Buffalo dairy products have a high nutritional value, beneficial to the health of consumers (Napolitano et al., Reference Napolitano, Guerrero-Legarreta, López, Gómez, Flores, Bertoni, Braghieri, Alvarez Macias, De Rosa, Mota-Rojas and Serrapica2021). Although buffalo milk and its derivatives are nutrient-rich they are influenced by various factors such as the feeding regime, the health of the aniamls, environmental conditions and, in general, by the production system (Sabia et al., Reference Sabia, Gauly, Napolitano, Cifuni and Claps2020). Seeking to maximize buffalo performance and the efficiency of the production system, it is essential to identify and explore the productive parameters of the different categories of animals on the property (Hernández-Herrera et al., Reference Hernández-Herrera, Lara-Rodríguez, Vázquez-Luna, Acar-Martínez, Fernández-Figueroa and Velásquez-Silvestre2018). In this context, exploring the weight gain capacity of growing dairy buffaloes is fundamental as it determines the evolution of the herd and its future reproductive and dairy performance and helps to establish optimal health and nutritional management, as well as assisting in the planning of housing and other facilites as buffalo farmoing transitions from traditional pracices to modern management, with consequential reduction in the final production cost (Kocaman et al., Reference Kocaman, Gurcan, Kurc and Soysal2017; Aquino et al., Reference Aquino, Palacpac, Molina, Lacanilao, Garcia, Del Barrio and Fujihara2024). Measurement of body weight requires relatively expensive equipment, so the use of easily-measured body characteristics as a proxy for body weight is an attractive option. Previously, we showed that the quadratic and allometric models are good predictors of body weight of lactating Murrah buffalo from body volume (Ramos-Zapata et al., Reference Ramos-Zapata, Dominguez-Madrigal, García-Herrera, Camacho-Perez, Lugo-Quintal, Tyasi, Gurgel, Ítavo and Chay-Canul2023; Cruz-Tamayo et al., Reference Cruz-Tamayo, Ramírez-Bautista, Mota-Rojas, Escobar-España, García-Herrera, Gurgel, Dias-Silva, Araújo, Santana, Aguiar, Ítavo and Chay-Canul2024). Currently, we hypothesize that body volume can also be used in growing animals, i.e. animals for herd replacement. Thus, our objective was to use the body volume to predict the body weight of growing dairy buffaloes.
Material and methods
The animals included in the present study were treated in accordance with the ethical guidelines and regulations for animal experimentation of the Division of Agricultural Sciences of the University of Juárez Autónoma de Tabasco (approval code: UJAT-2012-IA-18). The experiment was conducted in a commercial farm “Tres Bocas” in the municipality of Francisco Rueda(17°50′N 93°57′W), Tabasco State, México. The region has an average annual temperature of 25°C and rainfall of 2750 mm, with hot and humid summers. Data for body weight (BW, kg), heart girth (HG, cm) and body length (BL, cm) were collected from 160 replacement female dairy Murrah buffaloes aged between 8 months and 4 years. Water was available ad libitum and buffaloes had access to natural pasture. BW was recorded by weighing the animals on a fixed platform scale with a capacity of 2000 kg and an accuracy of 0.5 kg, while HG and BL were recorded using a flexible fibreglass tape measure (Truper®), as previously described by Ramos-Zapata et al. (Reference Ramos-Zapata, Dominguez-Madrigal, García-Herrera, Camacho-Perez, Lugo-Quintal, Tyasi, Gurgel, Ítavo and Chay-Canul2023). The body volume (BV, dm3) was estimated using the formula for calculating the volume of a cylinder according Paputungan et al. (Reference Paputungan, Hakim, Ciptadi and Lapian2015).
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, Reference Mckinney2010). Pearson's correlation coefficients between variables were estimated using PROC CORR using the SAS 9.4 statistical program (SAS Inst. Inc., Cary, NC). The ratio between BV and BW was determined by linear (Eq. 1), quadratic (Eq. 2) and allometric (Eq. 3) equations using the “lmfit” package (Newville et al., Reference Newville, Stensitzki, Allen and Ingargiola2014). The following allometric equation was fitted: Y = aX ** b, where Y represents BW, X represents BV and a and b are parameters of the model. The models and their residuals were plotted with the “matplotlib” package (Hunter, Reference Hunter2007). 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 (R2), the mean square error (MSE) and the root MSE (RMSE). The last three parameters were obtained using the “scikit-learn” package (Pedregosa et al., Reference Pedregosa, Varoquaux, Gramfort and Thirion2011). The accuracy of the regression models was evaluated by the coefficient of determination (R2), root mean square error (RMSE) and Akaike's information criteria (AIC) as explained by Eyduran et al. (Reference Eyduran, Akin and Eyduran2019) using the following equations:
1. Coefficient of Determination
2. Root-mean-square error (RMSE) given by the following formula:
3. Akaike Information Criteria (AIC):
Bayesian information criteria (BIC) and coefficient of variation (CV) were also calculated. The predictive capacity of the three models for BW was evaluated by cross-validating k-folds (k = 4). 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, R2, and the mean absolute error (MAE). The mean absolute error is an alternative to the mean squared prediction error (MSPE) 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 k-folds cross-validation was performed using the “scikit-learn” package (Pedregosa et al., Reference Pedregosa, Varoquaux, Gramfort and Thirion2011), which allowed a comparison of numerous multivariate calibration models.
Results
The growing dairy buffaloes had a mean BW of 256.6 ± 96.82 kg and a BV of 155.3 ± 74.87 dm3 (Table 1) with considerable variation between individuals. There were high and positive correlation among all variables studied (Table 2). In particular, BW presented a positive correlation with heart girth (r = 0.96), body length (r = 0.89) and body volume (r = 0.94).
Descriptive analysis of the body weight and body volume in growing dairy buffaloes reared in Mexican humid tropical conditions (n = 160)
SD – standard deviation; SEM – standard error of mean.
Pearson correlation coefficients among body weight, heart girth, body length, and body volume of growing dairy buffaloes
* P < 0.001.
All parameters (R2, MSE, RMSE, AIC and BIC) used to evaluate the regression equations showed that the quadratic regression model was more effective than the linear and allometric models for estimating BW using BV. When comparing the linear and exponential models, we verified that the BW prediction was better explained by the exponential model (Table 3). The behavior of weight and BV data allowed us to verify the relationship between observed and predicted values in the different models used (Fig. 1). The criteria for evaluating and validating models (R2, MSPE and MAE) using the k-folds technique (cross validation: Table 4), allows us to state that the quadratic model presented a better predictive performance than either the linear or exponential models due to better fit scores. Also, it allowed us to show that the exponential model presented a better fit than the linear model, considering internal validation.
Body weight (BW) prediction equations using the body volume formula (BV) in lactating buffaloes raised in tropical humid conditions (n = 160).
Regression equations to estimate body weight (kg) in growing dairy buffaloes reared in Mexican humid tropical conditions
* BW: body weight; BV: body volume; R2: determination coefficient; MSE: mean square error; RMSE: Root MSE; AIC: Akaike Information Criterion; BIC: Bayesian Information Criterion. Values in parentheses are the parameter estimates’ standard errors (SE). The indicates: *: P < 0.05; **: P < 0.01; ***: P < 0.001
Internal k-folds cross-validation of the proposed models
MSPE: mean squared prediction error; R2: coefficient of determination; MAE: mean absolute error.
Discussion
The correlation analysis indicates that body volume (BV) can predict the body weight (BW) of growing buffaloes. This raises the possibility of body measurements being used to predict nutritional maintenance requirements, thereby assisting in nutritional management for better productive performance (Chay-Canul et al., Reference Chay-Canul, García-Herrera, Salazar-Cuytun, Ojeda-Robertos, Cruz-Hernández, Fonseca and Canul-Solís2019). The quadratic regression model best predicted BW. Parameters such as withers height, rump height, body height, heart girth (HG), abdominal girth, pelvic girth and body length (BL) can be inserted in models, giving more robustness for estimating BW of mature female Murrah buffaloes (Ruiz-Ramos et al., Reference Ruiz-Ramos, Torres-Chable, Peralta-Torres, Ojeda-Robertos, Luna-Palomera, Portillo-Salgado, Tyasi, Gurgel, Ítavo and Chay-Canul2023), but we have not done that in this study. BV estimated from HG and BL has now been shown effective for growing animals, in the same way as we showed previously for mature lactating females (Ramos-Zapata et al., Reference Ramos-Zapata, Dominguez-Madrigal, García-Herrera, Camacho-Perez, Lugo-Quintal, Tyasi, Gurgel, Ítavo and Chay-Canul2023). However, in this case we have achieved a better adjustment of the data via quadratic regression. Analyzing the cross-validation criteria of the models (R2, MSPE and MAE), which guarantee the accuracy of the regression models, allowed us to reaffirm that the use of quadratic regression better fitted the BW and BV data, as described by Paputungan et al. (Reference Paputungan, Hendrik and Utiah2018) and Ramos-Zapata et al. (Reference Ramos-Zapata, Dominguez-Madrigal, García-Herrera, Camacho-Perez, Lugo-Quintal, Tyasi, Gurgel, Ítavo and Chay-Canul2023).
It is important to highlight that body characteristics such as those used here can be measured without the need for any expensive technology or equipment and can, therefore, be applied globally and in the most diverse animal production systems. The development of mathematical equations that predict BW could become an essential tool to assist in the decision-making of producers.
In conclusion, body weight of growing dairy buffaloes can be estimated from simply obtained measures of body characteristics. Body weight was best predicted by quadratic regression using body volume as the prediction variable.
Acknowledgements
We thank Carlos Mario Zurita Rueda who generously allowed us to sample their animals and use their facilities.
