The Morphometric Scale to Predict the Live Weight of Malpura Sheep in Semi-arid Region of Rajasthan

The Malpura  is a hardy sheep breed of semi-arid region of Rajasthan (Tonk, Jaipur and Sawai Madhopur districts) known for its higher growth rate and adaptability to harsh climate (Kumar et al., 2008; Gowane et al., 2010). This sheep is well-built having long legs, square compact body and medium to long tail. The ears are very small or stumpy and hence called as “Buchi” by local shepherds. The live weights in farm raised sheep were reported to be 3.27±0.03 kg, 17.52±0.16 kg, 26.43±0.25 kg and 33.42±0.30 kg at birth, three month, six month and at twelve month age, respectively (Jyoti et al., 2018).
       
In the field, animals are slaughtered across all the ages. The Malpura sheep has higher growth rate and hence lambs are slaughtered at early age too, however farmers do not get the due share for their heavy weight lambs as animals are never sold on weight basis. The primary reason for this is unavailability of the weighing balances at the farmer’s door and also unorganised market of the sheep that has led to complete dependence of the local shepherds on middlemen for sale of their produce. Recent study by our group revealed that there are nearly 50% losses in revenue earned by local shepherds as they are not directly involved in the terminal market for sale of their produce (Gowane et al., 2019). Researchers have worked out the ways of predicting the live weight of sheep or goats using body measurements. Agamy et al., (2015) reported that regardless of breed, the equation including body length, withers height and paunch girth could predict body weight of Egyptian ram-lambs with an accuracy of 75%. However, very few studies have tried to address this issue, especially in India. Our study aimed at construction of the morphometric scale using simple body measurements for prediction of the approximate live weight in sheep across all the ages in males and females. This study envisioned that the construction of such a scale will further benefit the shepherds to guess the live weight of the lambs sold and expect the desired price from the customer.

The present study was conducted at the ICAR-Central Sheep and Wool Research Institute, Avikanagar on a well organised flock of Malpura sheep maintained under the Malpura - Mega Sheep Seed Project (MSSP) from December 2018 to October 2019. The animals were weighed starting from three month of age to 12 month age and  adult animals were also weighed on the digital weighing scale. During each weighing the body length of the animals (L) and heart girth (G) were measured in centimeter (cm) using the measuring tape. Animals in the growth phase were followed up to adult stage (12 month) and morphometric measurements were also taken during each weighment. Total 1124 records on 823 animals (203 males and 620 females) were collected for present study. The grazing and management of the animals was followed as per the sheep management and health protocol followed at ICAR-CSWRI Avikanagar and mentioned elsewhere for Malpura sheep (Gowane et al., 2015a). The animals are managed on semi-intensive system and protected against the major health hazards by vaccinations and other prophylactic measures.
       
The data on live weight (N=1164 or 1124) and corresponding morphometric measures on G and L were digitalized and subjected to analysis. The sex wise or age group wise data was not separated for present study, as separate scale for each age class in each sex is not advisable as it will lead to the confusion for the end user. Our aim was to develop a scale which is common across the age as well as sexes in Malpura sheep. The data were also not corrected for the fixed effects of sex, season, etc. as the pragmatic scale will assume the bias of these factors. As the application of this study will be on the raw data, which will not be corrected by end user. Several predictive variables were created using arithmetic combination of L and G (Table 2). In present study 14 linear predictors were regressed on the live weight to obtain the estimates of regression, coefficient of determination and then the prediction equations using the regression coefficients for prediction of live weights were derived. Two extra predictors with additive linear regression of L and G with >10kg [(L+G)>10] and more than 15 kg [(L+G)>15] were used assuming mostly animals slaughtered are at least 10 kg in live weight.
       
The original predictive variables L and G, when used as additives, were found to yield the better estimates. However, in most of the linear regression analysis, the homoskedasticity of the residual variance is assumed, which is not always true and heteroscedasticity of the residual variance exists. Thus in such cases the weighted least squares (WLS) is actual maximum likelihood estimator. Thus WLS process were used to obtain the weights for noise variance
Where,
w_i is weight for noise variance σ2i at each measurement i.
       
Several powers for the weights starting from -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5 and 2 were used in the linear regression equations as well as in the WLS, separately. Thus total 9 WLS prediction models were compared using the log-likelihood values. The model with highest log-likelihood value was chosen for further analysis and construction of the prediction equation. Compared the best linear regression model with the best WLS model using root mean squared deviation (RMSD) which represents the mean deviation of predicted values with respect to the observed values in the same units as the model variable under evaluation (Kobayashi and Salam 2000).

The population under study had average mean live weight 28.54 kg and standard deviation of 8.90 kg. Out of 1164 records, 6.7% had live weight up to 15 kg and 2.1% had weights above 45 kg. Live weights between 25 to 35 kg dominated the records with 42.2% (Table 1). The data was normally distributed and had the range of 58.8 kg. Huge variability was also observed for body length and heart girth measurements across different live weight groups. There was linear relationship of the G and L with increased live weight class. The overall mean for L and G was 63.44 (7.12) and 74.35 (8.61) cm, respectively. The range was from 38.0-83.0 cm for L and 43.0-100.0 cm in G. The overall variance for G was 74.05 and for L it was 50.72 and variance was fairly high for G and L in the higher weight category. Earlier report for body measurements in Malpura sheep institute flock revealed similar results (Mishra et al., 2005). The body length and heart girth with little higher estimates were earlier reported in the same breed in the field flocks viz. body length estimate of 70.81±1.07 cm for 2-teeth animals, 71.62±1.08 cm for 4-teeth animals and 72.26±0.92 cm for full mouthed animals, similarly 78.79±1.33 cm in 2-teeth, 82.42±1.34 cm in 4-teeth and 85.47±1.14 cm in full mouth animals (Gowane et al., 2015b). Most of the animals in the current data set belong to growth phase and below 12 month age, thus reflecting the lower overall mean estimates. As expected, the average L and G in the >45 kg category in present study were 73.0 and 88.0 cm, respectively which is in accordance with the earlier estimates (Gowane et al., 2015b).
 

 

       
The results of linear regression analysis were interesting as the relationship of L with G in different arithmetic formats affected the predicted variable in significant way. The live weight was predicted using models as shown in Table 2. The R² was an indicator of predictability of the model. Result indicates  that use of only L had 72% predictability, whereas quadratic L explained 71.4% variation. Only G explained 76.3% whereas quadratic G explained 77.4% variability in live weight. Combination of L and G together significantly improved the predictability. The equation used in large ruminants (LG²) had 86.5% predictability, whereas GL² could explain 84.8% variability in live weight. Multiplicative relationship of L and G (LG) gave better prediction . The R² for LG was 87.0%. The predictability of LG was better than most other multiplicative predictors such as (LG)², LG³, √(LG) and √(LG²). Dividing the LG by either 100 or 300 resulted in similar R² as that of LG, i.e. 87.0%, however, the regression coefficient was better with LG/100 and LG/300. The regression equation developed using LG/300 was Y = -11.92 + 2.553(LG/300).
       
The additive predictor using L and G additively (L+G), resulted in highest predictability (R²=0.871), although non-significant from LG, LG/100 or LG/300. The prediction equation developed using L+G was Y=-49.743+0.576×L+ 0.562×G. The advantage of L+G over LG is the ease of use as no derived predictor needs to be worked out, apart from better predictability. Assuming that the animals slaughtered are usually more than 10 or 15 kg in live weight, data in set 1 have truncated with live weight more than 10kg viz. (L+G)_10 and set 2 with truncated data with live weight more than 15kg viz. (L+G)_15 and used the L+G predictor. The resulting R² values for set 1 was 86.5% and for set 2 it was 83.9%. The result indicates  that the un-truncated data was resulting in better prediction equation and hence using  L+G predictor is advisable. The Fig 1 clearly indicates the superior predictability of L+G and derivations of L+G over all other predictors, as the graph of predicted values over the observed values becomes more and more linear.
 

       
The variance of residuals (observed - predicted values) is not constant across the data points and hence the magnitude of the noise is not constant resulting in heteroskedasticity. In such case the ordinary least squares are no longer the maximum likelihood estimates (MLE) and needs a correction for MLE as it is no longer efficient. If we know the noise variance (σ²_i) at each measurement i then we can set weights: w_i=1/σ²_i and get the heteroskedastic MLE and recover the efficiency. The weighted least squares analysis (WLS) was used for this purpose. Various powers from -2 to +2 with 0.5 interval were used to obtain WLS estimates of regression for L and G for predicting the live weight (Table 3). The log-likelihood values for all the models when compared, we found that the model L+G with power -1 for the weights was the best (log-likelihhod = -2976.772). The estimate of R² obtained with this model (WLS^-1) was 88.3%, which is superior to all the other predictors. The regression equation developed using WLS-1 was Y = -48.53 +0.535×L+0.58´×G.
 

       
The plotted graph for residuals of L+G and WLS^-1 are given in Fig 2. The residuals for the two predictors were compared. The residuals plotted had no significant difference of magnitude or direction. For L+G, the average of the residuals was -0.002 and summation was -2.802. The squared residuals averaged 10.108 and summation was 11745.897. For the WLS^-1, the average of the residuals was 0.047 and summation was 54.915, whereas the squared residuals average was 10.155 and the summation was 11800.290. The predictive ability of the WLS^-1 was better but not significantly higher than L+G. The RMSD estimates were 3.178 for L+G and 3.185 for WLS^-1. There was no significant difference between the two and estimates indicated that use of L+G predictor is more logical. Thus looking in to the ease of use, use of L+G as the simple and most suitable measure for prediction of the live weight in Malpura sheep is recommended.
       

 
Several authors who worked on cattle show that the heart girth is the most precise and easy to apply of the linear body measurements (Delage et al., 1955). Thys and Hardouin (1991) in Poulfouli sheep of north Cameroon also developed a scale using only heart girth that resulted in allometric curve which explained 90.8% of variation of the body weight in ewes and 86.5% in rams. Nigm et al., (1995) found that heart girth was the best single predictor and accounted alone for 77% of the variation in body weight of Merino males. Afollayan et al., (2006) used the polynomial equation using chest girth as an independent variable and predicted body weight. Abdel-Moneim (2009) reported that body length and heart girth accounted for 47% and 86% in body weight of Barki and Rahmani sheep, respectively, whereas both paunch girth and body length represented 93% of the variation in Ossimi sheep body weight. Ambarcioðlu et al., (2017) also shown chest girth as most important predictor for live weight. Kumar et al., (2018) revealed that the heart girth is the most important trait for estimation of live weight in Harnali sheep and the prediction equation given was Y= -63.72+1.23HG; with R² = 0.87. The present study however, deviated from these observations and it was observed that the inclusion of L as well as G results in better prediction of live weight. In accordance with present finding, Yilmaz et al., (2012) reported the highest coefficients of determination from the models formed for body length or body length and chest girth together (R² = 0.79, R² = 0.87). 
       
The present study revealed that it is possible to create a measurement scale which is pretty accurate for prediction of live weight of sheep using simple arithmetic. However, the ease of its use must be kept in mind as the end user is the shepherd who usually does not have access to the high end technology and also knowledge. With the help of measuring tape, we can easily measure heart girth and body length of the sheep. The simple linear regression L+G and its prediction equation can be used to arrive at the approximate weight of the animal. The equation can be communicated in a layman language as make the measures of L and G to half and add them and then deduct nearly 50 from the estimate to arrive at the approximate weight of the animal (Y=-49.743+0.576×L+0.562×G). Hence, this scale may be used in field to estimate live weight of the animals with more accuracy for monetary benefit of the shepherds.

The authors acknowledge the Director, ICAR-Central Sheep and Wool Research Institute, Avikanagar for providing all kinds of support for the execution of this project. The authors are also thankful to the Mega Sheep Seed Project (MSSP) of ICAR for funding the project. The technical help provided by Mr. Yogiraj Meena (Technical Officer AGB Division) is highly acknowledged for collection of the data and its recording for morphometric characters.