Genetic parameter estimates for growth traits in Iran-Black sheep

Abstract

The present study was conducted to estimate variance components and genetic parameters for growth traits of Iran-Black sheep, maintained at the Abbasabad sheep breeding station, located in northeast of Mashhad, (Razavi Khorasan province of Iran) over a period of 24 years (1981 through 2004). Records of 4607 lambs descended from 155 rams, and 1227 ewes were used in the study. Traits included for the present study were birth weight (BW), weaning weight (WW), weight at 6 months (W6), weight at 9 months (W9), and yearling weight (YW). Analyses were carried out by restricted maximum likelihood (REML) fitting an animal model and ignoring or including maternal genetic or permanent environmental effects. Six different animal models were fitted for all traits. The most appropriate model was chosen after testing the improvement of the log-likelihood values. Heritability estimates for weight at birth; weaning; and 6, 9, and 12 months of age were 0.04, 0.14, 0.16, 0.19, and 0.18, respectively. Maternal heritability of body weight declined from 0.33 at birth to 0.04 at six months of age. The maternal permanent environmental component accounted for 6% to 15% to the total variance for all traits under study. The direct-maternal genetic correlation (r_am) was positive for all traits and ranged from 0.36±0.27 for BW to 0.99±0.98 for YW, but was never significant. The results showed that modest rates of genetic progress appear possible for all weights. Results also suggest that maternal additive effects were only important in early stages of growth, whereas a permanent environmental maternal effect existed at all ages up to 12 months of age, probably as a carry-over effect of maternal influences present at weaning. Direct genetic correlations (r_a1,a2) between traits were positive and ranged from 0.82 (BW-WW) to 0.99 (W6-YW). The estimates of correlation between permanent environmental maternal effect among traits were close to those of r_a1,a2. Phenotypic and environmental correlations for all traits were generally lower than direct genetic correlations.

Keywords:

• Iran-Black sheep
• body weight
• variance components
• heritability
• genetic correlation

1. Introduction

The efficiency of sheep production enterprises can be improved by enhancing the litter size, lamb weight, milk yield, and wool quantity and quality. In Iran, mutton is the traditional source of protein and the consumption level is high in comparison with beef and chevon. Moreover, lamb and mutton are the most important income source from sheep in Iran. The sale of lamb provides a considerable economic return in most Iranian breeds of sheep and accounts for 30–40% of the agriculture output value. Among 27 recognized sheep breeds in the country, most of the Iranian native sheep are fat-tailed and carpet-type wool-producing breed (Sefidbakht 2011). More than 42% of meat produced in the country was obtained from these native sheep breeds (Sefidbakht 2011). To increase economic returns from these animals, genetic improvement of growth-related traits is required; therefore, the selection objective should concentrate on these traits (Tosh & Kemp 1994). Further, for designing the effective selection programs to increase the efficiency of sheep production, the knowledge of genetic parameters for lamb weights at various ages and the genetic relationships among the traits are of utmost importance. In addition, estimates of genetic parameters can aid in determination of selection criterion, prediction of the response to selection, and construction of selection indexes.

Body weight and growth traits in sheep are known to be influenced by the direct and maternal genetic effects as well as by environmental effects. Early growth is influenced not only by direct genetic effects (i.e. the animal's own genetic potential) and the environment under which it is grown but also by maternal genetic and maternal environmental effects. Maternal effects are especially important in early life and also may have carry-over effects later in life (Mandal et al. 2006). Nasholm and Danell (1994) observed that when maternal genetic effects are important, but not considered in the statistical model, heritability estimates are biased upward and the realized efficiency of selection is reduced. A number of studies have demonstrated that maternal effects are substantial for growth-related traits in sheep and the inclusion of maternal effects in animal models has an important effect on the estimates of direct heritability (Maria et al. 1993; Ozcan et al. 2005; Mandal et al. 2006; Rashidi et al. 2008; Baneh et al. 2010). Genetic and environmental relationships between direct and maternal effects for growth have often varied from moderately positive to highly negative in various sheep breeds (Maria et al. 1993; Tosh & Kemp 1994; Snyman et al. 1995; Nasholm & Danell 1996; Yazdi et al. 1997; Notter 1998). Hence, to achieve optimum progress in a selection program, both direct and maternal components should be taken into account, especially if there is an antagonistic relationship between them.

Hence, there is no published information of genetic structure regarding growth traits in this breed. Therefore, the present study was conducted to estimate (co)variance components associated with direct and maternal genetic effects and variances associated with maternal permanent environmental effects on body weights and to estimate relationships among body weights in Iran-Black sheep.

2. Materials and methods

2.1. Breed and flock management

The Iran-Black is a breed of north-eastern part of Iran and is mainly reared for mutton production. This synthetic breed was developed in 1975 with the aim of increasing mutton production by crossing of Baluchi ewes with Chios rams and vice versa. The animals are well adapted to the dry and hot climate and low-quality pastures found in the north-eastern part of the country. The mating season commences in mid-August and ends in September. Normally one breeding ram is allowed to mate with 10–12 ewes and is kept in the flock until five years of age. The major reasons for culling of animal in the flock are infertility and natural causes (e.g. disease). The lambing season starts in mid-January and ends in February. During the lambing season, ewes were kept indoor and carefully managed. At lambing, the lambs were weighed and ear-tagged shortly after birth. The identities of newborn and their parents, date of birth, sex, type of birth, and birth weight were recorded. Lambs were weaned at approximately 90 days of age. The lambs were weighed at three months intervals from birth to 12 months of age, and the date of each weight was recorded. To protect the animals from the local prevalent diseases, vaccinations were performed twice per year and animals were dewormed with drugs twice per year.

2.2. Data

Data on 4607 records of lambs produced by 1227 ewes and 155 rams were collected from the breeding flock of Abbasabad (33°, 34′N and 58°, 23′E), located in northeast of Mashhad, Iran over a period of 24 years (1981 through 2004). The traits included in these analyses were birth weight (BW), weaning weight (WW), weight at six months (W6), weight at nine months (W9), and yearling weight (YW). A description of data used in the analyses is presented in Table 1.

Table 1. Characteristics of data structure for body weights at different ages in Iran-Black sheep.

Item	BW (kg)	WW (kg)	W6 (kg)	W9 (kg)	YW (kg)
Animal in pedigree	4923	4480	3881	3392	3149
Number of records	4607	4220	3636	3196	2955
Number of sires	135	155	152	133	132
Number of dams	1227	1213	1147	1075	1055
Number of sires with progeny	90	96	93	91	91
Number of dams with progeny	1103	1107	1045	1002	984
Number of sires with own records and progeny	76	81	81	82	82
Number of dams with own records and progeny	970	1026	971	928	909
Average number of records per dam	3.97	3.70	3.37	3.12	2.67
Average number of records per sire	37.76	29.72	26.35	26.86	24.83
Average weight (kg)	3.61	22.13	29.17	33.20	39.39
Standard deviation (kg)	0.83	5.19	5.67	5.71	7.05
CV (%)	22.88	23.45	19.43	17.20	17.89

BW, birth weight; WW, weaning weight; W6, 6-month weight; W9, 9-month weight; YW, yearling weight.

2.3. Statistical analyses

Estimates of variance and covariance components were obtained by restricted maximum likelihood using a derivative-free algorithm fitting an animal model (WOMBAT; Meyer 2007). To identify the fixed effects to be included in the model, the General Linear Model (GLM) procedures of SAS (1996) was performed considering effects of birth year (24 classes), sex of lamb (2 classes), birth status (3 classes: single, twin and triplet) of lamb, and age of dam (6 classes). All these effects were significant (P < 0.05) for all weights and hence were included in the final model. WW and W6 were adjusted for 100 and 180 days of age, respectively. Also, age of weighting were considered as covariate for W9 and YW (P < 0.05). Convergence of REML solutions was assumed when the average difference in likelihood function (2 log L, where L is the likelihood value) in successive iterations was less than 10⁻⁸. Analyses were restarted for additional rounds of iterations using results from the previous round as starting values to ensure that a global maximum was used. When estimates did not change, convergence was confirmed.

The following six single trait animal models incorporating various combinations of maternal genetic and permanent environmental effects were used to estimate genetic parameters for each trait:

(1)

(2)

(3)

(4)

(5)

(6)

where y is a n ×1 vector of observations for each trait; b, a, m, and c are vectors of fixed effects (birth year, sex of lamb, birth status of lamb, and age of dam), direct additive genetic effects, maternal additive genetic effects, and permanent environmental effects due to dam, respectively; X, Z₁, Z₂, Z₃ are the corresponding incidence matrices relating these effects to y; e is the vector of residual effects; A is the numerator relationship matrix; and σ_am is the covariance between additive direct and maternal genetic effects.

The (co)variance structure of the random effects in the analysis can be described as:

where A is the numerator relationship matrix; is the direct additive genetic variance; is the maternal additive genetic variance; σ_αm is the direct-maternal additive genetic covariance; is the maternal permanent environmental variance; is the residual variance; and I_d and I_n are identity matrices of order equal to the number of dams and records, respectively (Ekiz et al. 2004). Total heritability for each model and trait was calculated to predict the expected response to phenotypic selection according to the following equation (Willham 1972):

Log likelihood ratio test was applied to determine the significant random effects and consequently to identify the most appropriate model for each trait (Meyer 1992). An effect was considered to have a significant influence when its inclusion caused a significant increase in log-likelihood compared to a model in which it was ignored. Significance was tested at P < 0.05 by comparing differences in log-likelihoods (−2 log L, χ²: calculated χ²) to values for a chi-square distribution (: χ² of table) with degrees of freedom equal to the difference in the number of (co)variance components fitted for the two models. Where −2 log L values were not significantly different (P < 0.05), the model with the fewest random terms was chosen. Estimates of additive direct (h_a²) and maternal heritability (m²) and the maternal permanent environmental effect (c²) were calculated as ratios of estimates of additive direct (), additive maternal (), and permanent environmental maternal () variances, respectively, to the phenotypic variance (). The genetic correlation between direct and maternal genetic effects (r_am) was estimated as the ratio of the estimates of the σ_am to the product of the square roots of the estimates of and .

Genetic and phenotypic relationships between traits were estimated using multiple-trait analyses. The fixed and random effects included in the model were those that were significant for each trait in the single trait analyses.

3. Results and discussion

Numbers of observations, phenotypic means, standard deviations, and coefficients of variations for body weights of Iran-Black sheep at birth, weaning, and post-weaning at 6, 9, and 12 months of the age are shown in Table 1.

Number of observations decreased with increasing age from birth (n = 4607) to yearling (n = 2955) because of culling or death of animals and sale of some males. Coefficients of variation for body weights ranged from 17.2% to 23.5% and were within the range of reported values for other sheep breeds (Miraei-Ashtiani et al. 2007; Vatankhah & Talebi 2008; Mandal et al. 2008).

3.1. Environmental effects

Least squares means and standard errors for the traits studied are showed in Table 2. All the traits under study were significantly (P < 0.01) affected by the lamb's birth year, sex, birth type, and age of dam. Significant variation in body weights of lambs at all ages were found among different birth years and can be attributed to variation in climatic conditions (weather, temperature, moisture etc.), farmer accessibility to needed feedstuff, and management conditions (Baneh et al. 2010). Male lambs were heavier than their female counterpart by 0.20, 2.10, 2.98, 3.58, and 5.69 kg at birth, 3, 6, 9, and 12 months of age, respectively. Differences in body weights between sexes may be due to differences in the sexual hormones. This result was in agreement with those reported by Eftekhari-Shahroudi et al. (2002) and Rashidi et al. (2008). Single-born lambs were heavier than twin- and triplet-born lambs at all ages. Lambs born to ewes in their fifth and sixth parities were significantly heavier than lambs born to younger or older ewes. Significant variation in body weights of lambs due to dam age and birth status might be partially explained by differences in uterine capacity, milk production, and mothering ability of ewes at different ages. In addition, effects of litter size are probably explained by the competition for uterine space and capacity during pregnancy and for milk before weaning among multiple-born lambs (Rashidi et al. 2008; Baneh et al. 2010). Significant effect of various environmental factors on body weight have been reported in several breeds of sheep (Eftekhari-Shahroudi et al. 2002; Ozcan et al. 2005; Rashidi et al. 2008; Baneh et al. 2010).

Table 2. Least-squares means and standard errors of body weights at different ages in Iran-Black sheep.

	Traits
Fixed effects	BW (kg)	WW (kg)	W6 (kg)	W9 (kg)	YW (kg)
Birth year	**	**	**	**	**
Sex of lamb	**	**	**	**	**
Male	3.58±0.06^a	23.07±0.29^a	31.36±0.31^a	33.87±0.62^a	42.16±0.39^a
Female	3.38±0.06^b	20.97±0.28^b	28.38±0.30^b	30.29±0.62^b	36.47±0.38^b
Birth type	**	**	**	**	**
Single	4.16±0.06^a	24.93±0.29^a	32.52±0.30^a	34.30±0.62^a	41.58±0.38^a
Twin	3.44±0.06^b	21.19±0.28^b	29.13±0.30^b	31.52±0.62^b	38.79±0.38^b
Triplet and more	2.83±0.07^c	19.94±0.34^c	27.96±0.37^c	30.42±0.66^c	37.56±0.46^c
Dam's age (year)	**	**	**	**	**
2	3.13±0.06^c	21.08±0.30^b	28.99±0.32^b	31.38±0.63^b	38.58±0.41^b
3	3.46±0.06^b	22.32±0.30^a	30.42±0.32^a	32.48±0.63^a	39.93±0.40^a
4	3.52±0.07^b	22.41±0.29^a	30.03±0.31^a	32.34±0.62^a	39.79±0.39^a
5	3.60±0.07^a	22.49±0.33^a	30.29±0.36^a	32.37±0.65^a	39.73±0.45^a
6	3.62±0.07^a	22.36±0.37^a	29.93±0.42^a	32.52±0.69^a	40.02±0.52^a
7 or more	3.54±0.08^ab	21.44±0.44^b	29.57±0.49^ab	31.39±0.74^b	37.83±0.60^b

Note: Means with similar superscript in each sub-class did not differ significantly (P < 0.05); ** Significant effect at P<0.01.

BW, birth weight; WW, weaning weight; W6, 6-month weight; W9, 9-month weight; YW, yearling weight.

3.2. Genetic effects

Estimates of (co)variance components and genetic parameters for investigated traits including birth weight; weaning weight; weights at 6, 9, and 12 month of age; and likelihood values for each analysis under the six different models are summarized in Table 3.

Table 3. Estimates of (co)variance components (kg²) and genetic parameters for different body weights of Iran-Black sheep.

Trait	Model				σam			h^2	c^2	m^2	ram		log L	χ^2
BW	1	0.396	–	–	–	0.358	0.753	0.53±0.03		–	–	0.53±0.03	−233.53	467.07
	2	0.133	0.215	–	–	0.347	0.696	0.19±0.04	0.31±0.02	–	–	0.19±0.04	−40.04	80.09
	3	0.028	–	0.368	–	0.398	0.794	0.04±0.02	–	0.46±0.02	–	0.27±0.02	−5.97	11.94
	4	0.021	–	0.345	0.030	0.402	0.798	0.03±0.02	–	0.43±0.03	0.36±0.27	0.30±0.03	−5.09	10.19
	5	0.030	0.067	0.247	–	0.394	0.737	0.04±0.02	0.09±0.03	0.33±0.04	–	0.21±0.03	−1.24	2.49
	6	0.019	0.068	0.219	0.033	0.400	0.739	0.03±0.02	0.09±0.03	0.30±0.05	0.51±0.31	0.24±0.03	0	0
WW	1	10.601	–	–	–	15.918	26.519	0.40±0.04	–	–	–	0.40±0.04	−67.27	134.538
	2	4.251	4.323	–	–	16.083	24.657	0.17±0.04	0.17±0.02	–	–	0.17±0.04	−4.94	9.878
	3	2.311	–	6.416	–	17.416	26.143	0.09±0.04	–	0.25±0.03	–	0.21±0.03	−16.87	33.738
	4	1.871	–	4.930	2.403	17.615	26.820	0.07±0.03	–	0.18±0.03	0.79±0.19	0.30±0.04	−11.35	22.71
	5	3.344	3.639	1.097	–	16.512	24.592	0.14±0.04	0.15±0.03	0.05±0.03	–	0.16±0.04	−1.17	2.354
	6	2.332	3.135	1.149	1.362	16.996	24.975	0.09±0.03	0.13±0.03	0.05±0.02	0.83±0.29	0.20±0.04	0	0
W6	1	10.626	–	–	–	19.808	30.434	0.35±0.04	–	–	–	0.35±0.04	−28.01	56.01
	2	5.532	3.287	–	–	20.010	28.828	0.19±0.04	0.11±0.02	–	–	0.19±0.04	−3.73	7.46
	3	3.737	–	4.438	–	21.292	29.467	0.13±0.04	–	0.15±0.03	–	0.20±0.04	−6.52	13.04
	4	3.207	–	3.358	1.933	21.504	30.002	0.11±0.03	–	0.11±0.02	0.59±0.23	0.26±0.04	−3.60	7.18
	5	4.507	2.508	1.196	–	20.510	28.721	0.16±0.04	0.09±0.02	0.04±0.03	–	0.18±0.04	−1.75	3.50
	6	3.583	2.088	1.206	1.242	20.942	29.061	0.12±0.04	0.07±0.02	0.04±0.02	0.59±0.32	0.21±0.04	0	0.00
W9	1	9.144	–	–	–	19.497	28.641	0.32±0.04	–	–	–	0.32±0.04	−19.99	39.97
	2	5.243	2.903	–	–	19.298	27.443	0.19±0.05	0.11±0.02	–	–	0.19±0.05	−1.29	2.57
	3	4.913	–	2.978	–	20.223	28.114	0.18±0.05	–	0.11±0.03	–	0.23±0.04	−11.48	22.97
	4	3.077	–	2.162	2.359	20.974	28.571	0.11±0.03	–	0.08±0.02	0.92±0.22	0.27±0.04	−6.44	12.88
	5	5.243	2.903	00.00	–	19.298	27.443	0.19±0.05	0.11±0.02	0.00±0.00	–	0.19±0.05	−1.29	2.57
	6	3.776	2.446	1.017	0.274	19.999	27.512	0.14±0.05	0.09±0.02	0.01±0.01	0.99±0.98	0.17±0.04	0	0.00
YW	1	10.930	–	–	–	29.599	40.529	0.27±0.05	–	–	–	0.27±0.05	−6.12	12.23
	2	7.112	2.202	–	–	29.966	39.280	0.18±0.05	0.06±0.02	–	–	0.18±0.05	−1.43	2.85
	3	9.839	–	0.617	–	29.839	40.294	0.24±0.05	–	0.02±0.02	–	0.25±0.05	−5.85	11.69
	4	6.058	–	0.985	2.442	30.948	40.433	0.15±0.05	–	0.02±0.02	0.99±0.44	0.25±0.04	−1.20	2.40
	5	7.112	2.202	0.00002	–	29.966	39.280	0.18±0.05	0.06±0.02	0.00±0.00	–	0.18±0.05	−1.43	2.85
	6	5.736	1.443	0.381	1.479	30.601	39.641	0.14±0.05	0.04±0.02	0.01±0.02	0.99 (*)	0.21±0.05	0	0.00

Note: ²_a is the direct additive genetic variance; ²_m is the maternal additive genetic variance; _am is the additive direct-maternal genetic covariance; ²_c is the maternal permanent environmental variance; ²_e is the environmental variance; ²_p is the phenotypic variance; h² is the heritability; m² is the maternal heritability; r_am is the additive direct-maternal genetic correlation; c²=²_c/²_p; h²_T is the total heritability; and log L is the log likelihood expressed as a deviation from the model with highest likelihood.

The model in bold represents the most appropriate model and * indicates that the approximation failed.

χ²: −2 * (Log Likelihood_Reducedmodel – Log Likelihood_Fullmodel).

BW, birth weight; WW, weaning weight; W6, 6-month weight; W9, 9-month weight; YW, yearling weight.

3.2.1. Birth weight

Estimates of the direct heritability of birth weight (Table 3) depended on the model used, ranging from 0.03 to 0.53. For this trait, ignoring maternal effects (Model 1) yielded substantially higher estimates of ²_a and h² than other models. Fitting a permanent environmental maternal effect (Model 2) increased the log likelihood markedly over that for model 1 (Table 3) and showed a significant maternal effect contributing 31% of the total variation in this trait while correspondingly reducing estimates of ²_a and ²_e. Fitting a maternal genetic (Model 3) rather than permanent environmental effect also resulted in an increase in log L over Model 1 and 2. With an estimate of the maternal heritability of 46%, the estimate of the direct heritability was reduced to 4%. In model 4, the estimate of direct-maternal genetic covariance (_am) was positive (0.03) and the direct maternal genetic correlation (r_am) was 0.43, with corresponding small differences in likelihoods between models 3 and 4. Based on the logarithm of the likelihood function, fitting both genetic and environmental components of the dam (Model 5) resulted in a significantly better fit as compared to other models. The inclusion of both genetic and environmental components due to dam effect (m²+c²) reduced the estimate of ²_c to 9%. After adding σ_am in model 6, the estimate of _am was 0.03 with a corresponding estimate of r_am of 0.51. However, the likelihood value did not change significantly compared to a model ignoring _am (Model 5). The most appropriate model for birth weight included a maternal genetic as well as permanent environmental effect (Model 5).

The direct heritability estimate (0.04) for BW in the present study was in agreement with the finding of Rashidi et al. (2008) for Kermani sheep (0.04) and Mandal et al. (2006) for Muzaffarnagari sheep (0.08). However, higher estimates were reported by Vatankhah and Talebi (2008) for Lori-Bakhtiari sheep (0.31), Gizaw et al. (2007) for Menz sheep (0.46), Lobo et al. (2009) for a Brazilian multi-breed meat sheep population (0.35), and Shokrollahi and Baneh (2012) for Arabi sheep (0.42).The low heritability estimates for birth weight in the present study can be explained by the poor nutritional level of ewes at the sheep-breeding station creating large environmental variation. In addition, high contribution of maternal effects in this trait may be another reason of this situation.

The maternal heritability estimate for birth weight (0.33) obtained in this study was in accordance with the findings of Eftekhari-Shahroudi et al. (2002) in Kermani sheep (0.33) and Larsgard and Olesen (1998) in Norwegian sheep (0.42). However, a very high estimate for this trait was reported by Miraei-Ashtiani et al. (2007) in Sangsari sheep (0.65). The high maternal effect on birth weight indicates that the prenatal effect was important for this trait. The estimate of permanent environmental maternal effect (c²) for birth weight (0.09) in our study was in agreement with the findings of Maria et al. (1993) and Mandal et al. (2006) in other sheep breeds. However, the estimates reported by Tosh and Kemp (1994) in Hampshire, Polled Dorset, and Romanov sheep; Snyman et al. (1995) in Afrino sheep; Neser et al. (2001) in Dorper sheep; and Ekiz et al. (2004) in Turkish Merino lambs were higher as compared to the present findings. The permanent environmental effect ( c²) due to the dam can be ascribed to uterine environmental effects and the feeding level in late gestation of the ewe (Maria et al. 1993; Snyman et al. 1995). The high maternal effect at birth indicates that the maternal effect would have a considerable effect on selection response for this trait.

Comparison of Models 2, 3, and 5 in the present study showed that the estimates of m² and c² are biased upwards if both are important but only one is included in the analytical model. The estimate of h² from Model 1 was likewise biased upward by failure to include the significant maternal effects. Meyer (1992) also indicated that the relative values of m² and h² are influenced by the specific model. Estimates of m² could be biased upwards if a maternal permanent environmental effect exists but is not included in the model.

The total heritability, defined as the value used to calculate the expected response to phenotypic selection, (Table 3) was moderate in magnitude for birth weight (0.21). This result indicates that slow genetic progress appears possible for this trait under the prevalent management conditions. The total heritability for birth weight observed in this study was comparable to the findings of Ekiz et al. (2004) (0.14), Nasholm and Danell (1996) (0.24), and Neser et al. (2001) (0.21). Higher estimates of total heritability in comparison to this study were obtained by Assan et al. (2002) in Sabi sheep (0.77). The estimate reported by Maria et al. (1993) in Romanov sheep (0.02) was lower than the present value.

3.2.2. Weaning weight

Depending on the model used, estimates of direct heritability ranged from 0.07 to 0.40. Addition of a permanent environmental maternal effect (model 2) led to a reduction in additive direct heritability of 58% compared to model 1, and this effect accounted for 17% of phenotypic variance. Model 3, which included only direct and maternal additive effects, yielded an estimate of m² that explained only 25% of phenotypic variance with the reduction of direct heritability to 9%. Fitting a non-zero covariance (_am) along with a maternal genetic effect (Model 4) resulted with a large positive direct maternal covariance (2.40) along with large direct maternal genetic correlation (r_am) of 0.79. Model 5 attempted independent estimation of m² and c², but the estimate of m² was reduced to 5%, indicating low additive maternal variance for weaning weights in these data. Adding σ_am in model 6 led to an estimate of _am of 1.36 with a corresponding estimate of r_am of 0.83, but inclusion of the covariance component did not improve goodness of fit when compared to model 5. Model 5 was thus the preferred model for description of weaning weight: additive direct, additive maternal, and maternal permanent environmental components accounted for 14%, 5%, and 15% of phenotypic variance, respectively.

The estimate of the direct heritability of weaning weight in the present study (0.14, model 5) was similar to the findings of Snyman et al. (1995), Abegaz et al. (2002), Matika et al. (2003), and Ozcan et al. (2005) in different breeds of sheep. However, higher heritability estimates for weaning weight as compared to those from the present study were reported by other workers in various sheep breeds (Snyman et al. 1995; Notter 1998; El Fadili et al. 2000; Assan et al. 2002;Gizaw et al. 2007), and lower heritabilities for this trait were reported by Notter (1998) in Polypay sheep (0.07) and Ekiz et al. (2004) in Turkish Merino sheep (0.06).

The estimate of maternal heritability for weaning weight from our data (m²=0.05) was within the range of reported estimates for other sheep breeds (Yazdi et al. 1997; Notter 1998; Ozcan et al. 2005; Mandal et al. 2008; Miraei-Ashtiani et al. 2007). However, El Fadili et al. (2000), Abegaz et al. (2002), Safari et al. (2005), and Savar-Sofla et al. (2011) obtained higher estimates (0.10–0.24) than the present study. Further, our estimate of the proportion of variance associated with permanent environmental maternal effects for weaning weight (c²=0.15) was similar to the reported estimates of Rashidi et al. (2008) in Kermani sheep (0.13), Tosh and Kemp (1994) in Romanov sheep (0.12), and Mandal et al. (2008) in Muzaffarnagari sheep (0.10). Lower estimates were reported by Abegaz et al. (2005) in Horro sheep (0.06), Ozcan et al. (2005) in Merino sheep (0.08), and Matika et al. (2003) in Sabi sheep (0.07) as compared to the present findings. However, the estimate of 0.23 in Poly pay (Notter 1998) was higher than our estimate. The low productivity and the poor environment could partially explain low maternal effects at weaning for this breed in this study. These results also suggest that the importance of maternal effects, and particularly additive maternal effects, declined from birth to weaning, which agrees with results of Tosh and Kemp (1994), Snyman et al. (1995), Nasholm and Danell (1996), Yazdi et al. (1997), El Fadili et al. (2000), and Mandal et al. (2008).

The estimate of total heritability () for weaning weight was moderate in magnitude (0.16), indicating the phenotypic response to selection for this trait. Estimates of reported by Notter (1998) in Suffolk sheep and Yazdi et al. (1997) in Baluchi sheep were in agreement with those from this study. However, both lower (El Fadili et al. 2000; Ekiz et al. 2004; Ozcan et al. 2005) and higher (Snyman et al. 1995; Assan et al. 2002) estimates for for this trait have been reported in other studies involving different breeds of sheep.

3.2.3. Post-weaning weights

In model 1, where the maternal effect was ignored, heritability was biased upward for all post-weaning weights. Introducing apermanent environmental effects due to the dam (Model 2) explained 11%, 11%, and 6% of the total phenotypic variance for weights at 6, 9, and 12 months of age, respectively, and the corresponding reductions in the direct heritability was 46%, 41%, and 33% in comparison with model 1. Fitting the c² effect in the model also increased the log L value significantly over that for a simple animal model. Model 3, which includes maternal genetic effects in place of permanent environmental maternal effects, also identified a maternal effect contributing 15%, 11%, and 2% of total variation for this trait. Fitting a non-zero covariance (_am) along with a maternal genetic effect (Model 4) provided a large positive direct maternal covariance for all traits. In model 5, the genetic and environmental components of the effect of dam (m²+c²) are pulled apart and resulted the substantial reduction in the estimate of the maternal genetic effect for post-weaning weights. The maternal genetic effect was reduced drastically at six months of age and thereafter no evidence for an additive maternal effect on post-weaning weight was observed in these data. Allowing for a direct-maternal covariance (_am) yielded a positive direct maternal covariance (Model 6), ranging from 0.27 to 1.48 with a high estimate of r_am, ranging from 0.59 to −0.99 for post-weaning weights. The most appropriate model for weight at six months included a maternal genetic as well as permanent environmental effect (Model 5). The model with the permanent environmental effect due to the dam (Model 2) was the most suitable model for weights at 9 and 12 months of age.

The moderate estimates of direct heritability (0.16–0.18) observed for post-weaning weights in the present study was well within the range of results of other researchers (Abegaz et al. 2002; Mandal et al. 2008; Vatankhah & Talebi 2008) but lower than those reported by Snyman et al. (1995) in Afrino sheep(0.59), Yazdi et al. (1997) in Baluchi sheep (0.29), Gizaw et al. (2007) in Menz sheep (0.51), and Miraei-Ashtiani et al. (2007) in Sangsari sheep (0.49). Comparison of current results for maternal effects with those of other studies is difficult because of differences in the models fitted. However, the maternal heritability (0.04) for lamb with 6-month weight obtained in this study was similar to those reported by Nasholm and Danell (1996), Yazdi et al. (1997), and Safari et al. (2005) in different breeds of sheep.

Maternal heritability of different growth traits decreased with age, which confirms the findings of Tosh and Kemp (1994), Snyman et al. (1995), Nasholm and Danell (1996), Yazdi et al. (1997), and El Fadili et al. (2000) who observed that maternal effects are substantial in young animals but diminish with age. The moderate direct additive effects for post-weaning weights indicate that they represent a considerable proportion of genetic variation in Iran-Black lamb and suggest that moderate genetic progress may be obtained from selection under the prevalent management system. The low maternal effect on 6-month weight indicates that the maternal effect had less effect on selection response for this trait.

The c² effect for post-weaning weights of Iran-Black lambs contributed 6–11% of the total phenotypic variance. These results were also in accordance with those published in literature by several authors (Matika et al. 2003; Safari et al. 2005; Mokhtari et al. 2008). The c² effect increased from birth to weaning weight and thereafter declined. However, Tosh and Kemp (1994) observed that the permanent environmental effect decreased in importance as lambs became increasingly independent of the ewe. These analyses suggest that after weaning, maternal permanent environmental effects were still a source of variation up to yearling age. Similar trends were reported by Maria et al. (1993), Tosh and Kemp (1994), and Miraei-Ashtiani et al. (2007). This decrease in maternal permanent environmental effects at later ages presumably reflects an increasing impact on body weight of the animal's own genotype at more advanced ages.

Total heritability estimates for post-weaning weights in this breed were moderate in magnitude, ranging from 0.18 to 0.20, and were similar to direct heritability estimates. The moderate estimates of total heritability indicate the scope for some selection progress for these traits. These estimates of for post-weaning weights were comparable with the findings of other researchers (Abegaz et al. 2002; Ozcan et al. 2005; Safari et al. 2005) but lower than the estimates of Snyman et al. (1995) and Yazdi et al. (1997) in other sheep breeds.

3.2.4. Correlations estimates

Multivariate estimates of direct additive genetic correlations, maternal additive genetic correlations, maternal permanent environmental correlations, phenotypic correlations, and environmental correlations between body weights at different ages are presented in Table 4. The direct additive genetic correlations between body weights at different ages were high and positive, ranging from 0.82 (BW-WW) to 0.99 (W6-YW). High direct additive genetic correlations between body weights were also reported by Yazdi et al. (1997), Ozcan et al. (2005), and Bahreini-Behzadi et al. (2007) in different breeds of sheep. The high additive genetic correlations between body weights of lambs in this study indicated that selection based on any of these traits could lead to considerable genetically improvement of the other correlated traits because similar sets of genes appear to be responsible for body weights at various ages in this breed. The large direct additive genetic correlation (0.99) between W6 and YW of lambs in the present study confirms that selection to increase 6-month body weight would result in a substantial correlated genetic response in yearling weight.

Table 4. Estimates of correlations between various weightsb from multivariate analyses.

Trait 1	Trait 2	Number. of observations	ra1a2	rm1m2	rc1c2	re1e2	rp1p2
BW	WW	3872	0.82±0.09	0.25	0.88±0.07	0.31±0.02	0.43±0.02
BW	W6	3316	0.87±0.07	0.42	0.87±0.08	0.26±0.03	0.40±0.02
BW	W9	2898	0.91±0.06	–	0.85±0.08	0.22±0.03	0.38±0.02
BW	YW	2674	0.85±0.08	–	0.91±0.11	0.21±0.03	0.35±0.02
WW	W6	3591	0.92±0.04	0.98	0.95±0.03	0.68±0.02	0.76±0.01
WW	W9	3147	0.85±0.06	–	0.88±0.05	0.59±0.02	0.67±0.01
WW	YW	2917	0.89±0.05	–	0.91±0.06	0.52±0.02	0.63±0.01
W6	W9	3179	0.98±0.01	–	0.97±0.03	0.71±0.02	0.80±0.01
W6	YW	2944	0.99±0.02	–	0.95±0.05	0.64±0.02	0.75±0.01
W9	YW	2932	0.98±0.01	–	0.98±0.04	0.74±0.01	0.82±0.01

Note: r_a1a2 is the direct genetic correlation between traits 1 and 2; r_m1m2 is the maternal additive genetic correlation between traits 1 and 2; r_c1c2 is the maternal permanent environmental correlation between traits 1 and 2; r_e1e2 is the residual correlations between traits 1 and 2; r_p1p2 is the phenotypic correlations between traits 1 and 2.

BW, birth weight; WW, weaning weight; W6, 6-month weight; W9, 9-month weight; YW, yearling weight.

Estimates of maternal additive genetic correlations of birth weight with WW (0.25) and W6 (0.42) were positive and moderate in magnitude, but a high (0.98) maternal additive genetic correlation existed between WW and W6 of lambs. The maternal genetic correlation estimate between BW and WW in this study (0.25) was lower than the estimate of Abegaz et al. (2005) in Horro sheep (0.77) but was close to those of reported by Miraei-Ashtiani et al. (2007) in Sangsari sheep (0.33). VaezTorshizi et al. (1996) reported maternal additive genetic correlations between weaning and subsequent weights in Merino sheep that ranged from 0.61 to 0.91, which was in agreement with the present findings. Yazdi et al. (1997) reported correlations among weights at different ages in Baluchi sheep that varied from 0.53 to 0.78. The positive maternal genetic correlations between birth weight and body weights measured later in life indicated that maternal influences partly originate during the prenatal period. This result indicates that maternal additive genetic effects, which influence the growth of the fetus in the prenatal period could also have some favorable effects on postnatal growth. VaezTorshizi et al. (1996) concluded that the positive estimates of maternal additive genetic correlations among weights suggest that maternal effect at different ages of offspring is largely under the influence of similar genes of the dam.

In the current study, the estimates of maternal permanent environmental correlation (r_c) between the body weights at various ages were high and positive, ranging from 0.85 to 0.98. However, lower estimates of r_c between different body weights were reported by other workers (Miraei-Ashtiani et al. 2007; Shokrollahi & Zandieh 2012) in other sheep breeds.

Residual correlations between all body weights were positive and low to medium in magnitude, ranging from 0.21 between BW and YW to 0.74 between W9 and YW in our study (Table 4). Similarly, positive and small to moderate (ranging from 0.35 to 0.82) phenotypic correlations were observed among all body weights in the present study. The estimates of phenotypic and residual correlations among investigated traits were generally lower than the additive genetic correlations (Table 4). Birth weight had the lowest phenotypic correlation with the other traits, ranging from 0.35 to 0.43, whereas the remaining weights had moderate correlations, ranging from 0.63 to 0.82. In general, the phenotypic correlations among all traits at different ages decreased as the time between measurements increased. Our estimates for phenotypic correlations were comparable with those reported in the literature (Bahreini-Behzadi et al. 2007; Miraei-Ashtiani et al. 2007; Rashidi et al. 2008; Mokhtari et al. 2008).

4. Conclusion

The findings of the present study confirmed the importance of implementing the correct model of analysis for the estimation of (co) variance components and genetic parameters forgrowth traits of Iran-Black sheep. For example, ignoring the maternal effects in the model leads to overestimation of the direct and total heritability. Furthermore, the exclusion of a permanent environmental maternal effect results in overestimation of the maternal heritability for birth weight. The maternal influence diminished as age increased. The low to moderate estimates of heritability for growth traits in this study indicate that genetic improvement of growth traits is possible by selection. Results also suggest that both direct genetic and maternal effects were important for growth traits and hence both direct and maternal effects need to be considered in genetic evaluation of growth traits in this breed. The high positive genetic correlations between body weights of lambs suggest that selection to improve body weight at six months of age will result in genetic improvement in yearling weights of lambs.