Prediction of live weight in growing hair sheep using the body volume formula

Due to the conditions in which traditional sheep production systems operate, the evaluation of animal growth from live weight (LW) is limited by the high cost of the livestock scale as well as the sophisticated maintenance required. In this scenario, in recent years, biometric measurements have been investigated as an accurate indirect method to predict the LW of farm animals. Therefore, the present study was undertaken to examine different models for predicting the body weight of growing lambs using the body volume (BV) formula. Body volume, heart girth (HG) and body length (BL) data of 290 lambs aged between two and eight months were recorded. Body volume was calculated from HG and BL data using a formula that calculates the volume of a cylinder. The estimation of LW from the BV formula was achieved through regression equations using three mathematical models (linear, quadratic and exponential). The mean values of LW, HG, BL and BV of the lambs were 29.12±12.04kg, 70.00±11.69cm, 38.40±6.43cm and 23.93±9.90dm 3 , respectively. The correlation coefficient between LW and BV was r = 0.96 (P<0.001). The quadratic model showed the highest coefficient of determination (0.93) and the lowest prediction error (3.29kg). Under the experimental conditions adopted in this study, it is possible to predict the live weight of growing lambs using the body volume formula.


INTRODUCTION
Because of the conditions in which traditional sheep production systems operate, the evaluation of animal growth, which could be achieved using direct-measurement equipment such as livestock scales, often represents a challenge for producers due to its high cost (Chay-Canul et al., 2019;Canul-Solís et al., 2020;Salazar-Cuytun et al., 2021).Coupled with this, the calibration and maintenance of measurement equipment require trained technicians, who are not commonly available in rural areas (Málková et al., 2021;Salazar-Cuytun et al., 2021).As a result, the limitations of measuring equipment in traditional production systems cause the animals to be sold through negotiation or based on visual assessment, which leads to high errors in the estimation of body weight (BW), ultimately affecting the economic gains of producers (Kumar et al., 2018;Paputungan et al., 2018;Salazar-Cuytun et al., 2021).
In the case of sheep, several authors have developed equations to estimate BW from biometric measurements such as heart girt (HG), body length (BL), withers height, hip width, and rump height, mainly (Kumar et al., 2018;Chay-Canul et al., 2019;Huma and Iqbal, 2019;Worku, 2019;Canul-Solís et al., 2020;Gurgel et al., 2021).These researchers concluded that HG is the most important biometric measurement for the estimation of the animals' LW, since a high relationship was found between both body measurements.However, to improve the accuracy of prediction of LW, Paputungan et al. (2018) and Salazar-Cuytun et al. (2021) combined HG and BL data to calculate the body volume (BV) of the animals by adapting the formula used to calculate the volume of a cylinder.In this method, HG and BL represent the circular line and the height of the cylinder shape, respectively (Paputungan et al., 2018;Salazar-Cuytun et al., 2021).Despite the advantages the BV formula could offer to producers and researchers in estimating the LW of farm animals (Takaendengan et al., 2012;Paputungan et al., 2015Paputungan et al., , 2018;;Le Cozler et al., 2019), it has been poorly explored in hair sheep breeds at different physiological stages (Salazar-Cuytun et al., 2021).In this scenario, we hypothesize that body volume can be used to predict the live weight of hair lambs at different physiological stages.Therefore, the present study was carried out to predict the BW of growing hair lambs using the BV formula calculated from HG and BL data.

MATERIAL AND METHODS
The animals included in the present study were managed in compliance with the ethical guidelines and regulations for animal experimentation of División Académica de Ciencias Agropecuarias at Universidad Juárez Autónoma de Tabasco (approval code: UJAT-DACA-2015-IA-02).The animals were raised at the Sheep Integration Center of the Southeastern (Centro de Integración Ovina del Sureste; 17° 78" N, 92° 96" W; 10m asl), located on the Villahermosa-Teapa road, Mexico.
Live weight, HG and BL data were obtained from 290 clinically healthy hair lambs (Pelibuey and its crosses with Blackbelly and Katahdin) aged between two and 10 months.Live weight was recorded by weighing the animals on a fixed platform scale with a capacity of 300 kg and precision of 10 g, whereas HG and BL were recorded using a flexible fiberglass tape measure (Truper ® ), considering the anatomical references described by Bautista-Díaz et al. (2020).
Body volume was estimated using the formula to calculate the volume of a cylinder, by including the measurements of HG and BL in its composition.
For the statistical analysis and internal validation of the model, the data were read in the Python environment as follows: descriptive statistics were obtained using the description function of the "pandas" package (Mckinney, 2010).The ratio between BV and LW was determined by linear (Eq.1), quadratic (Eq.2) and allometric (Eq. 3) equations using the "lmfit" package (Newville et al., 2014).The following allometric equation was fitted: Y = aX ** b, where Y represents LW, X represents BV and a and b are parameters of the model.The models and their residuals were plotted with the "matplotlib" package (Hunter, 2007).The goodness-of-fit of the regression models was evaluated using the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), the coefficient of determination (R 2 ), the mean square error (MSE) and the root MSE (RMSE).The last three parameters were obtained using the "scikit-learn" package (Pedregosa et al., 2011).
The predictive capacity of the three models for LW was evaluated by cross-validating k-folds (k = 10).This approach was undertaken by randomly dividing the set of observation values into non-overlapping k-folds of approximately the same size.The first fold is treated as a validation set, and the model fits the remaining k-1 folds (training data).The ability of the fitted model to predict the actual observed values was evaluated using MSE, R 2 , and the mean absolute error (MAE).The mean absolute error is an alternative to the mean squared prediction error that is less sensitive to outliers and is related to the mean absolute difference between observed and predicted results.Lower values of root MSPE and MAE indicate a better fit.The kfolds cross-validation was performed using the "scikit-learn" package (Pedregosa et al., 2011), which allowed a comparison of numerous multivariate calibration models.The correlations indicated a positive and significant association (P<0.001) between LW and the biometric measurements (r=0.95 for HG and r=0.85 for BL).Likewise, LW showed a positive and significant correlation (P<0.001) with BV (r=0.96).Several studies with cattle (Paputugan et al., 2015, 2018), sheep (Taye et al., 2011;Iqbal et al., 2014;Chay-Canul et al., 2019;Worku, 2019) and goats (Adhianto et al., 2020;Dakhlan et al., 2021;Peña-Avelino et al., 2021;Ouchene-Khelifi and Ouchene, 2021) identified a high correlation between live weight and heart girth.In adult sheep, Kumar et al. (2018) found a genetic correlation of 0.51±0.13 between LW and HG, as well as a heritability of 0.61±0.16,confirming that LW can be estimated under field conditions using HG as a predictor.On the other hand, Paputugan et al. (2015) reported a correlation of r=0.72 between LW and BV in Ongole crossbred cows.This group of researchers also found a correlation of r≥0.90 between BV and HG in local Bali cattle of different ages.

RESULTS AND DISCUSSION
Three models were fitted to explore the relationship between LW and BV in growing lambs, as follows: 1) linear (Eq.1), 2) quadratic (Eq.2) and 3) allometric (Eq. 3) (Table 2; Figure 1).Salazar-Cuytun et al. (2021) found a correlation coefficient (r) of 0.89 between LW and BV (P <0.001) in Pelibuey lambs and sheep.Likewise, these authors reported that these variables better fitted a quadratic model, which showed the highest coefficient of determination (R 2 =0.81) and the lowest values of MSE (4.17), RMSE (2.04), AIC (1163.64)and BIC (1175.66).These results agree with those obtained in the present study, since although the three developed models showed a similar coefficient of determination (r 2 =0.93), the quadratic model exhibited lower values of MSE (9.74), RMSE (3.12), AIC (663.27) and BIC (674.28).Moreover, during the k-fold cross-validation Arq.Bras.Med.Vet.Zootec., v.74, n.3, p.483-489, 2022 process (k = 10), the quadratic model had the highest r 2 (0.92) and the lowest RMSPE (3.11) and AME (2.33) (Table 3).Therefore, the quadratic model was the mathematical model with the best performance according to the evaluation of goodness-of-fit to predict the LW of growing hair lambs using BV calculated from HG and BL data.Although the results agree with those reported by Salazar-Cuytun et al. (2021), it should be noted that their models were developed in Pelibuey lambs and sheep.In this respect, it has been established that body conformation and body fat deposition may differ between animals of different sexes and breedsaspects that may interfere with the correlation between some biometric measurements and LW in sheep (Wamatu and Alkhtib, 2021;Salazar-Cuytin et al., 2021).For this reason, models must be developed for animals of different physiological conditions and sexes, in different management scenarios, to improve decisionmaking and the economic benefits provided by determining and monitoring the LW of domestic animals (Sherwin et al., 2021;Málková et al., 2021;Salazar-Cuytun et al., 2021).could be predicted with high precision from BV with a coefficient of determination of r 2 = 0.92, which is higher than that obtained in the model in which only HG was used (r 2 = 0.90).The foregoing shows that the animals' LW could be predicted with greater precision from the BV formula that comprises HG and BL instead of a single biometric measurement.et al., 2017, 2020;Canul -Solís et al., 2020;Sabbioni et al., 2020).Some authors evaluated the use of biometric measurements as an alternative, practical and low-cost method that allows small producers to estimate the body weight of Pelibuey sheep in farming conditions.This approach consists of the development of mathematical equations from some biometric measurements that are taken directly on the animal (Chay-Canul et al., 2019;Canul-Solís et al., 2020).Multiple studies have reported variations in the ability of producers and veterinarians to accurately estimate the live weight of cattle visually, and most people underestimate the live weight of animals, which could lead to an increased risk of development of antibiotic and anthelmintic resistance (Málková et al., 2021;Sherwin et al., 2021;Salazar-Cuytun et al., 2021).

Figure 1 .
Figure 1.Relationship between live weight and body volume in growing Pelibuey lambs.

Table 1 .
Descriptive statistics of LW and biometric measurements recorded in growing hair lambs

Table 2 .
Live weight prediction equations using body volume in growing hair lambs MSE; BIC: Bayesian Information Criterion.Values in parentheses are the standard errors (SE) of the parameter estimates.The * indicates: *: P<0.05; **: P<0.01; ***: P<0.001On the other hand, Paputungan et al. (

Table 3 .
(Sabbioni et al., 2020)validation of the proposed modelsIn terms of management, determining LW is important in the design of animal nutrition and health programs(Sabbioni et al., 2020).In the specific case of sheep meat breeds, live weight is essential to choose the ideal time for slaughter and the optimal carcass endpoint (Bautista-Díaz