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Journal of Animal Science - Animal Genetics

Genomic predictions in Angus cattle: Comparisons of sample size, response variables, and clustering methods for cross-validation1

 

This article in JAS

  1. Vol. 92 No. 2, p. 485-497
    unlockOPEN ACCESS
     
    Received: Mar 28, 2013
    Accepted: Nov 27, 2013
    Published: November 24, 2014


    2 Corresponding author(s): Prashanth.Boddhireddy@Zoetis.com
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doi:10.2527/jas.2013-6757
  1. P. Boddhireddy 2,
  2. M. J. Kelly,
  3. S. Northcutt,
  4. K. C. Prayaga§,
  5. J. Rumph* and
  6. S. DeNise*
  1. Zoetis Inc., Kalamazoo, MI 49007
    Queensland Alliance for Agriculture and Food Innovation, University of Queensland, Brisbane St. Lucia, QLD, 4072, Australia
    American Angus Association, 3201 Frederick Ave, Saint Joseph, MO 64506
    Zoetis Inc., 45 Poplar Road, Parkville, Victoria, 3052, Australia

Abstract

Advances in genomics, molecular biology, and statistical genetics have created a paradigm shift in the way livestock producers pursue genetic improvement in their herds. The nexus of these technologies has resulted in combining genotypic and phenotypic information to compute genomically enhanced measures of genetic merit of individual animals. However, large numbers of genotyped and phenotyped animals are required to produce robust estimates of the effects of SNP that are summed together to generate direct genomic breeding values (DGV). Data on 11,756 Angus animals genotyped with the Illumina BovineSNP50 Beadchip were used to develop genomic predictions for 17 traits reported by the American Angus Association through Angus Genetics Inc. in their National Cattle Evaluation program. Marker effects were computed using a 5-fold cross-validation approach and a Bayesian model averaging algorithm. The accuracies were examined with EBV and deregressed EBV (DEBV) response variables and with K-means and identical by state (IBS)-based cross-validation methodologies. The cross-validation accuracies obtained using EBV response variables were consistently greater than those obtained using DEBV (average correlations were 0.64 vs. 0.57). The accuracies obtained using K-means cross-validation were consistently smaller than accuracies obtained with the IBS-based cross-validation approach (average correlations were 0.58 vs. 0.64 with EBV used as a response variable). Comparing the results from the current study with the results from a similar study consisting of only 2,253 records indicated that larger training population size resulted in higher accuracies in validation animals and explained on average 18% (69% improvement) additional genetic variance across all traits.



INTRODUCTION

Genomic selection methods add value to traditional breeding programs by improving the accuracy of breeding value estimates. The improved accuracy enables faster genetic improvement by decreasing generation intervals and providing more accurate selection decisions. Genomic selection involves using a training population with genotypes and phenotypes to simultaneously estimate effects of thousands of SNP across the genome (Meuwissen et al., 2001). These SNP effects can be used to predict genetic merit of any genotyped animal referred to as direct genomic values (DGV), which can be combined with EBV to compute genomically enhanced EBV (VanRaden et al., 2009).

The accuracy of the estimated DGV is important to the application of genomic selection in animal breeding. Several factors influence DGV accuracy including the number of records in the training population, the relationship between the discovery population and the target validation population (Habier et al., 2007, 2010; Clark et al., 2012), the type of response variable (e.g., raw phenotypes, EBV, or deregressed EBV [DEBV; Garrick et al., 2009]) used for estimating SNP effects, and the methodologies used for clustering training data for cross-validation (Saatchi et al., 2011). Others include the effective population size (Goddard and Hayes, 2009; Daetwyler et al., 2010), the extent oflinkage disequilibrium (LD) and density of genotypes (De Roos et al., 2008; Hayes et al., 2009a; Kim and Kirkpatrick, 2009; Wolc et al., 2011), the number of QTL contributing towards a trait of interest (Hayes et al., 2010), the heritability of the trait (Goddard and Hayes, 2009), the accuracy associated with the measurement of phenotypes, and statistical methodologies used for estimating DGV and corresponding accuracies (Moser et al., 2009; Su et al., 2010).

In this study we evaluate the effect of EBV and DEBV response variables, the utility of K-means and identical by state (IBS)-based clustering methods for cross-validation, and the effect of training population size on the prediction accuracy.


MATERIALS AND METHODS

Data

The study used genotypes on 11,756 registered Angus animals with expected progeny differences (EPD) records. The cryopreserved semen, hair follicles, or blood samples of these animals were procured from various commercial AI organizations, research organizations, and commercial breeders. The DNA was extracted from these samples and genotyped using the Illumina BovineSNP50 chip (Illumina Inc., San Diego, CA).

Seventeen traits were used in this analysis including birth weight(BIR_WT), calving ease direct (CED), calving ease maternal (CEM), carcass weight (CW), docility, fat thickness (FAT), DMI, heifer pregnancy (HP), marbling score (MARB), mature height (MHT), mature weight, maternal milking ability (MILK), rib eye area (REA), scrotal circumference, weaning weight (WW), yearling weight, and yearling height. By combining 3 generations of pedigree information on sires and dams, a total of 23,448 EPD and 52,164 pedigree records were available for this study. The EPD and their associated Beef Improvement Federation (BIF) accuracies were obtained from the American Angus Association (AAA) national cattle evaluation in March 2012. The number of records with both phenotypes and genotypes available varied across traits ranging from 573 records for HP to 7,976 records for CW (Table 1). Heritability estimates for the traits ranged from 0.12 for CEM to 0.64 for MHT as estimated using the entire AAA phenotypic database (Angus National Cattle Evaluation; http://www.angus.org/Nce/Heritabilities.aspx). The mean BIF accuracies are presented in Table 1.


View Full Table | Close Full ViewTable 1.

Heritability estimates and summary statistics for the traits used in this study. Cross-validation (CRV) and external validation (EXV) are data splits representing cross-validation and validation datasets, respectively

 
Trait H2 Animals EPD1 Mean EPD SD Mean BIF2 accuracy Mean BIF accuracy in CRV Mean BIF accuracy in EXV
Birth wt, kg 0.42 7,804 0.81 0.73 0.39 0.43 0.31
Calving ease direct, % 0.20 6,905 6.24 3.81 0.31 0.34 0.24
Calving ease maternal, % 0.12 6,905 7.64 2.97 0.18 0.22 0.10
Carcass wt, kg 0.28 7,976 9.25 4.00 0.17 0.21 0.10
Docility, % 0.37 2,012 11.31 10.27 0.36 0.42 0.24
Fat thickness, cm 0.42 7,974 0.03 0.05 0.19 0.23 0.13
DMI, kg/d 0.31 2,570 0.08 0.08 0.29 0.33 0.23
Heifer pregnancy, % 0.13 573 8.26 2.1 0.26 0.32 0.13
Marbling score 0.37 7,975 0.51 0.28 0.22 0.25 0.16
Mature height, cm 0.64 676 0.86 1.17 0.47 0.57 0.27
Maternal milking ability, kg 0.14 7,804 11.08 2.74 0.21 0.26 0.13
Mature wt, kg 0.37 676 33.4 29.6 0.45 0.53 0.29
Rib eye area, cm2 0.37 7,976 1.94 1.35 0.26 0.30 0.19
Scrotal circumference, cm 0.47 4,610 0.43 0.54 0.39 0.44 0.31
Weaning wt, kg 0.20 7,804 23.38 4.38 0.31 0.34 0.23
Yearling height, cm 0.50 3,103 0.81 0.81 0.44 0.50 0.34
Yearling wt, kg 0.20 7,804 42.27 7.29 0.27 0.31 0.18
1EPD = expected progeny differences.
2BIF = Beef Improvement Federation.

Quality Control for Genotypes.

Animals with identical genotypes (i.e., genomic twins) as well as animals with call rate less than 80% were removed from the analysis. Markers that had a call rate less than 70% were also removed from the analysis. Genotypes derived from both the version 1 and version 2 of the BovineSNP50 were used so only markers present on both chips were considered in this study. After editing, the total number of markers remaining for the analysis was 48,048.

Response Variables.

Estimated breeding values and DEBV were used as response variables for genomic analyses. For this purpose, initially EPD were multiplied by 2 to derive EBV and the BIF accuracies were converted into standard accuracies using the formula proposed in BIF guidelines (Beef Improvement Federation, 2010) as

Deregressed EBV were computed using EBV and their respective accuracies as per the approach proposed by Garrick et al. (2009). This approach is designed to eliminate the parental information and shrinkage inherent in EBV. The base-adjustment value required for calculation of DEBV was computed as the mean value of the EBV (for that trait). Furthermore, to ensure the quality of DEBV used in the study, only animals with DEBV accuracy greater than a 0.05 threshold were included in the analysis, similar to the study by Ostersen et al. (2011). The number of animals removed from the genomic analyses with DEBV as the response variable varied depending on the trait and associated accuracies (Fig. 1). As a consequence of the deregression methodology and the threshold imposed, DEBV records of CEM and MILK traits had only one-third the number of records compared to EBV response variables. Hence, these traits were not analyzed with DEBV response variables.

Figure 1.
Figure 1.

Number of observations in training cross-validation (CRV) group and validation group (external validation [EXV]) for response variables EBV and deregressed EBV (DEBV) for several traits studied.

 

Statistical Methodology

The estimation and evaluation of genomic selection results was undertaken in 2 steps denoted as cross-validation (CRV) and external validation (EXV). The available data for each trait were divided into 2 groups based on EBV accuracy: the top two-thirds high accuracy animals as the CRV dataset and the bottom one-third low accuracy animals as the EXV dataset.

Cross-Validation.

The training dataset was classified into 5 groups either using K-means or IBS-based clustering methods. During CRV, a prediction equation was developed using the marker effects estimated in 4 of the 5 groups and tested in the fifth group that was not used for marker effect estimation. This fifth group provided the CRV results from that calibration. This process was repeated 5 times leaving a different group out of the estimation of marker effects each time. The prediction equations applied to the EXV dataset were the average marker effects across 5 calibrations.

K-Means and Identical by State-Based Clusterings for Cross-Validation.

Both K-means and IBS-based clustering methods use a distance matrix that is a measure of the relationship among the animals in the dataset. The distance matrix was computed from the pedigree and genotypes for K-means and IBS-based methods, respectively.

In the K-means methodology, the distance matrix was the A matrix (additive relationship matrix computed from the pedigree) with slight modifications to each of the elements in the matrix. If the elements of the A matrix were denoted as aij, the elements of the distance matrix for K-means methodology was computed as dij = 1 – [aij/(aiiajj)1/2] as described by Saatchi et al. (2011), in which dij is a measure of pedigree distance between individual i and individual j, aij is the additive genetic relationship between individual i and individual j, and aii and ajj are diagonal elements of the A matrix. The A matrix was computed using PyPedal (Cole, 2007) and both the relationship matrix and K-means methodology (Hartigan and Wong, 1979) were implemented in R (R Development Core Team, 2011).

In the IBS-based method, the distance matrix consisted of IBS distances computed from marker genotypes. An R package called GenABEL (Aulchenko et al., 2007) was used for the computation of the IBS distance matrix asin which fij is the relationship between animals i and j, xi,k is the genotype at marker k for animal i, xj,k is the genotype at marker k for animal j, and pk is the allele frequency for marker k. The IBS distance matrix was then subjected to principal component analysis to reduce the dimensionality of the relationship matrix from n × n to n × 1. Ranks derived from the first principal component (PC1), which explains the greatest amount of variation, were used for partitioning animals into 1 of 5; the first one-fifth records were assigned to group 1, the next one-fifth records were assigned to group 2, and so on.

The maximum relationship coefficients (amax) were computed to evaluate the relationship among animals within and across clusters for different clustering methods. For an animal k belonging to cluster i, amax(i,j)k was the maximum of the relationship value (in the numerator relationship matrix) across all the animals in cluster j. The average maximum relationship of all animals in cluster i to the animals in cluster j was amax(i,j). The estimate of amax_within for a cluster i was then amax(i,i) and amax_across for a given cluster i was computed as the average of (amax(i,j)), in which ji. In addition, the difference between amax_within and amax_across, denoted as amax_diff, was also computed. Although IBS-based and K-means clustering methods were of primary interest in the current study, for comparative purposes and to enable better understanding of the effect of clustering methods on CRV results, comparisons were also made against random clustering and IBS-based methodology with unequal cluster sizes (IBS_UnEqual) for BIR_WT. In the IBS_UnEqual clustering method, the clustering was solely driven by PC1 values ignoring cluster sizes. The difference between maximum and minimum PC1 values across all clusters within IBS_UnEqual method was similar whereas the same was not necessarily true in the case of IBS-based method with equal sized clusters.

Computation of Marker Effects and Direct Genomic Value.

The allele substitution effect for each marker was computed using Gensel (Fernando and Garrick, 2008) in which a Bayesian method called BayesC was used for estimation of marker effects. BayesC fits a statistical model assuming a known fraction of markers as having zero effects, which in the current analyses was set to be 0.95. This is referred to as πi denoting the proportion of markers excluded in the model in each Gibbs sampling run. The total number of Markov Chain Monte Carlo iterations used for estimating posterior means of marker effects and variances was 45,000, of which the first 5,000 were discarded for burn-in. For each trait, both EBV and DEBV were used as response variables. In the analyses with EBV as response variable, accuracies were used as weighting factors. In the analyses with DEBV as the response variable, respective weights were calculated according to Garrick et al. (2009). The weight for the ith animal was wi = (1 – h2)/{[c + (1 – r2i)/r2i]h2}, in which h2 was the heritability of the trait, c was the part of the genetic variance not explained by markers, and r2i was the reliability of the DEBV of the ith animal. Three different c values, 0.10, 0.50, and 0.70, were used for computing weights.

The basic statistical model used for estimating these marker effects for each trait wasin which yi is the response variable, m is the number of markers, xij denotes genotype codes 0, 1, and 2 (for the 0, 1, and 2 copies of “A” allele, respectively), bj is the substitution effect of marker j, and e is residual error. The DGV of the targeted animals in a validation dataset were calculated by summing the products of the estimated marker substitution effects () and their genotype codes xij as

Five sets of DGV were computed, 1 corresponding to each of the CRV group. A pooled correlation across the 5 CRV groups was computed as described in Snedecor and Cochran (1967). Direct genomic values were also computed for EXV animals. The marker effects for computing DGV were average of marker effects across the 5 CRV groups for both K-means and IBS-based strategies.

Parameters to Evaluate Direct Genomic Values

A perfect evaluation of genomic predictions requires the estimation of the correlation between true breeding values and DGV. As true breeding values were not available, an approximation to the evaluation was achieved by computing the correlation between predicted values (DGV) and EBV in both the CRV and EXV datasets in the current study. In the case of DEBV, the correlation was divided by the square root of the heritability since the DEBV were on the phenotypic scale.

In addition, the regression of EBV or DEBV on DGV was calculated to evaluate prediction bias. The DGV were unbiased, downward biased, and upward biased when regression coefficients were closest to, greater than, and less than 1, respectively. Percent genetic variation (%GV) explained was computed by squaring the correlation between DGV and EBV and then multiplying by 100.

Subset of the Data.

One of the objectives of this study was to evaluate the effect of size of the training dataset on the accuracy of genomic predictions. A subset of the above mentioned dataset with 10 traits was analyzed in 2010, referred to as the year 2010 study in this publication. A total of 2,253 records with both genotypes and EPD were available for the year 2010 study. The EPD were obtained from AAA national cattle evaluation in November 2010. The EPD were initially multiplied by 2 to derive EBV and BIF accuracies were converted into standard accuracies as described earlier. The animals were genotyped on version 1 of the Illumina BovineSNP50 chip. The 10 traits common with the current study were BIR_WT, CED, CEM, CW, FAT, DMI, MARB, MILK, REA, and WW. Heritability estimates were similar for most of the traits between the studies. The number of records available ranged from 1,722 records for CED to 2,253 records for DMI. Summary statistics for this data subset are presented in the Table 2. Similar to the current study, the year 2010 dataset was divided into training and validation groups consisting of two-thirds higher accuracy bulls and one-third lower accuracy animals, respectively. The genomic analyses methodology was the same as the current study. However, only the EBV response variable with IBS-based clustering method was used in the CRV.


View Full Table | Close Full ViewTable 2.

Number of observations and summary statistics for several traits used in the year 2010 study1. Cross-validation (CRV) and external validation (EXV) are data splits representing cross-validation and validation datasets, respectively

 
Trait H2 Animals EPD2 mean EPD SD Mean BIF3 accuracy Mean BIF accuracy in CRV Mean BIF accuracy in EXV
Birth wt, kg 0.31 1,783 0.98 0.37 0.39 0.42 0.32
Calving ease direct, % 0.10 1,722 4.67 1.95 0.30 0.32 0.22
Calving ease maternal, % 0.14 1,722 5.67 1.42 0.16 0.18 0.09
Carcass wt, kg 0.29 1,812 4.63 0.73 0.14 0.18 0.08
DMI, kg/d 0.48 2,253 0.12 0.14 0.28
Fat thickness, cm 0.42 1,844 0.03 0.03 0.20 0.23 0.13
Marbling score 0.37 1,844 0.27 0.1 0.20 0.24 0.14
Maternal milking ability, kg 0.12 1,783 9.80 1.15 0.30 0.32 0.21
Rib eye area, cm2 0.37 1,844 0.90 0.58 0.23 0.27 0.17
Weaning wt, kg 0.25 1,783 21.41 1.96 0.30 0.33 0.23
1This dataset refers to a subset data of the current study that was analyzed in year 2010.
2EPD = expected progeny differences.
3BIF = Beef Improvement Federation.


RESULTS

Estimated Breeding Value vs. Deregressed EBV Response Variables

The correlations, regression coefficients, and %GV for training CRV and EXV are presented in Table 3. The results indicate that the CRV and EXV mean correlations were higher and consistent across traits when using EBV response variable than those obtained using DEBV. The mean CRV correlations across all traits were 0.64 and 0.57 using EBV and DEBV traits, respectively (Table 3). With EXV data sets, the mean correlations were 0.63 and 0.44 for EBV and DEBV traits, respectively (Table 3). These results demonstrate that DEBV prediction accuracies were higher when EBV accuracies were higher. The accuracies obtained with c values of 0.1, 0.5, and 0.7 (used in computation weights of DEBV) resulted in similar accuracies across all traits indicating that the accuracies were not sensitive to choice of c used for DEBV weights. The DEBV results presented in the tables were based on c value of 0.50.


View Full Table | Close Full ViewTable 3.

Accuracies of direct genomic values (DGV), regression coefficients, and percent genetic variation explained by DGV with EBV and deregressed EBV (DEBV) response variables

 
Training (cross-validation)
External validation
EBV DEBV EBV DEBV
Trait r1 b1 %GV1 r b %GV r b %GV r b %GV
Birth wt, kg 0.55 0.90 30 0.54 1.01 29 0.57 0.86 32 0.44 1.02 19
Calving ease direct, % 0.59 0.91 34 0.70 1.20 49 0.59 0.99 35 0.54 1.31 30
Calving ease maternal, % 0.65 0.92 42 0.62 0.92 39
Carcass wt, kg 0.74 0.91 55 0.43 0.95 18 0.62 0.88 39 0.54 1.75 30
Docility, % 0.64 0.80 41 0.71 0.78 50 0.69 0.91 48 0.58 1.22 34
Fat thickness, cm 0.74 1.19 54 0.48 1.12 23 0.61 1.19 37 0.46 1.44 21
DMI, kg/d 0.44 1.01 19 0.34 0.95 12 0.39 0.99 15 0.22 0.86 5
Heifer pregnancy, % 0.57 0.95 31 0.54 2.22 29 0.71 0.87 51 0.12 1.25 2
Marbling score 0.76 1.00 58 0.51 1.05 26 0.78 1.01 61 0.48 1.24 23
Mature height, cm 0.56 1.04 31 0.52 0.97 27 0.66 1.11 43 0.34 1.12 11
Maternal milking ability, kg 0.72 0.91 52 0.72 0.87 52
Mature wt, kg 0.47 0.73 22 0.28 0.21 8 0.55 0.90 30 0.24 0.35 6
Rib eye area, cm2 0.71 0.97 50 0.62 0.95 38 0.65 0.97 42 0.50 1.17 25
Scrotal circumference, cm 0.62 0.91 38 0.60 1.03 36 0.63 0.94 40 0.41 1.11 17
Weaning wt, kg 0.71 0.92 50 0.77 1.16 59 0.68 0.88 46 0.62 1.21 39
Yearling height, cm 0.62 0.94 37 0.57 1.05 32 0.61 0.85 37 0.41 1.00 16
Yearling wt, kg 0.74 0.93 55 0.91 1.15 83 0.68 0.83 47 0.71 1.20 51
AVG 0.64 0.94 41 0.57 1.05 35 0.63 0.94 41 0.44 1.15 22
1r = accuracy of DGV estimated as correlation between DEBV or EBV and DGV; b = regression of DEBV or EBV on DGV; %GV = percent genetic variance explained by DGV.

The predictive ability of DGV was further explored by contrasting the response variables used in developing prediction equations (Fig. 2). Estimated breeding values were predicted with higher accuracies using prediction equations developed with EBV than those developed with DEBV response variables. In contrast, DEBV were predicted with similar accuracies with prediction equations developed with EBV response variables as those developed with DEBV response variables at least in some traits.

Figure 2.
Figure 2.

Direct genomic value (DGV) accuracies compared for EBV and deregressed EBV (DEBV) response variables in the external validation dataset. Direct genomic values, DGV_EBV and DGV_DEBV were computed with EBV and DEBV response variables, respectively. For EBV response variables, accuracy was measured as correlation between DGV and EBV. For DEBV response variables, accuracy was computed as correlation between DGV and DEBV divided by square root of heritability.

 

Identical by State-Based vs. K-Means Clustering

The training CRV mean correlations obtained with IBS-based clustering were higher than those obtained using K-means clustering methodology. The average correlation across all traits was 0.64 and 0.58 with IBS based and K-means, respectively (Table 4), with EBV as the response variable. The average correlation across all traits was 0.57 and 0.51 with IBS based and with K-means, respectively, when DEBV was used as the response variable. The correlation between IBS-based and K-means correlations across all the traits was approximately 0.96. In general, correlations were higher in IBS-based clustering methods with the exception of marbling for which accuracies were slightly higher for K-means clustering method.


View Full Table | Close Full ViewTable 4.

Accuracies of direct genomic values (DGV), regression coefficients of deregressed EBV (DEBV) or EBVon DGV and percent genetic variation explained by DGV with EBV and DEBV as response variables comparing identical by state (IBS)-based and K-means cross-validation methods

 
Trait IBS based (EBV) K-means (EBV) IBS based (DEBV) K-means (DEBV)
r1 b1 %GV1 r b %GV r b %GV r b %GV
Birth wt, kg 0.55 0.9 30 0.49 0.87 24 0.54 1.01 29 0.47 0.99 22
Calving ease direct, % 0.59 0.91 34 0.51 0.86 26 0.70 1.20 49 0.61 1.21 38
Calving ease maternal, % 0.65 0.92 42 0.59 0.84 34
Carcass wt, kg 0.74 0.91 55 0.68 0.91 46 0.43 0.95 18 0.38 0.95 15
Docility, % 0.64 0.80 41 0.63 0.79 39 0.71 0.78 50 0.70 0.79 50
Fat thickness, cm 0.74 1.19 54 0.70 1.21 49 0.48 1.12 23 0.42 1.00 18
DMI, kg/d 0.44 1.01 19 0.41 0.92 17 0.34 0.95 12 0.33 0.95 11
Heifer pregnancy, % 0.57 0.95 31 0.54 0.97 29 0.54 2.22 29 0.58 4.64 34
Marbling score 0.76 1.00 58 0.77 0.95 60 0.51 1.05 26 0.55 1.12 30
Mature height, cm 0.56 1.04 31 0.43 0.97 18 0.52 0.97 27 0.36 0.83 13
Maternal milking ability, kg 0.72 0.91 52 0.66 0.87 44
Mature wt, kg 0.47 0.73 22 0.33 0.62 11 0.28 0.21 8 0.14 0.12 2
Rib eye area, cm2 0.71 0.97 50 0.69 0.94 48 0.62 0.95 38 0.58 0.89 34
Scrotal circumference, cm 0.62 0.91 38 0.55 0.90 30 0.60 1.03 36 0.52 1.01 27
Weaning wt, kg 0.71 0.92 50 0.62 0.87 39 0.77 1.16 59 0.68 1.22 47
Yearling height, cm 0.62 0.94 37 0.58 0.94 33 0.57 1.05 32 0.55 1.07 30
Yearling wt, kg 0.74 0.93 55 0.66 0.87 44 0.91 1.15 83 0.81 1.16 65
AVG 0.64 0.94 42 0.58 0.9 35 0.57 1.05 35 0.51 1.2 29
1r = accuracy of DGV estimated as correlation between DEBV or EBV and DGV; b = regression of DEBV or EBV on DGV; %GV = percent genetic variance explained by DGV.

Relationship of Animals Within and Across Clusters with Different Clustering Methods

The number of records, amax_within, amax_across, and amax_diff values, indicating the relationship among animals within and across clusters created through K-means, IBS-based, random, and IBS_UnEqual clustering methods are presented in Table 5. As expected, these results demonstrate that K-means method and IBS_UnEqual methods disproportionately allocate animals to different clusters. One of the 5 clusters had more than 40% of the animals while another had less than 6% of the animals. The amax_diff values for K-means, IBS based, random, and IBS_UnEqual are 0.23, 0.12, 0.00, and 0.20, respectively, indicating that the K-means method provides tighter clustering followed by IBS_UnEqual, IBS-based, and random method, respectively. The average correlation between EBV and DGV for BIR_WT trait was 0.48, 0.55, 0.59, and 0.52 for K-means, IBS-based, random, and IBS_UnEqual methods, respectively. The confidence interval range around the correlations was smaller (0.08–0.09) for IBS-based and random methods while the range was larger for K-means (0.06–0.19) and IBS_UnEqual (0.06–0.34).


View Full Table | Close Full ViewTable 5.

Comparison of relationship among animals within (amax_within) and across (amax_across) clusters in various methods

 
Method Cluster Animals amax_within amax_across amax_diff1 r2 CI3 of r
K-means Cluster 1 284 0.56 0.24 0.32 0.43 0.33 to 0.52
K-means Cluster 2 2,150 0.47 0.31 0.17 0.49 0.46 to 0.52
K-means Cluster 3 1,243 0.50 0.31 0.18 0.52 0.48 to 0.56
K-means Cluster 4 1,039 0.37 0.21 0.16 0.46 0.41 to 0.51
K-means Cluster 5 434 0.55 0.23 0.32 0.52 0.45 to 0.59
Average 0.49 0.26 0.23 0.48
IBS4based Cluster 1 1,030 0.55 0.28 0.27 0.50 0.45 to 0.54
IBS based Cluster 2 1,030 0.43 0.32 0.11 0.55 0.51 to 0.59
IBS based Cluster 3 1,030 0.38 0.32 0.06 0.55 0.51 to 0.59
IBS based Cluster 4 1,030 0.37 0.32 0.05 0.59 0.55 to 0.63
IBS based Cluster 5 1,030 0.45 0.30 0.15 0.58 0.54 to 0.62
Average 0.44 0.31 0.13 0.55
Random Cluster 1 1,093 0.38 0.39 –0.01 0.58 0.54 to 0.62
Random Cluster 2 999 0.37 0.37 0.00 0.62 0.58 to 0.66
Random Cluster 3 1,030 0.37 0.37 0.00 0.60 0.56 to 0.64
Random Cluster 4 1,032 0.37 0.38 –0.01 0.56 0.52 to 0.60
Random Cluster 5 996 0.40 0.39 0.01 0.60 0.56 to 0.64
Average 0.38 0.38 0.00 0.59
IBS_UnEqual5 Cluster 1 71 0.43 0.16 0.27 0.53 0.34 to 0.68
IBS_UnEqual Cluster 2 2,423 0.45 0.35 0.10 0.53 0.50 to 0.56
IBS_UnEqual Cluster 3 1,731 0.44 0.35 0.09 0.52 0.48 to 0.55
IBS_UnEqual Cluster 4 638 0.49 0.29 0.19 0.54 0.48 to 0.59
IBS_UnEqual Cluster 5 287 0.57 0.24 0.33 0.47 0.37 to 0.56
Average 0.48 0.28 0.20 0.52
1amax_diff = the difference between amax_within and amax_across.
2Training cross-validation correlations (r) between EBV and direct genomic values for birth weight.
3CI = confidence interval of correlations.
4IBS = identical by state.
5IBS_UnEqual = IBS-based methodology with unequal cluster sizes.

The distribution of amax values for different clustering methods is shown in Fig. 3. The results demonstrate that in IBS-based and IBS_UnEqual clustering methods, the animals in cluster i are more closely related to the animals in cluster i – 1 and i + 1 than to those in clusters i – 2 and i + 2. Similar distinctions could not be made for K-means clusters since the clustering was not driven by values on a linear scale as in IBS method. The distribution of amax for random clustering method is uniform across all clustering methods.

Figure 3.
Figure 3.

The mean of the maximum relationship coefficients (amax) values between different clusters for identical by state (IBS)-based, K-means, random, and IBS-based methodology with unequal cluster sizes (IBS_UnEqual) clustering methods.

 

Current Study vs. Year 2010 Study

The results of this study were compared to the results obtained from a previous study with the same methodology but with fewer records (see Table 6). The comparison is based on results obtained using only EBV response variables. The average CRV correlations are comparable in both studies albeit with moderate increases in the current study. However, EXV results demonstrate a significant improvement in accuracy (0.49 vs. 0.65; Table 6). Significant improvement was observed for CED, CW, MARB, MILK, REA, WW, and YW. The average amount of genetic variance explained increased from 26 to 44%, an average improvement of 69%.


View Full Table | Close Full ViewTable 6.

Comparison of accuracies of direct genomic values (DGV) and percent genetic variation explained by DGV across the current study and year 2010 study in cross-validation (CRV) and external validation (EXV) datasets

 
Year 2010 study results Current results
Trait Animals r1 – CRV %GV1 – CRV r – EXV %GV – EXV Animals r – CRV %GV – CRV r – EXV %GV – EXV
Birth wt, kg 1,783 0.55 30 0.52 27 7,804 0.55 30 0.57 32
Calving ease direct, % 1,722 0.57 32 0.41 17 6,905 0.59 35 0.60 36
Calving ease maternal, % 1,722 0.53 40 0.67 45 6,905 0.65 43 0.62 39
Carcass wt, kg 1,812 0.63 40 0.50 25 7,976 0.74 55 0.73 53
Fat thickness, cm 1,844 0.70 49 0.61 37 7,974 0.74 55 0.74 55
DMI, kg/d 2,253 0.39 17 0.28 11 2,570 0.44 19 0.39 15
Marbling score 1,844 0.77 59 0.49 24 7,975 0.76 58 0.76 58
Maternal milking ability, kg 1,783 0.68 46 0.43 18 7,804 0.72 52 0.73 53
Rib eye area, cm2 1,844 0.65 42 0.48 23 7,976 0.71 50 0.70 49
Weaning wt, kg 1,783 0.64 41 0.53 28 7,804 0.71 50 0.70 49
AVG 1,839 0.61 40 0.49 26 7,169 0.66 45 0.65 44
1r = accuracy of DGV estimated as correlation between EBV and DGV; %GV = percent genetic variance explained by DGV.


DISCUSSION

Genomic selection has made significant contributions in improving the accuracy of selection decisions, especially in dairy breeds. Similar efforts in beef cattle have been constrained by the lack of large pedigreed and recorded resource populations. In this study, we assembled a relatively large resource population for Angus beef cattle to generate robust genomic predictions across a wide range of economic traits. Furthermore, the effects of methodological variations on accuracy were also presented with a view to compare the response variables, the CRV groupings, and the size of the training dataset.

In the current study, a 2-step validation was implemented. In general, the accuracies obtained from CRV and EXV datasets were comparable and consistent within the EBV response variable while the accuracies obtained with DEBV response variables were considerably higher in CRV datasets than those observed in EXV datasets. One reason for such lower DEBV prediction accuracies in EXV dataset is that DEBV (obtained with low accuracy EBV) are expected to have smaller genomic contribution due to Mendelian sampling and have more noise added during deregression process, in which parental contribution is removed. It should be noted that in the current study, no effort was made to minimize the additive genetic relationships between CRV and EXV datasets and the split was driven strictly by EBV accuracies of various traits. Therefore, it is reasonable to expect that CRV and EXV datasets are related, with additive genetic relationships and LD determining the accuracy of DGV in the validation dataset as expected in a real world scenario. In a similar study in Angus cattle, Saatchi et al. (2011) reported DGV accuracies with DEBV response variables. The accuracies ranged from 0.22 to 0.69 with an average of 0.44. For the same traits, response variable, and clustering method, the correlation in our study ranged from 0.14 to 0.81 with an average of 0.50. The differences in the results could be attributed to a greater number of records used in this study.

The results of both CRV and EXV indicated that the accuracies obtained with EBV response variables were higher than those achieved with DEBV. In a dairy study, Aguilar et al. (2010) reported consistently slightly lower accuracies when using daughter deviations (DYD) as a response variable than EBV. In another dairy study, Gredler et al. (2010) found similar accuracies with EBV and DEBV for protein yield with an average accuracy of 94%. However, the prediction accuracies obtained with EBV response variables were markedly better than those obtained with deregressed EBV for the interval between first and last insemination in heifers and cows that had average EBV accuracies of 54 and 63%, respectively. Guo et al. (2010) compared the accuracies with EBV and DYD as response variables and found that using EBV resulted in slightly higher accuracies (approximately 1.9%) across several simulated scenarios.

On the contrary, Ostersen et al. (2011) found that DEBV as response variable resulted in higher reliabilities of DGV than those obtained using EBV in pigs. The improvement was about 39 and 18% for daily gain and feed conversion ratio. Thus, the results in the literature vary even though most results suggest that using EBV response variables resulted in higher accuracies than those obtained with DEBV or DYD. In some cases the improvement was marginal but was significant in other cases. In particular, the EBV response variables performed better for traits with lower EBV accuracies than for those traits with higher EBV accuracies relative to DEBV. This has important implications for development of genomic-enhanced evaluations in beef breeds where accuracy may be constrained by the number of available records.

While DEBV (Garrick et al., 2009) have reported to be more appropriate as response variables than EBV, the proposed advantage in predictive power is not supported in the current study. There can be several reasons for this result. The positive effect of using DEBV as response variable will depend on the degree of double counting and the amount and heterogeneity of information for genotyped animals (Ostersen et al., 2011). It can be postulated that in the current study, compared to pigs or dairy cattle, the degree of genetic relationships are lower among the individuals in the training population and therefore the advantage of DEBV in addressing double counting may have been reduced. Furthermore, the perceived disadvantage associated with variable EBV accuracies when used as response variables was addressed in the current study by including accuracies as weighting factors in the genomic analyses. In support of the current results, Guo et al. (2010) also reported that with sires having unequal number of progeny in a simulated dairy study, the reliabilities using the EBV approach were slightly higher than those using weighted DYD approach. In the same study, the simulated results showed that for traits of moderate to high heritability and relatively more number of progeny and hence high accuracies, EBV and DEBV generate DGV of similar accuracy and hence it can be stated that the relative advantage of 1 response variable over the other depends on the nature of the dataset.

Cross-validation is often used in predictive modeling studies to judge the generalizability of the statistical estimates to an unseen independent validation data set. The data in this study have been clustered for CRV using various strategies. The rationale for using clustering methods that use relationship among animals for CRV is that if the SNP underlying the prediction equations are causal mutations or in close proximity to causal mutations, then the estimates should hold up in a genetic background slightly further from the training dataset. However, some of the estimates that are based on weaker LD signals may not validate well in unseen data sets that might otherwise work in a data set that is similar to the training data set. By increasing tightness of clustering (i.e., increased amax_diff), one may lose weaker LD signals that contribute to prediction accuracy in the validation set of animals. It is therefore necessary to maintain a balance between the tightness of the clusters in CRV methodology and the possibility of losing LD signals that may improve prediction accuracy.

In this study we compared the accuracies of DGV across 17 traits analyzed with IBS-based and K-means clustering methods. Both these methods, as implemented in this study, partition the training animals based on the relationship among animals, 1 using information from computed genotypes and the other from pedigree. K-means tended to cluster animals into groups that were more homogenous (average amax = 0.49) compared to IBS (average amax = 0.44). Each group was more genetically distant to other groups within K-means compared to IBS (0.26 and 0.31, respectively). This was reflected in the lower CRV correlations in K-means compared to IBS based. This supports the results of Clark et al. (2012) and Habier et al. (2010) who showed that the genetic relationships between the training and the validation datasets impact realized genomic selection accuracy.

While the groups formed by K-means clustering had slightly less genetic diversity within groups (amax within = 0.49) compared to IBS or random clustering, the groups formed by this clustering were quite unbalanced. Unequal cluster sizes lead to difference in sampling variance between the CRV groups. Groups with smaller sizes will have accuracy estimates with larger sampling variance. This is reflected in the confidence intervals around the correlations where the confidence interval range for IBS based was stable (0.08–0.09) while the range was much larger for K-means (0.06–0.19) and IBS_UnEqual (0.06–0.34).

Another way of decreasing the relationship between calibration clusters and validation cluster while maintaining equal number of animals in calibration clusters is by excluding animals in clusters i – 1 and i + 1 from calibration. This is possible in IBS-based methods because of the linear scale on which the cluster group allocations are made. Therefore, it can be argued that IBS-based method offers better a balance between uniformity of cluster sizes and the difference in relatedness within and across clusters.

Increasing the number of animals in training has been shown to increase the accuracy of genomic selection in both theoretical (Daetwyler et al., 2008; Hayes et al., 2009b) and empirical studies (VanRaden et al., 2009). The results of the current study demonstrate that these prediction equations explained an additional 18% genetic variance across 10 traits in the validation dataset, where the size of the training population was increased from approximately 1,300 to 5,250 records.

Most studies comparing the effect of size of the training population have been in dairy cattle with limited comparable studies in beef cattle. In one of the first such empirical studies on genomic predictions, VanRaden et al. (2009) found that the gain from genomic prediction was linear for net merit when training size was increased from 1,151 bulls to 3,576 bulls in U.S. Holsteins. In the current study, while such an overall increase in accuracy across all traits was observed owing to increase in the training population, trait to trait variation was also evident. This also emphasized the fact that such an increase could not continue linearly with an increase in the training population and that different traits tend to slow down at differing rates depending on the additive genetic variation of the trait and the relationships among the training population. On the contrary, Moser et al. (2009) did not find any consistent improvement with increase in training size in an Australian dairy cattle study when the size was varied from 1,239 to 1,880, which could be attributed to fewer number of markers (about 7,000) and the addition of relatively fewer animals.

In a German Holstein study, Habier et al. (2010) reported an improved DGV accuracy due to LD alone with increasing training size in milk yield, fat yield, protein yield, and somatic cell score. For the same traits, a North American Holstein study (Habier et al., 2011) further confirmed that the accuracy of DGV improved markedly with training data size increase from 1,000 to 4,000 bulls albeit with slight improvement or a reduction from 4,000 to 6,500 bulls. Furthermore, there were trait and statistical method specific differences in the extent of increase in accuracy. In summary, there is overwhelming evidence in the literature to suggest that an increased training population size has a positive effect on DGV accuracies in cattle and in other species such as poultry (Wolc et al., 2011). This is consistent with the knowledge that with additional records, there will be more observations per SNP allele and hence greater accuracy in estimating SNP effects. This was summarized in a review describing the differences in accuracies of DGV achieved in various countries due to differing number of bulls used in the reference population (Hayes et al., 2009b). Increasing training population size increases the accuracy of genomic predictions by influencing several factors, for example, by increasing the relationship between the animals in the training and validation animals, especially in North American pure-bred Angus cattle where the effective population size is approximately 650 (Saatchi et al., 2011). Increasing the training population size also allows for the relaxation in cutoff thresholds such as decreasing minor allele frequency thereby retaining rare SNP in the genotype data. Furthermore, there could be a potential increase in the number of high EBV accuracy animals in the training with an indirect effect on the increased accuracy of predictions with an associated decrease in the sampling variance.

Conclusions

This study presented a comprehensive analysis of accuracies of genomic predictions using both CRV and EXV datasets in U.S. Angus cattle. Estimated breeding value response variables resulted in higher accuracies than those obtained with deregressed response variables. The marker effects estimated from EBV were as successful in predicting DEBV as marker effects computed from DEBV while the opposite was not true. Training CRV accuracies with K-means methodology resulted in accuracies that were consistently lower than those obtained with the IBS-based clustering method. Increasing the discovery population size increased the prediction accuracies and explained an average of 18% of additional genetic variance in the EXV data.

 

References

Footnotes


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