Livestock Research for Rural Development 24 (11) 2012 Guide for preparation of papers LRRD Newsletter

Citation of this paper

Estimation of genetic parameters of milk production traits of Iranian Holstein dairy cattle using multi-trait random regression model

Mehdi Bohlouli and Sadegh Alijani

Department of Animal Science, University of Tabriz, Tabriz, Iran
M.bohluly@gmail.com

Abstract

The objective of this research was to estimate genetic parameters of milk yield, fat yield and protein yield in Iranian Holstein dairy cattle. A total of 868460 test day records of milk production traits from 109574 first-parity Iranian Holstein dairy cattle were analyzed with multi-trait random regression sire model based on Restricted Maximum Likelihood (REML). Bivariate analyses between the production traits were used and correlations between traits were calculated from (co)variance components estimated in these analyses.

 

The heritability of milk yield, fat yield and protein yield as a function of days in milk were estimated between 0.09 to 0.23, 0.06 to 0.12 and 0.07 to 0.23, respectively. The repeatability for these traits ranged from 0.68 to 0.76, 0.32 to 0.59 and 0.52 to 0.67, respectively. Genetic correlations for 305-d yield among production traits were high, and for milk and fat, for milk and protein and for fat and protein yields were 0.81, 0.94 and 0.86, respectively. Genetic correlations between test-day milk and fat yields, between milk and protein yields and between fat and protein yields at the same stage of lactation were 0.63 to 0.90, 0.84 to 0.94 and 0.66 to 92, respectively. However, Genetic correlations were lower between milk and fat yields and between fat and protein yields than between milk and protein yields. As relatively large data set was used in this research, thus estimated (Co)variance components for random regression coefficients could be used for national genetic evaluation of dairy cattle in the Iran by random regression.

Key words: dairy cattle, genetic parameters, heritability


Introduction

Traditionally, aggregated 305-d yields have been used in dairy cows genetic evaluation in Iran. However, the 305-d yields predicted from few observations may give rise to bias. The use of test-day (TD) models to analyze milk production data has several advantages over the use of models based on 305-d yield. TD models account for environmental factors that could affect the performance of cows throughout the lactation period. Therefore, temporal environmental effects of individual test days can be taken into account (Meyer et al 1989 and VanRaden 1997). Several models have been used for estimation of (co) variance components for test-day yields.

 

Repeatability model assumes that the sequence of measurements of an individual is repeated measurements of the same trait. A multi-trait model has been applied as well (Meyer et al 1989 and Hammami et al 2008). In this model, every test day is considered as a separate trait. Random regression model (RRM) has been extensively used for analyzing test day yields as suggested by Schaeffer and Dekkers (1994). In random regression models, curves are estimated for random effects. The benefits of TD models and analyzing TD yields by random regression methodology have been thoroughly discussed (Swalve 2000 and Jensen 2001).

 

In recent years, there has been increased emphasis on estimating genetic parameters of TD milk production traits using RRM that have been reported for several cow populations by fitting various functions to model (Jamrozik and Schaeffer 1997; Jakobsen et al 2002 and Hammami et al 2008). Legendre polynomials, suggested by Kirkpatrick et al (1990) are used in many analyses by random regression models as basic functions. The objective of this research was to estimate (co)variance components for relatively large data set of production traits in first parity Iranian Holsteins dairy cattle with multi-trait random regression sire model using restricted maximum likelihood (REML) method.


Material and methods

Data

Total of test-day records for first lactation Iranian dairy cows, between 2001 and 2010, were extracted from the Animal Breeding Center database at Karaj, Iran. Only records of the first lactations of cows with age at first calving between 21 and 46 month were considered in the analyses. Daily records for milk yield, fat percentages, and protein percentages were in the ranges 1.0 to 75 kg, 1 to 9% and 1 to 7%, respectively. Only records from the first lactation that had data for all production traits on a given test day were kept. Cows were required to have a minimum of five TD records between 5 and 305 days in milk (DIM). Data edits eliminated sires that had progeny in fewer than three herds and herds that used fewer than three sires; and also herd-year of calving subclasses were required to have a minimum of 10 cows. Finally, edited data set consisted of 868460 records, produced by 109574 Holstein cows with known sire (1616 bulls) in 18610 herd-year-months of test-days (HTD). Pedigree were traced as far back as possible; therefore, all sires have genetic relationship with these sires (recorded daughters) kept in analysis.

Statistical models and analyses

For multi-trait analysis, the sire model fitted was as follows:

 

 

 The first five polynomials were calculated from the normalized Legendre polynomial (Kirkpatric et al 1990): 

 

 


Results and discussion

Summary statistics for the milk production traits along days in milk are shown in Table 1. The data show an increase in milk yield in early lactation, and then a decrease. The records were produced by 109574 Holstein cows with known sires (Table 2) in 318 herds.


Table  1: The mean and standard deviation of milk production traits in different stage of first lactation

 

 

 

Milk (kg)

 

Fat yield (kg)

 

Protein yield (kg)

DIM

 

Number

Means

SD

 

Means

SD

 

Means

SD

5-35

 

84720

28.5

6.83

 

1.03

0.333

 

0.862

0.222

36-65

 

88701

32.3

6.83

 

1.06

0.331

 

0.933

0.224

66-95

 

91186

32.6

6.80

 

1.05

0.323

 

0.955

0.224

96-125

 

92948

32.2

6.81

 

1.04

0.315

 

0.959

0.225

126-155

 

93554

31.4

6.94

 

1.03

0.312

 

0.952

0.228

156-185

 

93201

30.6

6.96

 

1.01

0.311

 

0.940

0.228

186-215

 

90869

29.8

6.98

 

1.00

0.311

 

0.925

0.229

216-245

 

87790

28.7

6.93

 

0.981

0.303

 

0.902

0.227

246-275

 

81022

27.5

6.92

 

0.964

0.301

 

0.875

0.228

276-305

 

64469

26.6

6.94

 

0.946

0.298

 

0.857

0.230

5-305

 

868460

30.2

7.16

 

1.01

0.317

 

0.919

0.229


Table  2: Number of sires and daughters by class of daughters per Sire

Class of number of daughters per sire

Number of sires

Total number of daughters

5-9

372

2609

10-19

388

5417

20-49

376

11624

50-99

174

12339

100-199

152

20973

200-499

129

39597

>500

25

17015

Sum

1616

109574


-2log of likelihood function (L) and Akaike information criterion (AIC) for each of the univariate analyses for milk, fat, and protein yields are shown in Table 3. The random regression models fitted by 2-4 orders of Legendre polynomial (M2, M3 and M4) have been applied to the random parts (additive genetics and permanent environmental variances) of the sire models. Minimum of −2 ln (restricted likelihood) was used as criterion for best fit of the applied function of the random part of the model within trait and generally, residual variances estimated by M2 to M4 models indicated that lowest residual variance was found for M4 model (Table 3). Therefore, The M4 models were best for data of milk, protein and fat yields.

 

Cobuci et al (2005) and Costa et al (2008) reported that the Legendre polynomials of orders 3 and 4 were the most appropriated for fitting test-day of milk yield, by random regression model.


Table  3: Analysis of goodness of fit for random regression models with different orders of Legendre polynomial

Trait

Model1

No of parameters

-2Log(L)2

AIC3

Residual variance

 

M2

13

5029474

5029500

12.2

Milk

M3

21

4991568

4991610

11.0

 

M4

31

4971860

4971922

10.3

 

 

 

 

 

 

 

M2

13

88264

88290

0.0472

Fat

M3

21

86445

86487

0.0463

 

M4

31

85572

85634

0.0454

 

 

 

 

 

 

 

M2

13

704925

704951

0.0162

Protein

M3

21

702245

702287

0.0155

 

M4

31

701342

701404

0.0150

1 M2 to M4 = random regression models fitted by 2-4 orders of Legendre polynomial for both additive genetics and permanent environmental variances.

2 value of -2log of likelihood function (L)

3 Akaike information criterion, and AIC= -2Log (L) + 2(number of parameters)   


The estimated additive genetic variances and permanent environmental and covariances for univariate model with the smallest -2 log (L) (Table 3) are given in Table 4; also these estimated based on multi-trait random regression model for milk and fat yields and for milk and protein yields are shown in Table 5 and Table 6 , respectively.


Table 4: Sire additive genetic (G) and permanent environmental (P) (co)variances for curve parameters for each traits are in the up triangle.  Correlations between curve parameters in bold are in lower off diagonal. Residual (R) variances are shown in the bottom row. (Co)variances for all traits are multiplied by 103   

 

 

Milk yield

 

Fat yield

 

Protein yield

G

 

2911

546

-289

88.9

-73.6

 

2.33

0.357

-0.0431

-0.00621

-0.0391

 

2.40

0.605

-0.162

0.0272

-0.0160

 

0.553

336

-60.2

11.0

-1.12

 

0.398

0.345

-0.0429

-0.0179

0.00723

 

0.640

0.372

-0.0452

-0.00952

0.0166

 

-0.483

-0.297

123

-30.4

15.6

 

-0.0773

-0.200

0.133

-0.0553

0.0216

 

-0.385

-0.272

0.0739

-0.0216

0.00972

 

0.363

0.133

-0.605

20.6

-11.2

 

-0.0205

-0.154

-0.764

0.0394

-0.0198

 

0.119

-0.106

-0.540

0.0217

-0.0104

 

-0.408

-0.0183

0.421

-0.741

11.2

 

-0.193

0.0926

0.446

-0.750

0.0176

 

-0.104

0.274

0.359

-0.709

0.00991

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P

 

36010

2742

-1930

434

-807

 

34.4

0.425

-0.973

-0.209

-0.564

 

28.1

3.03

-1.333

0.0146

-0.388

 

0.185

6113

-472

-323

59.8

 

0.0284

6.50

-1.72

-0.258

0.308

 

0.245

5.42

-0.407

-0.281

-0.0299

 

-0.206

-0.122

2435

-515

-164

 

-0.0932

-0.378

3.18

-1.32

0.0954

 

-0.170

-0.118

2.19

-0.492

-0.106

 

0.0696

-0.126

-0.318

1078

-379

 

-0.0267

-0.0758

-0.556

1.79

-0.898

 

0.00273

-0.119

-0.328

1.03

-0.359

 

-0.161

0.0289

-0.126

-0.436

698

 

-0.0857

0.108

0.0476

-0.598

1.26

 

-0.0905

-0.0159

-0.0888

-0.438

0.654

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R

 

10310

 

45.4

 

15.0


Table 5: Sire additive genetic (G), Permanent environmental (P), and residual (R) (co)variances parameters estimated in a bivariate sire model analysis between milk yield (m) and fat yield (f). Genetic correlations between curves parameters are in bold. All (co)variances were multiplied by 103

 

 

m0

m1

m2

m3

m4

f0

f1

f2

f3

f4

G

m0

2913

544

-287

91.2

-74.1

67.9

13.9

-0.752

-0.832

-0.842

m1

0.550

337

-61.5

8.83

-0.331

13.0

9.23

-1.01

-0.193

-0.161

m2

-0.484

-0.305

121

-30.7

15.2

-5.24

-1.10

2.61

-0.695

0.350

m3

0.363

0.103

-0.600

21.7

-11.4

2.68

-0.245

-0.376

0.362

-0.232

m4

-0.401

-0.005

0.404

-0.714

11.7

-1.78

0.333

0.102

-0.163

0.276

f0

0.814

0.457

-0.308

0.372

-0.336

2.39

0.352

-0.0652

0.000120

-0.0409

f1

0.435

0.850

-0.169

-0.0871

0.163

0.383

0.354

-0.0412

-0.0101

0.00952

f2

-0.0372

-0.147

0.635

-0.212

0.0778

-0.104

-0.181

0.143

-0.0510

0.0189

f3

-0.0720

-0.0485

-0.296

0.364

-0.220

0.000

-0.0801

-0.630

0.0450

-0.0173

f4

-0.110

-0.0621

0.225

-0.349

0.558

-0.183

0.120

0.378

-0.667

0.0164

P

m0

36010

2724

-1943

438

-808

957

64.4

1.85

-20.2

-8.20

m1

0.184

6111

-472

-325

60.9

64.3

173

-14.8

-0.323

-2.98

m2

-0.207

-0.122

2438

-512

-160

-43.3

-16.2

65.8

-11.7

-0.768

m3

0.0701

-0.126

-0.316

1080

-372

10.9

-8.78

-14.4

29.1

-10.2

m4

-0.160

0.0295

-0.122

-0.426

707

-24.0

1.03

-4.20

-9.27

20.0

f0

0.852

0.139

-0.148

0.0564

-0.153

35.1

0.81

-0.73

-0.238

-0.582

f1

0.128

0.830

-0.123

-0.101

0.0153

0.0512

7.06

-1.44

-0.108

0.243

f2

0.00501

-0.0992

0.697

-0.229

-0.0832

-0.0651

-0.284

3.65

-1.09

0.0586

f3

-0.0732

-0.00321

-0.161

0.603

-0.237

-0.0283

-0.0283

-0.388

2.16

-0.842

f4

-0.0356

-0.0315

-0.0123

-0.249

0.603

-0.0782

0.0725

0.0254

-0.458

1.56

R

m

 

10310

 

 

 

300

 

 

 

f

 

 

 

 

 

44.7

 

 


 

Table  6: Sire additive genetic (G), Permanent environmental (P), and residual (R) (co)variances parameters estimated in a bivariate sire model analysis between milk yield (m) and protein yield (p). Genetic correlations between curves parameters are in bold. All (co)variances were multiplied by 103  

 

 

m0

m1

m2

m3

m4

p0

p1

p2

p3

p4

G

m0

3084

560

-315

98.5

-77.2

82.6

22.6

-5.86

0.0697

-0.163

m1

0.550

336

-63.4

11.1

-1.24

15.4

9.49

-1.06

0.0611

0.101

m2

-0.512

-0.312

123

-30.8

15.7

-8.42

-2.96

2.77

-0.479

0.103

m3

0.385

0.131

-0.603

21.2

-11.5

3.06

0.838

-0.723

0.431

-0.134

m4

-0.405

-0.0201

0.413

-0.728

11.8

-2.12

-0.321

0.387

-0.221

0.223

p0

0.937

0.528

-0.479

0.419

-0.389

2.52

0.604

-0.171

0.0925

0.000

p1

0.637

0.810

-0.419

0.286

-0.144

0.658

0.408

-0.052

-0.0175

0.0281

p2

-0.384

-0.210

0.910

-0.571

0.414

-0.395

-0.278

0.083

-0.0167

0.00925

p3

0.00783

0.0186

-0.273

0.586

-0.399

0.048

-0.212

-0.475

0.0312

-0.00680

p4

-0.0232

0.0453

0.0732

-0.227

0.521

0.00685

0.369

0.261

-0.681

0.0101

P

m0

36070

2709

-1961

436

-801

967

113

-42.2

-2.93

-11.5

m1

0.182

6116

-480

-322

55.3

75.5

172

-11.6

-8.33

-1.43

m2

-0.209

-0.124

2444

-518

-159

-52.1

-10.6

67.7

-13.4

-5.26

m3

0.070

-0.125

-0.318

1088

-375

11.6

-8.12

-12.4

30.1

-9.28

m4

-0.158

0.0274

-0.120

-0.426

713

-22.5

-0.667

-5.56

-8.17

18.9

p0

0.958

0.182

-0.198

0.0647

-0.159

28.2

3.10

-1.31

-0.0312

-0.359

p1

0.253

0.934

-0.0908

-0.105

-0.0108

0.248

5.55

-0.385

-0.281

-0.0310

p2

-0.149

-0.0986

0.917

-0.252

-0.140

-0.165

-0.111

2.23

-0.469

-0.116

p3

-0.0155

-0.101

-0.258

0.867

-0.290

-0.00464

-0.113

-0.299

1.11

-0.338

p4

-0.0718

-0.0216

-0.125

-0.332

0.834

-0.0802

-0.0149

-0.095

-0.380

0.72

R

m

 

10300

 

 

 

310

 

 

 

p

 

 

 

 

 

14.9

 

 


Heritabilities of milk production traits as a function of DIM for single trait model are shown in Figure 1. Clearly the estimates of heritability of TD records were not constant throughout the lactation. The heritability of milk yield, fat yield and protein yield as a function of DIM were estimated between 0.09 to 0.23, 0.06 to 0.12 and 0.07 to 0.23, respectively. The repeatability for these traits ranged from 0.68 to 0.76, 0.32 to 0.59 and 0.52 to 0.67, respectively. For milk and protein yields there are higher heritability estimates than for fat yield based on DIM, which are in accordance with many other similar investigations (Shadparvar and Yazdanshenas 2005; Abdullahpour et al 2010; Hammami et al 2008 and Bohlouli and Alijani 2012). Permanent environmental variances were higher at the beginning of lactation for all traits; therefore, heritabilities are lower in the beginning of lactation. These results are similar to those observed by Cobuci et al (2011) and Biassus et al (2011) and also repeatabilities are higher in this stage of lactation.


The small differences in heritability estimates between models with third and fourth order of Legendre polynomials (M3 and M4) do not indicate a preferred order of the Legendre polynomial (Cobuci et al 2011).

Figure  1: Heritability (h2) for milk (m), fat (f), and protein (p) yield as a function of days in milk (DIM)
for models with third and fourth order Legendre polynomials (M3 and M4, respectively).

Genetic correlations for 305-d yield among production traits were high, and for milk and fat, for milk and protein and for fat and protein yields were 0.81, 0.94 and 0.86, respectively (Table 7). These estimates were similar with those obtained by Miglior et al (2009) using a multiple-trait-multiple-lactation random regression model in Chinese Holsteins. Larger genetic correlation for 305-d yield between milk and protein yield than between milk and fat yield was reported also by Hammami et al (2008), and Jakobsen et al (2002). The permanent environmental correlations for 305-d yield between yield traits were also high. The large permanent environmental correlations (from 0.97 to 0.99) were found among first lactation yields (Hammami et al 2008).

Table 7: Estimates of heritabilities (diagonal and bold), genetic (above diagonal) and permanent environmental (below diagonal) correlations for 305-d milk, fat, and protein yields

Trait

Milk

Fat

Protein

Milk

0.30

0.81

0.94

Fat

0.85

0.25

0.86

Protein

0.96

0.88

0.31

 

Estimated genetic and environment correlations between test-days of milk yields, test-days of fat yields, and test-days of protein yields at different stages of lactation are shown in Figure 2 and Figure 3. Genetic correlations between test-day close together are close to unity, and the genetic correlations gradually decline as the distance between test-days increases. These figures indicate that correlations between individual test-day are more alike for milk and protein yield than for fat yield. A similar pattern of genetic correlations for daily milk production traits has been reported using a comparable random regression model (Jensen et al 2001 and Jacobsen et al 2002 and Cobuci et al 2011).  

 

Jakobsen et al (2002) reported genetic correlations estimates higher than 0.40 for first lactation test-day milk yield of Holstein dairy cattle, therefore much higher than some estimates observed in this study. However, lower estimates, even close to zero, were obtained for genetic correlations between test-day milk yields in first lactation by Cobuci et al (2005) and Biassus et al (2011).

Figure  2: Genetic (G) correlations between test-day milk yields, test-day fat yields, and test-day protein yields at different days in milks (DIM) for the same trait Figure 3: Permanent environmental (PE) correlations between test-day milk yields, test-day fat yields, and test-day protein yields at different days in milks (DIM) for the same trait   

Genetic correlations between test-day milk and fat yield, between milk and protein yield and between fat and protein yield at the same stage of lactation are shown in Figure 4. Genetic correlations between milk and fat, milk and protein and fat and protein were 0.63 to 0.90, 0.84 to 0.94 and 0.66 to 92, respectively. As expected, genetic correlations between traits were high. However, genetic correlations were lower between milk and fat yields and between fat and protein yields than between milk and protein yields (Zavadilova et al 2005).

For milk and protein, the correlations between the same DIM in the consecutive lactations were below 0.9 at the beginning of the lactation and above 0.9 at the end of lactation. However, for milk and fat yields, and for fat and protein yields, the correlations were clearly lower. Similar shapes of correlation at the same DIM were also reported by Jakobsen et al (2002) and Zavadilova et al (2005).

Figure  4: Genetic correlations between the same DIM of two traits (milk-fat, milk-protein and fat-protein) 

Low heritabilities for fat yields in this study is in accordance with results in other studies using RR models (Hammami et al 2008; Biassus et al 2011 and Bohlouli and Alijani 2012). As found by Ravagnolo et al (2000), fat production seems to decline more strongly than milk or protein yield as a response to heat stress. The decline for fat yield was observed over the whole range of temperatures, whereas for milk and protein, the yields appeared relatively constant until about 24C and then declined. (Hammami et al 2008)

 

Genetic parameters of milk yield and protein yield obtained in this study were moderate compared with major reports on Holstein populations but were low for fat yield. However, low heritability estimates are caused by reduced additive genetics and increased permanent environmental and residual variances. Generally, the resulting estimates of (co)variances, heritabilities, genetic and permanent environmental correlations followed the general pattern reported in other studies.


Conclusion


Acknowledgment

The authors thank the Animal Breeding Center of Karaj, Iran for providing the data.


References

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Received 3 September 2012; Accepted 21 October 2012; Published 6 November 2012

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