Estimates of Maternal Effect and (co)Variance Components for BodyWeight at Different Ages by Animal Model in Chokla Sheep

Small ruminants serve the mankind in multiple ways of providing protein rich food, supplementing farmers’ income, facilitating rural employment and improving soil fertility. So these animals play an important role for the socio-economic upliftment of small, marginal farmers and landless labourers in our country. Growth is a merit of interest in livestock animals. Information about growth model parameters is very serviceable for selection polices in Madras Red sheep (Ganesan et al., 2015). A number of non-genetic factors affect these growth traits and directly obscure recognition of the genetic potential. Improvement in production, without affecting adaptability can be brought about only by genetic improvement through selection and breeding. Formulation of breeding programmes require accurate values of genetic parameters, for which precise estimates of (co)variance components, obtained after adjustment for various non-genetic factors are a pre-requisite.
       
An animal model like DFREML takes into accounts all relationship in the pedigree and is therefore expected to provide estimates of genetic parameters with higher precision. DFREML estimates of covariance components through a derivate free methods while, the AI algorithm (AIREML) is an iterative method which needs initial values of variance components. In mammals, including most livestock species, because there are long periods of maternal dependence, the early growth traits are not controlled only by direct additive genetic effects but also by maternal effects (Gowane et al., 2015 and Aguirre et al., 2016). Maternal effects have been defined as any influence from a dam on its offspring, excluding the effects of directly transmitted genes that affect performance of the offspring. Maternal environmental effect can be partitioned in to permanent and common sectors. However, the later has been ignored in most genetic studies on growth traits. It was observed by various authors that when maternal genetic effects are important and not considered in the statistical model, heritability estimates are biased upwards and the realised 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. Recently many studies have attributed most of the variation in lamb weights to maternal effects (Prince et al., 2010; Abbasi et al., 2012; Gowane et al., 2015; Aguirre et al., 2016; Radwan et al., 2018; Latifi and Mohammadi, 2018 and Mahala et al., 2020).
       
Hence, present study was undertaken to estimate various (co)variance components and genetic parameters for body weight at different ages.

Data and management at research station
 
Data and pedigree information on 6785 Chokla sheep belonging 459 sires and 2102 dams maintained at the Central Sheep and wool Research institute, Arid Region Campus Beechwal, Bikaner were collected over a period of 47 years (1974 to 2020). This institute is geographically located at an altitude of 234.84 meters above mean sea level on 28°3'N Latitude and 37°5'E Longitude.Chokla sheep were reared under semi intensive system of management and all animals grazed during the day (7 to 8 h) on natural pasture with supplementation depending upon the status and age category of the animals and were penned at night. At birth each lamb was identified and date of birth, sex, type of birth and weight were recorded. Lambs were normally weaned at three months of age. Dry fodder supplementation, 300 g of concentrate mixture was also provided during the post-weaning period. The main breeding season generally commenced towards the mid of August and continued for 2-3 oestrus cycles (up to beginning of November). However, a minor season of mating was also executed in the month of March-April to augment the more lambing per year. The prophylactic measures such as vaccination, deworming, dipping and hygienic measures like dusting, spraying, disinfection of sheds, watering channels, feeding troughs and protection of lambs against inclement weather conditions and prophylactic antibiotic treatment of lambs were implemented.
 
Classifications of data
 
The data were classified according to period, season and sex of lamb. These data were classified into eleven different periods of 4 years interval each except period P1, P2 and P11to provide unbiased allocation of observations in each period or to avoid the unequal distribution in each period.These periods were P1 (1974-1978), P2 (1979-1983), P3 (1984-1987), P4 (1988-1991), P5 (1992-1995), P6 (1996-1999), P7(2000-2003), P8(2004-2007), P9(2008-2011), P10(2012-2015) and P11 (2016-2020). According to season of lambing data were classified into two season viz. spring (January to June) and autumn (July to December). Data were classified according to sex into male and female group.
 
Statistical analyses of data
 
The data were analysed to examine the effects of period, season, sex and ewe weight at lambing using least-squares analysis of variance with software SPSS VERSION 26.0 (2005). The model was as follows:
   
Where,
Y_ijklm = Growth performance record of the m^th progeny of i^th sire born in j^th period, k^th season belonging to l^th sex.
ì = Overall mean.
S_i = Random effect of ith sire.
A_j = Fixed effect of jth period of birth (j = 1, 2, 3 ...11).
B_k = fixed effect of kth season of birth (k = 1, 2).
C_l = Fixed effect of lth sex of lamb (l = 1, 2).
DW_ijkl = Dam’s weight at lambing.
DW = Mean dam’s weight at lambing.
b (DW_ijkl - DW) = The regression of the corresponding trait on dam’s weight at lambing.
e_ijklm = Residual random error under standard assumption which make the analysis valid, i.e. NID (0,𝛔²).
       
The differences between the least-squares means for subclass under a particular effect were tested by Duncan’s multiple range test (Kramer, 1957).
       
(Co)Variance components and corresponding genetic parameters for the studied traits were estimated by average information Restricted Maximum Likelihood (AIREML)using the WOMBAT programme (Meyer, 2007) by fitting an animal model throughout.
       
Only significant effects (P<0.05) were included in the models which were subsequently used for the estimation of genetic parameters.
       
The following animal models by ignoring or including various combinations of maternal genetic and permanent environmental effects were fitted to estimate genetic parameters for each trait:
   
Where,
 
Y = N×1 vector of record
 
b = Fixed effects in the model with association matrix X.
a = Vector of direct genetic effect with the association matrix Z₁.
c = Vector of permanent maternal environmental effect with the association matrix W.
m = Vector of maternal genetic effects with the association matrix Z₂.
ε = Vector of residual (temporary environmental) effect.
X, Z₁, Z₂, and W = Incidence matrices that relate these effects = to the records such as for b, a, m and c, respectively.
       
Cov (a,m) indicates  covariance between direct and maternal additive genetic effects.
       
Generally, the (co)variance structure for studied traits was as follows:
 
Additive direct and maternal genetic effects were assumed to be normally distributed with mean 0 and variance A𝛔_a²and A𝛔_m², respectively, where A is the additive numerator relationship matrix and 𝛔_a² and 𝛔_m² are direct additive genetic and maternal additive genetic variances, respectively. 𝛔_am is the covariance between additive direct and maternal genetic effect. Permanent environmental effects of the dam and residual effects were assumed to be normally distributed with mean 0 and variances I_d𝛔_c² and I_n𝛔_e², respectively, where Id and In are identity matrices with orders equal to the number of dams and individual records, respectively and 𝛔_c² and  𝛔_e²are maternal permanent environment and residual variances, respectively.
       
Assumptions for variance (V) and covariance (Cov) matrices involving random effects were:  
The total heritability (h²_t), was calculated using the following formula:  
       
Heritability estimates of additive direct (h²), additive maternal (m²) and permanent environmental effects (c²) were calculated as ratios of estimates of additive direct (𝛔²a), additive maternal (𝛔²m) and permanent environment maternal (𝛔²c) variance to total phenotypic variance (𝛔²p), respectively.
         
The direct-maternal correlation (ram) was calculated in the following manner:        
Maternal across year repeatability for ewe performance was calculated for all the traits as follows:
   
Goodness of fit for the models was examined using likelihood based criteria as:
   
Where,
log L_i = Maximised log likelihood of model i at convergence. p_i = Number of parameters obtained from each model; the model with the lowest AIC was chosen as the best approximating model.
       
Bivariate animal model analysis was carried out in order to estimate genetic and phenotypic correlations between the traits based on the most appropriate single-animal models.

Genetic parameters are important because of the significant information available from ewes and their progeny, allowing for the proper partitioning of genetic variance. Descriptive statistics as estimated by the animal model was summarized for body weights at different ages in Table 1. In contrast to the current findings, Dangi and Poonia (2006) calculated means of WT3 and WT6 being 10.36±0.21 and 13.41±0.27 kg, respectively in crossbred sheep to be lower than those obtained in this paper. Mallick et al., (2017) calculated the overall least squares means for weights to be 3.28±0.02, 19.08±0.23 and 25.00±0.35 kg for BW, WT3 and WT6, respectively which higher to current means. They also concluded that genetic parameters estimated of WT6 indicated the possibility for using this trait as a selection criterion to improve body weight in Bharat Merino lambs.
       
The effect of period of lambing and sex of lamb was found highly significant (P<0.01) on all the studied traits. The effect of season of lambing was reported highly significant (P≤0.01) on all body weights except nine-month body weight. The regression of these traits on weight of ewe at lambing was significant.
 

 
(Co) variance components and genetic parameter estimates
 
One of the fundamental objectives of genetic evaluation exercises is to partition the genetic variance in direct and maternal effects, where applicable. The findings of the present study confirmed the importance of implementing the correct model for estimation of (co)variance components and genetic parameters for growth traits of Chokla sheep. (Co)variance components and genetic parameters estimated by most appropriate model in univariate analysis by WOMBAT for various growth traits of Chokla sheep are summarized in Table 2.
 

       
The results presented (Table 2) shows an incremental increase in (co)variance component and heritability values for the body weight traits according to age of the animal. This trend was similar, but not of the same magnitude, as that reported by Mohammadi et al., (2015), Gowane et al., (2015). Gowane et al., (2015) found that in Malpura sheep the h²_a for weight at 90, 180, and 270 days was 0.40, 0.50, and 0.37, respectively and studies reported a negative direct-maternal correlation.
       
In most studies on growth traits, it has been frequently reported that direct heritability for body weights have a tendency to increase with age (Eskandarinasab et al., 2010). The h² values for all the body weight traits except BW were moderate (0.3-0.5). The moderate heritability estimates for growth traits in this study indicates that modest rates of genetic progress may be possible for these traits from selection under the prevailing management system. The estimates for BW were low (0.17). The maximum h2 estimates were obtained for 9W and YW, with values of 0.510 and 0.515, respectively. The heritability of birth weight (0.173) was in accordance with findings of Gowane et al., (2010) as 0.19± 0.04 in Malpura sheep. The direct additive heritability estimates for weaning weight (0.392) and for 6W (0.471) were in close agreement with estimate obtained by Gowane et al., (2015) as 0.40±0.06 and 0.50±0.05, for WW and 6W, respectively in Malpura sheep. The value of 9W was found in close agreement with the findings of Aguirre et al., (2016) as 0.49 ± 0.06 in Santa Ines and Mahala et al., (2020) as 0.50±0.05 in Aviklain sheep. Similarly, Manoj et al., (2014) estimated heritability coefficients and their standard errors at different ages of Sahiwal heifers to be 0.13 ± 0.06 and 0.15 ± 0.09 for BW and WT6, respectively. Also, they documented that BW was significant for body weight trait selection in this breed.
       
The maternal genetic effect (m²) was found to be important and sizeable at weaning stage (Table 2). In these data, the maternal influence diminished as age increases, but modest genetic progress appears possible for all pre-weaning growth traits analyzed for the Chokla sheep. Maternal genetic effects contributed only 2.4% of the total phenotypic variance from birth to 30 days of age and this effect diminished further with increasing age. These results indicated as lambs grow up, the influence of maternal genetic effects on their growth decreases. The maternal heritability estimated from model 6 for BW and WW and model 3 for remaining different body weight traits show a decreasing trend with advancement in age. The maternal effect is particularly important for early growth traits in sheep as it is influential during pregnancy and lactation, but its importance decreases during the post-weaning stages (Gholizadeh and Ghafouri-Kesbi, 2015). The low maternal effect on pre-weaning growth indicates that the maternal effect would have less effect on selection response for these traits. When maternal effects are of high importance, total heritability values are more efficient than direct heritabilities for estimation of selection response based on phenotypic values.
       
The permanent environmental effect (c²) of the dam on birth weight is mainly determined by uterine capacity, feeding level especially at late gestation. Maternal permanent environmental variance was found to influence the early body weight traits of BW and WW and estimates of environmental effects (c²) for these traits were 0.121 and 0.028, respectively.
       
Addition of covariance between direct and maternal effects in model 3 and model 6 has shown negative and high estimate of r_am, which resulted in highly inflated values of heritability and maternal effect in these models. It might be due to some hidden mechanism underlying phenotypic relation, which restricts genetic covariance at higher negative magnitude (Prince et al., 2010). To prevent the use of biased estimates of additive direct heritability especially when maternal effects are important it is more useful to use the total heritability (h²_t) for evaluation of the response for selection based on phenotypic values. Total heritability estimated for BW, WW, 6W, 9W and YW was 0.071, 0.118, 0.193, 0.213, 0.188, respectively.
       
Reason behind high and negative r_am was found by various researchers (Tosh and Kemp 1994; Roff, 2002; Robinson 1996; Berweger et al., 1999 and Notter and Hough, 1997). Antagonism between the effects of an individual’s genes for growth and those of its dam for a maternal contribution may be due to natural selection for an intermediate optimum (Tosh and Kemp 1994). According to Roff (2002), antagonistic pleiotropy has long been considered a probable mechanism for the maintenance of genetic variance. Inclusion of sire year interaction in the model could lead to reduction in the negative correlation between the animal effects (Robinson 1996; Berweger et al., 1999). The data structure in the present study has not included this interaction. One more peculiar thing observed for pre weaning traits was large negative estimate of r_am, direct and maternal estimates tend to be higher than in models that assume 𝛔_am to be zero. As noted by Notter and Hough (1997), estimates that don’t involve ram can be properly used for genetic prediction only if the user also accepts and incorporate the additive maternal covariance into the prediction model.
 
Correlations among body weight at different ages
 
The estimates of different correlations among body weights at different ages are presented in Table 3. Genetic correlations among body weights at different ages were positive and ranged from medium to high except correlations between BW-6W, BW-9W and BW-YW, for which negative r_g was estimated (Table 3). In, general, all the estimates were significantly different from zero. 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.
 

       
The phenotypic correlations among body weights at different ages were positive and medium to high in magnitude. The phenotypic correlations were high between adjacent weights and declined in magnitude as the interval between the weights being related increased (Table 3). The significantly high phenotypic correlation (among 6W, 9W and YW) at this stage indicated that a lamb weighted heavier at 6 months of age, was likely to be heavier at 9 and 12 months of age. In the field condition, the earliest age at which sheep are purchased is around six months and hence weight at six months would be important criteria for evaluation of lambs in field conditions. The findings were in close agreement with the findings of Gowane et al., (2010) in Malpura and Parihar et al., (2017) in Magra sheep.
       
Only two traits i.e. birth weight and weaning weight showed maternal permanent environmental correlation in present study. This result indicates that in the existing management conditions, good maternal environment pose positive effects on lambs from birth to weaning stage. The highest maternal correlation between WW and 6W (0.999±0.109) was estimated highly positive and significant in present study. Maternal genes sharing dependence gradually declines as is evident from the decline are genetic correlation of maternal effects as the animal grows.

For formulation of breeding programmes at any farm/research station, there is requirement of accurate values of genetic parameters and (co)variance components. An animal model like DFREML takes into accounts all relationship in the pedigree and is therefore expected to provide estimates of genetic parameters with higher precision. The study revealed that the moderate heritability indicates that modest rates of genetic progress may be possible for these traits from selection under the prevailing management system. The maternal influence diminished as age increases and maternal genetic effect was found to be important and sizeable at weaning stage. It is more useful to use the total heritability for evaluation of the response for selection based on phenotypic values to prevent the use of biased estimates of additive heritability caused by high and negative correlation between additive and maternal effect.

Authors declare that there is no conflict of interest for this work.