic parameters and to perform a genome‐wide association study (GWAS) for predicted methane‐related traits in Japanese Black steers. The methane production and yield traits were predicted using on‐farm measurable traits, such as dry matter intake and average daily gain. A total of 4,578 Japanese Black steers, which were progenies of 362 sires genotyped with imputed 551,995 single nucleotide polymorphisms (SNPs), had phenotypes of predicted methane‐related traits during the total fattening period (52 weeks). For the estimation of genetic parameters, the estimated heritabilities were moderate (ranged from 0.57 to 0.60). In addition, the estimated genetic correlations of methane production traits with most of carcass traits and feed‐efficiency traits were unfavorable, but those of methane yield traits were favorable or low. For the GWAS, no genome‐wide significant SNP was detected, but a total of four quantitative trait locus (QTL) regions that explained more than 5.0% of genetic variance were localized on the genome, and some candidate genes associated with growth and feed‐efficiency traits were located on the regions. Our results suggest that the predicted methane‐related traits are heritable and some QTL regions for the traits are localized on the genome in Japanese Black steers. The descriptive statistics of carcass traits were the same as those described by Takeda et al. (The feed conversion ratio (FCR), residual feed intake (RFI), residual BW gain (RG), and residual intake and BW gain (RIG) based on DMI were regarded as feed‐efficiency traits and were calculated by the method of Koch, Swiger, Chambers, and Gregory  and Takea et al. , and thohttp://ftp.ensembl.org/pub/release‐97/variation/vcf/bos_taurus/). After quality control by excluding SNPs with a minor allele frequency of <0.01, a call rate <0.95, and Hardy‐Weinberg equilibrium test with a p value <.001, a total of 551,995 SNPs on autosomal chromosomes was used in this study.A complete description of the genotypic data was previously reported by Takeda et al. . Briefly2.24, CH4 per DMI (CH4/DMI), and methane conversion factor (MCF), which was the percentage of feed energy converted to methane and was calculated by CH4 divided by GEI, were calculated in this study. BW, DG, DMI, TDN, and Rrate were used as independent variables to predict CH4, CH4/DMI, and MCF using the following prediction equations, as shown by Uemoto et al. , which has been adopted in the Japanese national evaluation  and linear covariate age at the beginning of the test; u and e are the vectors of random effects. The ASReml 4.1 software , and I is an identity matrix. The estimated heritabilities of carcass traits were the same as those described by Takeda et al. variance matrix and R is the residual (co)variance matrix.For the relationship among predicted methane‐related traits, carcass traits, and feed‐efficiency traits, the genetic and residual correlations were estimated by a two‐trait animal model based on the model above. 2.4y, X, Z, b, and e are the same as described above. a is the vector of a random effect due to GEBV with a∼N0,Hσa2, where σa2 is the additive genetic variance accounted for by SNP information, and H is a matrix that combines pedigree and genomic information ; W is a matrix related to genotypes; and the element of W is wij=xij-2pj, where xij is the number of the second allele of the i‐th animal at the j‐th SNP. The variance components and the genome‐based heritabilities σa2/σa2+σe2 were estimated, and the estimated variance components were then used to predict the GEBV.The GWAS for predicted methane‐related traits was performed. The single‐step GWAS (ssGWAS) approach  was calculated using the following equation:a^g is a vector of the GEBV of genotyped animals. The refinement of SNP weights through two iterations was performed to estimate the SNP effect, as described by Wang et al. (r2 = 0.2) in this population .Next, the estimate of the SNP effect  was calculated as follows:sd is the standard deviation. The single run of the ssGWAS, which had no iterations for SNP weight refinement, was performed in this analysis as previously suggested .The significant test for SNP effects using the ssGWAS  was higher than that of CH4 . The pedigree‐based genetic variances, residual variances, and heritabilities for predicted methane‐related traits were estimated and are presented in Table 4, and CH4S) and between the two traits (CH4/DMI and MCF) were both positive, and the correlations between the three and two traits were negative.Descriptive statistics of predicted methane‐related traits are shown in Table 4S, and CH4 were unfavorably positive, and those with CH4/DMI and MCF were favorably negative. The estimated genetic correlations of predicted methane‐related traits with DG were similar to those with CW. Regarding feed‐efficiency traits, the estimated genetic correlations of DMI, CH4S, and CH4 with RFI were favorably moderate (0.52–0.57), those with RIG was favorably low (−0.24 to −0.21), and those with FCR and RG were unfavorably low . The estimated genetic correlations of CH4/DMI and MCF with FCR and RG were favorably moderate , those with RFI was unfavorably low (−0.27), and those with RIG was very low (about −0.10).The estimated genetic correlations of predicted methane‐related traits with carcass traits, DG, and feed‐efficiency traits are shown in Table 3.24S, and CH4 exhibited similar trends, and the QTL regions with genetic variance (%)>5.0 were detected on BTA 5 and 14. The QTL region on BTA 14 (21.4–23.7 Mbp) had the highest genetic variance for all three traits (approximately 10.0%). The results of CH4/DMI and MCF exhibited similar trends, and the QTL regions with genetic variance (%)>5.0 were detected on BTA 3 and 8. The QTL region on BTA 8 (88.5–91.1 Mbp) had the highest genetic variance (more than 20.0%). Next, the genome‐wide significance test was performed for predicted methane‐related traits, and p values for the ssGWAS were shown in Figure The estimated genome‐based heritabilities are shown in Table 44.14 from cattle is a heritable and a repeatable trait, and the heritability and repeatability estimates for CH4 were not very different among studies when a short‐term dataset is used  was less than that of CH4 and was variable among studies, when a short‐term dataset was used . In dairy cattle, the estimated heritabilities for CH4 and CH4 per milk production were low (0.21) for a short‐term dataset  during milking over the long‐term (5 consecutive months). Thus, the heritability of methane‐related traits, especially methane yield traits, such as CH4/DMI and MCF, could be underestimated in beef cattle, if a short‐term dataset is used. However, there have been no studies for heritability of methane‐related traits estimated using long‐term dataset in beef cattle. Here, we performed heritability estimation for predicted methane‐related traits using long‐term datasets (52 weeks). Our results showed that the larger heritabilities of predicted methane‐related traits could be estimated in beef cattle using a long‐term dataset, when the methane‐related traits were evaluated by the prediction equations. Some of the non‐genetic effects were considered because of health conditions at the time, the amount of ingested feed before the measurement, time points along the growth curve, and further studies were needed to unveil the reasons.The CH4 in beef cattle without reducing beef cattle productivity. Donoghue et al.  without those for RFI. Those of CH4/DMI and MCF were favorably moderate to high or low . These genetic correlations displayed similar trends as those described by Donoghue et al.  for CH4/DMI. Using estimates of SNP effects or explained genetic variance was useful in increasing the accuracy of GEBV by allowing unequal SNP variance in the ssGBLUP approach  gene, which is one of the candidate genes for CW in Japanese Black cattle  and two traits (CH4/DMI and MCF). The QTL region on BTA 14 had the highest genetic variance in DMI, CH4S, and CH4, and the PLAG1 gene was the best candidate gene in the QTL region. PLAG1 regulates several growth factors, and the variants of the PLAG1 gene are strongly associated with cattle stature and growth traits  gene was the best candidate gene in the QTL region. SHC3 is a signal transduction protein involved in recognition of phosphorylated tyrosine, and the SHC3 gene is suggested to be a potential QTL for RFI by GWAS  gene was located. There has been no report on the direct association between the SH3BP4 gene with not only CH4 but also growth and feed‐efficiency traits. The variants on the SH3BP4 gene were associated with the sensitivity of beef cattle to environmental variation (Carvalheiro et al., In this study, a total of four QTL regions that explained more than 5.0% of genetic variance in any one of the traits was detected, and some candidate genes were located on the QTL regions. In addition, the distribution of QTL regions was different between three traits (DMI, CHn Figure . The QTL4.34 correctly, but high costs and logistical efforts make it difficult to measure over a long period with a large number of cattle. Actually, only a few studies have estimated genetic parameters (Donoghue et al., 4 in beef cattle, and no such studies have been reported in dairy cattle. Methane‐related traits strongly depend on DMI, because the variation in DMI accounted for 52%–64% of the variation in CH4 (Knapp et al., 4 obtained by open circuit respiration chambers was mainly dependent on DMI and BW in beef cattle. Thus, the methane‐related traits were predicted using the prediction equations that use these traits as independent variables in our study.The use of open circuit respiration chambers is the “gold standard” method to measure CH4 in this study. The prediction equation by Shibata et al. (4 on DMI. The prediction equation by Uemoto et al. (4 strongly depends not only on the quantity of feed intake but also on the composition of the diet (de Haas et al., 4 by Shibata et al. (4 (Moss et al., We applied two prediction equations developed by Shibata et al.  and Uemoa et al.  is highlo et al.  can accoa et al.  was over4S showed higher predictive values than CH4, which is the same trend as described by Uemoto et al. (4S is likely to be overestimated. However, the estimated genetic correlations among DMI, CH4S, and CH4 were very close to 1.0, and the distribution of QTL regions showed very similar trends among these traits in our study. The results of genetic parameter and GWAS were similar to those of Manzanilla‐Pech et al. (4 was mainly dependent on DMI and BW. These results suggested that the genetic background of these traits had a close relationship with each other. In addition, the difference in the prediction equations for CH4 had no large effect on the genetic and genomic analyses, if DMI was used as an independent variable in a prediction equation.In this study, CHo et al. . Actuallh et al. , who con4 predicted by DMI, milk yield and maintenance traits (de Haas et al., 4 itself in beef cattle, one of the most important indicators is the residual CH4, which is a measure of the actual minus predicted CH4 with a concept similar to that of RFI (Donoghue et al., 4, the actual values of CH4 are required. Thus, it is necessary to develop low‐cost on‐farm measuring methods, such as spot breath samples similar to the sniffer method (Hammond et al., 4 contained in spot breath samples have been reported in dairy cattle (Breider et al., 4 over a long period at a low cost in beef cattle.Many studies have estimated genetic parameters and performed GWAS for CH54S, and CH4 with most of the carcass traits and feed‐efficiency traits were unfavorable, but those of CH4/DMI and MCF were favorably moderate to high or low. For the GWAS, no genome‐wide significant SNP was detected, but the QTL regions with low to moderate genetic variance were localized to several regions with some candidate genes on the genome. Our results showed that predicted methane‐related traits were heritable and the information regarding the genetic parameter estimates and QTL regions could be useful in the genetic improvement for predicted methane‐related traits in beef cattle. A breeding strategy such as a combination of methane‐related traits, carcass traits, and feed‐efficiency traits will be important to increase cattle productivity and reduce greenhouse gases in beef cattle.In this study, we estimated genetic parameters and performed a GWAS for predicted methane‐related traits measured over the long‐term fattening period in Japanese Black steers to clarify and better understand the genetic architecture of predicted methane‐related traits. For genetic parameter estimation, the moderate heritabilities of predicted methane‐related traits were estimated. In addition, the estimated genetic correlations of DMI, CHThe authors declare that they have no competing interests.Fig S1Click here for additional data file.Table S1Click here for additional data file.Table S2Click here for additional data file.


The growing sample size of genome-wide association studies has facilitated the discovery of gene-environment interactions (GxE). Here we propose a maximum likelihood method to estimate the contribution of GxE to continuous traits taking into account all interacting environmental variables, without the need to measure any. Extensive simulations demonstrate that our method provides unbiased interaction estimates and excellent coverage. We also offer strategies to distinguish specific GxE from general scale effects. Applying our method to 32 traits in the UK Biobank reveals that while the genetic risk score (GRS) of 376 variants explains 5.2% of body mass index (BMI) variance, GRSxE explains an additional 1.9%. Nevertheless, this interaction holds for any variable with identical correlation to BMI as the GRS, hence may not be GRS-specific. Still, we observe that the global contribution of specific GRSxE to complex traits is substantial for nine obesity-related measures (including leg impedance and trunk fat-free mass). Most gene-by-environment interaction methods rely on the availability of the interacting environment. Here, the authors propose a robust maximum likelihood method for estimating the overall statistical interaction between a genetic risk score for a continuous outcome and all environmental variables. While dozens or even hundreds of SNPs have been found to be associated with each trait, the effect contributed by each individual marker is typically very small2. In addition to their marginal effects, many genetic factors are suspected to alter susceptibility to the effects of environmental factors on the trait. The detection of these gene–environment (G x E) interactions has become possible with the large sample sizes of current GWAS, and many methods have been proposed to achieve this. However, most of these methods assume that the genetic marker(s) and the interacting environmental factor have been measured without noise, and often require that the outcome and/or environment be binary. While model misspecification may have a more limited impact in single SNP-association analysis, this can result in biased estimation of the interaction term in GxE analysis3. For example, testing a noisy or dichotomised version of a continuous environmental variable can bias the estimation in an arbitrary direction, depending on the dichotomisation threshold4. Observing the outcome variable on a transformed scale  is also liable to introduce bias in any direction and magnitude.Genome-wide association studies (GWAS) have been instrumental in the discovery of tens of thousands of genetic variants  associated with complex traits and diseases5 including a filtering first step based on either the marginal SNP–trait association7, SNP–environment association8, a mixture of the two (cocktail method)9 or their combination10. Mixed effect models have been proposed to evaluate the differences in heritability in subgroups based on environmental exposure11. All these methods, however, require that the environment be measured (accurately), whereas in most studies only some of the relevant environmental variables are reported. Furthermore, many potentially crucial factors may be difficult to define precisely or measure accurately, such as physical activity, accessibility of fast food, sleep and diet which are all key factors in obesity and are suspected to interact with genetic risk. Even in cases where a potentially relevant factor has been measured accurately, it is impossible to determine whether any detected interaction is due to the tested variable or one of its correlates. For example, many environmental factors have been shown to interact with the genetic risk score for body mass index (BMI)12, such as physical activity13, alcohol consumption14, socio-economic status (as measured by the Townsend deprivation index)15, sugary drink consumption16, certain types of diet17, etc. Many of these environmental variables are correlated with one another, and little is known about how these interactions relate to each other14.More advanced methods adapt a two-step procedure20. This has the advantage of accounting for all interacting environmental variables, without requiring their observation. However, these methods were not designed to assess the extent of the interaction strength, and are mostly restricted to single SNP analysis. In addition, these studies do not seek to account for general scale effects that are not specific to the genetic markers. Due to their low statistical power, variance tests have rather been used to improve power of classical G × E tests where the environment is measured and testable21. Others also proposed variance component analysis22, assuming that the environment is emerging as cumulative effect of multiple observed molecular phenotypes, which is less feasible for complex human traits and the method is not scalable to hundreds of thousands of samples.Another approach which has been proposed is to detect G × E interaction based on differences in variance across genotype groupshttps://github.com/zkutalik/GRSxE_software).In this work, we propose a method to establish statistical interaction between a genetic risk score (GRS) for a continuous outcome and all environmental variables. Furthermore, this method quantifies the total contribution of G × E to the trait variance beyond that of the GRS alone. The structure of the paper is as follows: first, we set up the normal linear interaction model and derive how to quantify the total G × E contribution. Next, we demonstrate through extensive simulations that any violations of the model assumptions  do not introduce noticeable bias in the interaction parameter estimation. Further, we show that our bootstrap procedure produces close to nominal coverage probability of the produced confidence intervals regardless of the noise distribution. In addition, we propose an approach to determine whether the observed variance inflation is specific to the tested GRS or simply due to general heteroscedasticity. Finally, we apply our method to the GRSs of 32 continuous complex traits from the UK Biobank to reveal the contribution of G × E to their variability. The code implementing the algorithm is available in R and Matlab .Our proposed method (see “Methods” for details) calculates the overall contribution of G × E interaction between a fixed genetic factor  and all of its interaction partners, which do not need to be measured in the study. We treat the environment as a random effect and integrate it out, hence we require only data on the outcome and the genetic factor. Even without observing E, G × E will result in differences in trait variance across the different GRS groups. The rate of change of the outcome variance allows us to infer the underlying G × E contribution to the outcome. We first explored the performance of our method through extensive set of simulations. In summary, most violations of our model assumptions do not lead to bias or incorrect coverage of the 95% confidence interval  on the estimation bias. For this set of analyses, we fixed other parameters  = t) and varied only these two (E[e3] and E[e4]) in the simulations. We also explored the effect of skewness and kurtosis of the residual noise (ϵ) on the estimation bias in the same way but setting E[ϵ3] and E[ϵ4]. We ran simulations for all 21 possible (skewness2 + 1 < kurtosis) pairs of skewness  and kurtosis  of the environmental or noise variables and for each setting we repeated the simulation 100 times. Our results confirm that already at relatively low sample size , the central limit theorem ensures unbiased results for all explored non-normal distributions for both the environmental variable and the noise .First, we explored the effect of skewness and kurtosis of the environmental variable (entclass1pt{miniman = 1000), the coverage probability may deviate slightly from the nominal 95% for high kurtosis  using power transformations (f(t) = tp) with different exponents . As described in the “Methods”, we also generated a fake GRS (fGRS) as a control to see how specific the observed GRS interaction is and to what extent it is due to scale/transformation effect. Results show , but they are significantly different from those obtained from the fGRS analysis. These results indicate that—in the case of transformed outcome and Gaussian noise—comparing interaction effect estimates coming from data with true vs counterfeit GRS can clearly distinguish null vs non-null interaction effects in most tested outcome transformation scenarios. However, more extreme transformations (f(t) = t3, see Supplementary Fig. E (or ϵ) is similar to the skewness/kurtosis of a Gaussian random variable upon applying the scale transformation function (f(t)), INQT of the outcome before applying our method can reduce type I error rate and increases power. For example when E (or ϵ) has positive skewness and f(t) is convex , INQT is beneficial, because the transformation that renders the outcome normally distributed reasonably agrees with the inverse of the scale transformation (f−1). On the other hand when positive skewness is combined with a concave transformation  but a true interaction effect exists for the GRS, the interaction estimate for the GRS imitation will be non-zero  or the environmental variable (E). By simulations, we have shown  transforms the outcome to have quantiles identical to that of a Gaussian distribution, while preserving the original ranks. For marginal effect inference, since SNP effects are tiny, INQT has been useful to ensure the normality of the residuals and the resulting test statistics. This however, is not necessary when the sample size is in excess of 10,000 samples unless the minor allele frequency is very lowY∣G), thus our recommendation is conservative.In the light of the extensive simulation and empirical results, we can formulate the following recommendation for analysis. In case we lack evidence for (significantly) non-zero interaction effect estimate n = 10,000–100,000). The simulation experiment showed that studies with sample size of n = 20,000 are well-powered (>80% power at P < 10−3) to detect interaction effects (γ2) of at least 2% and applying it to (currently considered as) large studies n = 100,000 we can detect effects as low as 0.005 . We have also observed that our approach is more powerful than the BF test for any bin choice  test used in most recent vQTL applicationsP-value thresholds (P < 10−3) using the estimated GRSs yields unbiased interaction effect estimates and inclusive GRSs  lead to conservative estimates. For this reason in all other simulation in this paper, we assume the GRS to be known, since it gives indistinguishable estimates for γ from those where the GRS is estimated from the data. Also, these calculations confirm that although our GRSs for traits in the UK biobank were estimated from the same data, given the stringent P-value threshold (5 × 10−8), the G x E estimates are not affected by the fact that the GRS coefficients are slightly overestimated.Our results showed . We used the first set to select 110 SNPs associated with BMI at (strictly) genome-wide significant level (P < 10−8) and estimated a GRS using within-sample effect size estimates (GRS1) and a second GRS (GRS2) using out-of-sample effect size estimates from the second subset. We then applied our method to the first data set using both definitions of GRSs and obtained that the interaction estimates were not significantly different . Due to this fact, we only used traits for which the GRS (built from genome-wide significant independent SNPs) explained at least 2% of the respective trait variance. We declared a trait to have significant GRS × E contribution if the interaction effect estimate could be rejected to be zero with a P-value  < 1.5 × 10−3(= 0.05∕32). To be conservative, when >10% of the bootstrap estimates ended up on the boundary  = 0), the trait was not analysed further. Such situations may emerge when there is no interaction effect, hence β cannot be estimated or the likelihood surface was difficult to navigate. The estimates ), the interaction is not specific to the GRS and any similarly correlated variable would exhibit comparable interaction effect (Y) confirmed that such apparent interaction estimate could be obtained from a transformed version of an interaction-free trait estimated the global uncorrected G × E contribution . The estimates for the marginal effect Y-based sensitivity analysis. The strongest difference was observed for leg impedance where fGRS shows negative interaction (P < 10−175)) in sharp contrast to the actual GRS, which shows a positive and significant interaction (P < 1.4 × 10−7)). The result is a consequence of a very different mean–variance relationship for the true GRS and the fake GRS as shown in Fig. Y sensitivity analysis showed that the observed data could result from an interaction-free trait with leptokurtic noise transformed by a tail-expanding function, producing similar parameter estimates Y approach pointed to a non-Gaussian noise in the underlying trait, violating the assumption of the fake GRS-based sensitivity analysis.While for the majority (59%) of the 22 traits the interaction effect of the GRS was not specific, 9 traits yielded significant difference between the interaction estimate and that for a counterfeit GRS (see Table P < 10−52)), however, the counterfeit GRS reveals a significantly (P = 1.3 × 10−15) stronger interaction effect (P < 10−300)). This indicates that the observed heteroscedasticity is due to the observed trait being a result of a convex transformation and on the untransformed scale the GRS would have a negative interaction. Forced vital capacity (FVC) and both arm and trunk predicted mass show a similar pattern, whereby the fGRS yields close to double-sized interaction effect as the true GRS. The robustness of these findings is corroborated by the fake-Y sensitivity analysis, which showed that such data could not be produced as a transformed version of an interaction-free trait, as such traits would result in discordant β or γ estimates.For trunk fat-free mass, the GRS shows pronounced interaction effect , but upon correction for overall heteroscedasticity the correlation was substantially reduced (P < 0.05∕376)  and the combination of all possible continuous environmental variables. Our method is designed for a continuous outcome, but it can be extended to binary traits  our method is well-powered to detect GRS × E contribution even as low as 0.5%, but this is still 2.5 times larger than the largest detected interaction for an FTO variant and alcohol consumption frequency14. Therefore, even in such large data sets, our method is underpowered to detect interaction between an environmental factor and individual SNPs. Its primary use is therefore for GRS × E interaction, which does implicitly assume that SNP × E interaction effect sizes are proportional to the marginal effect of the SNPs, and only captures the contribution of an environmental variable interacting with many SNPs of the GRS. Others have explored evidence for trait variability at the single SNP level, but found very little evidence for it19. They also attempted to account for inherent mean–variance relationship of heteroscedastic traits (such as BMI), although their approach assumed that the majority of SNP should show no real interaction effect and the function of the mean–variance relationship was very simplistic, which may not be accurate for SNPs (like the one near FTO) with larger effects. Our approach to control for transformation-induced heteroscedasticity instead tested for the interaction effect expected for an artificial GRS with similar correlation with the outcome as the true GRS.We have shown that our approach—despite its derivation relying on the normality of both the environmental factor and residual noise—provides unbiased estimates and accurate coverage probabilities of the 95% confidence interval for a wide range of environmental and noise distributions. In addition, we can also estimate the explained variance of the global interaction partner. Furthermore, our power analysis found that in modern biobank-sized studies 25. We, however, used a specific model  variance QTL analysis was performed for 13 traits in the UK biobank and found several associations using the Levene testf(t)) can be attenuated, masked or even reversed by the positive skew of the noise, hence the INQT function becomes very different from f−1. We have also shown that when the trait is not transformed and true interaction exists, INQT can introduce bias in arbitrary direction, depending on the skewness of E and ϵ  and hence may distort the G × E estimation even further.For main effect GWAS, the outcome is often inverse normal quantile transformed . We believe that this is not necessarily the right approach for G × E interaction analysis, as such transformation will also introduce bias . Our simulation studies confirmed  was tested, the interaction effect was double of the one obtained for the corresponding fake GRS. In general, if any two variables that are correlated with an outcome also show an interaction effect, we suspect that it is due to the trait being observed on a transformed scale, and hence an observed interaction effect may not be specific. Instead of trying to guess the underlying transformation, we rather estimate how much interaction effect is attributed to a non-specific correlate of the outcome, mimicking the original risk factor. However, published G × E studies do not correct for this phenomenon. Note that our reported uncorrected total GRS × E contributions are typically much larger than any of the previously reported ones using specific environmental factors. In the UK Biobank, alcohol intake frequency—GRS interaction explained 0.19% of the BMI, representing less than the tenth of the global uncorrected G × E contribution of 1.93% estimated by our method.Applying our method to complex traits from the UK Biobank revealed that modelling untransformed BMI would point to substantial GRS × E contribution (increasing the 5% explained variance of the GRS by 2%), however this contribution is not specific to the GRS, any variable with comparable effect on BMI would yield very similar interaction effect. In line with this claim, log(BMI) or INQT(BMI) show no interaction effect. Note, however, that this observation is specific to the GRS and when a more inclusive GRS  distribution. Both excess skew of ϵ and convex trait transformation can lead to positive interaction estimate for the fGRS. While the latter situation equally biases the interaction estimate of both the real GRS  the interaction effect estimate  for this range of selection strength30. Finally, our tool is not designed to pick up interaction with non-continuous E, e.g., a G-sex interaction, which may be the most important contributor for WHR.As any method, ours has its own limitations. It requires access to the individual-level genetic and phenotypic data to be able to estimate the G × E contribution to a trait. Fitting a likelihood function can be time consuming, but even for UK Biobank-scale data it takes only a few seconds on four CPUs and a further 10 min to perform the 100 bootstraps. The proposed method assumes that any outcome heteroscedasticity  is driven by G × E interaction, although it could be due to variance controlling genetic effectsThe proposed method could be used as a tool to establish the contribution of G × E to different traits and subsequently prioritise those with substantial global interaction effect for follow-up G × E analysis with specific environmental factors. Such traits may show particular potential for public health interventions, where the genetic predisposition could be modified the most by lifestyle changes.18. These methods, like ours, do not need to observe the interacting environment, as they treat the environment as a nuisance variable and integrate it out. This results in loss of statistical power, as we only look at the consequence of such interaction in terms of the change in the outcome distribution as a function of the GRS value. The presence of G × E would lead to a different distribution of the outcome  in higher genetic risk groups, which is captured by the fitted likelihood function. Our maximum likelihood approach does not require any arbitrary grouping of the population into subgroups according to their genetic predisposition and the interaction effect size is directly estimated.In the past, methods have been proposed to detect G × E based on variance heterogeneity of the outcome in different genotype groupsn individual and g) on the outcome (gene–environment interaction) and to quantify the extent of this modification. Here, we are particularly interested in an abstract environmental variable  that modifies the genetic predisposition of a complex trait (y). The corresponding capital letters represent the random variables. We assume that the true underlying model is as followsY, G and y0 refers to the constant intercept. We allow for G being correlated . The model can then be rewritten asϵ is assumed to be normally distributed with zero mean. Note that due to the properties of G, E and Y, all terms on the right hand side have zero mean, except G-independent environmental effect and G and the G-independent environment. Note that we cannot distinguish between an interaction model with pure linear G term with correlated G–E  asE and ϵ are normally distributed, i.e., Pr(E = e) = ϕ(e) and Pr(ϵ = e) = ϕ(e), where ϕ( ⋅ ) is the probability density function of the standard normal distribution. Therefore, the integral simplifies toθ = {α1, α2, β, γ}, μθ,g = α1 ⋅ g + α2 ⋅ (g2 − 1) and Y, G)) can be written asϵ) ≥ 0. Covariates,  can be incorporated into the model by modifying μθ,g to α1 ⋅ g + α2 ⋅ (g2 − 1) + C ⋅  c, where C is the matrix with all the covariates listed as columns and c is the coefficient vector that will be estimated in the ML procedure.We can write the density function of (ϵ) = 0  the analysed trait was discarded to be on the safe side. To reduce computational time when testing large number of single SNPs (instead of one GRS), one can compute the Fisher information matrix to obtain standard error for the interaction estimates and use bootstrapping only for SNPs showing the most evidence for interaction. Note that when γ = 0, parameter β cancels out in the formula and hence not identifiable. For this reason, likelihood ratio test is not ideal to derive confidence interval for When the error term substantially deviates from normal distribution (the deviation limit depending on sample size), the variance of the parameter estimates (ion (Eq. ), e.g., y = f(z), g} with the model Z = α1G + α2(G2 − 1) + βE + γ(G × E) + ϵ. Such a transformation may induce general heteroscedasticity, which translates to mean–variance relationship that is not specific to any predictor of Y. In Supplementary Note It is possible that the linear interaction model does not describe the observed outcome, but only a transformed version of it, i.e., our observed data is {G  by simuentclass1pt{minimaG, we use the data  to estimate E[η ⋅ Y] = E[η ⋅ Y2] = 0. Let us define μi= E[Yi] for i = 1, 2, …, 5 with μ1 = 0 and μ2 = 1. These can be estimated from the data as Y were normally distributed, μ3 = μ5 = 0 and μ4 = 3. To find a0, a1, a2 that satisfies a0 = −a2, the second yields a1 = b1 − a2μ3. Therefore, knowing a2 directly yields a0, a1 and τ. Plugging these into the last equation givesa2 and hence its solution isμis and bis from the data, we can obtain ais and τ2, which can be used to simulate many counterfeit y, g) to the distribution of G represents a GRS with only a few SNPs, its distribution is not Gaussian and hence G do not come from the same distribution. This can be solved by using a permuted version of G multiplied by τ to generate η. The comparison was done using the test statistic ϵ is not Gaussian, g, i.e., the counterfeit G can show apparent interaction, which is not due to a potential transformation, but to the non-normality of ϵ.To create a fake G variable, another option is simulate a counterfeit Y, while explicitly modelling the trait transformation. In particular, we will generate an underlying trait f( ⋅ ), such that for trait y⋆, defined as f(z), the following hold: (i) y⋆ ~ α1g + α2(g2 − 1); (ii) the distribution of y⋆ matches that of y; (iii) applying our MLE method to  yields estimates for α, β, γ as similar as possible to the ones obtained for . Note that it is relatively easy to find parameters to fulfil the first two criteria, but the third is more difficult to satisfy. To simplify computation, in the following we ignored the α2(g2 − 1) term, as for most traits α2 = 0.Alternative approach: Instead of simulating a counterfeit y⋆, we first simulated a large number of error variables, ϵ, with 93 different combinations of skewness  and kurtosis  and 51 different α1 − 0.25, α1 − 0.24, …, α1 + 0.24, α1 + 0.25). Next, we generated 100 instances of f in order to obtain a variable (f(z)) as close as possible in distribution to the observed phenotype y. To allows for flexible transformation functions, we fitted polynomials up to 7th degree, where the outcome is the sorted phenotype y and the regressors are powers of the sorted version of z. Finally, for each skewness and kurtosis of ϵ, we chose the parameter combinations (z) with respect to the first two criteria. For each skewness and kurtosis of ϵ, the 100 realisations of y⋆  were then subjected to our MLE method to estimate α, β and γ and compared these to the ones obtained for . We report the results for the skewness and kurtosis combination (for ϵ) that resulted in the best match also w.r.t. α, β and γ. If we could identify a combination of parameters y⋆ matching y in terms of all three criteria, we conclude that the observed interaction effect of the phenotype may be due to trait transformation.To obtain such e and ϵ. The latter two were simulated from a Pearson distribution (R function rpearson / Matlab function pearsrnd), for which we set the first four moments . First, we explored whether the correlation between G and E has any impact on the parameter estimates. For these set of simulations, we used the original parameterisation (ϵ and e could lead to biased estimation of the key parameters (γ and β). Therefore, we conducted extensive simulations including 21 different distributions with a wide range of values for skewness  and kurtosis  both for e and ϵ  second (q2) and third quartiles (q3) and the lower/upper whiskers are at q1 − 1.5 ⋅ (q3 − q1), q3 + 1.5 ⋅ (q3 − q1), respectively.We systematically explored the robustness of our method to various simulation settings. As a basic setting, we assume that the generated phenotype is governed by the interaction model defined in Eq. . To thismentclass2pt{minimf(t) = tk, k = 0, 1, 2, 3), where instead of observing/modelling  directly, we observed (f(Y), G). Note that k = 0 represents the log-transformation. As the interaction effects are not the same on the transformed scale as on the original one, in these analyses our aim was only to distinguish between true and null interaction effects. Thus, we tested γ = 0 and γ2 = 0.05, while fixing other parameters at f(t) = tk, skewness  and kurtosis  both for e and ϵ, resulting in further 126 (3 × 21 × 2) parameter combinations.Next, we tested the impact of trait transformations  and interaction effects . Since in a typical scenario one would test a few dozen outcome traits, we used a P-value threshold of 10−3 to establish power. For these simulations, we set other parameters to E against linear interaction model with observed E under fixed setting of E.We then explored the power to discover G × E interactions for various combinations of realistic sample sizes  was assumed to be known . To examine whether using an estimate (g) results in estimation error, we simulated 1000 independent genotypes for a sample of 10,000 participants. The phenotype was then generated based on a polygenic model, where the effects of SNPs are drawn from a normal distribution and explain in total 30% of the trait variance. We then added an environmental factor (E) and an interaction term (GRS × E) to this genetic component, explaining 30% and 10% of the trait variance, respectively. Finally, we added normally distributed noise, contributing the remaining 30% to the phenotypic variance. Note that we used here larger SNP and G × E effects, because as opposed to the other simulations, here we created GRS not only based on genome-wide significant SNPs, while almost all previous settings mimic real scenarios, where the GRS is composed of only genome-wide significant SNPs. Using the simulated phenotype and genotype data, we derived GRS at different P-value thresholds. We computed two different GRSs, one based on ordinary least squares (OLS) and another one using the best linear unbiased predictor (BLUP). The emerging GRSs were then plugged into the likelihood function.Note that for real data we have to use P-value  < 5 × 10−8 and pruned them based on distance, eliminating SNPs that lie within 1 Mb vicinity of a stronger associated variant. We define an outcome trait continuous if the variable takes at least 100 different values in the UK Biobank sample. The analysis was restricted to a sub-sample of the UK Biobank comprising 378,836 unrelated, white British participants. We fitted the likelihood function both to the real data  and To explore whether we can find evidence of interaction between GRS and environmental variables, we looked at 32 continuous complex traits, where the GRS—composed of all independent, genome-wide significant SNPs in the UK Biobank—explained at least 2% of the variance of that trait. For this we first selected SNPs with association γ) values down to 0.02% latter point. To reduce computational time when testing large number of single SNPs, one can use the likelihood ratio test to obtain standard error for the interaction estimates and use only bootstrapping for SNPs showing the most evidence for interaction.Single SNP interaction testing differs in two aspects from the standard GRS analysis. On one hand, the expected interaction effects are much smaller and the bootstrapping procedure is not feasible for millions of SNPs genome-wide. To address the first point, we extended the simulations to smaller interaction (Further information on research design is available in the Supplementary Information NewPeer Review FileReporting Summary


As introduced species expand their ranges, they often encounter differences in climate which are often correlated with geography. For introduced species, encountering a geographically variable climate sometimes leads to the re‐establishment of clines seen in the native range. However, clines can also be caused by neutral processes, and so it is important to gather additional evidence that population differentiation is the result of selection as opposed to nonadaptive processes. Here, we examine phenotypic and genetic differences in ragweed from the native (North America) and introduced (European) ranges. We used a common garden to assess phenotypic differentiation in size and flowering time in ragweed populations. We found significant parallel clines in flowering time in both North America and Europe. Height and branch number had significant clines in North America, and, while not statistically significant, the patterns in Europe were the same. We used SNP data to assess population structure in both ranges and to compare phenotypic differentiation to neutral genetic variation. We failed to detect significant patterns of isolation by distance, geographic patterns in population structure, or correlations between the major axes of SNP variation and phenotypes or latitude of origin. We conclude that the North American clines in size and the parallel clines seen for flowering time are most likely the result of adaptation. Clines in invasive species can be due to adaptation or non‐adaptive mechanisms. We use a combination of common garden field experiments and population genetic analysis of GBS data to show that clines in common ragweed are likely adaptive. In addition to the dual economic and ecological damage introduced plants can cause when they proliferate, they also offer opportunities to study evolutionary ecology during colonization  is a globally invasive species with a wide range in its native continent of North America and a presence in Europe, Asia, and Australia  is an annual outcrosser in the Asteraceae family . In Eastern Europe, ragweed populations now extend north up into Poland and south into the Baltic states . Blocks were subdivided into plots, each containing 64 plants in an 8x8 configuration, except for the final plot. We continued to remove interspecific vegetation and provide the seedlings with water for four weeks after transplantation to promote establishment.For this experiment, we randomly chose 10 maternal families per population, except in cases where there were fewer than 10 families, in which case we used all available. We chose three germinants from each family (one for each of three blocks) for a total of 1,110 plants. Each individual was randomly assigned a position within a block. We planted germinants in seedling trays and kept in a greenhouse where we sprayed and bottom watered them for three weeks. At the end of June 2014, we planted seedlings into a plowed field at the Koffler Scientific Reserve  . We ran initial models including latitude and block to assess whether block had a significant effect on traits; block was not significant for any trait and was thus dropped in subsequent models. To test for clines in phenotypic traits, we used linear regressions on maternal family means. For each continent, we conducted regressions for three phenotypic traits  and the two fitness traits on latitude. We used separate regressions for each continent rather than ANCOVA for three reasons: first, because the latitudinal ranges between Europe and North America were only partially overlapping; second, because the relationship between latitude and climate differs dramatically between Europe and North America; and third, because our goal was to test for clines independently in each continent. Similar results were obtained using population means for traits and latitude. Unless otherwise specified below, statistical analyses were conducted in R (R Development Core Team 2016).We measured final height, final number of branches, and date of first flower. Since the vast majority of ragweed plants are monoecious  grown in seedling trays in growth chambers at the University of Toronto. These plants were from a subset of the populations used in the common garden, but were separate plants. GBS library prep was conducted by the Hodgins lab at Monash University Australia. In brief, DNA was digested from the dried leaves and adapters were ligated to the strands. A double enzyme digest with Pst1 and Msp1 was implemented using the same protocol as in van Boheemen et al (2018). DNA libraries were sent to Genome Quebec for sequencing on an Illumina HiSeq 2,500, using PE125 sequencing.We used Stacks , we used the R package Jombart, . AdegeneIn addition to STRUCTURE and IBD, patterns in genetic data can also be understood with principal component analysis , and to run an AMOVA to partition genetic variation between the range, population, and individual levels. We used SplitsTree to construct a NeighborNet for all the individuals , but otherwise there is not much geographic structure . The significant European principal component explained 4.5% of genetic variation. Altogether, the significant North America principal components explained 14.6% of genetic variation. There were no significant relationships between significant SNP principal component scores and either latitude or phenotype . These results suggest that axes of  SNP variation are not related to either latitude or the phenotypic traits, suggesting that latitudinal clines are unlikely to be generated by neutral or stochastic processes.Tracy–Widom tests indicated that there was one significant SNP principal component in Europe and seven for the North American dataset  and invasive (0.0566) ranges. Past work on ragweed has found similarly low FST values ; Data curation ; Formal analysis ; Investigation ; Methodology ; Project administration ; Writing‐original draft ; Writing‐review & editing . Kathryn A. Hodgins: Conceptualization ; Investigation ; Methodology ; Project administration ; Resources ; Writing‐review & editing . John R. Stinchcombe: Conceptualization ; Funding acquisition ; Project administration ; Resources ; Supervision ; Writing‐original draft ; Writing‐review & editing . BVM and JRS designed the study; BVM and KAH carried out the study; BVM and KAH analyzed the data; BVM wrote the manuscript; and BVM, KAH, and JRS edited, commented, and revised the manuscript. Click here for additional data file. Click here for additional data file. Click here for additional data file.


Growth differentiation factor 15 (GDF-15), a stress responsive cytokine, belongs to transforming growth factor β cytokine superfamily. Some evidence support that it’s involved in inflammation, coagulation, oxidative stress, endothelial dysfunction, and hemostasis. However, it’s still controversial whether GDF-15 directly contributes to the morbidity and mortality of patients suffered with cardiovascular disease (CVD). Besides prospective cohort study and randomized controlled trial, Mendelian randomization (MR) is a genetic epidemiological method that exploits genetic variants as unbiased proxies for modifiable to determine the causal relationships between exposures and health outcomes. Herein, we introduced a two-sample MR approach to evaluate the causal relationships of circulating GDF-15 levels with major CVDs incidence.Genetic instruments and summary statistics for two-sample MR analysis were obtained from 5 independent large genome-wide association studies (GWAS) to investigate the causal correlation between circulating GDF-15 levels and 9 CVDs, respectively. Conventional inverse variance weighted method was adopted to evaluate the causality of GDF-15 with different outcomes; weighted median and MR egger were used for sensitivity analyses.Among 9 SNPs identified from 5 GWASs in 2.6 million individuals, 5 SNPs  coming from chromosome 19 and containing the PGPEP1 and GDF-15 genes were employed. Based on the instruments, circulating GDF-15 levels significantly linked to the increased risk of cardioembolic stroke, atrial fibrillation, coronary artery disease and myocardial infarction. However, no significant causal association was observed for circulating GDF-15 levels with the incidence of any ischemic stroke, large-artery atherosclerotic stroke, small vessel stroke, heart failure and nonischemic cardiomyopathy.The MR study provides with genetic evidence for the causal relationship of circulating GDF-15 levels with the increased risk of cardioembolic stroke, atrial fibrillation, coronary artery disease and myocardial infarction, but not any ischemic stroke, large-artery atherosclerotic stroke, small vessel stroke, heart failure and nonischemic cardiomyopathy. It indicates that GDF-15 might be a promising biomarker or potential therapeutic target for some CVDs. Together with the economic growth and lifestyle change, the incidence of cardiovascular disease is also increasing in the global countries. Cardiovascular disease (CVD) has become an overwhelming cause of morbidity and mortality of population health, which contribute to the current public health concern. Subsequently, the increasing medical insurance costs become an important social economic burden. It’s crucial and significant to figure out the causal elements and therapeutic targets to reduce CVD morbidity and mortality, improve life quality and alleviate medical insurance burden.Recent researches have demonstrated that metformin, a classical and first-line glucose-lowering drug, is beneficial to cardiovascular outcomes and reduction of total mortality independent of glycemic control. Many different mechanisms beyond glycemic control have been implicated in cardiovascular protection induced by metformin, such as improvements of inflammation, coagulation, oxidative stress, endothelial dysfunction, and hemostasis . Growth The PARADIGM-HF trial has shown that GDF-15 plays independently a prognostic value in patients with heart failure with reduced ejection fraction (HFrEF) in which higher baseline and incremental GDF-15 levels were significantly relevant to mortality and all cardiovascular events, even after adjusting circulating concentrations of N-terminal pro-B-type natriuretic peptide (NT-proBNP) and high-sensitivity cardiac troponin T (cTnT) , stable Mendelian randomization (MR) is an epidemiological robust tool by using genetic variants as proxies for the exposure to infer causality between risk factors and outcome or disease . BecauseHerein, we obtained genetic instruments and summary statistics for two-sample MR analysis from 5 GWASs to investigate the causal correlation between circulating GDF-15 levels and 9 CVDs, including any ischemic strokes , AF, HF, nonischemic cardiomyopathy, CAD and MI. The present study concluded that GDF-15 might be a promising diagnostic biomarker and potential therapeutic target of some CVDs.p < 5 × 10–8). All the SNPs were on chromosome 19 containing the PGPEP1 and MIC-1/GDF15 genes. LD-Link [Circulating GDF-15 level was predicted by the exposure genetically. A meta-analysis of GWAS which including 5440 individuals of European ancestry from four community-based cohorts (the mean age was 62 years and 53% were women) was utilized to obtain GDF-15 genetic associations , as desc LD-Link  was appl LD-Link  for the The summary statistics for the selected SNPs with stroke were extracted from a large-scale meta-analysis of GWAS of 446,696 subjects of European ancestry , conducted by the MESTROKE consortium . Specifip values of < 0.05 were considered indicative of significant heterogeneity. All statistical analyses were performed by R version 3.6.1  and the MR package.Two-sample MR method was performed to access the causality in genetic-predicted circulating GDF-15 levels with stroke, AF, HF, and NICM. The casual effect estimates of SNP instruments on CVD outcomes were calculated using the Wald Estimator , with st2 ≥ 0.8) and rs16982345 had not reach the genome-wide threshold (p > 5 × 10−8). The rest of SNPs  coming from chromosome 19 and containing the PGPEP1 and GDF-15 genes displayed in Additional file Among 9 SNPs which identified from the GWAS, 4 SNPs were discarded since rs1054564, rs3746181, rs1363120 were high linkage disequilibrium (LD)  whereas reduced risk of CAD and MI incidence . While there was no robust evidence support the causal relationship of AIS, LAS, SVS, HF and NICM risk with circulating GDF-15 levels (p > 0.05). And validation and sensitivity analyses of relationship of circulating GDF-15 levels and outcomes conducted by IVW, MR-Egger test and Weighted Median method as shown in Table Casualty between circulating GDF-15 levels and 9 CVDs was shown in Fig. The present study investigated whether there was a causal association between circulating GDF-15 levels and nine CVDs including AIS, CES, LAS, SVS, AF, HF, NICM, CAD and MI by using two-sample MR based on 5 GWASs and 2.6 million cases. The result suggested that circulating GDF-15 level had a significant causal association with the incidence of CES, AF, CAD and MI, whereas no significant relationship could be concluded when coming to AIS, LAS, SVS, HF and NICM. In addition, a higher circulating GDF-15 was associated with the higher risk of CES and AF and lower risk of CAD and MI. Therefore, our study indicated a crucial role of circulating GDF-15 levels for the prevention and intervention of CVDs.CES has tripled in the past few decades and would persistently triple by 2050 worldwide. It’s the predominantly increasing proportion in ischemic strokes and eventually causes more severe strokes than other ischemic stroke subtypes . The prep < 0.05) [AF is the most common arrhythmia, currently affecting over 33 million individuals worldwide. The prevalence of AF is expected to more than double in adults over the next 40 years. AF is associated with a twofold increase in premature mortality and major adverse cardiovascular events such as HF, stroke and MI. Our result suggested that the circulating GDF-15 level was positive associated with the risk of AF. In community-based Individuals , postope < 0.05) . However < 0.05)  and pati < 0.05) . Potenti < 0.05) . In addiCAD is the most prevalent and important cause of ischemic heart disease, with major implications on global morbidity and mortality. The present result suggested that higher circulating level of GDF-15 was related to the lower risks of CAD and MI. GDF-15 may have a protective effect on atherosclerosis process. Consistently, overexpression of GDF-15 in macrophages significantly attenuated atherosclerotic lesions in the apoE knockout mouse model of atherosclerosis . In addip < 0.001) and first morbid event . Increases in GDF-15 over 12 months were independently associated with the risks of future mortality and first morbid event. Taken together, serum GDF-15 concentration had not only a promising value of diagnosis but also a superior prognostic biomarker. However, patient with HF usually have some comorbidities such as hypertension, AF, stroke, diabetes, and chronic renal dysfunction, which may influence the circulating GDF-15 level and need to be eliminated.Though the present MR study did not support a causality of the circulating GDF-15 with the risk of HF, there are some reports that GDF-15 may be related to disease severity and prognosis HF patients . In Val-This MR study firstly described the causal association between GDF-15 and 9 CVDs. Our work provided with a new perspective to clarify the role of GDF-15 in the development of CVDs. However, limitations should be considered while interpreting the results. The MR method have some common defects . FirstlyIn summary, this MR study provides with genetic evidence for the causal relationship of circulating GDF-15 levels with the increased risk of CES, AF and reduced risk of CAD, MI, but not for AIS, LAS, SVS, HF and NICM. It indicates that GDF-15 might be a promising biomarker or potential therapeutic target for some CVDs.Additional file 1. SNP predicting GDF-15 identified in GWAS.


Body size traits as one of the main breeding selection criteria was widely used to monitor cattle growth and to evaluate the selection response. In this study, body size was defined as body height (BH), body length (BL), hip height (HH), heart size (HS), abdominal size (AS), and cannon bone size (CS). We performed genome-wide association studies (GWAS) of these traits over the course of three growth stages  using three statistical models, single-trait GWAS, multi-trait GWAS and LONG-GWAS. The Illumina Bovine HD 770 K BeadChip was used to identify genomic single nucleotide polymorphisms (SNPs) in 1217 individuals.SOX2, SNRPD1, RASGEF1B, EFNA5, PTBP1, SNX9, SV2C, PKDCC, SYNDIG1, AKR1E2, and PRIM2 identified by single-trait analysis; SLC37A1, LAP3, PCDH7, MANEA, and LHCGR identified by multi-trait analysis; and P2RY1, MPZL1, LINGO2, CMIP, and WSCD1 identified by LONG-GWAS.In total, 19, 29, and 10 significant SNPs were identified by the three models, respectively. Among these, 21 genes were promising candidate genes, including Multiple association analysis was performed for six growth traits at each growth stage. These findings offer valuable insights for the further investigation of potential genetic mechanism of growth traits in Simmental beef cattle. In China, the production of beef cattle is a very important agribusiness, and the Simmental breed accounts for more than 70% of beef-producing herds. Beef producers use body size to monitor the growth of each animal throughout the fattening period , 2, as tGenome-wide association studies (GWAS) are robust statistical tools are that broadly identify candidate genes with significant SNPs involved in production traits –16, growIn this study, six body size traits were routine measured from the time cattle entering farm to slaughter, which provides valuable resources to study the complete growing period. The aim of our study was to comprehensively analyze of candidate genes and QTL regions associated with growth traits by conducting three GWAS approaches in Simmental beef cattle. Our findings offer valuable insights for the further investigation of the potential mechanism of growth traits in Simmental beef cattle.Figure p values are listed in Table Briefly, we found 45, 66 and 19 SNPs significantly were associated with six body size traits by single-trait GWAS, multi-trait GWAS and LONG-GWAS, respectively. There were no significant loci for single-trait BH6 , single-trait AS6, single-trait CS6, and LONG-AS. In addition, ten SNPs were associated with at least one of the six traits and eight SNPs were strongly associated with these traits in at least one of the three models. While according to their biological functions, 21 suggestive genes were selected as candidate genes and some details of them, including their positions in the genome, the nearest reported genes, the minor allele frequencies (MAF) and the p-value ranging from 9.99 × 10− 6 (BovineHD0700018941 for BL18) to 2.11 × 10− 8 (BovineHD0200014365 for HS18), and the MAF ranging from 0.003 (BovineHD0700034055) to 0.497 (BovineHD2600012755). Among these, two SNPs near SOX2 (SRY-Box 2) on BTA1 were also identified in the liver and stomach [RASGEF1B (RasGEF Domain Family Member 1B). On BTA7, one SNP (BovineHD0700034055) was associated with single-trait HS12 and single-trait AS12, namely EFNA5 and another SNP (BovineHD0700012966) was associated with single-trait HH6 and multi-trait6, namely PTBP1. On BTA10, one SNP (BovineHD1000002378) was associated with single-trait BH6 and multi-trait6, namely SV2C. While on BTA11, four loci in 0.04 Mb region were associated with the single-trait HS12 and one of them (BovineHD1100007368) was also associated with multi-trait12, all of which were near PKDCC. On BTA13, SNP BovineHD1300012489 and BovineHD1300012894 were associated with single-trait BH18 and single-trait AS18, respectively. These two SNPs also strongly associated with multi-trait18. On BTA23, two SNPs were found within PRIM2.A total of 45 SNPs achieved genome-wide significance associated with at least one of the six traits, with the  stomach . On BTA2SLC37A1. On BTA6, two suggestive loci were detected, one near LAP3 that associated with multi-trait12 and another near PCDH7. Two genome-wide loci were identified within the 0.02 Mb region of MANEA on BTA9. Furthermore, four promising loci were detected within in 0.04 Mb region of LHCGR on BTA11, and 13 loci were identified within the 0.03 Mb region of AKR1E2 on BTA13, which were also detected by single-trait analysis.Multi-trait GWAS identified 66 SNPs within or near 36 genes that were distributed on 21 chromosomes, including 8 loci that were also identified by single-trait GWAS, which indicated that these loci suggestively regulate the development of the body growth  was also associated with LONG-CS, LONG-BH and LONG-HH. Another two loci in the 4.2 Kb region near MPZL1 were identified, and the latter SNP (BTA-68271-no-rs) was also associated with LONG-HH and LONG-BH. Furthermore, one suggestive SNP near LINGO2 on BTA8 was associated with LONG-HS. In addition, four promising loci in the 0.03 Kb region were associated with LONG-HH, namely CMIP, a key gene in the T-cell signaling pathway. On BTA19, a suggestive locus near WSCD1 was associated with LONG-CS. No loci were associated with AS in our research.Nineteen loci were identified by LONG-GWAS, including three significant loci on 12 chromosomes , which encodes a transcription factor involved in the regulation of embryonic development [SOX17, which positively affects the growth traits of cattle, and the conserved regions of this gene in human genome is closely related to body development [SNRPD1 , which is a member of the ghrelin receptor family, and the encoded protein is involved in zinc-dependent signaling in epithelial tissue [RASGEF1B (RasGEF domain family member 1B) were associated with body height [EFNA5 (ephrin A5) was associated with two traits (HS and AS) at the same stage. It was also identified as a candidate gene for growth traits in broiler chicken [PTBP1 (polypyrimidine tract binding protein 1) was found to show genome-wide association with growth traits at 6 months by both single-trait and multi-trait GWAS. Its expression level determined the release of insulin, thereby affecting development [SNX9 (sorting nexin 9), as olfactory receptor, was associated with growth traits in Yorkshire pigs [SV2C (synaptic vesicle glycoprotein 2C) was associated with BH by both single-trait and multi-trait GWAS. This gene was reported to modulate dopamine release in neural and endocrine cells [PKDCC  was associated with HS in both single-trait and multi-trait analyses. This gene was involved in the maintenance of bone density in humans [SYNDIG1 (synapse differentiation inducing 1) has been reported as a factor influencing the final weight and backfat thickness of Landrace pigs [AKR1E2  variant was associated with body length and girth in cattle [PRIM2 (DNA primase subunit 2) was associated with body weight and trait changes in pigs [On BTA1, two SNPs were near elopment , 33. Theelopment . On BTA2l tissue . On BTA6y height . In addiy height . On BTA7 chicken . Anotherelopment . On BTA9ire pigs . The SNPne cells . On BTA1n humans . On BTA1ace pigs , whereasn cattle . On BTA2 in pigs , 46.p values for the three stages were 3.90E-07, 9.92E-07 and 2.11E-08 respectively. These three values decreased to 8.23E-13, 1.73E-09 and 3.84E-10 in the multi-trait GWAS, respectively. We also identified several critical loci as follows. On BTA1, the SLC37A1  gene, which encodes a glucose-6-phosphate transporter that is involved in the homeostasis of blood glucose [LAP3 (leucine aminopeptidase 3) was reported to play critical roles in the regulation of hormone levels and protein maturation. Another study demonstrated that putative regulatory elements in the PCDH7 (protocadherin 7) gene may have roles in residual feed intake in Nelore cattle [MANEA , which has roles in proteolysis, was associated with the birth weight of Canchim beef cattle [LHCGR (luteinizing hormone/choriogonadotropin receptor) gene was as the cause of empty follicle syndrome [Multiple-trait analysis of linkage experiments has been reported to significantly enhance the power to detect common SNPs across traits , 48. The glucose . On BTA6e cattle . In addif cattle . On BTA1syndrome .P2RY1 (purinergic receptor P2Y1), a candidate gene that affects the serum Ca2+, encoded for a member of the family of G protein-coupled receptor family that works as receptor for extracellular ATP and ADP [MPZL1 (myelin protein zero like 1) gene could significantly enhance the migratory and metastatic potential of hepatocellular carcinoma cells by phosphorylating and activating the pro-metastatic protein [LINGO2 (leucine rich repeat and Ig domain containing 2), which is expressed in the central nervous system of mouse embryos, has been reported to associate with the body mass in a cohort of elderly Swedes [CMIP (C-Maf inducing protein), a candidate gene for reading-related traits, was also associated with plasma lipoprotein levels [WSCD1 (WSC domain containing 1), which encodes a protein with sulfotransferase activity that participates in the metabolism of glucose, was a candidate gene for feed efficiency and feeding behaviors in the White Duroc × Erhualian F2 population [We used LONG-GWAS, which involved multiple phenotype measurements for each individual . One dis and ADP . On BTA3 protein . Besidesy Swedes . On BTA1n levels . Moreovepulation .In conclusion, a total of 58 SNPs corresponding to 21 genes were found to be associated with six body size traits at 6, 12 and 18 months. Future studies characterizing the functions of these candidate genes may uncover the genetic architecture underlying the body size traits in Simmental beef cattle.Simmental beef cattle (born between 2008 and 2015) were established in Ulgai, Xilingole League, Inner Mongolia of China. Six body size traits at three growth stages  were measured simultaneously for each individual. The details of trait measurement are as follows: BH, also named wither height, the height from wither to ground; BL, the length from the front edge of the scapula to the back edge of the ischial tuberosity; HH, height from hip to ground; HS, also named heart girth, the chest girth in the back edge of scapula; AS, the girth of the thickest part of the abdomen; CS, the girth of the thinnest cannon bone. In addition, only cattle . Finally, 671,192 SNPs on 29 autosomal chromosomes with an average distance of 3 kb were generated for the analysis.Genomic DNA was isolated from blood samples using the TIANamp Blood DNA Kit . DNA quality was acceptable when the A260/A280 radio was between 1.8 and 2.0. Genotyping was performed with the Illumina BovineHD Beadchip  and the PLINK v1.07 Software was used for quality control . In thisQ matrix was reflected by the PCA. To replace the incomplete pedigrees, the K matrix was calculated by the VanRaden algorithm [y is a vector of the observed phenotypes; W was a vector of SNP genotype indicators, which was coded as 0, 1 and 2 corresponding to the three genotypes AA, AB, and BB with B being the minor allele. υ was the effect of marker, which is treated as a fixed effect; Variable X is an incidence matrix for non-genetic fixed effects, and β is a non-genetic vector of fixed effects including month ages (time of birth to measurement), enter weight (weight of just entering the farm), fattening days (time of entering farm to measurement) and principal component effects (the top three eigenvectors of the Q matrix). Variable Z is an incidence matrix for a vector of polygenic effects, and parameter u is a vector for residual polygenic effects with an assumed N  distribution, where σ2 is the polygenic variance and K is a marker inferred kinship matrix. While е is a vector for random residual errors with a putative N  distribution, where h2) is defined as: h2 = http://www.maizegenetics.net/gapit). Quantile–quantile (Q–Q) plots were generated to visualize the goodness of fitting for the GWAS model accounted by the population structure and familial relatedness. The negative logarithm of the p value from the model was calculated against the expected value based on the null hypothesis. The threshold p value after Bonferroni correction was 0.05/N = 7.45 × 10− 8, where N is the number of SNPs. In light of the fact that the Bonferroni correction results were too stringent with low statistical power [n is the number of P < 0.01 in the results, and m is the total number of SNPs [For six body size traits in three growth stage, we performed single-trait GWAS, respectively. The compressed mixed linear model (CMLM) was called because it reduced computing time by clustering individuals into groups, increased the power in QTN detection by eliminating the need to re-compute variance components, and enhanced the effectiveness in correcting the inflation from the polygenic background and controlling the bias of population stratification , 60. Brilgorithm . This moal power . Hence,  of SNPs .For the three growth stages, the multi-trait GWAS were conducted to detect pleiotropic SNPs and the model was a Chi square statistic, which approximately followed a Chi square distribution with the number of traits tested as the number of degrees of freedom. It was calculated for each SNP using the following formula :\documev and the corresponding variance ti is the 6 × 1 vector of the signed t-values of the ith SNP from the above-mentioned single-trait GWAS for the six traits. Matrix ti, and V−1 is the inverse of the 6 × 6 correlation matrix between traits, which was calculated by the estimated effects of the qualified SNPs .where β vector), polygenic effects, time stage effects and residual variance. Moreover, numerous studies have reported that the longitudinal design could facilitate the identification of time-dependent and consistent loci, which increased the statistical power due to their effectiveness in incorporating the correlation structure of multiple measurements and alleviating the multiple testing burden [http://genetics.cs.ucla.edu/longGWAS/. This model is as follows:For these individuals that completely obtained body size information at three growth stages, we conducted a longitudinal GWAS by LONG-GWAS . This mog burden , 27, 66.y∗ is the adjusted phenotype . The incidence matrix W, Z, the vector v, u and e are consistent with CMLM mentioned above. Differently, the parameter γ is a vector for time stage effects with a putative N  was applied to search for related QTL regions.The UMD3.1 genome assembly was used to located genes for annotation, and the QTLdb database  are illustrated by the Manhattan plots on the left panel. The deviations of the signals from null hypothesis are illustrated as the Quantile-Quantile (QQ) plots on the right panel. The negative logarithms of the observed (y axis) and the expected (x axis) P values are plotted for each SNP (dot). GWAS were performed six body size traits months 6, 12 and 18 after birth separately. Each analysis is labeled as trait (BH or HH) and month on the far right. The number neighboring each trait indicates the age of measurement . The 29 chromosomes are color coded.Additional file 2: Figure S2. The strengths of genome-wide association studies (GWAS) are illustrated by the Manhattan plots on the left panel. The deviations of the signals from null hypothesis are illustrated as the Quantile-Quantile (QQ) plots on the right panel. The negative logarithms of the observed (y axis) and the expected (x axis) P values are plotted for each SNP (dot). GWAS were performed six body size traits months 6, 12 and 18 after birth separately. Each analysis is labeled as trait (BH or HH) and month on the far right. The number neighboring each trait indicates the age of measurement . The 29 chromosomes are color coded.Additional file 3: Table S1. Descriptive statistics of 133 phenotypic records in LONG-GWAS method.


The possibility of assessing meat quality traits over the meat chain is strongly limited, especially in the context of selective breeding which requires a large number of phenotypes. The main objective of this study was to investigate the suitability of portable infrared spectrometers for phenotyping beef cattle aiming to genetically improving the quality of their meat. Meat quality traits  were appraised on rib eye muscle samples of 1,327 Piemontese young bulls using traditional  laboratory analyses; the same traits were also predicted from spectra acquired at the abattoir on the intact muscle surface of the same animals 1 d after slaughtering. Genetic parameters were estimated for both laboratory measures of meat quality traits and their spectra-based predictions.2 from 0.52 to 0.80), low for pH and purge losses (R2 around 0.30), and very poor for cooking losses and tenderness (R2 below 0.20). Except for lightness and purge losses, the heritability estimates of most of the predicted traits were lower than those of the measured traits while the genetic correlations between measured and predicted traits were high .The prediction performances of the calibration equations, assessed through external validation, were satisfactory for color traits (RResults showed that NIRS predictions of color traits, pH, and purge losses could be used as indicator traits for the indirect genetic selection of the reference quality phenotypes. Results for cooking losses were less effective, while the NIR predictions of tenderness were affected by a relatively high uncertainty of estimate. Overall, genetic selection of some meat quality traits, whose direct phenotyping is difficult, can benefit of the application of infrared spectrometers technology. Improving meat quality attributes through genetic selection proved to be theoretically feasible as many quality traits display moderate to medium heritability values . HoweverVisible and near-infrared spectroscopy (Vis-NIRS), which is based on the principle that different chemical bonds in organic matter absorb or emit light of different wavelengths when the sample is irradiated, offers a number of important advantages over conventional methods: ability to take rapid and frequent measurements, fast and simple or no sample preparation, suitability for on-line use, ability to simultaneously determine different attributes .Several studies have assessed the use of reflectance spectroscopy to accurately predict the chemical composition of beef –5 and, wHowever, with regards to genetic improvement, scientific knowledge is very scarce in beef cattle although genetic parameters of NIRS predictions of meat quality traits have been estimated in pigs . In a prThe availability of new, portable NIR and Vis-NIR spectrometers able to collect spectra directly from the muscle surface at the slaughterhouse  means thIn the absence of large-scale studies on the prediction of meat quality using portable NIR spectrometers, a research project  was set up with the aims of analyzing meat quality traits in Piedmontese young bulls, and of proposing innovative selection strategies for their improvement. The first steps taken were: to evaluate beef farming systems and other phenotypic sources of variation in carcass and meat quality traits using gold standard laboratory analyses ; to estiThe main objective of this study was, therefore, to investigate the suitability of portable infrared spectrometers for phenotyping beef cattle as a basis for genetically improving the quality of their meat. The specific aims were: 1) to analyze the genetic variation in meat quality traits as predicted by two very different portable spectrometers on the intact cross-sectional muscle surface in the abattoir; 2) to compare this with the genetic variation in traits measured in the laboratory after sampling, aging, transport and analysis; 3) to assess the genetic relationships between laboratory measures of meat quality traits and their spectrum-based predictions.The study was carried out on samples from 1,327 Piemontese young bulls slaughtered at the same commercial abattoir over 106 slaughter days. The young bulls were progeny of 204 A.I. purebred sires and 1,286 dams, all registered in the Italian Piemontese Herd Book.The animals were fattened on 115 farms representative of the beef production systems in the Piemonte region . The beef farming systems, feeding regimes, fattening conditions and slaughter performances of the young bulls are described in detail by Savoia et al. [2.The sampled young bulls had an average carcass weight of 438.1±43.6 kg, and an average age at slaughter of 541±63 days, giving an average daily carcass gain of 0.818±0.107 kg/d. Average carcass conformation score  was 14.66, corresponding to an average evaluation close to “E+” in the EU linear grading system; the average rib eye area measured at the 5th rib was 92±14.3 cmVis-NIRS: LabSpec 2500 , which has a spectral range in the visible and near-infrared sections of electromagnetic radiation (wavelengths 350 to 1830 nm), measurements taken every 1 nm producing 1481 data points per sample; the instrument’s dimensions are 12.7 cm × 36.8 cm × 29.2 cm, and it weighs 5,600 g; the spectra are collected with a probe (26 cm × 10 cm × 5 cm) connected to the instrument with an optical fiber;Micro-NIRS: Micro NIR Pro , which has a spectral range in the near-infrared region , measurements taken every 6 nm producing 125 data points per sample; the instrument’s dimensions are 4.5 cm × 4.4 cm × 4.0 cm, and it weighs 60 g; the spectra are collected directly by the instrument, which should be connected to a lap-top or tablet via a USB cable.Spectra collection and the technical characteristics of the instruments are described in detail by Savoia et al. . BrieflyThe right side of each carcass was divided into 2 quarters between the 5th and 6th ribs (pistol cut) in the abattoir the day after slaughter (about 24 h post-mortem). The spectra were collected on the cross-sectional surface of the longissimus thoracis muscle using the scanning head of the fiber-optic contact probe (10 mm in diameter) of the Vis-NIRS or by applying the Micro-NIRS to the surface of the muscle. Five spectra were acquired with each instrument from different positions on the cut surface of the same muscle.Twenty-four hours after slaughter and immediately following spectra collection, individual samples (4.0 cm thick) of the longissimus thoracis muscle were collected from between the 5th and 6th ribs, then were individually vacuum packed and transferred under refrigerated conditions to the laboratory, where they were stored in a chilling room at 4 °C for 6 d (meat aging), after which meat quality traits were measured on all samples.Meat quality was assessed 7 d after slaughter by measuring: muscle pH in triplicate using a digital pH-meter; lightness (L*), redness (a*), yellowness (b*), hue angle (h*), chroma (C*) in triplicate after 1 h blooming using a Minolta CR-331C colorimeter; purge losses  by difference between the weight of the sample cut at carcass dissection (day 1 after slaughtering) and before analyses (day 7); cooking losses  by difference between of the meat subsample before and after cooking meat sample in a water-bath till an internal temperature of 70 °C; tenderness  on 6 cylindrical 1.27 cm-diameter cores of cooked meat. Details of the procedures used to assess the meat quality traits can be found in Savoia et al. .The spectral data were edited and processed according to the model described in detail in the previous study by Savoia et al. . In brieA Bayesian model (Bayes B) implemented with the BGLR library  of the R2 values of external validation have been used to evaluate the prediction accuracy of calibration models. The “leave-one-batch-out” procedure’s details are described in Savoia et al. [In order to reproduce operational conditions, an external validation procedure was carried out to predict meat quality traits from the calibration equations based on the Vis-NIR and Micro-NIR spectra. As the most important source of variation was the slaughter batch , external validation consisted in predicting the observations of a given batch from the calibration equations developed using the measured meat quality data of animals slaughtered on all the other days (“leave-one-batch-out” procedure). This procedure has been repeated for each batch accumulating the predicted values. Therefore, the predictions of meat quality data for each animal were obtained using prediction equations developed without the observations measured on that animal and on all the animals slaughtered in the same batch. As a consequence, the entire set of predicted data could be used for the estimation of genetic parameters without any risk of inflation of the estimates. The Ra et al. .The final dataset used to estimate (co)variance components and to evaluate the magnitude of the genetic correlations contained the measured and predicted observations on a number of animals ranging from 1,117 to 1,134 depending on the trait.(Co)variance components were estimated by REML procedures using the VCE software . For eacy contains the observations for traits 1 and 2, β is the vector of non-genetic fixed effects, c is the vector of random herd effects (98 levels), q is the vector of the random batch effect (106 levels), u is the vector of animal additive genetic effects, e is the vector of random residual effects, and X, W1, W2 and Z are incidence matrices of proper dimensions. Fixed effects of parity of the dam  and age at slaughter  have been included in the model for pH and L*, respectively. Effects of different herds were assumed to be normally and independently distributed, c ~ N; effects of batch were assumed to be normally and independently distributed, q ~ N. A minimum cell size of 3 observations was required for both herd and batch effects. Animal additive genetic effects were assumed to be normally distributed, u ~ N, where G is the (co)variance matrix between the animal effects, and A is the numerator of the Wright’s relationship matrix. Additive relationships were computed using a pedigree file that included the phenotyped animals and all their known ancestors . Residuals were assumed to have a normal distribution, e ~ N.The general model can be written in matrix notation as:2a is the additive genetic variance, and σ2e is the residual variance. Intraherd heritability is equivalent to standard heritability under models treating contemporary groups (herds/batches) as fixed effects.To facilitate comparison with literature estimates, we estimated intra-herd heritability defined as:Descriptive statistics of the meat quality traits measured in the laboratory on aged samples according to gold standard methods, and their predictions obtained from the spectra acquired in the abattoir the day after slaughter are reported in Table 2EXT 0.52 to 0.80), low for pH and PL (R2EXT around 0.30), and very poor for CL and WBSF (R2EXT below 0.20). No relevant differences were observed between the two spectrometers in terms of the magnitude of R2EXT. Across traits, there was a clear relationship between loss of variability in the predictions with respect to the measurements and the quality of the prediction performance  and WBSF showed the highest variability followed by color traits, whereas the SD of the pH measurements was very low. For all the traits considered, the average values of the predictions obtained with both instruments were very similar to the corresponding laboratory measurements. On the other hand, the variability in the predicted traits was always much lower than in the measured traits. This was particularly marked for PL, CL, and WBSF, where the standard deviation of the predictions was 50% to 78% lower than that of the measured traits. The reduction was less pronounced (− 10% to − 27%) for color traits. Loss of variability was in general more marked in the predictions obtained with the Micro-NIRS spectrometer (− 40%) than with the Vis-NIRS instrument (− 30%). The externally validated prediction performance of the calibration equations was satisfactory for all color traits  and relatively high for WBSF (0.31), but those of the predicted traits were considerably lower. In particular, the predictions of CL obtained with Micro-NIRS and WBSF obtained with the Vis-NIRS instrument showed an almost null incidence of additive genetic variance, and the resulting heritabilities were close to zero. For both pH and PL, the estimated heritabilities of the predictions obtained from the Vis-NIRS instrument were higher than those from the Micro-NIRS . The heritability of measured pH was higher than that of the corresponding predictions, whereas the heritability of measured PL was similar to that of the Micro-NIRS predictions and markedly lower than that of the Vis-NIRS predictions.Estimates of the genetic and residual correlations obtained by bivariate analyses of color and meat quality traits measured on aged meat samples in the laboratory, and their predictions obtained from meat spectra acquired in the abattoir by both the Vis-NIRS and Micro-NIRS are presented in Table Overall, the prediction performances of the two spectrometers were quite similar for all the traits considered. The genetic parameters of the predictions for color traits were comparable, whereas the Vis-NIRS performed better than the Micro-NIRS in the other meat quality traits.The main objective of this research was to evaluate the possible use of NIRS technology to predict phenotypes for meat quality traits for genetic evaluation purposes. The use of portable instruments at the slaughterhouse, and spectra acquisition from the muscle surface naturally exposed during routine subdivision of half-carcasses into quarters could eliminate the need for meat sample collection, which depreciates the carcasses, and for the subsequent transport, aging and laboratory analyses. In a recent work from the same project, we described, compared and discussed in detail the Vis-NIR and Micro-NIR spectroscopic techniques in terms of instrument characteristics, repeatability, calibration, cross-validation, and external validation of the predictions, and their ability to capture the main phenotypic sources of variation in meat quality traits . In this2 values lower than those in most of the published studies using random cross-validation. In other foods, Bittante et al. [2 or RMSE), are not sufficient to establish the usefulness of spectral predictions for the purposes of genetic improvement. Although Soyeurt et al. [2 of cross-validation exceeding 0.75 to be necessary in order to use predictions of dairy traits for selection, some authors report satisfactory results with moderate or even low prediction performances for milk [2, the suitability of infrared predictions as indicator traits for selection relies especially on a combination of their heritability and loss of additive genetic variance with respect to measured traits and their genetic correlations with the corresponding measurements [In our investigation the predictive performance of NIRS was evaluated using external validation, which led to Re et al.  and Eskie et al.  showed tt et al.  considerfor milk , 21 and for milk . Aside furements .The heritabilities of the laboratory-measured meat quality traits were in the range of most literature reports , 24, andIn general, the predictions of meat quality traits obtained from spectra acquired in the abattoir yielded lower heritability values than the corresponding traits measured on aged meat samples in the laboratory, with the exception of L* and PL. The difference in heritabilities between the predicted and measured traits was on average 0.08 for both spectrometers, but there was variability across traits. Although the heritabilities of the meat quality predictions were lower than the heritabilities of the measured traits, in most cases they were large enough to be exploited for selection. Only the predictions of CL obtained with Micro-NIRS, and the predictions of WBSF obtained with Vis-NIRS were of no use, as their additive genetic variance was almost null. So far, our previous survey has been the only one to address the estimation of genetic parameters for meat quality traits predicted by NIR spectroscopy . That inIn this investigation, the lower heritability of the predictions compared with the measurements was due to the additive genetic variance being on average 70% lower, which exceeded the decrease observed in the phenotypic variance, ranging from 50% to 60%, depending on the instrument. These results are consistent with those of Bonfatti et al. , who fou2 of the external validations (Fig. 2 of the external validations of the calibration models, particularly with the Vis-NIR spectrometer (Fig. The lower phenotypic variability in the meat quality predictions observed in this study was strongly related to the accuracy of the calibrations measured by the Rons Fig. . As expe2a for the predictions.The genetic correlations between the infrared-predicted and laboratory-measured traits are important in determining the effectiveness of their use as indicator traits for selective breeding , 27. TheFor PL, the estimated genetic correlations obtained in the present study with both instruments were substantial, and larger than in the previous study. Similarly, the Vis-NIRS predictions of pH had rather high genetic correlations with the measurements, whereas the corresponding correlations with the Micro-NIRS predictions were only moderate. In the previous study , CL and As with the earlier findings , the genThe use of infrared predicted traits at the population level for genetic purposes has been shown to be possible for some milk traits , but theThis study investigated the feasibility of selection for meat quality traits using NIRS predictions obtained from spectra acquired in the abattoir from the intact muscle surface using portable instruments. The accuracy of the predictions was good for color traits, but low for the other traits investigated. Nevertheless, the estimated genetic parameters showed that NIRS predictions of color traits, pH and PL can be used as indicator traits of the corresponding measurements for selection purposes. The results for CL were more doubtful, while the estimates for WBSF predictions were unreliable.The two spectrometers compared in this study yielded similar results for the prediction of color traits and their relative genetic parameters. However, the Vis-NIRS instrument produced better estimates of the genetic parameters of the other predicted meat quality traits.On the whole, the selection of complex traits such as those related to meat quality, which are difficult to phenotype directly, can benefit from the application of NIRS technology.