Estimation of Genetic Parametersand Evaluation of Sires for Growth and Fleece Yield Traits Using Animal Model in Chokla Sheep  

Ravindra Kumar , Singh C.V. , Barwal R. S.
Department of Animal Genetics and Breeding, College of Veterinary and Animal Science, G.B. Pant Univ. of Agriculture and Technology, Pantnagar- 263145, Distt. U.S. Nagar (Uttarakhand)
Author    Correspondence author
Animal Molecular Breeding, 2013, Vol. 3, No. 2   doi: 10.5376/amb2013.03.0002
Received: 22 Feb., 2013    Accepted: 05 Mar., 2013    Published: 21 Mar., 2013
© 2013 BioPublisher Publishing Platform
Abstract

The data on 1 214 animals progeny of 110 sires of Chokla sheep maintained at CSWRI, Avikanagar, Rajasthan were used in the present study considering the traits birth weight, weaning weight, 6 months weight and first greasy fleece yield. The least squares means were (2.81±0.02) kg, (12.12±0.11) kg, (16.91±0.13) kg and (0.95±0.01) kg under model 2 and (2.82±0.02) kg, (11.87±0.10) kg, (16.86±0.12) kg and (0.96±0.01) kg, respectively, under model 8 for birth, weaning and 6 month weight and first greasy fleece yield. Multivariate REML analysis has estimated slightly higher coefficient of variation than the univariate and model 8 analyses. The fixed effect of year had highly significant (P<0.01) effect on all the traits studies under model 2 and model 8 analysis. The differences in body weight traits at birth, weaning and at 6 month of age due to sex were highly significant (P<0.01). On first greasy fleece weight, sex had significant (P<0.05) effect under model 8. Male lambs were heavier than female lambs at all ages and produced more wool than females. The sire effect accounted for more variation under model 2 than model 8 for all traits except birth weight. The coefficients of multiple determination under model 8 were, 13.32%, 30.80%, 33.52% and 26.11%, respectively, for birth, weaning, 6 month and first greasy fleece weights. The higher variation at 6 month weight suggests applying intense selection pressure at the age of 6 month. The sires have evaluated and ranked on the basis of solutions obtained through univariate and multivariate REML using animal model and BLUP value for sire effects under model 8. The superiority of the best sires were around 5% for the body weight traits under BLUP1 but above 17% under BLUP2 and BLUP3. In BLUP2 and BLUP3, more than 64% animals were superior to the population mean for body weight traits. The superiority of the best animals (as per cent of the raw mean) was above 19% under BLUP2 and BLUP3 for body weight traits but this value was 18.21% (BLUP2) and 15.18% (BLUP3) for first greasy fleece yield. From these results, it was observed that the REML using animal model could be used to evaluate the animals along with their sires and dams.

Keywords
Sire evaluation; Animal model; Best linear unbiased prediction; Chokla Sheep; Growth; Fleece

Introduction
The sheep population in India is estimated to be about 71.56 million (2007 livestock Census) ranking third in the world, and is about 6.13% of the world population. About 0.369 MT of Mutton, 0.459 MT of wool and 40 M. kg of skins are produced annually. There are 42 descript breeds of sheep, distributed in various agro-climatic zones of the country. About 15.64% of the Indian sheep population are found in Rajasthan (2007 Census) which is the major sheep rearing state in India.

Chokla sheep produce fine carpet wool compared to all the other Rajasthan breeds. It is also known as Rajasthan Merino. Population of Chokla sheep was 0.886 million during 2007 census. It is apparent that number are declining due to natural reasons and large scale crossbreeding programmes for converting Chokla for apparel wool production. If the economic traits are to be included in a breeding programme, accurate estimates of breeding values will be needed to optimize selection programmes. In order to make rapid genetic progress in performance through selection for traits of economic importance in sheep genotypes, selected animals must be chosen for their superior breeding value (The genetic worth of individuals as parent) (Bichard, 1988, Falconer, 1989; Nicholas, 1987). There are many source of information, which can provide clues about an individual’s breeding value. These include individual performance, family performance and combined performance of individual and family weighted appropriately (Dalton, 1985; Nicholas, 1987; Falconer, 1989) after correction for known environment effects. The Conditions under which the use of these different sources of information are appropriate and well documented in the literature (Falconer, 1989; Micholas, 1993). A point worth highlighting is that when heritability is low, combining individual and family performances, appropriately weighted, provides the maximum response to selection (Falconer, 1989). This is because the estimated breeding value of an individual using data from different relationships is more accurate than a single estimate from the individual alone (Falconer, 1989; Micholas, 1989).

In practical animal breeding, multiple traits are usually measured on each individual to collect as much information as possible about its productivity. In genetic studies, multivariate estimation of (Co) variance components and genetic values for sire evaluation has recently been received considerable attention. In most of the cases, the breeding values of sires have been estimated using single trait models. However, now-a-days, there is a constant thrust to get best linear unbiased prediction (BLUP) evaluations using a single or multitrait animal model.

As per objectives under the present study the sires have been ranked on the basis of solution obtained through univariate and multivariate REML using animal model and BLUP value for sire effects under model 8 and find out rank correlations among sires/animals on the basis of BLUP values.

1 Results and Discussion

The phenotypic mean (±S.E.) of body weights at birth, weaning and 6 month of age were (2.84±0.50) kg, (11.65±2.84) kg and (16.72±3.59) kg, respectively and first greasy fleece yield clipped at the age of 6 month was (0.95±0.33) kg. Phenotypic range of data were 1.00 kg to 4.50 kg for body weight at birth, 4.40 kg to 21.20 kg for weaning weight, 6.40 kg to 30.00 kg for 6 month body weight and 0.14 kg to 2.40 kg for first greasy fleece yield with corresponding standardized range of -3.17 to 3.36, -2.56 to 3.37, -2.88 to 3.70 and -2.49 to 4.45 respectively (Table 1). On standardized scale body weight had shown more variation than other traits, because at this stage culling by natural means may not take place. After that the standardized range has reduced at WWT and then almost stabilized. It appears reasonable that the weights become mort uniform after the maternal influence and weaning weight stress have passed (Bhathaci and Leroy, 1998). 

 
 Table 1 Phenotypic mean (X), Standard deviation (S.D.), Phenotypic standard deviation (6p), Phenotypic range (Pr) and Standardized range (Sr) of data


Under normal curve, 17.47% population falls on mean for BWT, where as the corresponding values for weaning weight, weight at 6 month and first greasy fleece yield wee, 24.36%, 21.45% and 34.31% respectively. The phenotypic standard deviation under univariate analysis were 0.477, 2.443, 3.029 and 0.288 respectively for BWT, WWT, 6WT and GFYI.

The least squares mean (±S.E.) estimated by model 2 and model 8 for birth weight, weaning weight, weight at 6 month and first greasy fleece yield different traits, are presented in Table 2. The means estimated by model 8 were slightly different from the means estimated by model 2. Kushwaha (1994), Kushwaha et al. (1997) and Anonmous (1998) reported similar birth weight in chokla where as, Arora et al. (1975), Acharya and Manimohan (1979), Acharya (1982) and Sahni (1985) reported lower means for birth weight than present study. Higher means were reported by Kushwaha et al., (1997) for body weights at weaning and 6 months of age, where as, Sahni (1985) reported lower values in chokla. For 4 FYI, Sahni (1985), Kushwaha (1994) and Anonymous (1993) reported lower estimates, where as, Kushwaha et al., (1997) and Anonymous (1998) reported slightly higher mean for the same breed. Acharya (1982) also reported higher means for GFYI. The standard error under model 2 was higher than model 8 for all the traits.


Table 2 Least squares means of birth, weaning, 6 month and first greasy fleece weight under model 2 and model 8 analysis


The coefficient of variation (C.V. %) presented in Table 3 was almost similar for different traits under model 8, univariate and multivariate. The C.V. increase with increase with increase in age up to WWT but it decreases at 6 WT and again increased at GFYI. GFYI was showing maximum variation under all methods followed by WWT and 6 WT birth weight showed least variation. Lower C.V. observed for 6 month weight was due to culling of some lambs between 3 and 6 month of age that may have reduced the variation. More over, the weights become more uniform after the maternal influence and weaning stress over, as reported by Bathaci and Leroy (1998). High C.V. at GFYI was because of the fact that all the animals were, practically, not shorn exactly at similar age i.e. 6 month of age. Forgrty (1995) reported declining trend in the mean coefficient of variation for live weights with increasing age form birth (17%) to weaning (15%) yearling (11%) and hogget (10%). He reported consistency among coefficients of variation. Multivariate analysis had explained more variation than model 8 and univariate. It indicates that data had shown multivariate distribution. In general REML analyses using animal model explained more variation than the model 8 of least squares. Malik et al. (1971) had also reported the similar results whereas Arora et al. (1981) and Chaudhary and Malik (1972) had reported higher values than the present study in Chokla sheep.


 Table 3 Coefficient of variation (C.V. %) under model 8, univariate and multi variate analysis


1.1 Factor Affecting Body Weights and First Greasy Fleece Yield
The fixed effect of year had highly significant effect on all the traits studies under model 2 (Table 4) and Model 8 (Table 5). Similar observations were reported by Malik et al. (1971), Chaudhary and Malik (1972) and Kushwaha et al. (1996). The significant effect of year of birth on the traits studied revealed that breeding, feeding and management practices were not followed similar at this farm during different years. The farm is situated in Arid Zone and affected by draught in different years. Least squares means revealed that the production performance of sheep lambs in year 1979 was poor for all the traits. However, highest values were observed at different age and fleece yield after 1987. It may be possible due to change in grazing management system. One possible explanation for the differing body weight at different years might be associated with variability in forage available in pasture (Bathaci and Leroy, 1998). In years of low forage availability, sheep spend more energy in seeking feed, thus leaving less energy surplus for fat deposition.


 Table 4 Analysis of variance under model 2

 


 Table 5 Analysis of variance under model 8


1.2 Sex of Lamb

Differences in body weights at birth, weaning and at 6 month of age due to sex was highly significant. Sex had a significant effect on GFYI under model 8 (Table 4) but non-significant under model 2 (Table 5). The males were heavier than the female lambs at all ages and produced more wool than the females (Table 2). Malik et al. (1971) and Arora et al. (1979) reported non-significant effect of sex on BWT. Arora et al. (1979) reported significant effect of sex on WWT but non-significant effect on 6 WT. Chaudhary and Malik (1972) reported significant sex effect on GFYI in chokla. Kushwaha et al. (1996) reported significant effect of sex on WWT, 6 WT and GFYI in the same breed.

1.3 Sire Effect
The random effect on birth weight and highly significant effect on WWT, 6 WT and GFYI (Table 4), indicating sizable genetic differences among sires. Singh and Kushwaha (1995b) had also reported highly significant effect of sires on WWT, 6 WT and GFYI.

Sire of lamb, under model 2 of least square, accounted for 3.43, 5.94, 6.11 and 10.36% of total variation for BWT, WWT, 6 WT and GFYI, respectively. The corresponding values under model 8, were 3.70, 4.63, 4.04 and 3.62 (Table 6). Burfering and Kress (1993) also reported 8.3% and 8.8% variation in birth and weaning weight, respectively due to sire in sheep. The sire had accounted more variation under model 2 than model 8 for all the traits, except BWT. With the advance of age the variation accounted by sire was increased under model 2, therefore, these may be some confounding among traits, which increased sire contribution in total variation with the advance of age. Model 8 had not shown any trend. At weaning weight, sire had maximum variation under model 8. 
 


 Table 6 Observed between and within sire variance (expressed as percentage of phenotypic variation) under model 2 and modle 8


The coefficients of multiple determination (R2) obtained under model 8, were 13.32%, 30.80%, 33.52% and 26.11% respectively for BWT, WWT, 6 WT and GFYI. For growth traits, as the age of the animal advanced the R2 increased. Higher variation at 6 WT indicates the need for applying intense selection pressure at the age of 6 months.

The spectacular improvement in the production capacity could be achieved from selection of rams. This is because with the use of rams at large scale very high intensity of selection could be practiced in males. With the increase in the intensity of selection the importance of accuracy also increases. Therefore, selection of rams based on their accurately predicted breeding value is of paramount importance. Prediction of breeding value depends upon the method of sire evaluation used. There is a constant thrust to get BLUP evaluations by using an animal model under single or multiple trait models depending upon the goal. As per the objectives, the sires have been ranked on the basis of solution obtained through univariate and multivariate REML using animal model and BLUP value for sire effects under Model 8. The sire/animal effect and list of ten tops ranking sires are presented in Table 1, Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, and Table 10. Rank correlation (Table 11) between these values worked out to evaluate the efficiency of sire evaluation.


Table 7
Range of solutions (LSC) for sire effect under model 8



Table8
Sire effects of ten top ranking sires for BWT, WWT, 6WT and GFY1 under model 8



Table 9
Range of solutions for sire effect under univariate animal model



Table 10
Sire effects of ten top ranking sires for BWT, WWT, 6WT and GFY1 under univariate animal model



Table 11 Range of solutions for sire effect under multivariate animal mode



Three solutions for sire evaluation were used: Best Liner Unbiased Prediction (BLUP1) values of Model 8, and univariate (BLUP2) and multivariate (BLUP3) solutions of REML. All the methods were based on progeny testing; the BLUP2 and BLUP3 were based on an animal model, which utilized information from all the known relationships. Under univariate and multivariate animal model no sire effect was fitted. The sire solution was sorted out from the solution of all the animals and used for comparison with BLUP values obtained under model 8.

The raw means estimated by the different methods were same, therefore, the sire effects taken as deviation of the sire ‘s value from the raw mean and have been presented and discussed for the purpose of sire evaluation and comparison under different methods. The sires were evaluated for BWT, WWT, and 6WT and GFY1 traits.

A total of 110 sires were evaluated. The information on sire evaluation viz. percent of sires with negative or positive sire effects, sire effect for the top ranking and bottom ranking sires, and percent superiority/inferiority of top/bottom ranking sires under various methods are presented in Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, and Table 16.
 


 Table 12 Sire effects of ten top ranking sires for BWT, WWT, 6WT and GFY1 under multivariate animal model

 


 Table13 Range of solutions for animal effects under univariate animal model

 


 Table14 Animal effects of ten top ranking animals for BWT, WWT, 6WT and GFY1 under univariate animal model

 


 Table15 Range of solutions for animal effects under multivariate animal model



 Table 16 Animal effects of ten top ranking animals for BWT, WWT, 6WT and GFY1 under multivariate animal model


1.4 Birth Weight
The estimated average BWT of 2.84 kg was used for BLUP1 BLUP2 and BLUP3. About half of the sires (49.1%) were superior to the population mean under BLUP1. The corresponding values were much high under BLUP2 (66.4%) and BLUP3 (64.6%).

The range of sire effect for BWT were -0.1190 to 0.1224, -0.3109 to 0.5262 and -0.3108 to 0.5028, respectively, under BLUP1, BLUP2 and BLUP3. The range of sire effects was almost same under BLUP2, BLUP3 and BLUP1. More than 61% animals were superior to the population mean. The superiority of the best sires (as percent of the raw mean) was 4.31, 18.53 and 17.70, respectively under BLUP1, BLUP2 and BLUP3. Whereas corresponding values of inferiority of the worst sires were -4.19, -10.95 and -10.94. BLUP2 had shown maximum value in terms of superiority and/or inferiority. The range of animal solution was -0.5084 to 0.6334 and -0.5118 to 0.6340, respectively, under BLUP2 and BLUP3. In BLUP2 and BLUP3, about 64.5% animals were superior to the population mean. The superiority of the best animal (as percent of the raw mean) was 22.30% and 22.32%, respectively under BLUP2 and BLUP3 whereas corresponding values for inferiority of the worst sires were 47.90% and - 18.02%, BLUP2 and BLUP3 had shown almost similar values in terms of superiority and/or inferiority of animal solutions.

The upper limit of sire effects for BWT was increased from 0.1224 kg in the BLUP1 solution to about 0.50 kg in BLUP2 and BLUP3 whereas the lower limits were reduced from 0.1190 in BLUP1 to about 0.31 in BLUP2 and BLUP3. The upper and lower limit of sire effect under BLUP1 was almost 1/4 and 1/3, respectively of the BLUP2 and BLUP3 methods.

1.5 Weaning Weight
The estimated average WWT of 11.65 kg was used for BLUP1, BLUP2 and BLUP3. Less than half of the sires (48.2%) were superior to the population mean under BLUP1. The corresponding values were much higher under BLUP2 (71.8%) and BLUP3 (74.6%).

The ranges of sire’s effect for WWT were -0.7076 to 0.6686, -0.2493 to 2.2562 and -1.3714 to 2.4870, respectively under BLUP1, BLUP2 and BLUP3. The range of sire effects was similar under BLUP2 and BLUP3 but low in BLUP1. The superiority of the best sire (as percent of the raw mean) were 5.74, 19.37 and 21.35, respectively under BLUP1, BLUP2, BLUP3 whereas corresponding values of terms of inferiority. The range -11.77 BLUP3 had shown maximum value in terms of superiority and/or inferiority. The range of animal’s solution was -0.3831 to 2.2562 and -1.6611 to 2.8140, respectively, under BLUP2 and BLUP3. More than 64% animals were superior to the population mean in BLUP2 and BLUP3. The superiority of the best animals (as percent of the raw mean) was 19.37% and 24.16%, respectively, under BLUP2 and BLUP3 whereas corresponding values for inferiority of the worst sires were -11.87% and -14.26%. BLUP3 had shown more range in terms of superiority and/or inferiority for animal solutions than BLUP2. It was observed that top ranking sire for WWT was same (i.e. CS 784) in BLUP2 and BLUP3.

The upper limit of sire effects for WWT was increased from 0.6686 kg in the BLUP1 solution to 2.2562 kg in BLUP2 and 2.4870 kg in BLUP3 whereas the lower limits were reduced from 0.7076 in BLUP¬1 to 1.2493 and 1.3714 in BLUP3.

1.6 Six Month Weight
The estimated average of 6 WT (16.72 kg) was used for BLUP1, BLUP2 and BLUP3. Less than half of the sires (41.8%) were superior to the population mean under BLUP1. The corresponding values were much higher under BLUP2 (61.9%) and BLUP3 (68.2%).

The range of sire effects for 6 WT were -0.7304 to 0.8365, -1.8118 to 2.9024 and -1.7834 to 2.9949, respectively under BLUP1, BLUP2 and BLUP3. The ranges of sire effects were similar under BLUP2 and BLUP3 but low in BLUP1. The superiority of the best sires (as percent of the raw mean) were 5.14, 17.36 and 17.91, respectively under BLUP1, BLUP2 and BLUP3 whereas corresponding values of inferiority of the worst sires were -4.49, -10.84 and -10.67 BLUP2 and BLUP3 had shown maximum and almost same value in terms of superiority and/or inferiority. The ranges of animal solutions were -1.9756 to 3.4847 and -2.3548 to 3.5931 respectively, under BLUP2 and BLUP3. More than 64% animals were superior to the population mean under BLUP2 and BLUP3. The superiority of the best animals (as percent of the raw mean) was 20.84 and 21.49%, respectively, under BLUP2 and BLUP3 whereas corresponding values for inferiority of the worst sires were -11.82 and -14.08%. BLUP3 had shown more range in terms of superiority and/or inferiority for animal solutions in comparison to BLUP2. It was observed that top ranking sires for 6WT were not same in BLUP1, BLUP2 and BLUP3.

The upper limits of sire for 6WT were increased from 0.8365 kg in the BLUP1 solution to 2.9025 kg in BLUP2 and 2.9949 kg in BLUP3 whereas the lower limits were reduced from 0.7304 kg in BLUP1 to 1.8118 kg in BLUP2 and 1.7834 kg in BLUP3.

1.7 First Six Monthly Greasy Fleece Yield (GFY1)
The estimated average GFY1 of 0.95kg was used for BLUP1, BLUP2 and BLUP3. About half of the sires (48.2%) were superior to the population mean under BLUP1. The corresponding values were much higher under BLUP2 (60.9%) and BLUP3 (63.6%). In BLUP2 and BLUP3, about 60.0% animals were superior to the population mean.

The ranges of sire effects for GFY1 were -0.0575 to 0.0851, -0.1036 to 0.1429 and -0.1002 to 0.1279, respectively under BLUP1, BLUP2 and BLUP3. The range of sire effects was bit higher under BLUP3 and BLUP2. The superiority of the best sires (as percent of the raw mean) was 8.96, 15.04 and 13.46, respectively under BLUP1, BLUP2 and BLUP3 whereas corresponding values of inferiority of the worst sires were -6.05, -10.91 and -10.55. The ranges of animal solutions were -0.1036 to 0.1730 and -0.1002 to 0.1442, respectively, under BLUP2 and BLUP3. About 60% animals were superior to the population mean, the superiority of the best animals (as percent of the raw mean) were 18.21 and 15.18%, respectively, under BLUP2 and BLUP3 whereas corresponding values for inferiority of the worst sires were 10.91 and -10.55% respectively. BLUP3 had shown more superiority for animal solutions in comparison to BLUP2, but the lower limit was almost same in both the methods.

The upper limit of sire effects for 6WT was increased from 0.0851kg in the BLUP1 solution to 0.1429 kg in BLUP2 and 0.1279 in BLUP3 whereas the lower limits were reduced from 0.0575 in BLUP1 to 0.1036 in BLUP2 and 0.1002 in BLUP3. It was observed that the top ranking sire for GFY1 was same (i.e. CO 170) under all the methods.

The higher percentages of superior sires to population mean were under BLUP2 and BLUP3, for all the traits, might be due to non-fitting of sire effect in the model. In BLUP2 and BLUP3, sires were sorted out from the animal solutions and then ranked. From these results, it can be summarized that the range of sire effects was more under BLUP2 and BLUP3. These findings are in close agreement with the findings of Ahmed (2002) in Avikalin sheep.

1.8 Rank Correlation
All 110 sires were ranked on the basis of the solution obtained under model 8 and univariate and multivariate REML using animal models for BWT, WWT, 6WT and GFY1. The rank correlation coefficients for ‘among methods within trait’ and ‘among traits within method’ are presented in Table 17


 Table 17 Rank correlation coefficients


Rank correlations for the trait under all the methods were highly significant, ranging from 0.724 (between model 8 and multivariate animal model for GFY1) to 0.997 (between model 8 and univariate animal model for BWT). Rank correlations were above 0.950 for all the traits when sires were ranked by univariate and multivariate animal model. So, the ranking by these two animal models was almost same. Rank correlations of model 8 with univariate and multivariate animal models were lower than univariate with multivariate animal models. The rank correlation among the different methods were though high and significant (P<0.01), yet not perfect, revealing that ranking of sires by different methods not similar.

The rank correlations ‘among traits within method’ were lower than ‘among within trait’. In ‘among traits within method’, the ranking of the sires changed resulting in to decreased rank correlation coefficients. The change in ranking of sires with increase in age or weights of their daughter might be due to non-unity in genetic correlations between different weights. Within the method, the rank correlation ranged from 0.124 (between 6WT and GFY1 in multivariate animal model) to 0.934 (between 6WT and GFY1 in multivariate animal model). All the rank correlation coefficients were significant, except between BWT and GFY1 in univariate animal model and between 6WT and GFY1 in multivariate animal model. Model 8 had higher rank correlations among traits as compared to other two. In general, WWT had highest rank correlation with 6WT in all the methods, ranging from 0.728 in model 8 to 0.934 in multivariate animal model. This high rank correlation might be due to high genetic correlation between WWT and 6WT. These findings are in close agreement with the reports of Ahmad (2002) in Avikalin sheep.

2 Materials and Methods
2.1 Data

The present study includes data collected from 1974 to 1998 in the Chokla sheep flock at of Chokla sheep was maintained at the Institute under “All India Coordinated Research Project on Sheep Breeding (AICRP-SP)” for fine wool until 1992 and from April 1992 the flock was maintained under, Network Project on Sheep Improvement in the research project “Evaluation and Improvement of Chokla Sheep for Carpet Wool”.

The animals with known pedigree and complete records on all traits viz. birth weight, weaning weight, 6 month weight and first greasy fleece yield were considered for the present study. The animals were given new identity on the basis of their date of birth to avoid the pedigree check. While the identity no of the animal must be higher, the point is the data checks are to make sure parents are, n fact, older ten progeny. The sires with less than 4 progeny were deleted from the analysis. Similarly, years in which less than 20 observations were deleted from the analysis.

2.2 Statistical Methodology
For the estimation of parameters and (co) variance components, least- squares analysis (LSA) and derivative free restricted maximum likelihood (DFREML) methods were employed. Data were subjected to LSMLMW and MIXMDL package of Harvey (1990) under different models. A total of two models were considered to examine the effect of genetic and non-genetic factors on various body weight traits and on first greasy fleece yield.

2.3 Model 2
The model 2 considered was from LSMLMW and MIXMDL package of Harvey (1990) which consists one set of cross classified non-interacting random effect. All four traits were analyzed simultaneously, the model is as follows.

Yijkl = ų + si + cj + pk + eijkl

where, Yijkl is observation on 1th progeny of jth sex in kth year; ų is the over all mean; si is the random effect of ith sire (i = 1,2,……., 110); cj is the fixed effect of the jth sex (j = 1, 2); pk is the fixed effect of kth year of birth (k =1, 2, ………., 20), and eijkl is the random error which is normally and independently distributed with mean 0 and variance σ2e.

The analysis was computed with the mixed model least squares program which utilizes the method 3 of Henderson (1953).

2.4 Model 8
The model 8 considered was same as above which also consists one set of cross classified non interacting random effect. The same model was fitted on all the traits and the traits were analyzed separately. The general formulation of the mixed model fitted is as follows.

Yijkl = ų + si + cj + pk + eijkl

where, all the abbreviations are same as described in first model. The formulation of model in matrix notation is as follows.

Y = 1 ų + xb + za + e

Where, 1 is the column vector of the means; ų is the over all mean; B is the column vector of fixed effects; a is the column vector of random effects; z is an incidence matrix of 0’ s and 1’ s; x is an incidence matrix of o’ s, 1’ s & -1’ s and x-x values for the discrete effects, and e is a column vector of the random errors. This model is same as first model, except the random effect may be correlated.

2.5 Univariate
In univariat analysis, birth weight, weaning weight, 6 month weight and first six monthly greasy fleece yield were analyzed separately. The same model was fitted on all four traits. The general formulation of the mixed model fitted is as followes.

Yijkl = µ+ Ai + cj + pk + eijkl

Where, Ai is random effect of it animal and all the other abbreviations are same as described in earlier models. The formulation of general single trait animal model is matrix notation is as follows:

y = xf + za + e

Where, y is a vector of Nx 1 records; f is a vector of fixed environmental effects of sex and year; and covariable was taken here; a is vector of breeding values for additive direct genetic effects fitted shich is random; s is a N* n F design matrix for fixed effects with column ranks N*F*; z is a N* NR design matrix for random animal effects, where z=1, and e is a vector of N random residual errors.

2.6 Multivariate Model
In multivariate analysis, all the four mentioned traits were taken simultaneously for analysis. The multi trait animal model used to estimate parameters is as follows.

Yijkl = µ+ Ai + cj + pk + eijkl

Where all the abbreviations are same as described in univariate model. The above multi trait animal model, in matrix notation, for 4 traits used is as follows:

y = xb + zu + e

where, y is a vector of Nt* 1 of records; b is a vector of fixed environmental effects of sex and years. No covariable was taken here; µ is a vector of breeding values for additive direct genetic effects fitted, which is random; e is a vector of N random residual errors and x and z are incidence matrices relating the records to the effects of the model.

Three solutions for sire evaluation were used as Best Linear Unbiased Prediction (BLUP1) values of model 8 of Least squares analysis (Harvey, 1990), univariate (BLUP2) and multivariate (BLUP3) solutions of REML using animal model (Mayer, 1998), which utilized information from all the known relationship. Under univariate and multivariate and multivariate animal model no sire effect was fitted. The sire solutions was sorted out from the solution of all the animals used for comparison with BLUP values obtained under model 8. On the basis of these BLUP values sires were ranked.

2.7 Rank Correlation
The spearman’s rank correlation between BLUP values obtained by above methods was worked out (Steel and Torrie, 1980) as follows.

Where, r is the rank correlation; n is the number of sires; di is the difference between rank of the sire ranked by two methods.

The significance of the rank correlation was tested by students t-test as follows:

Note: with (n-2) degree of freedom

Acknowledgements
The authors want to thank Director, Central Sheep and Wool Research Institute, Avikanagar, Rajasthan, for providing data for the present study.

References
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