Development and evaluations of equations to predict empty body weight in pre-weaned hair sheep lambs

[Desenvolvimento e avaliação de equações para predizer o peso do corpo vazio em cordeiros deslanados na fase de cria]

ABSTRACT

This research aimed to assess the relationships among shrunk body weight (SBW) and empty body weight (EBW) to develop equations to estimate EBW in 121 pre-weaned hair sheep lambs from different genotypes (Pelibuey, n=39; Katahdin, n=27 and crossbred Pelibuey × Black Belly, n=55), sex (non-castrated male, n=65 and female, n=56) and litter size (single, n=42 and double, n=79). Linear model with intercept, Linear model without intercept and exponential regression models were used for data analysis. The correlation coefficients among SBW and EBW was high (r = 0.89). The regression equations had high determination coefficients (r²) of 0.97. The final model fitted to estimate the EBW as a function of SBW was: EBW (kg) = 0.0065 (±0.14*) + 0.88 (±0.0124***) ×SBW, since it presented better fit values and was statistically significant (P<0.001). The equation developed and evaluated in the present study revealed that the linear relationship between SBW and EBW can be used to predict EBW in pre-weaned hair sheep lambs.

Keywords:
body weight estimation hair sheep; sheep requirements; mathematical models; nutritional requirements

RESUMO

Esta pesquisa teve como objetivo avaliar as relações entre o peso corporal (PC) e o peso do corpo vazio (PCVZ) para desenvolver equações de estimativa do PCVZ em 121 cordeiros deslanados na fase de cria de diferentes genótipos (Pelibuey, n=39; Katahdin, n=27 e cruzados Pelibuey × Black Belly, n=55), sexo (macho não castrado, n=65 e fêmea, n=56) e tipo de parto (simples, n=42 ou duplo, n=79). Modelos de regressão linear com intercepto, regressão linear sem intercepto e exponencial foram usados para a análise dos dados. Os coeficientes de correlação entre PC e PCVZ foram elevados (r = 0,89). As equações de regressão apresentaram elevados coeficientes de determinação (r²) de 0,97. O modelo final desenvolvido para estimar o PCVZ como função do PC foi o seguinte: PCV (kg) = 0,0065 (±0,14*) + 0,88 (±0,0124***) × PCVZ, pois apresentou melhores valores de ajuste e foi estatisticamente significativo (P<0,001). A equação desenvolvida e avaliada no presente estudo revelou que a relação linear entre PC e PCVZ pode ser usada para predizer o PCVZ em cordeiros deslanados na fase de cria.

Palavras-chave:
estimativa de peso corporal vazio em ovinos deslanados; requerimentos nutricionais de ovinos; modelos matemáticos; necessidades nutricionais

INTRODUCTION

The research on hair sheep or tropical sheep breeds has not been a focus of the scientific community as it has sheep in temperate zones (Chay-Canul et al., 2014, 2016). For this reason, the nutritional needs for energy and protein and weighing adjustments have not been determined targeting this animal category, inferences regarding your dietary requirements for protein, calories, and weighing adjustments may be incorrect as a result (Herbster et al., 2020; Salazar-Cuytun et al., 2022; Vazquez-Jimenez et al., 2024).

Recently, some authors have stated that body weight (BW) adjustments are an indispensable tool for estimating animal performance in feeding trials, nutrient requirement studies and production systems (Herbster et al., 2020; Salazar-Cuytun et al., 2022). In this sense, it has been established that the first step in determining the nutritional requirements of ruminants is the conversion of BW to empty BW (EBW); however, the EBW is the equivalent of BW minus the weight of the gastrointestinal tract (GIT) content, and for this it is necessary to sacrifice the animals, weigh and wash the GIT of the animals (Chay-Canul et al., 2016; Herbster et al., 2020; Salazar-Cuytun et al., 2022). Thus, the determination of the EBW is complicated and tedious, and some regression equations have been developed to estimate the EBW from the BW of animals close to slaughter (Salazar-Cuytun et al., 2022).

In addition, it has been reported that the relationship between EBW and BW can be influenced by several factors, including the effects of dietary fibre content, level of concentrate, physiological status, level of production and maturity (Chay-Canul et al., 2014, 2016; Campos et al., 2017; Herbster et al., 2020). For the specific case of lactating lambs, there is little information on the predictive equations for estimating EBW (Chay-Canul et al., 2014, Campos et al., 2017; Salazar-Cuytun et al., 2022).

In the case of hair sheep, prediction equations for estimating EBW are scarce in the literature (Campos et al., 2017; Herbster et al., 2020; Salazar-Cuytun et al., 2022). It is necessary to continue with experiments in which the EBW can be determined and, with these data, to construct predictive equations that allow predicting the EBW of hair sheep in different physiological states in the tropics (Chay-Canul et al., 2014; Salazar-Cuytun et al., 2022; Vazquez-Jimenez et al., 2024). Therefore, the objective of the present research was to evaluate the relationships between shrunk body weight (SBW) and EBW to develop and to identify the best linear or nonlinear prediction model for EBW in pre-weaned hair sheep lambs regardless of genotypes (Pelibuey, Katahdin and crossbred Pelibuey × Black Belly), sex (non-castrated male and female) and litter size (single or double).

MATERIALS AND METHODS

Animals were managed in compliance with the guidelines and regulations for ethical animal experimentation of the División Académica de Ciencias Agropecuarias of the Universidad Juárez Autónoma de Tabasco (ID project PFI: UJAT-DACA-2015-IA-02). The experiment was carried out at the Southeastern Center for Ovine Integration (Centro de Integración Ovina del Sureste [CIOS]; 17° 78" N, 92° 96" W; 10 masl) located at 25+3km of the Villahermosa-Teapa road in the town of Alvarado Santa Irene, 2nd Section, Tabasco, Mexico.

The experiment used 121 growing hair sheep lambs (Pelibuey, n=39; Katahdin, n=27 and crossbred Pelibuey × Black Belly, n=55), sex (non-castrated male, n=65 and female, n=56) and litter size (single, n=42 or and double, n=79). aged 56 days and BW ranging from 6.08 to 16.85kg.

Each ewe and their offspring were housed in individual pens (2 × 3 m) equipped with a raised-slatted floor cage system. The feed and water availability was ad libitum for ewe without access for their offspring. Additionally, ewes were dewormed with Cydectin NF® (Pfizer, Brazil) at a dosage of 0.2mg/kg of body weight. The diet supplied was formulated with star grass hay (Cynodon nlemfuemsis), ground corn, soybean meal, sugarcane molasses and minerals, with an estimated metabolizable energy of 12 MJ/kg dry matter and 15 % crude protein (Energy, 1993).

Before slaughter, SBW was recorded after feed and water were withdrawn for 24 h. Animals were slaughtered humanely following the Mexican Official Norms (NOM-08-ZOO, NOM-09-ZOO, and NOM-033-ZOO) established for slaughter and processing of meat animals. The gastrointestinal tract (GIT) content was recorded as the difference in weight of the GIT before and after emptying and flushing with running water. The EBW was computed as the difference between SBW at slaughter and contents of the GIT. The data recorded at slaughter included the weight of internal organs and that of the carcass (HCW). The carcass was then chilled at 6°C for 24 h, after which the CCW was recorded.

For the statistical analysis and the internal model validation of the research, initially descriptive statistics were obtained, and the normality assumptions were verified for the study variables. Subsequently, the relationship between EBW and SBW was studied using an analysis of (co)variance, fitting a linear model that included the fixed effects of genetic group (GG), sex (S), and litter size (LS), as well as the interactions between SBW and the fixed effects, in order to test the null hypothesis of equality of SBW slopes $\left({\beta }_{1}SBW\right)$ within each categorical variable.

The linear model expression used was:

$EB{W}_{ijkl}=\mu +G{G}_i+L{S}_j+S{x}_k+{\beta }_{1}SB{W}_l+\left({\beta }_{1}SB{W}_l*G{G}_i\right)+\left({\beta }_{1}SB{W}_l*T{P}_j\right)+\left({\beta }_{1}SB{W}_l*S{x}_k\right)+{\epsilon }_{ijkl}$

Where: $EB{W}_{ijkl}=emptybodyweight$ $\mu$= overall mean; $G{G}_i$= Fixed effect of i-th genetic group (1=Pelibuey, 2=Katahdin, and 3=crossbred Pelibuey × Black Belly); $G{G}_i$= Fixed effect of j-th litter size (1=Single, 2=Twins); $S{x}_k$= Fixed effect of k-th sex of lamb (1=machos, 2= hembras); ${\beta }_{1}SB{W}_l$= shrunk body weight regression (Covariate); $\left({\beta }_{1}SB{W}_l*G{G}_i\right)=$ Interaction or change in the slope of SBW due to GG; $\left({\beta }_{1}SB{W}_l*L{S}_j\right)=$ Interaction or change in the slope of SBW due to LS; $\left({\beta }_{1}SB{W}_l*S{x}_k\right)=$Interaction or change in the slope of SBW due to Sx;${\epsilon }_{ijkl}$= random residual effect.

The analyses of the linear model were performed using the PROC GLM procedure of the SAS statistical package, version 9.3.

However, no significant effects (P>0.05) of the fixed effects and interactions were found on the prediction of EBW. Only the covariate SBW was significant (P<0.001). Therefore, based on the results obtained, it was determined to continue with the evaluation of single linear or nonlinear equations for all hair lambs in the study, regardless of genetic group, litter size, and sex.

Subsequently, regression analyzes were performed to identify the best linear or nonlinear prediction model for EBW. According to recommendations carried out by Barcelos et al. (2020) three models to estimate EBW as a function of SBW were tested:

$EB{W}_{}={\beta }_0+{\beta }_{1}xSB{W}_{}+{\epsilon }_{}$ (Eq. 1)

$EB{W}_{}={\beta }_{1}xSB{W}_{}+{\epsilon }_{}$ (Eq. 2)

$EB{W}_{}={\beta }_{0}xSB{W}^{{\beta }_1}+{\epsilon }_{}$ (Eq. 3)

Where: $EB{W}_k=$ Empty body weight for i-th lamb; ${\beta }_0$ = Intercept and ${\beta }_1$= Slop are regression coefficients to be estimated; SBW= shrunk body weight; ${\epsilon }_{}$= random error.

The analyses of lineal models and the fit of lineal regression equations 1 and 2 were performed, using PROC GLM and in the case of Eq. 3, the fit of no lineal regression equation was performed using PROC NLIN of the SAS statistical package, ver. 9.3.

Outliers were tested, evaluating the studentized residuals in relation to the values predicted by the equations. The goodness-of-fit of the regression models was evaluated using the MSE, RMSE, R², Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC).

The predictive ability of the three models for EBW prediction was evaluated using k-folds validation (k = 10). This approach was performed by randomly dividing the set of observation values into k non-overlapping folds of approximately equal size. The first fold is treated as a validation set, and the model is fit to the remanding k - 1 folds (training data). The ability of the fitted model to predict the actual observed values was evaluated by the MSE, R² and mean absolute error (MAE). MAE is an alternative to the root mean square error of prediction (RMSEP) that is less sensitive to outliers, and it is related to the average absolute difference between observed and predicted outcomes. Lower values of RMSEP and MAE indicate a better fit. The k-folds validation was carried out in the “scikit-learn” package, which allowed for the comparison of numerous multivariate calibration models.

RESULTS

Mean (± SD), minimum and maximum weights of animals are shown in Table 1. The SBW ranged from 6.08 to 16.85 kg, while the EBW ranged from 5.18 to 14.38 kg. The results indicated that SBW had a highly significant positive correlation (P<0.01) with EBW (r=0.98).

The regression equations describing the estimation of EBW according to the three models are presented in Table 2 and the data are plotted in Figure 1. Regression equations 1 and 3 had the same coefficient of determination (r²) of 0.97 (Table 2, Figure 1), while equation 2 had the highest r² of 0.99. However, according to the AIC and BIC values, the equations 1 and 3 described the better relationship between SBW and EBW than the linear models without intercepts.

Although cross validation showed that all equations had a similar r² (0.97), the RMSEP and MAE were slightly lower for Eq. 1 than for Eq. 3 (Table 3). Nevertheless, the cross-validation showed that Eq. 1 tended to be slightly more accurate (lower RMSEP and MAE) than Eq. 3. Therefore, the following final model was fitted to estimate EBW as a function of SBW in lambs of different genotypes: EBW (kg) = 0.0065 (±0.14*) + 0.88 (±0.0124***) × SBW.

Table 1
Mean, minimum and maximum values of SBW and EBW in hair suckling lambs

Variable	N	Mean	Minimum	Maximum	SD
Pelibuey
SBW	39	10.54	6.06	16.85	2.51
EBW	39	9.45	5.18	14.88	2.30
Katahdin
SBW	27	11.11	6.22	15.15	2.68
EBW	27	9.91	5.51	13.37	2.40
Crossbreed
SBW	55	11.36	7.20	16.80	2.20
EBW	55	9.98	6.95	14.75	1.97
All
SBW	121	11.04	6.08	16.85	2.42
EBW	121	9.79	5.18	14.38	2.17

• ^S
  ^{BW: shrunk BW; EBW: empty BW; SD: Standard Deviation.}

Table 2
Prediction equations of EBW in hair suckling lambs, regardless of genetic group, litter size, and sex

Eq	Equations	MSE	RMSE	AIC	BIC	R2	P-value
1	EBW (kg)= 0.0065 (±0.14*) + 0.88 (±0.0124***)×SBW	0.107	0.33	-264.52	-258.75	0.97	P<0.001
2	EBW (kg)= 0.88 (± 0.003***)×SBW	0.106	0.33	-266.52	-263.73	0.99	P<0.001
3	EBW (kg)= 0.89±0.03*×SBW0.99± (0.01***)	0.107	0.33	-264.52	-258.96	0.97	P<0.001

• EBW: empty body weight; SBW: shrunk body weight; MSE= mean square error; RMSE = Root of MSE AIC: Akaike information criterion; BIC: Bayesian information criterion. Values in parentheses are the standard errors (SEs) of the parameter estimates. The * denotes: *: P < 0.05; **: P < 0.01; ***:P < 0.001.

Table 3
Internal k-fold cross-validation of the proposed models.

Eq	R2	MPE	RMSEP	MAE
1	0.97	0.316	0.562	0.246
2	0.97	0.326	0.570	0.255
3	0.97	0.321	0.566	0.249

• MPE: mean prediction error; RMSEP: root mean prediction error; R²: coefficient of determination; MAE: mean absolute error.

Figure 1
Linear and nonlinear relationship between empty body weight (EBW) a shrunk body weight (SBW) in hair suckling lambs, regardless of genetic group, litter size, and sex.

DISCUSSION

The EBW is calculated from the SBW, this relationship explains the high correlation between these variables. The use of a model that indicates EBW only from the SBW facilitates the extraction of zootechnical information from the herd, reducing the need to weigh the contents of the gastrointestinal tract (GIT), an action that is not routine in slaughterhouses. Chay-Canul et al. (2014) observed the same correlation when evaluating Pelibuey ewes. The proportion of GIT participation in the final weight of the animal varies according to the breed (Regadas Filho et al., 2103) but does not vary in relation to the physiological state of the animal (Chay-Canul et al., 2014), making it possible to use this model in pregnant or lactating animals. Barcelos et al. (2020) fitted the following final model to estimate SBW as a function of BW: SBW = 0.938× BW. They reported that the best relationship between SBW and BW was a linear model with no intercept. They showed that SBW accounted for 93.82% of BW, corresponding to a fitted relationship of 6.18% of fasting losses. In this study, based on regression tools and the cross-validation technique, we found that the linear model with intercept provided the best equation to describe the relationship between SBW and BW, accounting for approximately 12% of fasting losses.

Also, Salazar-Cuytun et al. (2022) found that the weight of the gastrointestinal content was equivalent to 5% of the animals' SBW in hair sheep reared in feedlot systems, demonstrating that the level of concentrates in the diet has a significant effect on the filling of the gastrointestinal tract. Recently, Vazquez-Jimenez et al. (2024) concluded that the linear relationship between BW and SBW and the linear and exponential relationships between SBW and EBW can be used to adjust body weight in growing Black Belly ewe lambs, with the weight of the gastrointestinal content being equivalent to 16% of the animals' SBW. These authors also noted that this confirmed that SBW could be calculated using an adjustment factor of 0.96 to full BW.

The choice of the ideal mathematical model should be based on the results of the indicators and not just on a single criterion. The first factor to be considered is the significance of the model and each parameter, this information is decisive for the applicability of the model. The use of models with non-significant parameters (p>0.05) leads to erroneous and inaccurate data. The ability of the predictor variable, in this case SBW, to explain the predicted data, in this case EBW, is elucidated from the coefficient of determination (R²), MSE= mean square error; RMSE = Root of MSE AIC: Akaike information criterion; BIC: Bayesian information criterion. The R² indicates the percentage of variation of the predicted by the predictor (Gurgel et al., 2023) in this case of the EBW that can be explained by the SBW, the higher the R² value, the greater the degree of accuracy of the model. Other parameters help you choose the most accurate model. The results of MSE, RMSE, AIC, BIC and the cross-validation values that present lower indices indicate the best models (Tedeschi, 2006).

Although equation 2 presents higher R², higher AIC and higher MPE, RMSEP and MAE from cross-validation. Eq 1 and Eq 3 presented the same MSE, RMSE, AIC and R², but the cross-validation data showed lower values of MPE, RMSEP and MAE for equation 1 chosen as the most accurate and precise to predict EBW values. EBW (kg) = 0.0065 (±0.14*) + 0.88 (±0.0124***) ×SBW. According to the chosen model, each kilogram of SBW is added 0.0065 kg, however the SBW is multiplied by 0.88, where each kilogram of SBW to EBW suffers a reduction of 0.12 grams, due to the participation of the GIT in the SBW.

CONCLUSION

The present study indicates that the weight of gastrointestinal contents was approximately 12% of the SBW in pre-weaned hair sheep lambs reared under tropical conditions. The equation developed and evaluated in the present study showed that the linear relationship between SBW and EBW can be used to predict EBW in pre-weaned hair sheep lambs.

REFERENCES

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Publication Dates

• Publication in this collection
  28 Apr 2025
• Date of issue
  May-Jun 2025

History

• Received
  31 Oct 2023
• Accepted
  11 Sept 2024