Description of the data set

The data set used to generate the models was composed of individual measurements from 569 sheep derived from sixteen studies (Pereira, Reference Pereira2011; Costa et al., Reference Costa, Pereira, Silva, Paulino, Mizubuti, Pimentel, Pinto and Rocha Junior2013; Oliveira et al., Reference Oliveira, Pereira, Pinto, Silva, Carneiro, Mizubuti, Ribeiro, Campos and Gadelha2014; Pereira et al., Reference Pereira, Fontenele, Silva, Oliveira, Ferreira, Mizubuti, Carneiro and Campos2014, Reference Pereira, Lima, Marcondes, Rodrigues, Campos, Silva, Bezerra, Pereira and Oliveira2017, Reference Pereira, Pereira, Marcondes, Medeiros, Oliveira, Silva, Mizubuti, Campos, Heinzen, Veras, Bezerra and Araújo2018a, Reference Pereira, Oliveira, Santos, Carvalho, Araújo, Sousa, Homem Neto and Cartaxo2018b; Rodrigues et al., Reference Rodrigues, Chizzotti, Martins, Silva, Queiroz, Silva, Busato and Silva2016; Gois et al., Reference Gois, Santos, Sousa, Ramos, Azevedo, Oliveira, Pereira and Perazzo2017; Brito Neto, Reference Brito Neto2020; Mendes et al., Reference Mendes, Souza, Herbster, Brito Neto, Silva, Rodrigues, Marcondes, Oliveira, Bezerra and Pereira2021; Silva et al., Reference Silva, Oliveira, Santos, Ramos, Cartaxo, Givisiez, Souza, Cruz, Cézar Neto, Alves, Ferreira, Lima and Zanine2021; Rocha, Reference Rocha2022; A. C. Rocha, unpublished data; A. S. Brito Neto, unpublished data; C. J. L. Herbster, unpublished data) with records of three sex classes: intact males (n = 416), castrated males (n = 51) and females (n = 102). The most representative hair sheep genotypes in the data set were: Santa Ines (n = 192); Morada Nova (n = 121), Brazilian Somali (n = 47), ½ Dorper × ½ Santa Ines (n = 63) and crossbred (n = 146). Within this data set, 429 records were originated from comparative slaughter (Pereira, Reference Pereira2011; Costa et al., Reference Costa, Pereira, Silva, Paulino, Mizubuti, Pimentel, Pinto and Rocha Junior2013; Oliveira et al., Reference Oliveira, Pereira, Pinto, Silva, Carneiro, Mizubuti, Ribeiro, Campos and Gadelha2014; Pereira et al., Reference Pereira, Fontenele, Silva, Oliveira, Ferreira, Mizubuti, Carneiro and Campos2014, Reference Pereira, Lima, Marcondes, Rodrigues, Campos, Silva, Bezerra, Pereira and Oliveira2017, Reference Pereira, Pereira, Marcondes, Medeiros, Oliveira, Silva, Mizubuti, Campos, Heinzen, Veras, Bezerra and Araújo2018a; Rodrigues et al., Reference Rodrigues, Chizzotti, Martins, Silva, Queiroz, Silva, Busato and Silva2016; Mendes et al., Reference Mendes, Souza, Herbster, Brito Neto, Silva, Rodrigues, Marcondes, Oliveira, Bezerra and Pereira2021; A. C. Rocha (unpublished data); A. S. Brito Neto (unpublished data); C. J. L. Herbster (unpublished data)). In these studies, 77 animals were slaughtered initially and named as reference or baseline group; 114 animals were fed at maintenance level, and 238 fed above maintenance. The remaining records (n = 140) were originated from feeding trials (Gois et al., Reference Gois, Santos, Sousa, Ramos, Azevedo, Oliveira, Pereira and Perazzo2017; Pereira et al., Reference Pereira, Oliveira, Santos, Carvalho, Araújo, Sousa, Homem Neto and Cartaxo2018b; Brito Neto, Reference Brito Neto2020; Silva et al., Reference Silva, Oliveira, Santos, Ramos, Cartaxo, Givisiez, Souza, Cruz, Cézar Neto, Alves, Ferreira, Lima and Zanine2021; Rocha, Reference Rocha2022), studies which did not use the comparative slaughter methodology, with animals fed above maintenance. Information on level of feeding for each study is described in the supplementary material (Table S1). The quantitative information body weight (BW), fasting body weight (FBW), CW, EBW, and RE were utilized to generate the models (Table 1).

Table 1. Descriptive statistics of the variables used to generate the prediction models

CW, carcass weight; CG, carcass gain; FBW, fasting body weight; EBW, empty body weight; EBWG, empty body weight gain; RE, retained energy; SD, standard deviation.

Slaughter procedures and chemical analyses

Slaughter procedures were similar in all studies. In summary, FBW was obtained before slaughter, after 18 h without feed and water. Slaughter was carried out by stunning with a captive bolt pistol, causing a cerebral concussion and severing of the jugular vein until the animals completely bled, followed by skinning and evisceration. The blood, internal organs, visceral fat, head, hooves, and skin were weighed, collected, and frozen. The gastrointestinal tract (GIT), bladder, and gallbladder were weighed full, emptied, washed, drained, and weighed empty. The EBW was obtained as the FBW minus the GIT, bladder, and gallbladder contents.

The carcasses were weighed, refrigerated at 4°C for 24 h, divided in half lengthwise, and then frozen. Subsequently, the non-carcass components, hides, and right half carcass samples were cut with a band saw and ground separately in an industrial meat grinder. After grinding and homogenization, samples were taken for chemical analysis. For determination of the body composition, the ground samples of the right half-carcasses, non-carcass parts, and hides were pre-dried at 55°C to constant weight and after this period, defatted by extraction with ether in a Soxhlet apparatus (AOAC, 1990; method number 920.39) for 12 h (Pereira et al., Reference Pereira, Lima, Marcondes, Rodrigues, Campos, Silva, Bezerra, Pereira and Oliveira2017). Subsequently, the fat-free samples were ground in a ball mill and analysed for dry matter (AOAC, 1990; method 967.03) and crude protein content (AOAC, 1990; method 984.13).

Models and estimation of variables

To estimate the initial EBW and CW of the performance animals in the comparative slaughter studies, regression equations of the FBW against the BW, EBW against the FBW, and CW against the EBW were generated from the data baseline animals. Likewise, the initial body energy of the performance animals was estimated by regression equations of the body energy contents against the EBW from the data baseline animals (Herbster et al., Reference Herbster, Oliveira, Brito Neto, Justino, Teixeira, Azevedo, Santos, Silva, Marcondes, Oliveira, Bezerra and Pereira2024).

The CG (kg/day) was obtained by the difference between the final and initial carcass weight, divided by the number of experimental days, within each study. The daily RE (MJ/day) was obtained by the difference between the final and initial body energy content (BEC). The BEC was obtained for each animal from the body content of protein and fat and their caloric equivalents (ARC, 1980) according to the following equation:

(1)$$BEC = ( {5.6405\;\times BPC} ) + ( {9.3929 \times BFC} ) $$

where BEC is the body energy content (MJ); BPC is body protein content (kg); and BFC is body fat content (kg).

The CW, EBW and EBWG were estimated through linear regressions using the following equations, respectively:

(2)$$CW = \beta 0 + \beta 1 \times FBW$$

(3)$$EBW = \beta 0 + \beta 1 \times CW$$

(4)$$EBWG = \beta 0 + \beta 1 \times CG$$

where CW is the carcass weight (kg); FBW is fasting body weight (kg); EBW is the empty body weight (kg); EBWG is empty body weight gain; CG is the carcass gain; and β0 and β1 correspond to the intercept and slope of the linear regression, respectively.

To predict the RE, the model suggested by the NRC (1984) was used, which describes the relationship between the RE and the EBWG for a given EBW, being the EBWG variable replaced by the CG variable, as suggested by Benedeti et al. (Reference Benedeti, Valadares Filho, Chizzotti, Marcondes and Silva2021):

(5)$$RE = \beta 0\;\times EBW^{0.75}\;\times \;CG^{\beta 1}$$

where RE is the retained energy (MJ/day); EBW^0.75 is metabolic empty body weight (kg); CG is carcass gain (kg/day); β0 is the antilogarithm of the intercept of the linear regression of the logarithm of RE (MJ/kg^0.75 EBW/day) as a function of the logarithm of CG (kg/day); and β1 corresponds to the slope of the regression.

To estimate EBWG and RE, only data from animals fed above the maintenance level were used, since the growth pattern of these animals differs from those feds at the maintenance level.

Statistical analysis

The parameters of the linear models were tested using the MIXED procedure of SAS (version 9.4, Inst. Inc., Cary, NC), and the significance level was set at 0.05. As the data set was composed of different studies, it was necessary to quantify the variance associated with the studies using the principles of meta-analysis, described by St-Pierre (Reference St-Pierre2001). The random effect of the study was included and tested in the intercept and slope of all models, considering the possibility of covariance. The fixed effect of sex class on models’ parameters was tested, and when the differences were significant, an equation was fitted for each sex class. Seventeen types of variance-covariance structures were tested, with the choice of structure for defining the most appropriate model based on Akaike's Information Criteria. Individual observations with Student residuals greater than 2.5 or below −2.5 were considered outliers (Pell, Reference Pell2000; Tedeschi, Reference Tedeschi2006) and excluded from the data set. When Cook's distance was greater than 1.0, the study was considered an outlier and removed from the analysis (Cook and Weisberg, Reference Cook and Weisberg1982).

Validation of equations

An independent validation framework was adopted, which consisted of searching for studies conducted with hair sheep raised in tropical conditions that had the same input information as the models generated to predict CW, EBW, EBWG and RE.

For CW and EBW we used values of mean of treatments, from published manuscripts, as described in Table 2 and 3. Although, for EBWG and RE we used raw (individual) values extracted from four independent studies.

Table 2. Summary of studies used to validate the generated equations

CW, carcass weight; EBW, empty body weight; EBWG, empty body weight gain; n, in the number of observations in the study; RE, retained energy; T, is the number of treatments in the study.

^a Compilation of means of treatments reported by independent publications.

^b Study included only in the validation data set of the CW prediction equations.

^c Study included only in the validation data set of the EBW prediction equations.

^d Compilation of individual information originating from independent study data sets.

Table 3. Characteristics of the data sets used to validate the generated equations

CW, carcass weight; CG, carcass gain; FBW, fasting body weight; EBW, empty body weight; EBWG, empty body weight gain; RE, retained energy.

^a Compilation of means of treatments reported by independent publications.

^b Compilation of individual information originating from independent study data sets.

Model validation analyses were carried out using the Model Evaluation System (MES) software, version 3.1.13 (Tedeschi, Reference Tedeschi2006), and the significance established was 0.05. The predicted and observed values were compared using the following regression model:

(6)$$Y = \beta 0 + \beta 1 \times X$$

where Y represents the observed values; X represents the predicted values; and β0 and β1 correspond to the intercept and slope of the regression, respectively. The regression was evaluated according to the following statistical hypotheses (Neter et al., Reference Neter, Kutner, Nachtsheim and Wasserman1996): H₀: β0 = 0 and β1 = 1; H_a: rejection of H0. If the null hypothesis is not rejected, it is concluded that the tested equation estimates precisely and accurately. The coefficient of determination (R ²) was used as an indicator of precision, with values closer to 1 being better. The correlation and concordance coefficient (CCC) or reproducibility index, was used to evaluate the model in terms of prediction efficiency (Deyo et al., Reference Deyo, Diehr and Patrick1991; Nickerson, Reference Nickerson1997; Liao, Reference Liao2003) and varies from –1 to +1, with values closer to +1 being better. The models’ prediction errors were evaluated using the estimated mean squared error of prediction (MSEP; the closer to 0 the better), and its components (squared bias, SB; systematic bias, MaF; and random errors, MoF; Bibby and Toutenburg, Reference Bibby and Toutenburg1977). The root mean square error of prediction (RMSEP) was used to evaluate model accuracy, and the lower the RMSEP, the better the model accuracy.