Estimation of variance components and heritabilities for body weight from birth to six years of age in Merino sheep using random regression models

 

K.R. Nemutandani1, M.A. Snyman1, W.J. Olivier1 & C. Visser2

1 Grootfontein Agricultural Development Institute, Private Bag X529, Middelburg (EC), 5900, South Africa

2 Department of Animal and Wildlife Sciences, University of Pretoria, Pretoria, 0084

Carina Visser (Corresponding author)

 

Summary

Genetic parameters and (co)variance components for body weight in sheep estimated with random regression models are relatively scarce. The aim of this study was to identify the most appropriate random regression model for estimation of variance components and genetic parameters for body weights recorded from birth until six years of age in Merino sheep. The dataset used in this study comprised body weight data recorded from birth until six years of age in the Grootfontein Merino stud from 1968 to 2012. Random regression models fitted included direct genetic, maternal genetic and animal and maternal permanent environmental effects as random effects in various combinations. The model fitting second order polynomials for the direct and maternal genetic effects and 11 splines separating ages 1, 2, 4, 8, 12, 15, 20, 32, 44, 56 and 68 months was the most suitable model. Three datasets were created. The first included data on all ewes from birth until six years of age and rams from birth until 15 months of age; the second included data from only ewes from birth until six years of age; the third included data from ewes and rams from birth until 15 months of age. The additive genetic variance and consequently the phenotypic variance, as well as the direct heritabilities obtained in this study are much higher than those obtained elsewhere with random regression models in sheep. However, in all but one of the other studies, the datasets included body weights up to much younger ages (16 months) than the current study. The model fitting one polynomial for direct and maternal genetic effects and including 11 splines was compared for the three datasets. It was evident that direct genetic variances and heritabilities were similar until 15 months of age between the dataset including all animals and the one including rams and ewes up till the age of 15 months. These values were, however, higher than published literature values. The direct variances obtained with the dataset including only data from ewes, yielded much lower values, which were comparable to literature values up until 15 months of age. Including records for ram lambs up until 15 months of age together with ewes from birth until adult ages yielded direct genetic variances that fall outside the normal values reported for sheep. This raises the question if random regression is the most suitable procedure for the analysis of body weight in sheep when including data on all available animals from birth until adult age. 

 

Keywords: direct genetic variance, phenotypic variance

 

 

INTRODUCTION

Recently, random regression models have become a more common method to use for the analyses of growth traits. The random regression model (RR) allows environmental effects specific to the time of recording to be accounted for and can also accommodate genetic differences in the shape of each animal's growth curve (Meyer, 2004; Schaeffer, 2004). Additionally it can estimate variances for any age or between any pair of ages in the data set (Ghafouri-Kesbi et al., 2008). The ability of the RR model to properly account for the changing correlation structure results in an increase in prediction accuracy of estimated breeding values when compared to that of the multivariate model (Meyer, 2004).

Genetic parameters and (co)variance components for body weight in sheep estimated with random regression models are relatively scarce (Molina et al., 2007; Ghafouri-Kesbi et al., 2008; Kariuki et al., 2010; Wolc et al., 2011; Bohlouli et al., 2013; Jannoune et al., 2015; Venkataramanan, 2016), as opposed to parameters obtained with single trait analyses.

Genetic parameters obtained with random regression models are comparable with those estimated with general linear models (Ghafouri-Kesbi et al., 2008; Kariuki et al., 2010) on data sets including body weights up to 16 months of age. The aim of this study was to identify the most appropriate random regression model for estimation of variance components and genetic parameters for body weights recorded from birth until six years of age in Merino sheep.

 

MATERIALS AND METHODS

The dataset used in this study comprised body weight data recorded from birth until six years of age in the Grootfontein Merino stud from 1968 to 2012. The total number of ram and ewe lambs for which birth weight was recorded, were 7794 and 8317 respectively. These were the progeny of 3814 dams and 359 sires. The number of records available for adult ewes at six years of age was 703. The data set comprised 58214 records in total. The estimation of variance components and genetic parameters with random regression models was done with the ASReml program (Gilmour et al., 2009). Fixed effects for year-season of birth, sex, rearing status and age of the dam were included in the models. Random regression models fitted included direct genetic, maternal genetic and animal and maternal permanent environmental effects as random effects in various combinations. These models were fitted either with splines with knots at ages 1, 2, 4, 8, 12, 15, 20, 32, 44, 56 and 68 months, splines with knots at ages 1, 4, 15 and 68 months or no splines. The random effects were modelled using cubic spline functions. Polynomials up to the second degree were fitted for the direct genetic and maternal genetic random effects. Output values were processed to obtain (co)variances and genetic parameters for the specific body weights at the different ages. Three datasets were created. The first included data on all ewes from birth until six years of age and rams from birth until 15 months of age; the second included data from only ewes from birth until six years of age; the third included data from ewes and rams from birth until 15 months of age.

 

RESULTS AND DISCUSSION

The description of the models and log-likelihood value (LogL), Akaike information criterion (AIC) and Bayesian information criterion (BIC) for each model fitted are given in Table 1 (See Appendix A).      From the LogL, AIC and BIC values in Table 1 it follows that the models including splines with knots at 11 ages provided a better fit than those including 4 or 0 knots. Models M3-7, M3-7-ewes and M3-7-lambs were the most suitable models for each of the respective datasets used. For the purpose of this paper, only direct genetic variances and direct heritabilities for the various models including splines with knots at 11 ages are summarised in Tables 2 and 3 for body weight from birth until six years of age (See Appendix A).

The additive genetic variance and consequently the phenotypic variance, as well as the direct heritabilities obtained in this study are much higher than those obtained elsewhere with RR models in sheep. Direct genetic variances reported in literature varied between 0 and 25 kg2 for body weight from birth to 16 months of age, with one exception of 0 to 50 kg2 for Santa Ines sheep from birth to 196 days (Saramento et al., 2016). Corresponding literature direct heritabilities varied from 0.02 for birth weight to 0.55 for the older ages up to 16 months of age (Molina et al., 2007; Ghafouri-Kesbi et al., 2008; Kariuki et al., 2010; Wolc et al., 2011; Bohlouli et al., 2013; Jannoune et al., 2015; Zamani et al., 2016). Only one other study where random regression models were fitted to 4 years of age could be found (Venkataraman (2016). However, additive genetic variance (1 to 50 kg2) and direct heritabilities (0.13 to 0.12) in that study was also much lower than for the current study.

The trends in direct genetic variance for body weight with age differ between models that included one-degree polynomials and models including two-degree polynomials for the random effects (Figures 1 and 2).

 

Figure 1. Direct genetic variance for body weight from birth until 68 months of age obtained for models including one-degree polynomials for the random effects.

 

Figure 2. Direct genetic variance for body weight from birth until 68 months of age obtained for models including two-degree polynomials for the random effects.

 

Direct genetic variance was much higher for M3-1 at the older body weights than for M3-1-ewes (Table 2). It was similar between M3-1 and M3-1-lambs up to 15 months of age (Figure 1). Direct variances obtained with both M3-1 and M3-1-lambs were higher than values obtained in other studies, while those obtained with M3-1-ewes were similar to literature studies up to 15 months of age. The same applies to direct heritabilities obtained with these three models (Table 3). The direct variances obtained with M3-7-ewes followed the same trend as for those obtained with M3-7, although the values were much lower and more in line with published variances for sheep (Table 2).

 

CONCLUSIONS

Direct genetic and phenotypic variances estimated in this study with various random regression models for body weight from birth until six years of age were much higher than corresponding published estimates for sheep. The dataset including only records of ewes from birth until six years of ages yielded values more in line with other published values for sheep. Including records of ram lambs up until 15 months of age together with ewes from birth until adult ages yielded direct genetic variances that fall outside the normal values reported for sheep. As many animals are missing older weights, the extrapolation needed for those animals is probably one of the reasons for the poorly estimated values at the older ages. This raises the question if random regression is the most suitable procedure for the analysis of body weight in sheep when including data on all available animals from birth until adult age. 

 

REFERENCES

Bohlouli, M., Mohammadi, H., Alijani, S., 2013. Genetic evaluation and genetic trend of growth traits of Zandi sheep in semi-arid Iran using random regression models. Small Rumin. Res. 114, 195-201.

Ghafouri Kesbi, F., Eskandarinasab, M., Shahir, M.H., 2008. Estimation of direct and maternal effects on body weight in Mehraban sheep using random regression models. Arch. Anim. Breed. 51, 235-246.

Gilmour, A.R., Gogel, B.J., Cullis, B.R. & Thompson, R., 2009. ASReml User Guide Release 3.0 VSN International Ltd, Hemel Hempstead, HPI 1ES, UK.

Jannoune, A., Boujenane, I., Falaki, M., Derqaoui, L., 2015. Genetic analysis of live weight of Sardi sheep using random regression and multi-trait animal models. Small Rumin. Res. 130, 1-7.

Kariuki, C.M., Ilatsia, E.D., Wasike, C.B., Kosgey, I.S., Kahi, A.K., 2010. Genetic evaluation of growth of Dorper sheep in semi-arid Kenya using random regression models. Small Rumin. Res. 93, 126-134.

Meyer, K., 2004. Scope for a random regression model in genetic evaluation of beef cattle for growth. Livest. Prod. Sci. 86, 69-83.

Molina, A., Menendez-Buxadera, A., Valera, M., Serradilla, J.M., 2007. Random regression model of growth during the first three months of age in Spanish Merino sheep. J. Anim. Sci. 85, 2830-2839.

Sarmento, J.L.R., Torres, R.A., Sousa, W.H., Lôbo, R.N.B., Albuquerque, L.G., Lopes, P.S., Santos, N.P.S.& Bignard, A.B., 2016. Random regression models for the estimation of genetic and environmental covariance functions for growth traits in Santa Ines sheep. Genet. Molecular Res. 15(2), gmr.15025749.

Schaeffer, L.R., 2004. Application of random regression models in animal breeding. Livest. Prod. Sci. 86, 35-45.

Venkataramanan, R., 2016. Random regressions to model growth in Nilagiri sheep of South India. Small Rumin. Res. 144 242–247.

Wolc, A., Barczak, E., Wójtowski, J., Ślósarz, P., Szwaczkowski, T., 2011. Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models. Small Rumin. Res. 100, 15-18.

Zamani, P., Moradi, M.R., Alipour, D., Ghafouri-Kesbi, 417 F., 2016. Combination of B-Spline and Legendre functions in random regression models to fit growth curve of Moghani sheep. Small Rumin. Res. 145, 115-122.

 

APPENDIX A


Table 1. Order of fit of direct (ka) and maternal (km) genetic effects, maternal (kmpe) and animal (kape) permanent environmental effects, number of knots, number of parameters (Np), log-likelihood value (LogL), Akaike information criterion (AIC) and Bayesian information criterion (BIC) for the different models fitted.

Model

ka

km

kmpe

kape

Splines

Np

LogL Value

AIC

BIC

Data set including records from ewes and rams from birth to 6 years of age

M1-1

1

     

11

5

-126 243

252 491

252 510

M1-2

1

     

4

5

-127 042

254 089

254 108

M1-3

1

     

0

4

-151 709

303 421

303 436

M1-4

1

 

 

1

11

6

-126 243

252 491

252 510

M1-5

1

 

 

1

4

6

-127 042

254 089

254 108

M1-6

1

 

 

1

0

5

-151 709

303 421

303 436

M1-7

2

     

11

8

-124 294

248 596

248 626

M1-8

2

     

4

8

-125 625

251 259

251 289

M1-9

2

     

0

7

-133 820

267 647

267 674

M2-1

1

 

1

 

11

8

-124 366

248 740

248 770

M2-2

1

 

1

 

4

8

-125 180

250 369

250 399

M2-3

1

 

1

 

0

7

-150 167

300 340

300 367

M2-4

1

 

1

1

11

9

-124 366

248 740

248 770

M2-5

1

 

1

1

4

9

-125 180

250 369

250 399

M2-6

1

 

1

1

0

8

-150 167

300 340

300 367

M2-7

2

 

1

 

11

11

-123 072

246 155

246 196

M2-8

2

 

1

 

4

11

-124 282

248 576

248 617

M2-9

2

 

1

 

0

10

-132 495

265 000

265 038

M3-1

1

1

   

11

8

-124 366

248 740

248 770

M3-2

1

1

   

4

8

-125 180

250 369

250 399

M3-3

1

1

   

0

7

-150 167

300 340

300 367

M3-4

1

1

 

1

11

9

-124 366

248 740

248 770

M3-5

1

1

 

1

4

9

-125 180

250 369

250 399

M3-6

1

1

 

1

0

8

-150 167

300 340

300 367

M3-7

2

2

   

11

14

-122 409

244 831

244 884

M3-8

2

2

   

4

14

-123 717

247 449

247 502

M3-9

2

2

   

0

13

-132 193

264 399

264 448

M4-1

1

1

1

 

11

9

-124 364

248 736

248 770

M4-2

1

1

1

 

4

9

-125 180

250 368

250 402

M4-3

1

1

1

 

0

8

-150 167

300 341

300 371

M4-4

1

1

1

1

11

10

-124 364

248 741

248 794

M4-5

1

1

1

1

4

10

-125 180

250 373

250 426

M4-6

1

1

1

1

0

9

-150 167

300 346

300 395

M4-7

2

2

1

 

11

15

-122 409

244 832

244 889

M4-8

2

2

1

 

4

15

-123 718

247 450

247 507

M4-9

2

2

1

 

0

14

-132 193

264 400

264 452

Data set including records form only ewes from birth to 6 years of age

M3-1-ewesa

1

1

 

 

11

8

-69 280

138 568

138 599

M3-2-ewes

1

1

 

 

4

8

-70 881

141 770

141 800

M3-3-ewes

1

1

 

 

0

7

-89 450

178 908

178 934

M3-7-ewes

2

2

 

 

11

14

-67 968

135 946

135 987

Data set including records form ewes and rams from birth to 15 months of age

M3-1-lambsb

1

1

 

 

6

8

-100 615

201 235

201 254

M3-2-lambs

1

1

 

 

3

8

-101 406

202 817

202 836

M3-3-lambs

1

1

 

 

0

7

-107 445

214 895

214 910

M3-7-lambs

2

2

 

 

6

14

-95 699

191 405

191 435

M3-1-ewes - Models done on datasets including records form only ewes from birth to 6 years of age

M3-1-lambs - Models done on datasets including records form ewes and rams from birth to 15 months of age

 

Table 2. Direct genetic variances obtained with the different models.

Model 

Age (months)

1

2

4

8

12

15

20

32

44

56

68

M1-1

0.0

1.0

13.4

78.8

198.8

324.5

602.3

1616.2

3120.1

5114.2

7599.2

M1-7

0.4

1.6

18.7

99.1

220.3

324.6

500.7

788.2

734.0

384.4

59.9

M2-1

1.0

1.7

12.0

67.6

170.1

277.6

515.4

1384.5

2674.5

4385.5

6518.3

M2-7

0.4

1.4

17.7

95.5

213.2

314.6

485.3

761.5

702.1

356.5

45.2

M3-1

1.0

1.7

12.0

67.6

170.1

277.6

515.4

1384.5

2674.5

4385.5

6518.3

M3-7

0.1

1.1

15.4

82.8

184.5

272.0

419.3

658.3

609.4

314.8

50.3

M4-1

0.0

0.7

11.0

66.6

169.1

276.6

514.4

1383.5

2673.5

4384.5

6517.3

M4-7

0.3

1.3

15.5

82.8

184.5

271.9

419.3

658.3

609.4

314.8

50.2

M3-1-Ewes

1.4

1.8

2.9

5.9

10.1

14.0

22.1

49.3

87.5

136.6

196.6

M3-7-Ewes

0.5

1.3

3.5

10.5

19.7

27.1

39.3

58.6

57.4

43.2

42.1

M3-1-Lambs

0.2

1.6

14.2

78.0

193.4

313.9

         

M3-7-Lambs

0.2

4.6

28.7

97.0

185.1

318.5

         

 

 

Table 3. Direct heritabilities obtained with the different models.

Model 

Age (months)

1

2

4

8

12

15

20

32

44

56

68

M1-1

0.00

0.07

0.48

0.85

0.93

0.96

0.98

0.99

1.00

1.00

1.00

M1-7

0.03

0.11

0.58

0.88

0.94

0.96

0.97

0.98

0.98

0.97

0.81

M2-1

0.07

0.11

0.41

0.71

0.78

0.81

0.83

0.84

0.84

0.85

0.85

M2-7

0.03

0.09

0.56

0.87

0.93

0.95

0.97

0.97

0.97

0.92

0.54

M3-1

0.07

0.11

0.42

0.71

0.79

0.81

0.83

0.84

0.85

0.85

0.85

M3-7

0.01

0.08

0.48

0.73

0.79

0.81

0.82

0.83

0.83

0.82

0.71

M4-1

0.00

0.05

0.40

0.71

0.79

0.81

0.83

0.84

0.85

0.85

0.85

M4-7

0.02

0.08

0.48

0.73

0.79

0.81

0.82

0.83

0.83

0.82

0.71

M3-1-Ewes

0.09

0.11

0.16

0.27

0.39

0.46

0.57

0.73

0.81

0.86

0.89

M3-7-Ewes

0.04

0.08

0.20

0.43

0.59

0.66

0.74

0.80

0.79

0.72

0.68

M3-3-Lambs

0.01

0.05

0.38

0.70

0.78

0.80

 

 

 

 

 

M3-7-Lambs

0.02

0.44

0.83

0.91

0.86

0.83

         

 

Published

Proc. 11th Wrld. Congr. Gen. Appl. Livest. Prod., Auckland, New Zealand, 11-16 February