Estimates of (co)variance components and genetic parameters of growth traits in Marwari sheep

Abstract

The present investigation was undertaken to estimate the (co)variance components and genetic parameters for different growth traits in Marwari flock comprising records of 1649 animals distributed over a period of 12 years (1999–2010), maintained at Arid Region Campus of Central Sheep and Wool Research Institute, Bikaner, Rajasthan, India. The estimation was done by restricted maximum likelihood procedures, fitting six animal models with various combinations of direct and maternal effects. As per likelihood ratio test, direct heritability estimates from the best model for body weight at birth, weaning, 6, 9 and 12 months of age, and average daily gain during birth to weaning, weaning to 6 and 6–12 months of age were 0.28 ± 0.058, 0.27 ± 0.050, 0.28 ± 0.049, 0.30 ± 0.080, 0.29, 0.26 ± 0.050, 0.16 ± 0.040 and 0.31, respectively. Maternal genetic effect declined from 4% at 6 months weight to 1% at 9 months and was zero at 12 months of age. Maternal genetic effect on the post-weaning traits was a carryover effect of the maternal influences during pre-weaning age. Maternal permanent environmental effects contributed 19% of the total phenotypic variation in birth weight and 8% for weaning weight. The evidence for maternal genetic effect for average daily gain was observed only during 6–12 months of age where the additive maternal heritability was estimated as 8%. The genetic correlation between direct and maternal genetic effects was found significantly large and negative for all the traits, indicating antagonistic pleiotropy, which must be considered while formulating breeding plans. A modest rate of genetic progress seems possible in the flock through selection. Genetic correlations between body weight traits were positive and ranged from 0.23 between birth weight and weight at 6 months to 0.88 between weaning weight and weight at 9 months of age. The positive and high genetic correlation of weaning weight with weight at subsequent ages suggests that genetic gain in post-weaning weight will be maintained even if selection age is reduced to 3 months.

Keywords:

• growth
• direct heritability
• genetic correlations
• maternal genetic effect
• Marwari sheep

1. Introduction

Sheep is an important economic livestock species that helps to strengthen the backbone of rural economy of India. Marwari breed of sheep is widely distributed in Jodhpur, Jalore, Nagaur, Pali, Sirohi and Barmer districts of Rajasthan and is reared for its medium and coarse quality carpet wool and mutton. However, the source of income from this breed depends mainly upon mutton production as earnings from its wool are of little value due to its coarse texture. The importance of this breed can be judged from the fact that this was numerically the largest breed of the north-west region of the country, well known for its high disease resistance, draught tolerance, capacity to travel longer distances in search of forage and is the lifeline of the Raika/Rebari communities who rear it (Yadav & Paul 2009).

With the rising prices of mutton in the market, fast-growing and heavier lambs are in great demand. The economics of sheep production is greatly affected by the growth performance as heavier lambs with high growth rate would fetch relatively more economic returns in lesser time span compared to weaker lambs (Narula et al. 2009). Thus, it is necessary to have knowledge of genetic parameters of these economically important growth traits to formulate optimum breeding policies for improved production.

Early expressed traits are determined not only by animal’s own genetic potential but also by its maternal environment (Robinson 1981). Maternal environment represents mainly the mother’s milk yield, mothering ability and also the uterine environment. Maternal genotype affects the phenotypic expression of the young ones through her genotype for maternal effects and through her direct additive genes for growth. Nasholm and Danell (1994) observed that when maternal genetic effects are important and not considered in the statistical model, heritability estimates are biased upwards and the realized efficiency of selection is reduced when compared with the expected. Thus, both direct and maternal components must be considered in order to achieve optimum genetic progress especially in growth traits. In the present study, an attempt has been made to estimate the variance and covariance components due to additive and maternal effects in Marwari sheep for various economically important growth traits by determining the most important animal model. Estimation of genetic and phenotypic correlations among these traits was also done to understand the relationships among the traits and also to formulate breeding strategies to improve combinations of the desired characters.

2. Materials and methods

2.1. Data

Data for the investigation were obtained from the records of Sheep Research Project entitled ‘Improvement of Marwari Sheep for Carpet Wool Production through Selection’ under Network Project on Sheep Improvement, located at the Arid Region Campus of the Central Sheep and Wool Research Institute (CSWRI), Bikaner. Different economic traits included in the study were body weight at birth (BWT), three (3WT), six (6WT), nine (9WT) and twelve (12WT) months of age and average daily gain between adjacent stages of growth i.e., from birth to 3 (ADG1), 3–6 (ADG2) and 6–12 (ADG3) months of age. Characteristics of the data structure, number of sire and dam, least-squares mean (LSM), standard deviation and coefficient of variation for respective traits are summarized in Table 1. Data were collected over the years 1999–2010, with records on total of 1649 lambs descended from 107 sires and 562 dams. All the animals in this flock were kept under semi-intensive management system. Regarding feeding, concentrate mixture was provided ad-libitum to suckling lambs from 15 days’ age until weaning (90 days). In addition, they were grazed separately from their ewes in morning and evening. After weaning period, all the sheep were allowed to graze from 8.00 am to 6.00 pm daily, except during summer months from April to September when split grazing during cooler hours of the day was practiced from 6.00 am to 12 Noon and 3.00 pm to 7.00 pm. In addition to this, 300 g concentrate mixture was provided during post-weaning period. The pasture consisted primarily of annual grasses such as Aristida funcunilata (Lampla) and Cenchrus saggitarius (Bhurat); perennial grasses such as Lasiurus sindicus (Sewan), Dactyloctenium sindicum (Ganthia) and Cenchrus ciliarus (Anjan); legumes like Indigofera spp. (Bakaria), Tephrosis purpurea and Tribulus terrestris (Gokhru) and trees and shrubs like Prosopis cineraria (khejri), Zizyphus nummularia (Pala), Calligoneum polygonoides (Phog), Aerva pseudotomentosa, Crotolaria burchea and Cymbopogan spp. Birth weight was taken within 24 hrs of birth, and 3, 6, 9 and 12 month weights were taken on exact dates.

Table 1. Characteristics of data structure for economic traits of Marwari sheep.

Trait*	BWT	WWT	6WT	9WT	12WT	ADG1	ADG2	ADG3
No. of records	1649	1545	1385	850	612	1525	1371	644
Sires with progeny records	107	107	107	90	88	107	107	85
Dams with progeny records	562	535	492	300	217	531	476	210
Mean	3.04	14.82	21.29	26.15	28.91	131.50	70.73	37.23
Standard deviation	0.52	3.11	3.85	4.41	3.98	31.51	24.69	13.96
Coefficient of variation (%)	15.60	16.88	14.25	11.09	9.90	19.39	30.56	35.65

* indicates that mean and standard deviation for BWT to 12WT are in kg and for ADG1 to ADG3 are in gm.

2.2. Statistical methods

Data were first analyzed by least-squares analysis of variance (SPSS 2005) to identify the fixed effects to be included in the model. The model included the fixed effects of period of birth (four levels), sex of lamb (two levels) and parity of ewe (four levels). Ewe weight at lambing was fitted as a covariate. Only significant effects (p ≤ 0.05) were included in the models which were subsequently used for the genetic analysis. (Co)variance components were estimated by restricted maximum likelihood procedures (REML) using a derivative-free algorithm fitting an animal model (DFREML; Meyer 2000). Convergence of the REML solutions was assumed when the variance of function values (–2 log-L) in the simplex was less than 10^–8. To ensure that a global maximum was reached, analysis was restarted. When estimates did not change up to two decimals, convergence was confirmed. Six models which accounted for the direct and maternal effects were fitted as follows:

(1)

(2)

(3)

(4)

(5)

(6)

Where, Y is the vector of record; β, a, m, c and ε are vectors of fixed, direct additive genetic, maternal additive genetic, permanent environmental effects of the dam and residual effects, respectively; with association matrices X, Z_a, Z_m and Z_c; A is the numerator relationship matrix between animals; and σ_am is the covariance between additive direct and maternal genetic effects. Assumptions for variance (V) and covariance (Cov) matrices involving random effects were:

Where, I represents identity matrix; , , , are additive genetic variance, additive maternal, maternal permanent environmental and residual variances, respectively. The direct-maternal correlation (r_am) was obtained for all the traits under analysis. Maternal across year repeatability for ewe performance was calculated for all the traits as: t_m = (¼) h² + m² + c² + r_am √m²√h² (Al-Shorepy 2001). The total heritability () was calculated using the formula: = (+ 0.5 + 1.5 σ_am)/σ_p² (Willham 1972).

The most appropriate model for each trait was selected based on likelihood ratio test (LRT; Meyer 1992). An effect was considered to have a significant influence when its inclusion caused a significant increase in log-likelihood, compared with a model in which it was ignored. Significance of an effect was tested at p < 0.05 by comparing the differences in log-likelihoods (–2 log-L) with values for a chi-square distribution with degrees of freedom equal to the differences in the number of (co)variance components fitted for the two models. The model with fewest random terms was chosen where log-L values did not differ significantly. Subsequently, a series of bivariate animal model analysis under the model 1 was carried out in order to estimate genetic and phenotypic correlations between the traits with starting values obtained from single trait analysis.

3. Results and discussion

LSM along with the standard deviation and per cent coefficient of variation for different traits under study are given in Table 1. The LSM ± SE for various traits were: BWT = 3.04 ± 0.01 kg; WWT = 14.82 ± 0.08 kg; 6WT = 21.29 ± 0.10 kg; 9WT = 26.15 ± 0.15 kg; 12WT = 28.91 ± 0.16 kg; ADG1 = 131.50 ± 0.81 g; ADG2 = 70.73 ± 0.67 g and ADG3 = 37.23 ± 0.55 g. (Co)variance components and genetic parameters estimated by univariate analysis for various growth traits of Marwari sheep are presented in Table 2. As per LRT, the best model for BWT and 3WT was model 4, which included direct additive and permanent environmental effects of the dam. For post-weaning weights and ADG3, model 2 was considered best which included additive direct and maternal genetic effects. For ADG1 and ADG2, model 1, a simple animal model, was the best that included only direct additive effect. The complete estimates from all six models for all the growth traits are given in Table 2. So the discussion is being stuck to the best fitted model.

Table 2. Estimates of (co)variance components (kg²) and genetic parameters for different growth traits.

Items^a	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Trait: BWT
	0.11	0.05	0.06	0.06	0.06	0.06
	–	0.05	0.05	–	0.02	0.02
σam	–	–	−0.48 E-2	–	–	0.26 E-02
	–	–	–	0.04	0.02	0.02
	0.12	0.13	0.12	0.12	0.12	0.12
	0.23	0.23	0.23	0.22	0.22	0.22
h^2	0.48 ± 0.03	0.23 ± 0.052	0.24^b	0.28 ± 0.058	0.25 ± 0.056	0.25^b
m^2	–	0.21 ± 0.033	0.23^b	–	0.10 ± 0.065	0.09^b
ram	–	–	−0.09	–	–	0.08
c^2	–	–	–	0.19 ± 0.031	0.11 ± 0.059	0.11^b
	0.48	0.34	0.33	0.28	0.30	0.31
tm	0.12	0.27	0.27	0.26	0.27	0.27
Log-L	180.19	186.61	186.67	239.75	153.60	153.62
3WT
	1.82	1.71	4.09	1.69	1.69	4.02
	–	0.41	2.60	–	0.11	2.27
σam	–	–	−3.01	–	–	−2.92
	–	–	–	0.48	0.38	0.34
	4.42	4.16	2.69	4.08	4.07	2.65
	6.24	6.28	6.37	6.25	6.26	6.36
h^2	0.29 ± 0.05	0.27 ± 0.05	0.64^b	0.27 ± 0.050	0.27 ± 0.050	0.63^b
m^2	–	0.07 ± 0.029	0.41^b	–	0.02 ± 0.048	0.36^b
ram	–	–	−0.92	–	–	−0.97
c^2	–	–	–	0.08 ± 0.030	0.06 ± 0.050	0.05^b
	0.29	0.30	0.14	0.27	0.28	0.12
tm	0.07	0.13	0.10	0.14	0.15	0.11
Log-L	−2373.92	−2441.26	−2408.06	−2358.57	−2451.94	−2419.00
Trait: 6WT
	2.64	2.60	6.30	2.63	2.61	6.30
	–	0.35	3.95	–	0.36	3.94
σam	–	–	−4.92	–	–	−4.91
	–	–	–	0.19	0.17 E-03	0.39 E-04
	6.55	6.28	3.88	6.40	6.28	3.88
	9.20	9.24	9.20	9.21	9.24	9.20
h^2	0.29 ± 0.048	0.28 ± 0.049	0.68^b	0.29 ± 0.049	0.28^b	0.68^b
m^2	–	0.04 ± 0.027	0.43^b	–	0.04^b	0.43^b
ram	–	–	−0.99	–	–	−0.99
c^2	–	–	–	0.02 ± 0.030	0.00	0.00
	0.29	0.30	0.10	0.29	0.30	0.10
tm	0.11	0.11	0.07	0.09	0.11	0.07
Log-L	−2630.73	−2228.68	−2180.88	−2445.98	−2413.18	−2365.38
9WT
	2.55	2.53	3.92	2.43	2.44	2.47
	–	0.47 E-01	1.21	–	0.25 E-05	0.97 E-03
σam	–	–	−1.61	–	–	−0.49 E-01
	–	–	–	0.51	0.51	0.54
	5.85	5.83	4.97	5.47	5.46	5.45
	8.40	8.40	8.49	8.41	8.41	8.41
h^2	0.30 ± 0.079	0.30 ± 0.080	0.46^b	0.29^b	0.29^b	0.29^b
m^2	–	0. 01 ±0.045	0.14^b	–	0.00	0.10^b E-03
ram	–	–	−0.74	–	–	−1.0
c^2	–	–	–	0.06^b	0.06^b	0.06^b
	0.30	0.30	0.25	0.29	0.29	0.29
tm	0.08	0.08	0.07	0.13	0.13	0.13
Log-L	−1497.91	−1397.78	−1395.68	−1450.32	−1443.44	−1443.22
12WT
	2.37	2.37	3.29	2.36	2.37	2.83
	–	0.37 E-04	0.56 E-01	–	0.49 E-05	0.74 E-01
σam	–	–	−0.43	–	–	−0.46
	–	–	–	0.53 E-04	0.92 E-06	0.84 E-07
	5.82	5.82	5.31	5.83	5.82	5.68
	8.19	8.19	8.23	8.19	8.19	8.12
h^2	0.29 ± 0.091	0.29^b	0.40^b	0.29^b	0.29^b	0.35^b
m^2	–	0.00	0.68^b E-02	–	0.00	0.91^b E-01
ram	–	–	−1.00	–	–	−1.00
c^2	–	–	–	0.00	0.00	0.00
	0.29	0.29	0.33	0.29	0.29	0.27
tm	0.07	0.07	0.05	0.07	0.07	0.04
Log-L	−1065.03	−1004.63	−1001.89	−1040.08	−1029.57	−1026.45
Trait: ADG1
	169.25	164.68	410.91	162.40	163.07	408.89
	–	26.54	266.60	–	7.49	254.14
σam	–	–	−322.17	–	–	−318.53
	–	–	–	32.45	25.85	12.88
	480.98	461.80	305.49	456.60	455.71	303.27
	650.22	653.02	660.83	651.45	652.12	660.65
h^2	0.26 ± 0.050	0.25 ± 0.051	0.62^b	0.25 ± 0.050	0.25 ± 0.051	0.62^b
m^2	–	0.04 ± 0.027	0.40^b	–	0.01 ± 0.044	0.38^b
ram	–	–	−0.97	–	–	−0.99
c^2	–	–	–	0.05 ± 0.030	0.04 ± 0.048	0.02^b
	0.26	0.27	0.09	0.25	0.26	0.09
tm	0.07	0.10	0.07	0.11	0.11	0.08
Log-L	−5750.29	−6060.74	−6023.33	−5828.06	−5981.08	−5943.95
ADG2
	72.47	72.56	144.43	72.53	72.46	133.31
	–	0.93 E-03	26.38	–	0.15 E-03	13.98
σam	–	–	−61.72	–	–	−43.17
	–	–	–	0.11 E-02	0.33 E-03	0.13 E-01
	394.57	394.50	357.28	394.52	394.58	362.63
	467.04	467.06	466.37	467.05	467.04	466.77
h^2	0.16 ± 0.040	0.16^b	0.31^b	0.16^b	0.16^b	0.29^b
m^2	–	0.00	0.06^b	–	0.00	0.03^b
ram	–	–	−1.00	–	–	−1.00
c^2	–	–	–	0.00	0.00	0.00
	0.16	0.16	0.14	0.16	0.16	0.16
tm	0.04	0.04	0.16 E-02	0.04	0.04	0.88 E-02
Log-L	−5060.23	−5137.65	−5125.70	−5058.11	−5139.77	−5130.12
ADG3
	55.39	55.41	148.33	55.41	55.45	101.86
	–	0.45 E-03	66.17	–	0.29 E-03	9.15
σam	–	–	−99.07	–	–	−30.53
	–	–	–	0.45 E-03	0.57 E-03	0.24 E-03
	122.68	122.66	60.71	122.66	122.63	94.98
	178.07	178.07	176.14	178.07	178.08	175.46
h^2	0.31 ± 0.064	0.31^b	0.84^b	0.31^b	0.31^b	0.58^b
m^2	–	0.00	0.38^b	–	0.00	0.05^b
ram	–	–	−1.00	–	–	−1.00
c^2	–	–	–	0.00	0.00	0.00
	0.31	0.31	0.19	0.31	0.31	0.35
tm	0.08	0.08	0.24 E-01	0.08	0.08	0.23 E-01
Log-L	−2166.96	−1968.42	−1939.56	−2091.69	−2043.69	−2028.81

^a , , , and are additive genetic, maternal additive genetic, maternal permanent environmental, residual variance and phenotypic variance, respectively; h² is heritability; c² is /; t_m is maternal across year repeatability for ewe performance; is total heritability and log-L is log-likelihood for the best model obtained from DFREML (Meyer 2000).

^b Indicates that the approximation used to define standard errors of parameter estimates failed.

Column in bold values represents estimates from best model as per LRT.

3.1. Pre-weaning weights

(Co)variance components along with the genetic parameters for BWT from six different models are given in Table 2. The model including direct additive and permanent environmental effects of the dam (model 4) was sufficient to explain the variation in the birth weight of lambs. In the model 4, the heritability for BWT was 0.28 ± 0.058. This moderate heritability estimate suggests further scope for improvement due to selection in the flock for higher birth weight. The estimate was similar with the findings of Prince et al. (2010) as 0.28 ± 0.03 in Avikalin sheep. However, lower estimates than the present study as 0.04, 0.056, 0.20 and 0.19 were reported by Rashidi et al. (2007) in Kermani, Kushwaha et al. (2009) in Chokla and Gowane et al. (2010a, 2010b) in Bharat Merino and Malpura sheep, respectively.

The permanent environmental maternal effect for BWT was moderate in this study (c² = 0.19 ± 0.031). This indicates the importance of maternal environment and care at birth of lamb. The estimates were similar with the findings of Gowane et al. (2010a) in Bharat Merino sheep where c² was 0.19 ± 0.02. The estimates of repeatability of ewe performance (t_m) and total heritability () were moderate in magnitude as 0.26 and 0.28, respectively. Gowane et al. (2010b) reported slightly lower estimates of t_m and as 0.25 and 0.19, respectively in Malpura sheep.

The direct heritability estimates for weaning weight from the best model was 0.27 ± 0.050. Lower estimates than the current study were obtained by Notter (1998) as 0.21 and 0.07 in Suffolk and Polypay, Kushwaha et al. (2009) as 0.18 in Chokla and Gowane et al. (2010a) as 0.04 ± 0.02 in Bharat Merino sheep. The c² estimate of 0.08 ± 0.030 in this study also indicates the decline of maternal effect from birth to weaning in Marwari sheep. Ekiz et al. (2004) and Ozcan et al. (2005) both reported c² = 0.08 in Turkish Merino sheep. Gowane et al. (2010a) in Bharat Merino and Prince et al. (2010) in Avikalin sheep reported lower estimates of c² as 0.06 ± 0.02 and 0.03 ± 0.02, respectively.

Estimate of repeatability of ewe performance (t_m) for weaning weight was low in magnitude as 0.14 in Marwari sheep. In the current study, total heritability () was moderate as 0.27, which is higher than the reports of Kushwaha et al. (2009) for Chokla sheep, Gowane et al. (2010b) for Malpura sheep and Prince et al. (2010) for Avikalin sheep as 0.18, 0.18 and 0.20, respectively. Moderate additive variability for 3WT in Marwari sheep and also the estimate of t_m and indicates further scope of genetic improvement in weaning weight through mass selection.

For WWT, correlation estimates between direct additive and maternal genetic effect (r_am) were negative and higher which means improvement in one will result in reduction of another. Inclusion of sire × year interaction in the model could lead to a reduction in the negative correlation estimate between the animal effects (Robinson 1996; Berweger et al. 1999). The data structure in the present study however did not include this interaction. For WWT, it was also observed that in the presence of large negative estimate of r_am, direct and maternal estimates tend to be higher than in models that assume r_am to be zero. As noted by Notter and Hough (1997), estimates that do not involve r_am can be properly used for genetic prediction only if the user also accepts and incorporates the additive maternal covariance in to the prediction model.

3.2. Post-weaning weights

Estimates of (co)variance components calculated for the weights at 6, 9 and 12 months of age are presented in Table 2. For 6WT, model 1 explained 29% variance through direct heritability. Addition of m² in model 2 and c² in model 4 did not influence the heritability estimate. However, addition of σ_am in model 3 inflated the heritability estimate due to very high negative covariance between direct and maternal effects (r_am = –0.99). Similar finding was seen in model 6 where σ_am was taken in the analysis. In spite of the fact that maternal genetic variance tends to converge to zero as the age advances, high and negative r_am is suggestive that there is some hidden mechanism underlying phenotypic relation, which restricts genetic covariance at higher negative magnitude. Similar conclusion was drawn by Prince et al. (2010) in Avikalin sheep. Thus, model 2, second best model as per LRT, was studied for genetic parameter estimates of 6WT.

Thus, the direct heritability estimates from the best model (model 2) for the post-weaning weights were 0.28 at 6WT, 0.30 ± 0.080 at 9WT and 0.29 at 12WT for Marwari sheep. The estimates were higher than those of the earlier reported by Kushwaha et al. (2009) in Chokla sheep (0.16 for 6WT, 0.22 for 9WT and 0.23 for 12WT), Gowane et al. (2010a) in Bharat Merino sheep (0.00 for 6WT, 0.03 for 9WT and 0.09 for 9WT) and Prince et al. (2010) in Avikalin sheep (0.28 for 6WT and 0.15 for 12WT). Higher estimate than the present study for 6WT was reported by Notter (1998) as 0.55 in Suffolk sheep. Additive maternal heritability (m²) declined from 0.04 at 6 months weight to 0.01 ± 0.045 at 9 months and was zero at 12 months of age. Similar reports of declining maternal effects with the advancement of age were reported by Maria et al. (1993), Tosh and Kemp (1994) and Mandal et al. (2009).

Estimate of repeatability of ewe performance (t_m) for post-weaning weights were low in magnitude as 0.11, 0.08 and 0.07 for 6WT, 9WT and 12WT. Gowane et al. (2010b) and Prince et al. (2010) reported similar estimates in Malpura and Avikalin sheep, respectively. Total heritability () estimates for Marwari sheep were 0.30, 0.30 and 0.29 for 6WT, 9WT and 12WT, respectively which is higher than the reports of Gowane et al. (2010a) for Bharat Merino sheep. However, Gowane et al. (2010b) in Malpura sheep reported lower values for than the present study. Reports suggest scope of further genetic improvement in post-weaning weights through selection.

3.3. Average daily gain

(Co)variance estimates for average daily gain from six different models are presented in Table 2. Based on logarithm of the likelihood function, model 1 was best for ADG1 and ADG2, whereas for ADG3, model 3 was the best. However, addition of σ_am, due to high negative association (r_am = –1.00), inflated heritability estimate of ADG3 to 0.84. Therefore, although for ADG3 model 3 was best as per LRT, model 2 (second best model) was studied for discussion of genetic parameter estimates.

Additive genetic heritability for ADG1 from most suitable model was 0.26 ± 0.050. Our estimates were similar to estimates of Mohammadi and Edriss (2007) in Mehraban breed of sheep. However, Prince et al. (2010) reported lower estimates as 0.15 ± 0.04 in Avikalin sheep. Estimates of t_m and were 0.07 and 0.26, respectively.

For post-weaning gain during 3–6 months of age (ADG2), direct additive heritability (h²) from the best model (model 1) was 0.16, indicating reasonable scope of improvement in the trait through selection. The estimate was exactly similar with the findings of Prince et al. (2010) in Avikalin sheep (0.16).

For post-weaning gain during 6–12 months of age (ADG3), model 1 explained 31% of total variance due to direct additive effect that was found not to be changed by addition of m² or c². The direct heritability estimate for ADG3 from the best model was found to be extremely high (0.84) which can be explained by a very high negative covariance between direct and maternal effects (r_am = –1.00). Thus, model 2 was studied for genetic parameter estimates and the estimated value of heritability by this model was 0.31. Lower estimates of 0.21 and 0.22 were reported by Notter (1998) in Suffolk and Polypay sheep, respectively; and 0.03 ± 0.03 by Prince et al. (2010) in Avikalin sheep. Maternal additive effect was found unexpectedly high (m² = 0.38) in the best model for ADG3. However, in rest of the models, that do not include the covariance between maternal and additive effects, no evidence of maternal effect was found namely in the most inclusive model 5, estimates of h², m² and c² were 0.31, 0.00 and 0.00, respectively. Generally, for improvement in daily gains direct animal effects are important only up to 6 months and after that environmental effects supervenes the direct effects. But the heritability estimated for ADG3 by the author suggests that direct effects are still dominating over the environmental factors and must be exploited to bring about genetic improvement in this flock of Marwari sheep.

3.4. Correlation estimates

Estimates of genetic, phenotypic and residual correlations for growth traits were calculated by DFREML bivariate analysis under the model 1 and are summarized in Table 3. Genetic and phenotypic correlations between body weight traits were positive and of medium to high magnitude showing no genetic antagonism between them. Estimates of genetic correlations were larger than the majority of corresponding phenotypic and residual correlations. Genetic correlations between body weights at different ages ranged from 0.23 ± 0.110 for BWT–6WT to 0.88 ± 0.079 for 3WT–9WT. For average daily gains, it was observed that genetic correlation between ADG1–ADG2 was positive, but ADG1–ADG3 and ADG2–ADG3 had negative genetic correlations. Negative genetic correlations suggest that these traits tend to compensate for the high or low gain in the corresponding traits. ADG1–ADG3 and ADG2–ADG3 also had negative phenotypic correlations indicating that different factors were responsible for expression of these traits. Negative but non-significant genetic correlations were observed for BWT–ADG2, 3WT–ADG3, 6WT–ADG3, 9WT–ADG1 and 12WT–ADG1. Similarly, negative phenotypic correlations were observed between BWT–ADG2, 3WT–ADG2, BWT–ADG3, 3WT–ADG3 and 6WT–ADG3, which might have resulted due to compensatory growth of 3–12 months of age to that of growth up to weaning. Estimates of residual correlations were almost equal in magnitude with their respective phenotypic correlations.

Table 3. Estimates of genetic (above the diagonal) and phenotypic and residual correlations (below the diagonal with residual correlations in parentheses) for different growth traits in Marwari sheep.

Trait	BWT	3WT	6WT	9WT	12WT	ADG1	ADG2	ADG3
BWT	–	0.48 ± 0.09	0.23 ± 0.11	0.37 ± 0.12	0.44 ± 0.14	0.25 ± 0.11	−0.42 ± 0.15	0.13 ± 0.14
3WT	0.38 ± 0.02 (0.34 ± 0.05)	–	0.83 ± 0.05	0.88 ± 0.08	0.56 ± 0.12	0.97 ± 0.01	0.12 ± 0.18	−0.10 ± 0.16
6WT	0.28 ± 0.03 (0.32 ± 0.05)	0.72 ± 0.02 (0.68 ± 0.02)	–	0.84 ± 0.07	0.39 ± 0.14	0.86 ± 0.05	0.65 ± 0.11	−0.37 ± 0.15
9WT	0.32 ± 0.03 (0.29 ± 0.06)	0.64 ± 0.03 (0.55 ± 0.04)	0.78 ± 0.02 (0.76 ± 0.02)	–	0.76 ± 0.09	−0.13 ± 0.12	0.46 ± 5.44	0.19 ± 0.18
12WT	0.30 ± 0.04 (0.22 ± 0.07)	0.55 ± 0.03 (0.56 ± 0.05)	0.60 ± 0.03 (0.68 ± 0.04)	0.74 ± 0.03 (0.73 ± 0.04)	–	−0.93 ± 0.47	0.05 ± 0.22	0.61 ± 0.15
ADG1	0.22 ± 0.03 (0.20 ± 0.05)	0.98 ± 0.01 (0.99 ± 0.00)	0.71 ± 0.02 (0.65 ± 0.03)	0.42 ± 0.03 (0.99 ± 0.04)	0.50 ± 0.04 (0.66 ± 0.04)	–	0.21 ± 0.19	−0.18 ± 0.17
ADG2	−0.02 ± 0.03 (0.13 ± 0.05)	−0.01 ± 0.03 (−0.04 ± 0.05)	0.60 ± 0.02 (0.60 ± 0.03)	0.46 ± 0.03 (0.53 ± 0.04)	0.34 ± 0.04 (0.42 ± 0.06)	0.01 ± 0.03 (−0.04 ± 0.04)	–	−0.39 ± 0.18
ADG3	−0.032 ± 0.04 (−0.14 ± 0.07)	−0.22 ± 0.04 (−0.27 ± 0.07)	−0.39 ± 0.04 (−0.39 ± 0.06)	0.01 ± 0.04 (−0.07 ± 0.08)	0.37 ± 0.04 (0.27 ± 0.07)	−0.23 ± 0.04 (−0.24 ± 0.06)	−0.35 ± 0.04 (−0.35 ± 0.06)	–

The estimates of genetic correlation for birth weight with other traits was in the range of 23–48%, which gives an evidence for the fact that BWT is not the good criteria of selection of animals for higher gain at adult stage. The genetic correlation estimate of 0.48 for BWT–3WT was in accordance with the estimate of 0.52 by Hanford et al. (2003) in Targhee sheep, 0.45 by and 0.41 by Gowane et al. (2010a, 2010b) in Bharat Merino and Malpura sheep, respectively. The genetic correlation of 3WT with 6WT, 9WT and 12WT were 0.83 ± 0.049, 0.88 ± 0.079 and 0.56 ± 0.124, respectively. Similar results were observed by Swain et al. (2004) in Bharat Merino sheep and Gohil (2010) in Marwari sheep. The genetic correlation of 6WT with 9WT and 12WT were 0.84 ± 0.067 and 0.39 ± 0.143, respectively. The genetic correlation between 9WT–12WT was 0.76 ± 0.090. The estimates of genetic correlation between these body weight traits in current study were in accordance with the findings of Gowane et al. (2010a) in Bharat Merino sheep. For average daily gains, the estimates of genetic correlation between ADG1–ADG2, ADG1–ADG3 and ADG2–ADG3 are 0.21 ± 0.188, –0.18 ± 0.170 and –0.39 ± 0.182, respectively.

High genetic correlations between body weight traits suggest that many of the genetic factors that influence body weight at weaning to adult stage were the same. On the basis of high genetic correlation of 6WT–9WT and moderate 6WT–12WT, it can be said that animals with above average 6WT would tend to be above average in genetic merit for 9WT and 12WT. High genetic correlation between 3WT and post 3WT’s are indicative of similar response to the selection, if selection is carried out at weaning instead of the present practice of selection at 6 months.

4. Conclusions

Additive genetic variability for all the growth traits was moderate to high, suggesting further scope for genetic improvement in the flock. Along with direct effects of the animal, additive maternal effects also need to be considered for genetic evaluation of post-weaning body weight traits and post-weaning average daily gain from 6–12 months of age. Maternal permanent environmental effect was evident only up to weaning for body weight traits and not evident in daily gains. Genetic and phenotypic correlations between body weight traits were moderate to high indicating that there is no genetic antagonism between these traits; however, post-weaning daily gains have negative relationship due to compensatory growth effects. In present study, direct maternal as well as maternal permanent effect was found negligible at WWT which can be explained as in addition to dam’s milk, lambs are also sent for grazing for short duration in a day as separate flock at very early age. Moreover there is high genetic correlation among WWT and 6WT suggesting scope of early selection of animals at weaning instead of present practice of selection at 6 months of age.

Acknowledgements

Authors are thankful to the Director, Central Sheep and Wool Research Institute; Head, Arid Region Campus, Central Sheep and Wool Research Institute; Vice-chancellor, Rajasthan University of Veterinary and Animal Sciences; and Dean, College of Veterinary and Animal Science; for providing the facilities for the execution of work. The technical help rendered by Mr. Vimal Mehrotra T-7-8 at Arid Region Campus, Central Sheep and Wool Research Institute, Bikaner, during data collection is deeply acknowledged.