Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: I. Variance component estimation.

Birth weight and calving difficulty were analyzed with Bayesian methodology using univariate linear models, a bivariate linear model, a threshold model for calving difficulty, and a joint threshold-linear model using a probit approach. Field data included 26,006 records of Gelbvieh cattle. Simulated populations were generated using parameters estimated from the field data. The Gibbs sampler was used to obtain estimates of the marginal posterior mean and standard deviation of the (co)variance components, heritabilities, and correlations. In the univariate analyses, the posterior mean of direct heritability for calving difficulty was .23 with the threshold model and .18 with the linear model. Maternal heritabilities were .10 and .08, respectively. In the bivariate analysis, posterior means of direct heritability for calving difficulty were .21 and .18 for the bivariate linear-threshold and linear-linear model, respectively. Maternal heritabilities were .09 and .06, respectively. Direct heritability for birth weight was .25 for the univariate model and .26 for bivariate models. Maternal heritability was .05 for the linear-threshold model and the univariate model and .06 for the bivariate linear model. Genetic correlation between direct genetic effects in both traits was .81 for the linear-threshold model and .79 for the bivariate linear. Residual correlation was .35 for the bivariate linear model and .50 for the bivariate linear-threshold. A simulation study confirmed that the posterior mean of the marginal distribution was suitable as a point estimate for univariate threshold and bivariate linear-threshold models.     

Comparison of models for missing pedigree in single-step genomic prediction

Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u₂) were assumed to be adjusted for UPG effects (g) using matrix Q₂ as u2∗=u2+Q2g before incorporating genomic information. The Quaas–Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g′). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g′)=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.     

Evaluation of the utility of diagonal elements of the genomic relationship matrix as a diagnostic tool to detect mislabelled genotyped animals in a broiler chicken population

This study explored distributions of diagonal elements of genomic relationship matrix (G), evaluated the utility of G as a diagnostic tool to detect mislabelled animals in a genomic dataset and evaluated the effect of mislabelled animals on the accuracy of genomic evaluation. Populations of 10 000 animals were simulated with 60 000 SNP varying in allele frequency at each locus between 0.02 and 0.98. Diagonal elements of G were distributed with a single peak (mean = 1.00 ± 0.03) and ranged from 0.84 through 1.36. Mixed populations were also simulated: 7 000 animals with frequencies of second alleles ranging from 0.02 through 0.98 were combined with 1750 or 7000 animals with frequencies of second alleles ranging from 0.0 through 1.0. The resulting distributions of diagonal elements of G were bimodal. Body weight at 6 weeks was provided by Cobb-Vantress for broiler chickens, of which 3285 were genotyped for 57 636 SNP. Analysis used a combined genomic and pedigree relationship matrix; G was scaled using current allele frequencies. The distribution of diagonal elements was multimodal and ranged from 0.54 to 3.23. Animals with diagonal elements >1.5 were identified as coming from another chicken line or as having low call rates. Removal of mislabelled animals increased accuracy by 0.01. For the studied type of population, diagonal elements of G may be a useful tool to help identify mislabelled animals or secondary populations.     

Genome-wide marker-assisted selection combining all pedigree phenotypic information with genotypic data in one step: An example using broiler chickens

Data of broiler chickens for 2 pure lines across 3 generations were used for genomic evaluation. A complete population (full data set; FDS) consisted of 183,784 and 164,246 broilers for the 2 lines. The genotyped subsets (SUB) consisted of 3,284 and 3,098 broilers with 57,636 SNP. Genotyped animals were preselected based on more than 20 traits with different index applied to each line. Three traits were analyzed: BW at 6 wk (BW6), ultrasound measurement of breast meat (BM), and leg score (LS) coded 1 = no and 2 = yes for leg defect. Some phenotypes were missing for BM. The training population consisted of the first 2 generations including all animals in FDS or only genotyped animals in SUB. The validation data set contained only genotyped animals in the third generation. Genetic evaluations were performed using 3 approaches: 1) phenotypic BLUP, 2) extending BLUP methodologies to utilize pedigree and genomic information in a single step (ssGBLUP), and 3) Bayes A. Whereas BLUP and ssGBLUP utilized all phenotypic data, Bayes A could use only those of the genotyped subset. Heritabilities were 0.17 to 0.20 for BW6, 0.30 to 0.35 for BM, and 0.09 to 0.11 for LS. The average accuracies of the validation population with BLUP for BW6, BM, and LS were 0.46, 0.30, and <0 with SUB and 0.51, 0.34, and 0.28 with FDS. With ssGBLUP, those accuracies were 0.60, 0.34, and 0.06 with SUB and 0.61, 0.40, and 0.37 with FDS, respectively. With Bayes A, the accuracies were 0.60, 0.36, and 0.09 with SUB. With SUB, Bayes A and ssGBLUP had similar accuracies. For traits of high heritability, the accuracy of Bayes A/SUB and ssGBLUP/FDS were similar, and up to 50% better than BLUP/FDS. However, with low heritability, ssGBLUP/FDS was 4 to 6 times more accurate than Bayes A/SUB and 50% better than BLUP/FDS. An optimal genomic evaluation would be multi-trait and involve all traits and records on which selection is based.     

Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.     

Genotype by environment interaction for growth due to altitude in United States Angus cattle

The objectives of this study were to determine if sires perform consistently across altitude and to quantify the genetic relationship between growth and survival at differing altitudes. Data from the American Angus Association included weaning weight (WW) adjusted to 205 (n = 77,771) and yearling weight adjusted to 365 (n = 39,450) d of age from 77,771 purebred Angus cattle born in Colorado between 1972 and 2007. Postweaning gain (PWG) was calculated by subtracting adjusted WW from adjusted yearling weight. Altitude was assigned to each record based upon the zip code of each herd in the database. Records for WW and PWG were each split into 2 traits measured at low and high altitude, with the records from medium altitude removed from the data due to inconsistencies between growth performance and apparent culling rate. A binary trait, survival (SV), was defined to account for censored records at yearling for each altitude. It was assumed that, at high altitude, individuals missing a yearling weight either died or required relocation to a lower altitude predominantly due to brisket disease, a condition common at high altitude. Model 1 considered each WW and PWG measured at 2 altitudes as separate traits. Model 2 treated PWG and SV measured as separate traits due to altitude. Models included the effects of weaning contemporary group, age of dam, animal additive genetic effects, and residual. Maternal genetic and maternal permanent environmental effects were included for WW. Heritability estimates for WW in Model 1 were 0.28 and 0.26 and for PWG were 0.26 and 0.19 with greater values in low altitude. Genetic correlations between growth traits measured at different altitude were moderate in magnitude: 0.74 for WW and 0.76 for PWG and indicate possibility of reranking of sires across altitude. Maternal genetic correlation between WW at varying altitude of 0.75 also indicates these may be different traits. In Model 2, heritabilities were 0.14 and 0.27 for PWG and 0.36 and 0.47 for SV. Genetic correlation between PWG measured at low and high altitude was 0.68. Favorable genetic correlations were estimated between SV and PWG within and between altitudes, suggesting that calves with genetics for increased growth from weaning to yearling also have increased genetic potential for SV. Genetic evaluations of PWG in different altitudes should consider preselection of the data, by using a censoring trait, like survivability to yearling.     

Heat stress effects on farrowing rate in sows: genetic parameter estimation using within-line and crossbred models

The pork supply chain values steady and undisturbed piglet production. Fertilization and maintaining gestation in warm and hot climates is a challenge that can be potentially improved by selection. The objective of this study was to estimate 1) genetic variation for farrowing rate of sows in 2 dam lines and their reciprocal cross; 2) genetic variation for farrowing rate heat tolerance, which can be defined as the random regression slope of farrowing rate against increasing temperature at day of insemination, and the genetic correlation between farrowing rate and heat tolerance; 3) genetic correlation between farrowing rate in purebreds and crossbreds; and 4) genetic correlation between heat tolerance in purebreds and crossbreds. The estimates were based on 93,969 first insemination records per cycle from 24,456 sows inseminated between January 2003 and July 2008. These sows originated from a Dutch purebred Yorkshire dam line (D), an International purebred Large White dam line (ILW), and from their reciprocal crosses (RC) raised in Spain and Portugal. Within-line and crossbred models were used for variance component estimation. Heritability estimates for farrowing rate were 0.06, 0.07, and 0.02 using within-line models for D, ILW, and RC, respectively, and 0.07, 0.07, and 0.10 using the crossbred model, respectively. For farrowing rate, purebred-crossbred genetic correlations were 0.57 between D and RC and 0.50 between ILW and RC. When including heat tolerance in the within-line model, heritability estimates for farrowing rate were 0.05, 0.08, and 0.03 for D, ILW, and RC, respectively. Heritability for heat tolerance at 29.3°C was 0.04, 0.02, and 0.05 for D, ILW, and RC, respectively. Genetic correlations between farrowing rate and heat tolerance tended to be negative in crossbreds and ILW-line sows, implying selection for increased levels of production traits, such as growth and reproductive output, is likely to increase environmental sensitivity. This study shows that genetic selection for farrowing rate and heat tolerance is possible. However, when this selection is based solely on purebred information, the expected genetic progress on farrowing rate and heat tolerance in crossbreds (commercial animals) would be inconsequential.     

Impact of including the cause of missing records on genetic evaluations for growth in commercial pigs

It is of interest to evaluate crossbred pigs for hot carcass weight (HCW) and birth weight (BW); however, obtaining a HCW record is dependent on livability (LIV) and retained tag (RT). The purpose of this study is to analyze how HCW evaluations are affected when herd removal and missing identification are included in the model and examine if accounting for the reasons for missing traits improves the accuracy of predicting breeding values. Pedigree information was available for 1,965,077 purebred and crossbred animals. Records for 503,716 commercial three-way crossbred terminal animals from 2014 to 2019 were provided by Smithfield Premium Genetics. Two pedigree-based models were compared; model 1 (M1) was a threshold-linear model with all four traits (BW, HCW, RT, and LIV), and model 2 (M2) was a linear model including only BW and HCW. The fixed effects used in the model were contemporary group, sex, age at harvest (for HCW only), and dam parity. The random effects included direct additive genetic and random litter effects. Accuracy, dispersion, bias, and Pearson correlations were estimated using the linear regression method. The heritabilities were 0.11, 0.07, 0.02, and 0.04 for BW, HCW, RT, and LIV, respectively, with standard errors less than 0.01. No difference was observed in heritabilities or accuracies for BW and HCW between M1 and M2. Accuracies were 0.33, 0.37, 0.19, and 0.23 for BW, HCW, RT, and LIV, respectively. The genetic correlation between BW and RT was 0.34 ± 0.03, and between BW and LIV was 0.56 ± 0.03. Similarly, the genetic correlation between HCW and RT was 0.26 ± 0.04, and between HCW and LIV was 0.09 ± 0.05, respectively. The positive and moderate genetic correlations between BW and other traits imply a heavier BW resulted in a higher probability of surviving to harvest. Genetic correlations between HCW and other traits were lower due to the large quantity of missing records. Despite the heritable and correlated aspects of RT and LIV, results imply no major differences between M1 and M2; hence, it is unnecessary to include these traits in classical models for BW and HCW.     

Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.