Comparison on genomic predictions using three GBLUP methods and two single-step blending methods in the Nordic Holstein population

  • Hongding Gao1, 3,

    Affiliated with

    • Ole F Christensen1,

      Affiliated with

      • Per Madsen1,

        Affiliated with

        • Ulrik S Nielsen2,

          Affiliated with

          • Yuan Zhang3,

            Affiliated with

            • Mogens S Lund1 and

              Affiliated with

              • Guosheng Su1Email author

                Affiliated with

                Genetics Selection Evolution201244:8

                DOI: 10.1186/1297-9686-44-8

                Received: 28 October 2011

                Accepted: 28 March 2012

                Published: 6 July 2012

                Abstract

                Background

                A single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population.

                Methods

                The data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the single-step blending method and the GBLUP method with a polygenetic effect.

                Results

                Averaged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method (without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method, respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP methods.

                Conclusions

                The single-step blending method is an appealing approach for practical genomic prediction in dairy cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the genomic relationship matrix.

                Background

                Selection based on dense markers across the genome [1] has become an important component of dairy cattle breeding programs [27]. The accuracy of genomic prediction relies on the amount of information used to derive the prediction equation. In many genomic selection programs, thousands of bulls which have been progeny tested over the last decades have been genotyped and are used as national reference populations. These have been extended by sharing data across countries to include much more information, such as the North American cooperation [8], the EuroGenomics project [7], and the joint Brown Swiss project [9]. Generally, genomic predictions are based on the data of all genotyped animals. However, in practice, not all individuals can be genotyped. To make use of as much information as possible for genetic evaluation, it is appealing to blend the genomic predicted breeding value and the traditional estimated breeding values (EBV) into genomically enhanced breeding values (GEBV) or to perform genomic prediction using all information available simultaneously.

                Many studies have shown that a linear model which assumes that effects of all single nucleotide polymorphisms (SNP) are normally distributed with equal variance performs as well as variable selection models for most traits in dairy cattle [2, 4]. Because such BLUP models are simple and have low computational requirements, they have become popular approaches for practical genomic prediction. De-regressed proofs (DRP) [10, 11] are generally used as the response variable for genomic prediction since they can be easily derived from the EBV that are usually available.

                Several blending strategies, including multi-step and single-step approaches, have been proposed to estimate GEBV [4, 5, 1218]. The core of a single-step procedure is the integration of the marker-based relationship matrix into the pedigree-based relationship matrix such that information of genotyped and non-genotyped animals is used simultaneously [1315]. Previous study by Su et al. [18] reported that a single-step procedure resulted in more accurate GEBV than a multi-step procedure.

                Some studies [1315, 18] have reported that the combined relationship matrix in a single-step method may need to be adjusted because the marker- and pedigree-based relationship matrices may not be on the same scale, and different methods to adjust for this have been proposed [1922]. These adjustments may also benefit genomic prediction using other models that integrate marker- and pedigree-based relationship matrices, such as a GBLUP model with a polygenic effect.

                The purpose of this study was to compare single-step blending and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population. De-regressed proofs were used as response variables in both GBLUP and the single-step blending methods.

                Methods

                Data

                Data consisted of 5 214 genotyped bulls born between 1974 and 2008 and 9 374 non-genotyped bulls born between 1950 and 2008. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Thus, the training data contained 3 045 genotyped and 8 822 non-genotyped bulls born before this date, and the validation data contained 2 169 genotyped bulls born after this date. Non-genotyped bulls born after October 1, 2001 were not used in training or validation. For the GBLUP methods described below, the training data only included the 3 045 genotyped animals. All 16 traits (sub-indices) in the Nordic Total Merit index were assessed, including yield, conformation, fertility, and health traits. For each trait, the DRP with reliability less than 0.20 were excluded from the training and the validation data. This removed 1.3%, 2.8% and 3.2% of DRP for birth index, fertility and health, respectively, and less than 0.5% for the other traits. The numbers of individuals in the training and validation datasets differed between traits (Table 1).
                Table 1

                Heritability (h 2 ) of the traits, number of bulls in training (Train) and validation datasets (Valid gen ) for GBLUP and single-step blending

                Trait

                h2

                TrainGBLUP

                Trainsingle

                Dif1

                Validgen 2

                Milk

                0.39

                3003

                9137

                6134

                1395

                Fat

                0.39

                3003

                9137

                6134

                1395

                Protein

                0.39

                3003

                9137

                6134

                1395

                Growth

                0.30

                2538

                6690

                4152

                1640

                Fertility

                0.04

                3037

                10909

                7872

                1378

                Birth index

                0.06

                3045

                10586

                7541

                2167

                Calving index

                0.03

                3040

                11538

                8498

                1501

                Mastitis

                0.04

                3006

                9174

                6168

                1461

                Health

                0.02

                3026

                9050

                6024

                1214

                Body conf.

                0.30

                2884

                7492

                4608

                1380

                Feet & Leg

                0.10

                2925

                7727

                4802

                1379

                Udder conf.

                0.25

                2928

                7743

                4815

                1380

                Milkingspeed

                0.26

                2928

                7725

                4797

                1380

                Temperament

                0.13

                2926

                7691

                4765

                1371

                Longevity

                0.10

                2980

                8740

                5760

                916

                Yield

                0.39

                3003

                9137

                6134

                1395

                1Number of additional non-genotyped bulls used in single-step blending compared to GBLUP (Col.4 – Col.3); 2 Only genotyped bulls in the validation dataset.

                Marker genotypes were obtained using the Illumina Bovine SNP50 BeadChip (Illumina, SanDiego, CA). The final marker data included 48 073 SNPs for 5 214 bulls after removing SNP with minor allele frequency (MAF) less than 0.01 and locus average GenCall score less than 0.60.

                De-regressed proofs (DRP) were used as response variables for genomic prediction in all approaches. Based on EBV data of 14 588 progeny-tested bulls and pedigree data of 42 144 animals, the de-regression was carried out by applying the iterative procedure described in [23, 24] using the MiX99 package [25] and with the heritabilities shown in Table 1, which were those used in Nordic cattle routine genetic evaluation. A detailed description of the Nordic cattle genetic evaluation and standardized procedures of EBV is given in http://​www.​nordicebv.​info/​Routine+evaluati​on/​.

                Statistical models

                Three GBLUP and two single-step blending methods were used. All analyses were performed with the DMU package [26, 27], for estimating both the variance components and breeding values.

                Simple GBLUP

                The basic GBLUP method [28, 29] used to predict direct genomic breeding values (DGV) was:
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ1_HTML.gif

                where y is the data vector of DRP of genotyped bulls, μ is the overall mean, 1 is a vector of ones, Z is a design matrix that allocates records to breeding values, g is a vector of DGV to be estimated, and e is a vector of residuals. It was assumed that http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq1_HTML.gif where http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq2_HTML.gif is the additive genetic variance, and G is the marker-based genomic relationship matrix [28, 29]. Allele frequencies used to construct G were estimated from the observed genotype data. Random residuals were assumed such that http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq3_HTML.gif where http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq4_HTML.gif is the residual variance and D is a diagonal matrix with elements http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq5_HTML.gif . The weights wi account for heterogeneous residual variances due to differences in reliabilities of DRP. They were defined as http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq6_HTML.gif , where http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq7_HTML.gif is the reliability of DRP. The reliability was calculated as http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq8_HTML.gif , where EDC is effective daughter contribution, and http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq9_HTML.gif . To avoid possible problems caused by extreme weight values, reliabilities larger than 0.98 were set to 0.98.

                GBLUP with a polygenic effect

                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ2_HTML.gif

                where u is the vector of residual polygenic effects that are not captured by the SNP.

                Here, we used an equivalent approach. Let http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq10_HTML.gif , http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq11_HTML.gif , where A is the pedigree-based relationship matrix. Define http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq12_HTML.gif and http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq13_HTML.gif , then http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq14_HTML.gif and http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq15_HTML.gif , such that http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq16_HTML.gif where ω is the ratio of residual polygenic to total additive genetic variance. Thus, the above model is equivalent to
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ3_HTML.gif

                It was assumed that http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq17_HTML.gif , where G ω is a combined relationship matrix, http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq18_HTML.gif . The estimates of g ω were defined as DGVω to distinguish from the simple GBLUP and the single-step blending methods.

                Adjusted GBLUP with a polygenic effect

                The model was the same as the above GBLUP method with a polygenic effect but G was adjusted to be on the same scale as A. Then, the combined relationship matrix was http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq19_HTML.gif , where G* is the adjusted genomic relationship matrix. The adjustment of G is described below.

                Original single-step blending

                The original single-step blending method [15, 17, 18] uses information from genotyped and non-genotyped individuals simultaneously by combining the genomic relationship matrix G with the pedigree-based numerator relationship matrix A, using the following model:
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ4_HTML.gif
                where y is the vector of DRP for both genotyped and non-genotyped bulls, 1 is a vector of ones, Z is a design matrix, and a is the vector of additive genetic effects, which are the sum of the genomic and the residual polygenic effects. It was assumed that http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq20_HTML.gif , where matrix H is the modified genetic relationship matrix that combines pedigree-based relationship information [13, 15]:
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ5_HTML.gif
                where A 11 is the sub-matrix of the pedigree-based relationship matrix (A) for genotyped animals, A 22 is the sub-matrix of A for non-genotyped animals, A 12 (or A 21) is the sub-matrix of A for relationships between genotyped and non-genotyped animals, and http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq21_HTML.gif , where ω is a weight (within the range from 0.05 to 0.40 in this study). The G matrix used in the single-step blending was the same as in the GBLUP method. The inverse of H[15, 17] is
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ6_HTML.gif

                Adjusted single-step blending

                In the adjusted single-step blending method, the G matrix was adjusted for the difference between the original genomic relationship matrix and pedigree relationship matrix (A 11), as proposed by previous studies [19, 20]. The G matrix was adjusted using two parameters α and β [21], i.e.,
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ7_HTML.gif
                which were derived from the following equations:
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ8_HTML.gif
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Equ9_HTML.gif

                Matrix G * was then used to replace G to construct the combined relationship matrix in the single-step blending method.

                The weights ω ranging from 0.05 to 0.40 were used to construct G ω and http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_IEq22_HTML.gif for the single-step blending methods and for the GBLUP methods with a polygenic effect.

                Validation

                The reliabilities of genomic predictions were measured as squared correlations between the predicted breeding values and DRP for bulls in the validation data, divided by the average reliability of the DRP in validation data. A Hotelling-Williams t-test was used to test the difference between the validation correlations obtained from these five prediction methods [30, 31]. Bias of genomic predictions was measured as the regression of DRP on the genomic predictions [32].

                Results

                Genomic predictions using the GBLUP method were improved when a polygenic effect was included (Tables 2 and 3). With a relative weight of 0.2 on the residual polygenic variance, the average reliability of genomic predictions for the 16 traits was 0.363, which was 0.3% points higher than the average reliability from the simple GBLUP. Moreover, the GBLUP method with a polygenic effect reduced bias of genomic predictions. Averaged over the 16 traits, the absolute deviation of the regression coefficient (DRP on genomic prediction) from 1 was 0.093 when using the GBLUP methods with a polygenic effect and 0.107 when using the simple GBLUP method. The GBLUP methods with a polygenic effect slightly reduced also bias in mean, as the intercept in the regression analysis was closer to 0, compared with the simple GBLUP. For the two GBLUP methods with a polygenic effect, adjustment of the genomic relationship matrix had no effect on predictive ability and bias.
                Table 2

                Reliabilities of genomic predictions using different methods

                Trait

                GBLUP

                GBLUPAG

                GBLUPAG*

                Milk

                0.431

                0.428

                0.428

                Fat

                0.455

                0.457

                0.457

                Protein

                0.429

                0.435

                0.435

                Growth

                0.468

                0.481

                0.481

                Fertility

                0.411

                0.419

                0.419

                Birth index

                0.258

                0.263

                0.263

                Calving index

                0.301

                0.303

                0.303

                Mastitis

                0.362

                0.359

                0.359

                Health

                0.435

                0.435

                0.435

                Body conf.

                0.313

                0.316

                0.316

                Feet & Leg

                0.311

                0.307

                0.306

                Udder conf.

                0.366

                0.357

                0.357

                Milkingspeed

                0.292

                0.295

                0.295

                Temperament

                0.184

                0.183

                0.183

                Longevity

                0.320

                0.334

                0.334

                Yield

                0.431

                0.437

                0.438

                Mean

                0.360

                0.363

                0.363

                GBLUP without a polygenic effect (GBLUP), GBLUP with a polygenic effect and a weight of 0.2 (GBLUPAG), and adjusted GBLUP (i.e., using adjusted G matrix) with a polygenic effect and a weight of 0.2 (GBLUPAG*).

                Table 3

                Intercept (INT) and regression coefficient (REG) of DRP on genomic predictions from different methods

                Trait

                GBLUP

                GBLUPAG

                GBLUPAG*

                INT

                REG

                INT

                REG

                INT

                REG

                Milk

                2.028

                0.920

                1.455

                0.960

                1.445

                0.961

                Fat

                2.837

                0.877

                2.385

                0.912

                2.377

                0.913

                Protein

                3.906

                0.847

                3.182

                0.883

                3.169

                0.884

                Growth

                −0.240

                1.045

                −0.246

                1.083

                −0.246

                1.084

                Fertility

                1.439

                0.980

                1.583

                1.032

                1.586

                1.034

                Birth index

                0.846

                0.865

                0.707

                0.926

                0.705

                0.927

                Calving index

                1.002

                1.016

                0.822

                1.060

                0.819

                1.061

                Mastitis

                0.365

                0.937

                0.283

                0.947

                0.281

                0.947

                Health

                0.585

                1.156

                0.579

                1.175

                0.579

                1.176

                Body conf.

                1.172

                0.864

                0.965

                0.895

                0.961

                0.896

                Feet & Leg

                1.389

                1.009

                1.284

                1.055

                1.283

                1.056

                Udder conf.

                2.973

                0.899

                2.705

                0.926

                2.701

                0.926

                Milkingspeed

                1.751

                0.836

                1.575

                0.886

                1.572

                0.887

                Temperament

                2.665

                0.727

                2.579

                0.751

                2.578

                0.752

                Longevity

                2.537

                0.905

                2.171

                0.939

                2.164

                0.940

                Yield

                3.975

                0.853

                3.286

                0.887

                3.273

                0.887

                Mean Dev.1

                1.857

                0.107

                1.613

                0.093

                1.609

                0.093

                GBLUP without a polygenic effect (GBLUP), GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG) and adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*); 1Mean of absolute deviation from 1 for regression coefficient and from 0 for intercept.

                Table 4 reports validation reliabilities of GEBV from the two single-step blending methods and DGVω from the GBLUP method with a polygenic effect (the adjusted GBLUP method is shown as an example) for the 16 traits, with a relative weight ω = 0.20. The adjusted single-step blending led to the highest reliability of genomic predictions, followed by the original single-step blending, and the GBLUP method resulted in the lowest reliability. Reliabilities ranged from 0.206 to 0.503 (average 0.379) for the original single-step blending, from 0.206 to 0.503 (average 0.382) for the adjusted single-step blending, and from 0.183 to 0.481 (average 0.363) for the GBLUP method. In general, single-step blending was better than the GBLUP method and adjusted single-step blending was better than the original single-step blending, especially for production traits. On average, reliabilities of genomic breeding values predicted using the original single-step blending were 1.6 % higher than reliabilities from the adjusted GBLUP method, but 0.3% lower than reliabilities from the adjusted single-step blending.
                Table 4

                Reliabilities of genomic predictions using different methods

                Traits

                GBLUPAG*

                Singleori

                Singleadj

                Singleori-GBLUPAG*

                Singleadj-GBLUPAG*

                Singleadj-Singleori

                Milk

                0.428

                0.450

                0.456

                0.022*

                0.028**

                0.006*

                Fat

                0.457

                0.458

                0.466

                0.001

                0.009*

                0.008**

                Protein

                0.435

                0.437

                0.446

                0.002

                0.011

                0.009**

                Growth

                0.481

                0.503

                0.503

                0.022**

                0.022**

                0.000

                Fertility

                0.419

                0.425

                0.431

                0.006

                0.012

                0.005

                Birth index

                0.263

                0.274

                0.274

                0.011

                0.011

                −0.001*

                Calving index

                0.303

                0.328

                0.329

                0.025**

                0.026**

                0.002

                Mastitis

                0.359

                0.383

                0.384

                0.024**

                0.025**

                0.000

                Health

                0.435

                0.467

                0.469

                0.032

                0.034*

                0.003

                Body conf.

                0.316

                0.317

                0.317

                0.001

                0.001

                0.000

                Feet & Leg

                0.306

                0.296

                0.296

                −0.01

                −0.01

                0.000

                Udder conf.

                0.357

                0.358

                0.358

                0.001

                0.001

                −0.001

                Milkingspeed

                0.295

                0.312

                0.312

                0.017*

                0.017*

                0.000

                Temperament

                0.183

                0.206

                0.206

                0.023*

                0.023*

                0.000

                Longevity

                0.334

                0.415

                0.415

                0.081**

                0.081**

                0.000

                Yield

                0.438

                0.436

                0.446

                −0.002

                0.008

                0.010**

                Mean

                0.363

                0.379

                0.382

                0.016

                0.019

                0.003

                Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*), original single-step blending (Singleori) and adjusted single-step blending (Singleadj) with a weight of 0.2; *significant difference at p < 0.05; **significant difference at p < 0.01.

                The regression coefficients (Table 5) ranged from 0.757 to 1.138 (average absolute deviation from 1 equal to 0.084) for the original single-step blending, from 0.760 to 1.148 (average absolute deviation 0.080) for the adjusted single-step blending, and from 0.752 to 1.176 (average absolute deviation 0.093) for the adjusted GBLUP method. Predictions from the single-step blending methods appeared to have less bias than predictions from GBLUP, and predictions from the adjusted single-step blending has slightly less bias than predictions from the original single-step blending method. In addition, the two single-step blending methods led to smaller absolute deviation of the intercept from 0 than the adjusted GBLUP method, indicating less bias in mean.
                Table 5

                Intercept (INT) and regression coefficient (REG) of DRP on genomic predictions using different methods

                Trait

                  

                GBLUPAG*

                Singleori

                Singleadj

                INT

                REG

                INT

                REG

                INT

                REG

                 

                Milk

                1.445

                0.961

                1.225

                0.963

                0.843

                0.975

                Fat

                2.377

                0.913

                2.136

                0.910

                1.752

                0.932

                Protein

                3.169

                0.884

                2.967

                0.877

                2.441

                0.898

                Growth

                −0.246

                1.084

                −0.133

                1.093

                −0.103

                1.095

                Fertility

                1.586

                1.034

                1.633

                1.023

                1.917

                1.044

                Birth index

                0.705

                0.927

                0.608

                1.054

                0.583

                1.057

                Calving index

                0.819

                1.061

                0.439

                1.009

                0.520

                1.019

                Mastitis

                0.281

                0.947

                0.206

                0.954

                0.246

                0.958

                Health

                0.579

                1.176

                0.677

                1.138

                0.793

                1.148

                Body conf.

                0.961

                0.896

                0.652

                0.913

                0.605

                0.918

                Feet & Leg

                1.283

                1.056

                1.058

                1.028

                1.051

                1.030

                Udder conf.

                2.701

                0.926

                2.144

                0.934

                2.114

                0.935

                Milkingspeed

                1.572

                0.887

                1.371

                0.858

                1.355

                0.861

                Temperament

                2.578

                0.752

                1.816

                0.757

                1.795

                0.760

                Longevity

                2.164

                0.940

                1.531

                0.963

                1.384

                0.969

                Yield

                3.273

                0.887

                3.079

                0.878

                2.524

                0.902

                Mean Dev.1

                1.609

                0.093

                1.355

                0.084

                1.252

                0.080

                Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*), original single-step blending (Singleori) and adjusted single-step blending (Singleadj) with weight a weight of 0.2; 1Mean of absolute deviation from 1 for regression coefficient and from 0 for intercept.

                Table 6 presents differences between groups of the top 300 bulls based on predictions from the different methods. For all 16 traits, more than 9% of the top 300 bulls based on the adjusted GBLUP method differed from the top 300 bulls based on the two single-step blending methods. Differences between the two single-step blending methods were small, except for production traits, which was in agreement with the small differences in reliabilities of GEBV from the two single-step blending methods.
                Table 6

                Differences between groups of the top 300 bulls based on genomic prediction using different methods

                Trait

                GBLUPAG*Vs. Singleadj

                GBLUPAG*Vs. Singleori

                SingleoriVs. Singleadj

                Milk

                39

                38

                18

                Fat

                33

                33

                11

                Protein

                36

                38

                17

                Growth

                42

                44

                3

                Fertility

                29

                33

                8

                Birth index

                32

                32

                2

                Calving index

                38

                39

                4

                Mastitis

                32

                33

                1

                Health

                33

                35

                6

                Body conf.

                32

                31

                3

                Feet & Leg

                36

                37

                2

                Udder conf.

                38

                40

                3

                Milkingspeed

                35

                35

                1

                Temperament

                48

                46

                2

                Longevity

                41

                44

                8

                Yield

                27

                31

                16

                Adjusted GBLUP with a polygenic effect with a weight of 0.2 (GBLUPAG*), original single-step blending (Singleori), and adjusted single-step blending (Singleadj) with a weight of 0.20, measured as the number of bulls that are not among the top 300 based on the second method.

                In order to test the effect of different weighting factors ω in forming G ω and H, eight values of ω between 0.05 and 0.40 were used for the two single-step blending methods and the two GBLUP methods with a polygenic effect. On average, reliabilities varied from 0.356 to 0.363 over the eight scenarios for the two GBLUP methods, from 0.372 to 0.379 for the original single-step blending, and from 0.374 to 0.382 for the adjusted single-step blending (Figure 1). The highest mean reliability was obtained when using a weight of 0.15 or 0.20 for the four methods. The mean absolute deviation of the regression coefficient from 1 varied from 0.080 to 0.104 for the two GBLUP methods, from 0.074 to 0.098 for original single-step blending and from 0.072 to 0.091 for adjusted single-step blending (Figure 2). Mean of absolute deviations tended to decrease with increasing weights.
                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Fig1_HTML.jpg
                Figure 1

                The impact of different weights on reliability of genomic predictions using different methods. GBLUP with a polygenic effect (GBLUP-AG), adjusted GBLUP with a polygenic effect (GBLUP-AG*), original single-step blending (Single-ori), and adjusted single-step blending (Single-adj).

                http://static-content.springer.com/image/art%3A10.1186%2F1297-9686-44-8/MediaObjects/12711_2011_2532_Fig2_HTML.jpg
                Figure 2

                The impact of different weights on the mean absolute deviation from 1 of the regression coefficient of DPR on prediction using different methods. GBLUP with a polygenic effect (GBLUP-AG), adjusted GBLUP with a polygenic effect (GBLUP-AG*), original single-step blending (Single-ori), and adjusted single-step blending (Single-adj).

                Discussion

                This study applied three GBLUP and two single-step blending methods for genomic prediction in Nordic Holsteins. Predictive abilities of the five methods were compared in terms of reliability and bias. Results indicated that both the original single-step blending and the adjusted single-step blending were more accurate than the three GBLUP methods because the two single-step blending approaches used much more information to predict breeding values. Similar results were reported by Su et al. [18] for the Nordic Red population. In the current study, the size of the training dataset for the single-step blending methods was almost three times as large as that for the three GBLUP methods (Table 1) since DRP of the non-genotyped animals also provided information through a combined relationship matrix. Including pedigree information may also improve genomic predictions because the SNP may not account for all additive genetic variance. As shown in this study, including a residual polygenic effect in the GBLUP methods led to slightly higher reliability of genomic predictions.

                A regression coefficient of DRP on genomic predictions less than 1 indicates overestimation of the variance of genomic predictions (inflation), while a coefficient larger than 1 indicates underestimation (deflation). The two single-step blending methods led to less bias than the three GBLUP methods, and the two GBLUP methods with a polygenic effect resulted in less bias than the simple GBLUP method without a polygenic effect. The problem of inflation of genomic predictions is critical in practice [3335] as it can give an unfair advantage to juvenile over older progeny test bulls [17]. Aguilar et al. [17] showed that this bias was reduced by weighting the G and A matrices, and Liu et al. [36] found that including a polygenic effect in a GBLUP model (random regressions on SNP genotypes) led to less bias in genomic predictions. The present study showed that the weighting factor had an effect on the bias of genomic predictions for all traits in the single-step blending approaches and the GBLUP methods with a polygenic effect. A weight of 0.40 resulted in the smallest minimum absolute deviation from 1 for the regression of GEBV or DGVω on DRP, averaged over the 16 traits, but a loss of reliability around 0.8%, compared to a weight of 0.20, which led to highest average reliability and an acceptable average absolute deviation of regression coefficient from 1 (Figure 1,2).

                The adjusted single-step blending method resulted in less bias than the original single-step blending for all settings of the weight factor. In a simulation study, Vitezica et al. [19] also found that the single-step method was less biased and more accurate when the genomic relationship matrix was adjusted by a constant. Using chicken data, Chen et al. [20] showed that unbiased evaluations can be obtained by adding a constant to the G matrix that is based on current allele frequencies and suggested that the optimal G has average of diagonal and off-diagonal elements close to those of A 11. Forni et al. [22] also showed that re-scaling the G matrix is a reasonable solution to avoid inflation in pig data. However, in the present study, the adjusted G matrix did not improve genomic predictions in the GBLUP methods with a polygenic effect. This suggests that, based on the present data, adjustment of G has little effect on genomic prediction when only genotyped animals are used, but may be important in other data where there is a large difference in scale between G and A.

                The results from the present study indicate that increasing the weighting factor (0.40) reduces bias and that weighting factors around 0.15 to 0.20 give the highest reliability but the optimal weighting factors differed between traits. Similarly, Liu et al. [36] observed that the optimal residual polygenic variance in a GBLUP model (random regressions on SNP genotypes) with a polygenic effect appears to differ among traits. Therefore, trait-specific weighting factors should be used in the single-step blending methods and the GBLUP methods with a polygenic effect. In the near future, both bulls and heifers may be pre-selected based on genomic EBV. This will lead to biased predictions of breeding values in both conventional and genomic evaluation procedures. In such situations, appropriate methods to correct the bias of predictions are required [37].

                Christensen et al. [21] compared the adjusted and original single-step blending methods on pig data. In their study, the improvement of prediction reliabilities by adjustment of G matrix is much larger, compared with the results from the current study. This may be because there was more inbreeding in the pig data, which resulted in average values of the diagonal and off-diagonal elements of A 11 equal to 1.145 and 0.298, and estimates of β and α equal to 0.895 and 0.298, respectively. In the present study, the averages of the diagonal and off-diagonal elements of A 11were 1.060 and 0.085, and estimates of β and α were 0.976 and 0.085, i.e. closer to one and zero, respectively. This means that the original G matrix was less adjusted in this study compared to the study on pig data by Christensen et al. [21].

                Conclusions

                The single-step blending methods can increase reliability and reduce bias of genomic predictions. The adjusted single-step blending method performed slightly better than the original single-step blending method, both with respect to reliability and bias of genomic predictions. The weighting factor used in these single-step blending methods had a small effect on reliability of genomic prediction but an important effect on bias.

                Declarations

                Acknowledgements

                The authors thank Danish Cattle Federation, Faba co-op, Swedish Dairy Association and Nordic Cattle Genetic Evaluation for providing data. This work was performed in the project “Genomic Selection – from function to efficient utilization in cattle breeding (grant no. 3405-10-0137)”, funded under GUDP by the Danish Directorate for Food, Fisheries and Agri Business, the Milk Levy Fund, VikingGenetics, Nordic Cattle Genetic Evaluation, and Aarhus University.

                Authors’ Affiliations

                (1)
                Department of Molecular Biology and Genetics, Aarhus University
                (2)
                Danish Agricultural Advisory Service
                (3)
                College of Animal Science and Technology, China Agricultural University

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                Copyright

                © Gao et al; licensee BioMed Central Ltd. 2012

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