**CASE STUDY**

**Genomic evaluation of Holstein cattle in Antioquia (Colombia):
a case study ^{¤}**

*Evaluación genómica de ganado Holstein en Antioquia (Colombia): estudio de caso*

*Avaliação genômica do gado Holandês de Antioquia (Colômbia): estudo de caso*

**Julián Echeverri ^{1*}, Zoot, MSc, PhD; Juan C Zambrano^{2}, Qco, MSc, PhD(c); Albeiro López Herrera^{1}, Zoot, MV, MSc, DrSci.**

^{1}*Grupo de investigación BIOGEM, Departamento de producción Animal, Facultad de Ciencias Agropecuarias, Universidad Nacional
de Colombia, Medellín, Colombia.*

^{2}*Grupo de investigación BIOGEM, Posgrado en Biotecnología, Facultad de Ciencias, Universidad Nacional de Colombia,
Medellín, Colombia.*

^{*} Corresponding author: Julián Echeverri. Departamento de producción Animal, Facultad de Ciencias Agropecuarias, Universidad Nacional de Colombia.
Calle 59A No 63–20 –Núcleo El Volador, Bloque 50, Oficina 306. Medellín, Colombia. Email: jjecheve@un al.edu.co

*Received: March 15
Accepted: December 10, 2013*

**Summary**

**Background:** DNA markers have been widely used in genetic evaluation throughout the last decade
due to the increased reliability of breeding values (BV) they allow, mainly in young animals. **Objective:** to
compare breeding values estimated through the conventional method (best linear unbiased predictor, BLUP)
with methods that include molecular markers for milk traits in Holstein cattle in Antioquia (Colombia).
**Methods:** predictions of breeding values were performed using three methods: BLUP, molecular best linear
unbiased predictor (MBLUP), and Bayes C. The breeding values were compared using Spearman's correlation
coefficient and linear regression coefficient. **Results:** all Spearman correlation coefficients between breeding
values obtained by different methods were greater than 0.5, while linear regression coefficients ranged between
–2.10 and 1.58. **Conclusions:** prediction of breeding values through BLUP, MBLUP and Bayes C showed
different results in terms of magnitude from the estimated values. However, animal ranking according to
breeding values was not significantly different.

**Keywords:** *genetic markers, genomic selection, breeding value, milk quality, milk traits.*

**Resumen**

**Antecedentes:** en la última década, los marcadores de DNA han sido ampliamente usados en evaluaciones
genéticas porque incrementan la confiabilidad de valores genéticos principalmente en animales jóvenes.
**Objetivo:** comparar valores genéticos (BV) estimados por el método convencional (mejor estimador lineal
insesgado, BLUP) y métodos que incluyen marcadores moleculares para algunas características lecheras en ganado Holstein de Antioquia (Colombia). **Métodos:** la predicción de valores genéticos se realizó mediante
tres métodos: BLUP, mejor predictor lineal insesgado molecular (MBLUP) y Bayes C. Los valores genéticos
fueron comparados usando el coeficiente de correlación de Spearman y el coeficiente de regresión lineal.
**Resultados:** todos los coeficientes de correlación de Spearman entre los valores genéticos obtenidos por los
diferentes métodos fueron mayores de 0,5. Mientras que los coeficientes de regresión lineal oscilaron entre
–2,10 y 1,96. **Conclusiones:** la predicción de valores genéticos empleando los métodos BLUP, MBLUP y Bayes
C fue diferente en términos de la magnitud de los valores estimados. Sin embargo el ranking o clasificación
de los animales por sus valores genéticos no fue alterado significativamente.

**Palabras clave**: *calidad de leche, características de la leche, marcadores genéticos, selección genómica,
valor de cría.*

**Resumo**

**Antecedentes:** na última década, os marcadores moleculares que identificam polimorfismos no DNA têm
sido utilizados amplamente nas avaliações genéticas porque aumentam a fiabilidade dos valores genéticos (BV)
estimados principalmente em animais jovens. **Objetivo:** comparar valores genéticos estimados pelo método
convencional (melhor preditor linear não–viesado, BLUP) e métodos que incluem marcadores moleculares para
algumas características leiteiras no gado holandês de Antioquia (Colômbia). **Métodos:** as predições dos valores
genéticos foram realizadas por meio de três métodos: BLUP, melhor preditor linear não–viesado molecular
(MBLUP) e Bayes C. Os valores genéticos foram comparados por meio de coeficientes de correlação de
Spearman e de coeficientes de regressão linear. **Resultados:** os coeficientes de correlação de Spearman entre
os valores genéticos obtidos pelos diferentes métodos foram maiores que 0,5. Enquanto os coeficientes de
regressão linear variaram entre –2,10 e 1,96. **Conclusões:** a predição dos valores genéticos usando os métodos
BLUP, MBLUP e Bayes C foi diferente em quanto à magnitude dos valores estimados. No entanto, o ranking
ou classificação de animais por seus valores genéticos não foi alterada significativamente.

**Palavras chave**
*características do leite, marcadores genéticos, qualidade do leite, seleção genômica,
valor genético.*

**Introduction**

Breeding values (BV) are commonly calculated by using the best linear unbiased prediction (BLUP; Henderson, 1984). BV have been very useful to select animals with high genetic merit. However, an important limitation of this method lies in obtaining continuous phenotypic records because of the high costs implied. Accordingly, since the presence of alleles carrying the fundamental causative mutations affecting quantitative traits can determine genetic merit, genetic evaluations in recent years have included information on DNA markers (Haley, 1995).

The use of DNA markers in selection schemes
is very useful due to the increased reliability of the
estimated breeding values (EBVs), mainly for young
animals (Meuwissen and Goddard, 1996). In spite
of considerable efforts for implementing markerassisted
selection (MAS), the low density of DNA
markers makes it difficult to find markers in linkage
disequilibrium (LD) with quantitative trait loci (QTL).
Many genes affect quantitative traits. Consequently,
the benefit from MAS is limited by the proportion
of the genetic variance explained by QTL (Meuwissen
*et al.*, 2001).

Meuwissen * et al.* (2001) devised genomic
selection, an excellent method to solve the limitations
of MAS. This process allows the estimation of
BVs using high–density SNP markers. The Single
Nucleotide Polymorphism (SNP) markers are
uniformly distributed across the entire genome;
therefore, each QTL is in LD with some of these
markers across the entire population. However, the
practical applications of genomic selection became
feasible only a few years later with the recent
development of DNA chip technologies, which have
led to a rapid adoption of this method in selection
schemes in order to improve dairy cattle (Schaeffer

Milk production in Colombia has taken increasing
importance. However, few genetic evaluations have
been conducted in dairy cattle in Colombia (Quijano *et al.*, 2011) and few studies including molecular
markers have been associated with milk production
traits (Rincon *et al.*, 2012). Thus, the current situation
of livestock in Colombia requires initiating new
research to improve the genetic composition of
domestic dairy herds.

The objective of this study was to compare BV estimated through the conventional method BLUP and methods that include molecular markers for milk production traits in Holstein cattle in Antioquia, Colombia.

**Material and methods**

*Population*

The traditional estimated breeding value (TEBV),
estimated breeding value (EBV), and molecular
estimated breeding value (MEBV) were obtained from
231 Holstein animals (cows and bulls); the genomic
estimated breeding value (GEBV) was obtained
from 13 Holstein bulls. Phenotypic information
was taken from 59 dairy herds located in the high
tropics of the Antioquia province, Colombia. The
number of lactations used for the analyses were:
1,494, 1,295, 1,645, and 1,140 for milk yield (MY),
milk fat percentage (FP), milk protein percentage
(PP) and somatic cell count (SCC), respectively.
SCC was transformed to somatic cell score (SCS)
using the following equation: SCS = [((SCC–100/12)
*0.5015) + 0.0434] in order to achieve normality of
data distribution (Roman, 2012). All the phenotypic
information was managed and analyzed using the
Control 1 software, version 1.0 (Echeverri *et al.*, 2010).

*Animal genotyping*

A total of 231 animals (cows and bulls) were
genotyped for bovine growth hormone (bGH), kappacasein
(KC), and prolactin (PRL) genes through
PCR–RFLP methodology as described by, Medrano
*et al.* (1990), Dybus (2002) and Rincon *et al.* (2012), respectively. Furthermore, 13 Holstein bulls were
genotyped using the Illumina BovineSNP50 Beadchip
(Illumina, San Diego, CA, USA). The Beadchip
provides information of 54,001 SNPs distributed
throughout the entire bovine genome (Matukumalli *et al.*, 2009). Upon editing the database of the SNPs, 13
bulls with 40,753 SNPs were available. The database
was edited using the SAS/STAT^{®} software, version
9.1 (SAS Institute Inc., Cary, NC, USA) and PLINK
programs (Purcell *et al.*, 2007).

*Statistical analysis*

Analysis of Association for Biallelic Markers. An analysis of association between each marker (bGH, PRL, and KC) and each trait (MY, FP, PP, and SCS) was conducted through a generalized linear model in which the markers were included as fixed effects. The model used for this analysis was:

Where:

y_{ijklmno}= dependent variable (MY, FP, PP, and SCS).

μ= overall mean.

PN_{i}= fixed effect of the *i*th parity.

H_{j}= fixed effect of the *j*th herd.

β_{k}= linear regression coefficient of lactation length.

DL_{k}= lactation length covariate.

GH_{l}= fixed effect of the *l*th genotype (+/+, +/–
and –/–) for the bGH marker.

KC_{m}= fixed effect of the *m*th genotype (AA, AB
and BB) for the KC marker.

PRL_{n}= fixed effect of the *n*th genotype (AA, AB
and BB) for the PRL marker.

e_{ijklmno} = residual.

The statistical analysis was conducted using the
General Linear Model (GLM) procedure of SAS/
STAT^{®} software, version 9.1 (SAS Institute Inc., Cary, NC, USA). Differences between treatment means
were determined by least squares and analyzed by
ANOVA. The Tukey's multiple comparison test was
used to compare treatment means (p<0.05).

*Calculation of traditional estimated breeding
value (TEBV).* A univariate animal model was used
for each trait to estimate TEBV, which was defined
as the breeding value obtained using the conventional
method (BLUP). The statistical model used for this
analysis was:

*y= Xb + Za + e*

Where:

y = vector of observations (MY, FP, PP, and SCS).

X = design matrix relating records and fixed effects.

b = vector of the following fixed effects: calving year, calving month, region, contemporary group (Herd–parity number), linear regression coefficients for lactation length covariate (for all traits) and milk production covariate (only for PP, FP, and SCS) respectively.

a = vector of random genetic additive effect.

Ζ = incidence matrix relating records and random genetic additive effect.

e = residual.

The estimate breeding values (EBV) were
predicted in the same way as the TEBV, but included
the molecular markers (bGH, PRL and KC) as fixed
effects. TEBVs and EBVs were estimated via a
derivative–free algorithm by using the MTDFREML
program (Boldman *et al.*, 1995).

*Calculation of molecular estimated breeding value
(MEBV).* The method used to estimate the molecular
marker effects (bGH, KC and PRL) and polygenic
effect was the MBLUP (Hayes *et al.*, 2009). The
model used for this analysis was:

Where:

y = vector of n traditional estimated breeding values (TEBV) corrected for fixed effects as described above (TEBV for MY, FP, PP, and SCS).

m = overall mean.

1_{n}= vector of 1s.

X = is (n x p) design matrix allocating records to
the p markers (KC, bGH and KC), with element X_{ij}
= 0, 1 or 2 if the genotype of animal *i* at marker *j *is
AA, AB, or BB for KC and PRL genes and +/+, +/– or
–/– for the bGH gene, respectively.

g = (p x 1) vector of molecular marker effects (g represents the sum of the linear regression coefficients of TEBV on genotype (0, 1 and 2) of three molecular marker (bGH, KC and PRL).

Ζ= design matrix allocating records to TEBVs.

u = vector of polygenic effects of the ith animal,
with variance *Aσ ^{2}_{u}*; where A: is the average
relationship matrix of the animals genotyped with p
molecular markers.

e = residual error also assumed to be normally
distributed, e ~ N(0, *Iσ*^{2}_{e}) ;

where:

I = the n x n identity matrix.

Molecular estimated breeding values (MEBV) were determined through the following equation:

MEBVs were estimated via a derivative–free
algorithm by using the MTDFREML software
(Boldman *et al.*, 1995).

*Accuracy of estimated breeding values.* The
reliabilities of the estimated breeding values
(TEBV, EBV and MEBV) were obtained through
the following equation: R^{2} = 1–d_{i}α,

where:

d_{i}= ith diagonal element of C^{22} of the generalized
inverse of the mixed model equations, α = σ^{2}_{e}/σ^{2}_{a}
and accuracy (R) is the square root of reliability
(Mrode and Thompson, 2005).

*Calculation of genomic estimated breeding values
(GEBV).* The estimation of GEBVs was carried out in
two steps through the Bayes C method. 1) Estimation
of the effects of each SNP marker and, 2) Prediction
of the genomic estimated breeding values (GEBV).
Bayes C method assumes a mixture of distributions for
the SNP effects reflecting the assumption that there is
a large number of SNPs with zero or near zero effect
and a second smaller set of SNPs with larger effect
(Kizilkaya *et al.*, 2010, Verbyla *et al.*, 2010). The
general statistical model may be written as:

Where:

y = is the vector of traditional estimated breeding values (TEBV) corrected for fixed effects as described above (TEBV for MY, FP, PP, and SCS) for n individuals (n = 13 bulls).

μ = overall mean.

1_{n}= vector of ones of length n.

X_{j} = vector of indicator variables representing the
genotypes of the jth marker for all individuals, at each
jth marker there are three possible combinations of two
alleles (A or B), the homozygote of one allele (AA),
the heterozygote (AB) and homozygote of the other
allele (BB); these are then quantitatively represented
by 0, 1 and 2 respectively (i.e., X_{ij} = 0, 1 or 2).

β_{j}= is the random substitution effect for locus *j*, which
is conditional on σ^{2}_{β} and is assumed normally distributed
N(0, σ^{2}_{β}) when δ_{j} = 1, but β_{j} = 0 when δ_{j} = 0.

δ_{j}= is a random 0/1 variable indicating the absence
(with probability π) or presence (with probability 1–π)
of locus j in the model.

u= vector of random polygenic effects of length
n (Z is the associated design matrix) and can be
thought of as fitting the genes no accounted for by the
markers–locus effects in β, additionally u is assumed
to be normally distributed, u ~ N(0, *Aσ*^{2}_{M}) where A
is the pedigree derived additive genetic relationship
matrix of the genotyped animals.

e = residual error, also assumed to be normally
distributed, e ~ N(0, *Iσ*^{2}_{e}) here I = the nxn identity
matrix.

GEBVs of the animals (whose genotype was known) were predicted through the following equation:

The SNP effects and GEBVs were obtained by
using the GS3 program (Legarra *et al.*, 2011a).

*Methods for comparing breeding values*

The Spearman's rank correlation coefficients
between the breeding values obtained by BLUP,
MBLUP and Bayes C methods (r_{TEBV;MEBV}, r_{EBV;MEBV}
and r_{EBV;GEBV}) were calculated and used as a measure
of the degree of similarity between the ranking or
classification of the animals by their breeding values.
The linear regression coefficients (b_{TEBV;MEBV},
b_{EBV;MEBV} and b_{EBV;GEBV}) were also calculated
and used as a measure of the change in magnitude
between the breeding values. A regression coefficient
of one indicates no bias between the methods of
prediction and that the breeding values are equal in
magnitude.

**Results**

*Descriptive analysis of milk traits*

The mean and standard deviations for MY, PP, FP and SCS were: 5324 ± 1437 L/lactation, 3.03 ± 0.24%, 3.67 ± 0.43%, and 17.7 ± 39.37, respectively (Table 1). MY and SCS were the traits with greatest coefficients of variation (26.9 and 222%, respectively).

*Association analysis for biallelic markers and
milk traits*

Table 2 shows the genotype frequencies of the PRL, bGH and KC genes and the means of each trait per genotype. Through the use of Tukey's multiple comparison test it was possible to determine that genotypes AA and AB of PRL gene (p<0.01) and genotype BB of KC gene (p<0.05) were the most favorable for MY. On the other hand, BB genotype of PRL gene (p<0.05), the genotype (+/–) of bGH gene (p<0.05) and genotype BB of KC gene were the most favorable for PP (p<0.05). In the case of FP, only genotype (–/–) of bGH gene showed significant association with greater fat content in milk (p<0.01).

*Estimated breeding values (including molecular
markers)*

The TEBV, EBV and MEBV means were close to zero in all cases, but the coefficient of variation (CV) and accuracy (R) differed among them. Accuracies (R) were greater for MEBVs compared to TEBVs in all traits except for MY (Table 3).

*SNP effects and genomic estimated breeding
values (GEBVS)*

The effects of 40,753 SNPs were determined for MY, PP, FP and SCS, and their means were: –0.03520 L/lactation, -0.000034, -0.00019 and 0.000048%, respectively (Table 4).

On the other hand, the GEBVs for MY, PP, FP and SCS were estimated and means and standard deviations were: 359 ± 311 L/lactation, 0.123 ± 0.19%, 0.276 ± 0.20%, 0.501 ± 0.75, respectively (Table 4).

*Correlation and regression coefficients between
breeding values*

The Spearman correlation coefficients between EBV and MEBV for MY, FP, PP and SCS were: 0.796, 0.763, 0.936 and 0.999, respectively; and between TEBV and MEBV were: 0.823, 0.783, 0.962 and 0.620, respectively. These results indicate a high and favorable degree of association between breeding values. Finally, the correlations between EBV and GEBV were medium: 0.780, 0.500, 0.500 and 0.580, since the number of phenotypic records for EBVs was greater than for GEBVs (Table 5).

The comparison of breeding values obtained by different methods (BLUP, MBLUP and Bayes C) shows that regression coefficients were highly variable. For example, the regression coefficients of EBV on MEBV for MY, FP, PP, and SCS were: –2.140, 0.205, –0.015 and 0.999, respectively; for TEBV on MEBV were: 1.227, 1.163, 1.958, and 0.003, respectively; and finally, the regression coefficients of EBV on GEBV were: 0.784, 0.077, 0.380, and 1.110, respectively (Table 5).

**Discussion**

Traditionally, breeding values are obtained by using the best linear unbiased predictor (BLUP) (Henderson, 1984), which assumes that phenotypic traits are determined by an infinite number of unlinked additive loci, each one having an infinitesimal small effect (infinitesimal model) (Fisher, 1918). However, the finite loci model has been proposed to explain the genetic variation observed in quantitative traits. This model assumes a finite number of loci that explains the genetic variation of quantitative traits (Thompson and Skolnick, 1977). In this perspective, several methods that include molecular markers have been evaluated to estimate breeding values.

Legarra *et al.* (2011b) evaluated five methods
that include molecular markers (Bayesian Lasso with
one variance (BL1Var), Bayesian Lasso with two
variances (BL2Var), GBLUP, MCMC–GBLUP and
Het–Var–GBLUP). The genomic estimated breeding
values (GEBV) obtained through those methods were
compared with the double daughter yield deviation
(2DYD) by the correlation coefficient (r_{2DYD;GEBV}).
The correlations between 2DYD and GEBV (obtained
through the methods mentioned previously) (r_{2DYD;GEBV})
for fat percentage (FP) were: 0.53, 0.73, 0.59, 0.61, and
0.71, respectively; and for protein percentage (PP) were:
0.36, 0.48, 0.44, 0.46, and 0.47, respectively. We found
similar results for PP and FP using MBLUP and Bayes
C methods (Table 5).

On the other hand, Moser *et al.* (2009) evaluated
the following methods: fixed regression–least squares
(FR–LS), random regression BLUP (RR–BLUP),
Bayes A, support vector regression (SVR), and partial
least squares regression (PLSR). They estimated the
molecular breeding value (MBV) of young Holstein
bulls using only genomic information and the GEBV
obtained from the same bulls (combining the MBV
with the pedigree). The MBVs and GEBVs obtained
through the previously mentioned methods were
compared with the Australian estimated breeding
value (EBV) by using the correlation coefficient.
Correlations between EBV and MBV (r_{EBV;MBV})
were: 0.43, 0.56, 0.56, 0.58 and 0.55, respectively;
and between EBV and GEBV (r_{EBV;GEBV}) were: 0.49,
0.57, 0.60, 0.62, 0.60, and 0.62, respectively. The
correlations obtained by Moser *et al.* (2009) were
medium, and the authors attributed these results to the
low amount of data. Legarra *et al.* (2011b) suggests
that if correlations are high (equal or close to 1),
prediction methods have the same accuracy and the
prediction errors of breeding values are very similar.

We calculated correlations between breeding values
(r_{EBV;MEBV}, r_{TEBV;MEBV}, and r_{TEBV;GEBV}) for milk traits
(MY, PP, FP, and SCS), which ranged from 0.500
to 0.999. Furthermore, considering the correlations
between EBV and MEBV (r_{EBV;MEBV}) for PP (0.936)
and SCS (0.999), and between TEBV and MEBV
(rTEBV;MEBV) for PP (0.962), the ranking was not affected

The regression coefficients of TEBV on MEBV
and EBV on GEBV (b_{TEBV;MEBV} and b_{EBV;GEBV})
obtained in this study were different from 1 (ranged from
–2.10 to 1.58). These regression coefficients should
ideally be 1. However, the regression coefficients were
less than 1 for MY (b_{EBV;GEBV} = 0.784), FP (b_{EBV;GEBV}
= 0.077) and PP (b_{EBV;GEBV} = 0.380) and were greater
than 1 for MY (b_{TEBV;MEBV} = 1.227), FP (b_{TEBV;MEBV}
= 1.163), and PP (b_{TEBV;MEBV} = 1.958).

Bennewitz *et al.* (2009) determined GEBVs using
Bayes–BLUP method and two nonparametric kernel
regressions methods (ELM, ULM). The GEBVs were
compared with true estimate breeding value (TEBV)
(obtained by simulation) and determined the regression
coefficients of TEBVs on GEBVs (b_{TEBV;GEBV}), which
were: 1.376, 0.722, and 0.626, respectively. On the
other hand, Legarra *et al.* (2011b) obtained regression
coefficients of 2DYD on GEBV (b_{2DYD;GEBV}) (using
the previously mentioned methods). The regression
coefficients (b_{2DYD;GEBV}) for PP were 0.35, 1.10, 0.83,
1.10, and 0.99, respectively; and for MY were 0.25, 0.67,
0.59, 0.66, and 0.67, respectively. Legarra *et al.* (2011b),
suggest that most of the methods frequently inflate the
variances of the genomic estimated breeding values
(GEBVs) for some production traits, thus obtaining
regression values below 1. Contrary to this, they also
suggest that genetic variance is captured by QTL with
large effect on some compositional traits, what leads to
regression values greater than 1.

The prediction of breeding values (TEBV, EBV, MEBV and GEBV) by using BLUP, MBLUP and Bayes C methods showed different results in terms of magnitude from the estimated values according to the regressions obtained. However, the correlations between breeding values obtained by using methods that include molecular markers were similar, despite the different assumptions underlying the models. Finally, the results suggest that it is necessary to increase the number of records and genotyped animals to improve the prediction of GEBVs.

**Acknowledgements**

**Conflicts of interest**

The authors declare they have no conflicts of interest with regard to the work presented in this report.

**Notes**

¤ To cite this article: Echeverri J, Zambrano JC, López–Herrera A. Genomic Evaluation of Holstein Cattle in Antioquia (Colombia): a case study. Rev Colomb Cienc Pecu 2014; 27:306–314.

**References**

Bennewitz J, Solberg T, Meuwissen THE. Genomic breeding value estimation using nonparametric additive regression models. Genet Sel Evol 2009; 41:20.

Boldman K, Kriese L, Van Vleck L, Van Tassell C, Kachman S. A Manual for Use of MTDFREML. A Set of programs to obtain estimates of variances and covariances. USDA, Agricultural Research Service; 1995.

Dybus A. Associations between Leu/Val polymorphism of growth hormone gene and milk production traits in Black and White cattle. Arch Tiertz 2002; 45:421–428.

Echeverri J, López A, Parra J. Software control 1. Manejo y control de producción para hatos lecheros. Universidad Nacional de Colombia sede Medellín; 2010.

Fisher R. The correlation between relatives on the supposition of mendelian inheritance. T Roy Soc Edin 1918; 52:399–433.

Haley S. Livestock QTLs–bringing home the bacon? Trends Genet 1995; 11:488–492.

Hayes BJ, Bowman PJ, Chamberlain AJ, Goddard ME. Invited review: Genomic selection in dairy cattle: Progress and challenges. J Dairy Sci 2009; 92:433–443.

Henderson CR. Applications of linear models in animal breeding. 3ra ed. Guelph (ON): CGIL Publications; 1984

Kizilkaya K, Fernando RL, Garrick DJ. Genomic prediction of simulated multibreed and purebred performance using observed fifty thousand nucleotide polymorphism genotypes. J Anim Sci 2010; 88:544–551.

Legarra A, Ricard A, Filangi O. GS3, Genomic selection, Gibbs sampling, Gauss Seidel and Bayes Cpi. 2011a. [Access date: Feb 10, 2011] URL: http://snp.toulouse.inra.fr/~alegarra/

Legarra A, Robert–Granié C, Croiseau P, Guillaume F, Fritz S. Improved Lasso for genomic selection. Genet Res Camb 2011b; 93:77–87.

Matukumalli LK, Lawley CT, Schnabel RD, Taylor JF, Allan MF, Heaton MP, Jeff O'Connell, Moore SS, Smith TPL, Sonstegard TS, Van Tassell CP. Development and Characterization of a High Density SNP Genotyping Assay for Cattle. PloS ONE 2009; 4:e5350.

Medrano J, Aguilar E. Genotyping of bovine kappa–casein loci following DNA sequence amplification. Biotechnology 1990; 8:144–146.

Meuwissen THE, Hayes B, Goddard M. Prediction of total genetic value using genome–wide dense marker maps. Genetics 2001; 157:1819–1829.

Meuwissen THE, Goddard ME. The use of marker haplotypes in animal breeding schemes. Genet Sel Evol 1996; 28:161–176.

Moser G, Tier B, Crump RE, Khatkar MS, Raadsma HW. A comparison of five methods to predict genomic breeding values of dairy bulls from genome–wide SNP markers. Genet Sel Evol 2009; 41:56.

Mrode RA, Thompson R. Linear models for the prediction of animal breeding values. 2nd ed. Cambridge (MA): CABI Publishing; 2005.

Purcell S, Neale B, Todd–Brown K, Thomas L, Ferreira M, Bender D, Maller J, Sklar P, Paul IW de Bakker, Daly M, Sham P. PLINK: a toolset for whole–genome association and population–based linkage analysis. Am J Hum Genet 2007; 81:559–575.

Quijano JH, Echeverri J, López A. Evaluación genética de toros Holstein y Jersey en Condiciones tropicales. Medellín (Colombia): Centro de Publicaciones Universidad Nacional de Colombia Sede Medellín; 2011.

Rincon JC, López A, Echeverri J. Genetic variability of the bovine prolactin–Rsal loci in Holstein cattle in Antioquia province (Colombia). Rev Col Cienc Pec 2012; 25:191–201.

Roman SI. Genomic aspects of genetic improvement for mastitis resistance in dairy cattle. (Thesis PhD). Universitá degli Studi di Milano, Italy; 2012.

SAS/STAT. User's Guide. Version 9.1. Cary (NC, USA): SAS Institute Inc; 2006.

Schaeffer LR. Strategy for applying genome–wide selection in dairy cattle. J Anim Breed Genet 2006; 123:218–223.

Thompson EA, Skolnick MH. Likelihoods on complex pedigrees for quantitative traits. In: Pollack E, Kempthorne O, Bailey TB, editors. Proc Int Conf Quant Genet. Ames, Iowa: Iowa State University Press; 1977. p.815–818.

Verbyla KL, Bowman PJ, Hayes BJ, Raadsma H, Goddard ME. Sensitivity of genomic selection to using different prior distributions. BMC Proceeding 2010, 4(1):S5.