Application of linear and machine learning models to genomic prediction of fatty acid composition in Japanese Black cattle.

We collected 3180 records of oleic acid (C18:1) and monounsaturated fatty acid (MUFA) measured using gas chromatography (GC) and 6960 records of C18:1 and MUFA measured using near-infrared spectroscopy (NIRS) in intermuscular fat samples of Japanese Black cattle. We compared genomic prediction performance for four linear models (genomic best linear unbiased prediction [GBLUP], kinship-adjusted multiple loci [KAML], BayesC, and BayesLASSO) and five machine learning models (Gaussian kernel [GK], deep kernel [DK], random forest [RF], extreme gradient boost [XGB], and convolutional neural network [CNN]). For GC-based C18:1 and MUFA, KAML showed the highest accuracies, followed by BayesC, XGB, DK, GK, and BayesLASSO, with more than 6% gain of accuracy by KAML over GBLUP. Meanwhile, DK had the highest prediction accuracy for NIRS-based C18:1 and MUFA, but the difference in accuracies between DK and KAML was slight. For all traits, accuracies of RF and CNN were lower than those of GBLUP. The KAML extends GBLUP methods, of which marker effects are weighted, and involves only additive genetic effects; whereas machine learning methods capture non-additive genetic effects. Thus, KAML is the most suitable method for breeding of fatty acid composition in Japanese Black cattle.

Evaluating the performance of genomic prediction accounting for effects of single nucleotide polymorphism markers in reproductive traits of Japanese Black cattle.

We examined the prediction accuracies of genomic best linear unbiased prediction (GBLUP), various weighted GBLUP according to the degrees of marker effects (WGBLUP) and machine learning (ML) methods, and compared them with traditional BLUP for age at first calving (AFC), calving difficulty (CD), and gestation length in Japanese Black cattle. For WGBLUP, firstly, BayesC and FarmCPU were used to estimate marker effects. Then, we constructed three weighted genomic relationship matrices from information of estimated marker effects in the first step: absolute value of the estimated marker-effect WGBLUP, estimated marker-variance WGBLUP, and genomic-feature WGBLUP. For ML, we applied Gaussian kernel, random forest, extreme gradient boost, and support vector regression. We collected a total of 2583 animals having both phenotypic records and genotypes with 30,105 markers and 16,406 pedigree records. For AFC, prediction accuracies of WGBLUP methods using FarmCPU exceeded BLUP by 25.7%-39.5%. For CD, estimated marker-variance WGBLUP using BayesC achieved the highest prediction accuracy. Among ML methods, extreme gradient boost, support vector regression, and Gaussian kernel increased prediction accuracies by 28.4%, 19.0%, and 36.4% for AFC, CD, and gestation length compared with BLUP, respectively. Thus, prediction performance could be improved using suitable WGBLUP and ML methods according to target reproductive traits for the population used.

Comparing pedigree and genomic inbreeding coefficients, and inbreeding depression of reproductive traits in Japanese Black cattle.

BACKGROUND: Pedigree-based inbreeding coefficients have been generally included in statistical models for genetic evaluation of Japanese Black cattle. The use of genomic data is expected to provide precise assessment of inbreeding level and depression. Recently, many measures have been used for genome-based inbreeding coefficients; however, with no consensus on which is the most appropriate. Therefore, we compared the pedigree- ([Formula: see text]) and multiple genome-based inbreeding coefficients, which were calculated from the genomic relationship matrix with observed allele frequencies ([Formula: see text]), correlation between uniting gametes ([Formula: see text]), the observed vs expected number of homozygous genotypes ([Formula: see text]), runs of homozygosity (ROH) segments ([Formula: see text]) and heterozygosity by descent segments ([Formula: see text]). We quantified inbreeding depression from estimating regression coefficients of inbreeding coefficients on three reproductive traits: age at first calving (AFC), calving difficulty (CD) and gestation length (GL) in Japanese Black cattle. RESULTS: The highest correlations with [Formula: see text] were for [Formula: see text] (0.86) and [Formula: see text] (0.85) whereas [Formula: see text] and [Formula: see text] provided weak correlations with [Formula: see text], with range 0.33-0.55. Except for [Formula: see text] and [Formula: see text], there were strong correlations among genome-based inbreeding coefficients ([Formula: see text] 0.94). The estimates of regression coefficients of inbreeding depression for [Formula: see text] was 2.1 for AFC, 0.63 for CD and -1.21 for GL, respectively, but [Formula: see text] had no significant effects on all traits. Genome-based inbreeding coefficients provided larger effects on all reproductive traits than [Formula: see text]. In particular, for CD, all estimated regression coefficients for genome-based inbreeding coefficients were significant, and for GL, that for [Formula: see text] had a significant.. Although there were no significant effects when using overall genome-level inbreeding coefficients for AFC and GL, [Formula: see text] provided significant effects at chromosomal level in four chromosomes for AFC, three chromosomes for CD, and two chromosomes for GL. In addition, similar results were obtained for [Formula: see text]. CONCLUSIONS: Genome-based inbreeding coefficients can capture more phenotypic variation than [Formula: see text]. In particular, [Formula: see text] and [Formula: see text] can be considered good estimators for quantifying inbreeding level and identifying inbreeding depression at the chromosome level. These findings might improve the quantification of inbreeding and breeding programs using genome-based inbreeding coefficients.

Performance of the No-U-Turn sampler in multi-trait variance component estimation using genomic data.

BACKGROUND: Multi-trait genetic parameter estimation is an important topic for target traits with few records and with a low heritability and when the genetic correlation between target and secondary traits is strong. However, estimating correlations between multiple traits is difficult for both Bayesian and non-Bayesian inferences. We extended a Hamiltonian Monte Carlo approach using the No-U-Turn Sampler (NUTS) to a multi-trait animal model and investigated the performance of estimating (co)variance components and breeding values, compared to those for restricted maximum likelihood and Gibbs sampling with a population size of 2314 and 578 in a simulated and real pig dataset, respectively. For real data, we used publicly available data for three traits from the Pig Improvement Company (PIC). For simulation data, we generated two quantitative traits by using the genotypes of the PIC data. For NUTS, two prior distributions were adopted: Lewandowski-Kurowicka-Joe (LKJ) and inverse-Wishart distributions. RESULTS: For the two simulated traits with heritabilities of 0.1 and 0.5, most estimates of the genetic and residual variances for NUTS with the LKJ prior were closer to the true values and had smaller root mean square errors and smaller mean absolute errors, compared to NUTS with inverse-Wishart priors, Gibbs sampling and restricted maximum likelihood. The accuracies of estimated breeding values for lowly heritable traits for NUTS with LKJ and inverse-Wishart priors were 14.8% and 11.1% higher than those for Gibbs sampling and restricted maximum likelihood, respectively, with a population size of 578. For the trivariate animal model with real pig data, the estimates of the genetic correlations for Gibbs sampling and restricted maximum likelihood were strongly affected by population size, compared to NUTS. For both the simulated and pig data, the genetic variances and heritabilities for NUTS with an inverse-Wishart prior were overestimated for low-heritability traits when the population size was 578. CONCLUSIONS: The accuracies of variance components and breeding values estimates for a multi-trait animal model using NUTS with the LKJ prior were equal to or higher than those obtained with restricted maximum likelihood or Gibbs sampling. Therefore, when the population size is small, NUTS with an LKJ prior could be an alternative sampling method for multi-trait analysis in animal breeding.

Hamiltonian Monte Carlo method for estimating variance components.

A Hamiltonian Monte Carlo algorithm is a Markov chain Monte Carlo method, and the method has a potential to improve estimating parameters effectively. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamilton's equations, which are expressed as two differential equations. In the sampling process of Hamiltonian Monte Carlo, a numerical integration method called leapfrog integration is used to approximately solve Hamilton's equations, and the integration is required to set the number of discrete time steps and the integration stepsize. These two parameters require some amount of tuning and calibration for effective sampling. In this study, we applied the Hamiltonian Monte Carlo method to animal breeding data and identified the optimal tunings of leapfrog integration for normal and inverse chi-square distributions. Then, using real pig data, we revealed the properties of the Hamiltonian Monte Carlo method with the optimal tuning by applying models including variance explained by pedigree information or genomic information. Compared with the Gibbs sampling method, the Hamiltonian Monte Carlo method had superior performance in both models. We have provided the source codes of this method written in the Fortran language at https://github.com/A-ARAKAWA/HMC.

Effects of parent-of-origin models with different pedigree information on beef carcass traits and fatty acid composition in Japanese Black cattle.

Genomic imprinting should be considered in animal breeding systems to avoid lead in bias in genetic parameter estimation. The objective of this study was to clarify the effects of pedigree information on imprinting variances for carcass traits and fatty acid composition in Japanese Black cattle. Carcass records [carcass weight, rib eye area, rib thickness (RT), subcutaneous fat thickness and beef marbling score (BMS)] and fatty acid composition were obtained for 11,855 Japanese Black feedlot cattle. To estimate and compare the imprinting variances for the traits, two imprinting models with different pedigree information [the sire-dam gametic relationship matrix (Model 1) and the sire-maternal grandsire (MGS) numerator relationship matrix (Model 2)] were fitted. The ratio of the imprinting variance to the total additive genetic variance for RT (6.33%) and BMS (19.00%) was significant in Model 1, but only that for BMS (21.09%) was significant in Model 2. This study revealed that fitting the sire-MGS model could be useful in estimating imprinting variance under certain conditions, such as when restricted pedigree information is available. Furthermore, the present result suggested that the maternal gametic effects on BMS should be included in breeding programmes for Japanese Black cattle to avoid selection bias caused by imprinting effects.

Differential Metabolomics Profiles Identified by CE-TOFMS between High and Low Intramuscular Fat Amount in Fattening Pigs.

The amount of intramuscular fat (IMF) present in the loin eye area is one of the most important characteristics of high-quality pork. IMF measurements are currently impractical without a labor-intensive process. Metabolomic profiling could be used as an IMF indicator to avoid this process; however, no studies have investigated their use during the fattening period of pigs. This study examined the metabolite profiles in the plasma of two groups of pigs derived from the same Duroc genetic line and fed the same diet. Five plasma samples were collected from each individual the day before slaughter. Capillary electrophoresis-time of flight mass spectrometry (CE-TOFMS) was used to analyze the purified plasma from each sample. Principle component analysis (PCA) and partial least squares (PLS) were used to find the semi-quantitative values of the compounds. The results indicate that branched-chain amino acids are significantly associated with high IMF content, while amino acids are associated with low IMF content. These differences were validated using the quantification analyses by high-performance liquid chromatograph, which supported our results. These results suggest that the concentration of branched-chain amino acids in plasma could be an indicative biomarker for the IMF content in the loin eye area.

Inferring phenotypic causal structure among farrowing and weaning traits in pigs.

Direct selection for litter size or weight at weaning in pigs is often hindered by external interventions such as cross-fostering. The objective of this study was to infer the causal structure among phenotypes of reproductive traits in pigs to enable subsequent direct selection for these traits. Examined traits included: number born alive (NBA), litter size on day 21 (LS21), and litter weight on day 21 (LW21). The study included 6,240 litters from 1,673 Landrace dams and 5,393 litters from 1,484 Large White dams. The inductive causation (IC) algorithm was used to infer the causal structure, which was then fitted to a structural equation model (SEM) to estimate causal coefficients and genetic parameters. Based on the IC algorithm and temporal and biological information, the causal structure among traits was identified as: NBA â†’ LS21 â†’ LW21 and NBA â†’ LW21. Owing to the causal effect of NBA on LS21 and LW21, the genetic, permanent environmental, and residual variances of LS21 and LW21were much lower in the SEM than in the multiple-trait model for both breeds. Given the strong effect of NBA on LS21 and LW21, the SEM and causal information might assist with selective breeding for LS21 and LW21 when cross-fostering occurs.

Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.

BACKGROUND: Hamiltonian Monte Carlo is one of the algorithms of the Markov chain Monte Carlo method that uses Hamiltonian dynamics to propose samples that follow a target distribution. The method can avoid the random walk behavior to achieve a more effective and consistent exploration of the probability space and sensitivity to correlated parameters, which are shortcomings that plague many Markov chain Monte Carlo methods. However, the performance of Hamiltonian Monte Carlo is highly sensitive to two hyperparameters. The No-U-Turn Sampler, an extension of Hamiltonian Monte Carlo, was recently introduced to automate the tuning of these hyperparameters. Thus, this study compared the performances of Gibbs sampling, Hamiltonian Monte Carlo, and the No-U-Turn Sampler for estimating genetic parameters and breeding values as well as sampling qualities in both simulated and real pig data. For all datasets, we used a pedigree-based univariate linear mixed model. RESULTS: For all datasets, the No-U-Turn Sampler and Gibbs sampling performed comparably regarding the estimation of heritabilities and accuracies of breeding values. Compared with Gibbs sampling, the estimates of effective sample sizes for simulated and pig data with the No-U-Turn Sampler were 3.2 to 22.6 and 3.5 to 5.9 times larger, respectively. Autocorrelations decreased more quickly with the No-U-Turn Sampler than with Gibbs sampling. When true heritability was low in the simulated data, the skewness of the marginal posterior distributions with the No-U-Turn Sampler was smaller than that with Gibbs sampling. The performance of Hamiltonian Monte Carlo for sampling quality was inferior to that of No-U-Turn Sampler in the simulated data. Moreover, Hamiltonian Monte Carlo could not estimate genetic parameters because of difficulties with the hyperparameter settings with pig data. CONCLUSIONS: The No-U-Turn Sampler is a promising sampling method for animal breeding because of its good sampling qualities: large effective sample sizes, low autocorrelations, and low skewness of marginal posterior distributions, particularly when heritability is low. Meanwhile, Hamiltonian Monte Carlo failed to converge with a simple univariate model for pig data. Thus, it might be difficult to use Hamiltonian Monte Carlo for usual complex models in animal breeding.

Genomic best linear unbiased prediction method including imprinting effects for genomic evaluation.

BACKGROUND: Genomic best linear unbiased prediction (GBLUP) is a statistical method used to predict breeding values using single nucleotide polymorphisms for selection in animal and plant breeding. Genetic effects are often modeled as additively acting marker allele effects. However, the actual mode of biological action can differ from this assumption. Many livestock traits exhibit genomic imprinting, which may substantially contribute to the total genetic variation of quantitative traits. Here, we present two statistical models of GBLUP including imprinting effects (GBLUP-I) on the basis of genotypic values (GBLUP-I1) and gametic values (GBLUP-I2). The performance of these models for the estimation of variance components and prediction of genetic values across a range of genetic variations was evaluated in simulations. RESULTS: Estimates of total genetic variances and residual variances with GBLUP-I1 and GBLUP-I2 were close to the true values and the regression coefficients of total genetic values on their estimates were close to 1. Accuracies of estimated total genetic values in both GBLUP-I methods increased with increasing degree of imprinting and broad-sense heritability. When the imprinting variances were equal to 1.4% to 6.0% of the phenotypic variances, the accuracies of estimated total genetic values with GBLUP-I1 exceeded those with GBLUP by 1.4% to 7.8%. In comparison with GBLUP-I1, the superiority of GBLUP-I2 over GBLUP depended strongly on degree of imprinting and difference in genetic values between paternal and maternal alleles. When paternal and maternal alleles were predicted (phasing accuracy was equal to 0.979), accuracies of the estimated total genetic values in GBLUP-I1 and GBLUP-I2 were 1.7% and 1.2% lower than when paternal and maternal alleles were known. CONCLUSIONS: This simulation study shows that GBLUP-I1 and GBLUP-I2 can accurately estimate total genetic variance and perform well for the prediction of total genetic values. GBLUP-I1 is preferred for genomic evaluation, while GBLUP-I2 is preferred when the imprinting effects are large, and the genetic effects differ substantially between sexes.

Parameters affecting genome simulation for evaluating genomic selection method.

The present study investigated the parameter settings for obtaining a simulated genome at steady state of allele frequency (mutation-drift equilibrium) and linkage disequilibrium (LD), and evaluated the impact of whether or not the simulated genome reached steady state of allele frequency and LD on the accuracy of genomic estimated breeding values (GEBVs). After 500 to 50,000 historical generations, the base population and subsequent seven generations were generated as recent populations. The allele frequency distribution of the last generations of the historical population and LD in the base population were calculated when varying the values of five parameters: initial minor allele frequency, mutation rate, effective population size, number of markers and chromosome length. The accuracies of GEBVs in the last generation of the recent population were calculated by genomic best linear unbiased prediction. The number of historical generations required to reach mutation-drift equilibrium depended on the initial allele frequency and mutation rate. Regardless of the parameters, LD reached a steady state before allele frequency distribution reached mutation-drift equilibrium. The accuracies of GEBVs largely reflect the extent of linkage disequilibrium with the exception of varying chromosome length, although there were no associations between the accuracies of GEBVs and allele frequency distribution.

Impacts of genotyping strategies on long-term genetic response in genomic selection.

The present study investigated the effects of the choices of animals of reference populations on long-term responses to genomic selection. Simulated populations comprised 300 individuals and 10 generations of selection practiced for a trait with heritability of 0.1, 0.3 or 0.5. Thirty individuals were randomly selected in the first five generations and selected by estimated breeding values from best linear unbiased prediction (BLUP) and genomic BLUP in the subsequent five generations. The reference populations comprise all animals for all generations (scenario 1), all animals for 6-10 generations (scenario 2) and 2-6 generations (scenario 3), and half of the animals for all generations (scenario 4). For all heritability levels, the genetic gains in generation 10 were similar in scenarios 1 and 2. Among scenarios 2 to 4, the highest genetic gains were obtained in scenario 2, with heritabilities of 0.1 and 0.3 as well as scenario 4 with heritability of 0.5. The inbreeding coefficients in scenarios 1, 2 and 4 were lower than those in BLUP, especially within cases with low heritability. These results indicate an appropriate choice of reference population can improve genetic gain and restrict inbreeding even when the reference population size is limited.

Including dominance effects in the genomic BLUP method for genomic evaluation.

We evaluated the performance of GBLUP including dominance genetic effect (GBLUP-D) by estimating variances and predicting genetic merits in a computer simulation and 2 actual traits (T4 and T5) in pigs. In simulation data, GBLUP-D explained more than 50% of dominance genetic variance. Moreover, GBLUP-D yielded estimated total genetic effects over 1.2% more accurate than those yielded by GBLUP. In particular, when the dominance genetic variance was large, the accuracy could be substantially improved by increasing the number of markers. The dominance genetic variances in T4 and T5 accounted for 9.6% and 6.3% of the phenotypic variances, respectively. Estimates of such small dominance genetic variances contributed little to the improvement of the accuracies of estimated total genetic effects. In both simulation and pig data, there were nearly no differences in the estimates of additive genetic effects or their variance between GBLUP-D and GBLUP. Therefore, we conclude GBLUP-D is a feasible approach to improve genetic performance in crossbred populations with large dominance genetic variation and identify mating systems with good combining ability.