Energy is the most important component in swine diets comprising the largest proportion of diets and playing a vital role in the maintenance and growth of pigs [1,2]. Digestible (DE), metabolizable (ME), and net energy (NE), which reflect the energy utilizations in pigs, are used to formulate diets that fulfil energy requirements for optimal growth [3]. The DE, ME, and NE values can be estimated using prediction equations that take into account the chemical composition in feeds [1,4–8]. Notably, the accuracy of the most prediction equations improves when the gross energy (GE) concentration is used as an independent variable. Consequently, accurate determination of GE in feeds is essential for effectively estimating DE, ME, and NE for diet formulations.

The GE in feed ingredients can be determined using a bomb calorimeter. This method is relatively inexpensive and accurate, but time-consuming and not commonly conducted in commercial practice [9]. Alternatively, prediction equations for estimating GE in feeds based on their chemical compositions have been developed in previous studies [10,11] and introduced in the swine NRC [12,13]. However, Urriola et al [9] reported that the GE concentration in corn distillers dried grains with solubles was underestimated when the GE was calculated using the prediction equation developed by Ewan [10]. To our knowledge, studies evaluating the accuracy of the previous prediction equations have been rather scarce. Therefore, the objectives of the present work were to evaluate the accuracy of prediction equations previously developed for estimating GE in feed ingredients and to develop the novel equations. Additionally, the novel equations were validated using the data that were not used for the model development.

The evaluation study based on the data from 2,279 ingredient samples indicated that the equation reported by Ewan [10] had both mean bias (intercept = 218; standard error = 4 and p<0.001) and linear bias (slope = −0.121; standard error = 0.025 and p<0.001; Figure 1a). The equation of Sauvant et al [11] also had the mean bias (intercept = 135; standard error = 4 and p<0.001; Figure 1b).

Based on the data from 2,279 ingredient samples, 3 prediction models for estimating GE concentration were developed using CP, EE, and ash as independent variables (Table 2). The best-fitting model was: GE, kcal/kg DM = 4,341+11×CP+ 54×EE–24×ash, with R² = 0.372 and p<0.001 (Eq. 3), where the nutrient components are in % DM.

A validation study based on the 62 ingredients from the swine NRC [13] indicated that the Eq. 2 did not have a mean bias (intercept = −7; standard error = 47 and p = 0.884) or a linear bias (slope = −0.018; standard error = 0.089 and p = 0.840) as presented in Figure 2a. The Eq. 3 also did not have any bias for intercept (−56; standard error = 38 and p = 0.140) or slope (0.014; standard error = 0.068 and p = 0.834; Figure 2b). However, the equation of Ewan [10] showed a mean bias (intercept = 101; standard error = 35 and p = 0.005; Figure 3a) and the equation reported by Sauvant et al [11] also had a mean bias tendency (intercept = 71; standard error = 36 and p = 0.056; Figure 3b).

The DE, ME, and NE systems represent energy concentrations available to animals, and thus, these systems have been employed to formulate swine diets that meet energy requirement estimates of animals [3]. An accurate determination of DE, ME, or NE of a feed ingredient requires animal experiments that are time-consuming, laborious, and expensive. Alternatively, prediction models for estimating biologically available energy values of ingredients and diets for pigs using nutrient concentrations as independent variables are available [1,4,6,16,17]. It should be noted that the inclusion of GE concentration as an independent variable in the models for estimating the DE and ME improves the precision of the equations represented by increased determination coefficients [1,4,6]. In addition, the inclusion of ME as an independent variable in the equation for estimating NE increases the determination coefficient [8,18]. Therefore, an accurate GE value is essential for accurately estimating the DE, ME, or NE of a feed ingredient.

The underestimation of GE of feed ingredients observed in the present evaluation of the previous equations [10,11] is well supported by Urriola et al [9] who reported that the predicted GE in corn distillers dried grains with solubles using the equation of Ewan [10] was approximately 188 kcal/kg DM less than the measured GE. A linear bias observed in the evaluation of the equation by Ewan [10] indicates that the equation underestimates GE more for low-GE ingredients. The inaccuracy of the equation by Ewan [10] may be partially due to the limited number of ingredients (n = 33) and diet (n = 53) used for developing the equation. Nevertheless, the high determination coefficient (R² = 0.98) of the equation of Ewan [10] may be attributed to the inclusion of some ingredients containing extremely high GE concentrations such as fats and oils.

The reason for the mean bias observed in the evaluation of the equation of Sauvant et al [11] remains unclear but is potentially associated with the differences in the characteristics of the ingredients. Although Sauvant et al [11] employed a large number of ingredient samples (n>2,000) for developing the equation, the ingredients included roughages as well as grains and oilseed meals whereas the ingredients used in the present evaluation study were mostly concentrate feeds (Table 1). In addition, the ingredients in the NRC [13] also are concentrate feed ingredients.

The 2,279 feed ingredients used for developing novel equations in the present study primarily consisted of grains, oilseed meals, and cereal by-products which are commonly used for non-ruminants. No bias observed in the validation of the novel equations using data from the swine NRC [13] suggests that GE concentrations in feed ingredients for non-ruminants can be more accurately estimated using the novel equations compared with the previous equations.

In the novel equations, only CP, EE, and ash concentrations were used as independent variables for estimating GE concentration. Although fiber, starch, or sugar as additional independent variables can potentially improve the accuracy of prediction of GE [11,19], the concentrations of these nutrients are often unavailable. As in the present work, Ewan [10] also employed only CP, EE, and ash concentrations as independent variables for estimating GE concentration.

A previous equation for estimating gross energy concentrations in feed ingredients for non-ruminants underestimated the energy value determined using the adiabatic bomb calorimeter. In the present work, novel equations were developed for gross energy based on the chemical compositions of 2,279 ingredient samples for non-ruminants and the equations were fairly accurate based on the validation study.