Metabolizable energy in energy food for growing pigs and cross-validation regression models 1

The present study aimed to determine the apparent metabolizable energy (AME) of six corn cultivars, two sorghum cultivars and two wheat brans and to evaluate the cross-validation of predictive models of AME for corn, sorghum and wheat bran for growing pigs, as estimated from the data of chemical composition. Forty-four pigs, with an average initial weight of 24.3 kg, were distributed in a randomized block design, with 11 treatments (ten food treatments and the reference diet), four replicates and one pig per experimental unit. The reference diet was replaced by 30% for the ground corn and sorghum conditions and 20% for the wheat bran condition. The values of AME for corn, sorghum and wheat meal for pigs ranged from 3161 to 3275, 3317 to 3457 and 2767 to 2842 kcal kg-1 as a feed basis, respectively. The average metabolizability of the gross energy did not differ between the corn and sorghum cultivars, which formed a homogeneous group of food. Next, linear regression models were fitted to the 1st degree of the observed values as a function of the predicted AME, to test the hypothesis β0 = 0 and β1 = 1 in an experimental sample and 200 bootstrap samples. Fourteen predictive models had low percentages of cross-validation, ranging from 0-29.5%. The AME1A= 2.547 + 0.969ADE model was validated in experimental sample and 68% of bootstrap samples, proving its accuracy in estimating the AME of corn and sorghum from national data for growing pigs.


INTRODUCTION
The precise quantification of energy that pigs can digest and metabolize from eating a food is essential for the formulation of balanced diets (SAKOMURA; ROSTAGNO, 2016) because protein, amino acid and other nutrient requirements are expressed in terms of energy levels of diets.Associated maladjustment may over-or underestimate nutrient intake and performance in pigs (ROSTAGNO et al., 2011).
In many situations, the formulation of diets for pigs has been carried out based on food composition tables (ROSTAGNO et al., 2011).Thus, the update of the chemical composition data of the food is indispensable for achieving greater precision in the formulation and performance of animals, because factors such as climate, genetics, among others, altering the nutritional quality of food and can modify the use of nutrients by pigs, as reported by National Research Council -NRC (2012).
Otherwise, the use of equations for predicting AME energy feed for pigs based on proximal composition of foods has been studied because of the difficulty that the pig industry has to adopt conventional methods to determine the AME food, which require experiments on live animals, and require infrastructure, time and financial resources (POZZA et al., 2010).
The prediction of AME energy feed for pigs using models that have chemical composition of predictors has the advantages of speed and low cost (PELIZZERI et al., 2013), in addition to considering the lot of food characteristics to prepare the diet.
Although many researchers have estimated prediction models for the AME of food for pigs based on food composition (FERREIRA et al., 1997;LEKULE et al., 1990;NOBLET;PEREZ, 1993), in recent studies reporting on assessment validation equations for independent-sample data (CASTILHA et al., 2011;PELIZZERI et al., 2013), the validation tests have been applied only once, which does not allow for a consistent evaluation of a given model's predictive ability.
The bootstrap method can simulate real situations and be used repeatedly in various samples, to test the power of validation and reliability of equations in independent sets of data.This method consists of a set of resampling procedures from the original database, to obtain a significant amount of estimates of linear regression of 1 st degree parameters, allowing the hypothesis test application in each sample bootstrap (COELHO-BARROS et al., 2008).
In the evaluation of the validity of regression models, the use of the bootstrap method is advantageous because from the original database, it is possible to increase the number of samples and tests to evaluate the joint null hypothesis β 0 = 0 and β 1 = 1 upon linear regression parameters (MONTGOMERY; PECK; VINING, 2006).
In this context, this research was conducted in order to determine the AME of six corn cultivars, two sorghum cultivars and two wheat brans for growing pigs and evaluates the cross-validation of the 15 predictive models of EMA in experimental sample and 200 bootstrap samples.

MATERIAL AND METHODS
The metabolism assay was conducted in the pig metabolism room of the Experimental Farm at the State University of Parana West, UNIOESTE.
Forty-four pigs, crossbred barrows with an average initial weight of 24.3 (1.12) kg, were distributed into completely randomized blocks design, with 11 treatments and 10 foods (six corn cultivars, two sorghum cultivars and two wheat bran) and the reference diet, four replicates and a pig for experimental unit (metabolism cage).The blocks were made during four periods.
The cultivars of corn and sorghum replaced by 30% basal diet, while the wheat brans replaced 20% (SAKOMURA; ROSTAGNO, 2016).The basal diet (Table 1), based on corn and soybean meal, was formulated considering the chemical composition of the ingredients and the nutritional requirements of high genetic potential swine, with average performance in the initial phase (15 to 30 kg body weight) presented by Rostagno et al. (2011), except for the crude protein level.
The trial period lasted 12 days, seven days for the animals to adapt to metabolism cages and feed, and five days of total collection of faeces and urine.
Faeces were individually identified, weighed, wrapped in plastic bags and stored in a freezer at -18 °C, until the end of the collection period.At the end of this period, the samples were thawed, homogenized and withdrawn individual samples equivalent to 20% of each plastic bag.Next, the individual samples were collected for treatment, dried in a forced air oven (55 °C/72 h), ground and stored for further analysis of dry matter and gross energy.
The urines were filtered as excreted and individually collected in plastic buckets with 20 ml of HCl 1:1.Then, the volumes were measured with the aid of measuring cylinder and in each collection, 10% of the total were removed and transferred to glass jars identified by animal, that were stored in the refrigerator (3 °C) for further analysis of gross energy.
The ten food and the reference diet were submitted to analysis of dry matter (DM), gross energy (GE), crude protein (CP), ether extract (EE), crude fibre (CF), neutral detergent fibre (NDF), acid detergent fibre (ADF), ash, calcium and phosphorus as described by Silva and Queiroz (2005).The diets and faeces samples were analysed for DM and nitrogen content (SILVA; QUEIROZ, 2005).The GE values of the ten food, reference diet, faeces and urine were quantified using an adiabatic calorimeter (Parr® -6200).
For each food were evaluated digestibility coefficient of GE (DCGE), apparent digestible energy (ADE), metabolizability coefficient of GE (MCGE), apparent metabolizable energy (AME) and the AME:ADE ratio (SAKOMURA; ROSTAGNO, 2016).The effects of food on the DCGE and MCGE were checked by analysis of variance and average values of foods were grouped by the Scott-Knott test.
In the evaluation phase of model validation, chemical and energetic composition values for corn, sorghum and wheat bran, as obtained in the laboratory, and ADE measurements obtained experimentally were replaced in 15 regression models estimated from the chemical and energetic composition of these foods, as reported in the national and international scientific literature, via meta-analysis, to obtain the predicted values of apparent metabolizable energy (PAME).The observed values of apparent metabolizable energy (OAME) were obtained in the experiment, based on dry matter.
The models AME 1A = 2.547 + 0.969ADE and AME 1B = 39.33 + 0.969ADE were obtained jointly to estimate the AME of corn and sorghum, but national and international origin, respectively.The models AME 1C = 2.547 + 0.969ADE -4.217CP and AME 1D = 39.33 + 0.969ADE -4.217CP have been proposed to estimate the AME wheat brans national and international source, respectively.These models were adjusted considering the additive effects of intercept, ADE, GE, CF, EE, CP, ash, source dummy (SD), food dummy 1 (FD 1 ), food dummy 2 (FD 2 ) and the effects of interactions between dummies with regressive chemical and energy composition (LANGER, 2013) (LANGER, 2013).
The AME of corn and sorghum from national and international sources was estimated using the AME 3A = 3675.39+ 50.02EE and AME 3B = 3675.39+ 50.02EE -25.62CF models, respectively.For national source wheat bran, the proposed model was AME 3C = 3675.39+ 50.02EE -91.23CF.The international origin wheat bran had the AME estimated from the model EMA 3D = 3675.39+ 50.02EE -116.85CF.These models were fitted without inclusion as regressive, of ADE, GE and interactions of ADE and GE with the auxiliary variables (LANGER, 2013).
The models AME 4A = 3824.44-105.29ash+ 45.01EE and AME 4B = 3824.44-105.29ash+ 45.01EE -37.26CP have been proposed to estimate the AME of corn and sorghum (AME 4A ) and wheat brans (AME 4B ) for both pooled sources.These models were fitted without initial inclusion of ADE, GE, CF and their interactions with the indicator variables (LANGER, 2013).
Before fitting linear regression models 1 st degree (y i = b 0 + b 1 x i + ε i ) of OAME values as a function of PAME values, using the method of ordinary least squares, we proceeded to the analysis of standardized residual Student (RStudent) to diagnose influential observations or outliers that could interfere with the estimates of the regression parameters β 0 and β 1 .Based on the normal distribution curve, RStudent values larger than two standard deviations, in absolute value, were considered influential and removed from its database.
The significance of the β 1 parameter estimates was checked using the partial "t" test to test the null hypothesis β 1 = 0. Validation of the 1 st -degree models and, therefore, the regression models was observed when the joint hypothesis β 0 = 0 and β 1 = 1 for linear regression parameters was accepted, while applying the "F" test (MONTGOMERY; PECK; VINING, 2006).
Then, pairs of observed and predicted values of AME were replicated using the resampling method nonparametric bootstrap, generating 200 bootstrap samples of the same size as the original database, with replacement, by selecting the values randomly (COELHO-BARROS et al., 2008).
To check the percentage of validation of the models in 200 bootstrap samples (PVB), in each bootstrap sample were fitted linear regression models 1 st degree of OAME values as a function of PAME values and applying the "F" test (MONTGOMERY; PECK; VINING, 2006), to test the joint null hypothesis β 0 = 0 and β 1 = 1.From the significance probability (p) values of 200 "F" validation tests, PVB was calculated by: PVB = (number of results probability (p) greater than 0.05/200) x 100.
The significance level of 0.05 was used for all statistical tests.The statistical analyses were performed using the R Core Team (2013).

RESULTS AND DISCUSSION
The dry matter of the food ranged from 87.43 to 89.83% (Table 2) and is in line with the recommendation of 10 to 14% moisture (ASSOCIAÇÃO NACIONAL DOS FABRICANTES DE RAÇÕES, 1985), to prevent fermentation and proliferation of fungi that affect the quality of the diet and grain.
The calcium (Ca) levels of corn ranged from 0.01 to 0.02% and phosphorus total (P) ranged from 0.18 to 0.52% (Table 2).The value of 0.52% was very discrepant in relation to others.The nutrients that showed higher coefficients of variation (CV) among the six corn cultivars were P (45.87%) and Ca (34.99%).These results partially corroborate those obtained by Pelizzeri et al. (2013), which found greater instability for the Ca (CV = 62.5%) and acid detergent fibre content (CV = 47.18%), in chemical composition data corn collected in scientific literature.The Ca content (0.11%) and P (1.09 and 1.12%) of wheat bran were higher than their respective levels of Ca and P of the corn and sorghum (Table 2).
The gross energy (GE) contents of corn ranged from 3780 to 3931 kcal kg -1 (Table 3), which are in accordance with the GE values of corn with different nutritional profiles (3825 to 3929 kcal kg -1 ) obtained by Oliveira et al. (2011), and the value of 3940 kcal kg -1 (ROSTAGNO et al., 2011).The variation between the GE values for two sorghum cultivars was low (3946 and 3953 kcal kg -1 ) and the values found were higher than 3910 kcal kg -1 (ROSTAGNO et al., 2011).GE values of the wheat brans were 4040 and 3999 kcal kg -1 (Table 3).These values were similar to 4023 kcal kg -1 and greater than 3914 kcal kg -1 of GE (ROSTAGNO et al., 2011).
The variability found between GE values of corn, sorghum and wheat brans was consistent with reports in the literature, and can be attributed to the observed variation in the chemical composition of food, because the GE of food is directly related to the amount of heat it can be released by each fraction of food (NRC, 2012).However, despite the lower content of EE (1.97 and 2.53%) compared to corn (from 3.51 to 4.28%), the GE values of sorghums were higher than those of corn (Table 3), with no plausible justification for this fact.
The variation of the ADE and AME values between samples of the same food can be attributed to the influence of factors such as soil conditions, climate, genetics, among others, that affect the food chemical composition, the main determinant of ADE (NRC, 2012).The experimental coefficient of variation was 6.41% (ADE) and 7.50% (AME).Therefore, nutritionists should perform routine chemical analysis of the respective lots of food, aiming to formulate diets that meet more precision the nutritional requirements of animals, as these variabilities can compromise the precision in the formulations of diets for pigs, interfering with the performance, given the amplitude of the average values of AME between corn (114), ( 140) and wheat brans (75 kcal kg -1 ) (Table 3).
The ether extract (EE) and crude protein (CP) have a positive correlation with the apparent metabolizable energy (AME), i.e., the higher the lipid or CP content, the greater the value of AME food (LEKULE et al., 1990).The EE has a positive effect in AME due to the high heat produced in the oxidation (POZZA et al., 2010).However, in CP are compounds that are not used by the animal and AME food depends on the quality and how much the animal can take advantage of the protein, because it can be catabolized, increasing nitrogen losses via urine and energy demand (NRC, 2012).Sorghum had higher CP values in relation to corn, but their EE values remained below those obtained for corn (Table 2), indicating that the high correlation between EE and AME, reported by Lekule et al. (1990), was not sufficient to explain the higher numerical values of AME sorghum compared to corn.The difference between the highest value of AME of sorghum ( 3457) and the highest value of AME of corn (3275) was 182 kcal kg -1 .The difference between the lowest energy value of sorghum and corn was 156 kcal kg -1 (Table 3).
The ash, CF and NDF had negative correlation with AME (NOBLET; PEREZ, 1993).The ash acted as dilutive effect of GE and reduced organic matter content of the food (PELIZZERI et al., 2013).In this study, the highest ADF value (4.74%) to one of sorghum may have contributed to reducing the value of AME (3317 kcal kg -1 ) when compared to the value of 3457 kcal kg -1 the other cultivar of sorghum.However, observing the AME values of all corn and sorghum (Table 3) and its fibrous and ash content (Table 2), it was not possible to establish reasons for the differences in AME values between these foods based the correlations exhibited by Noblet and Perez (1993), except for the fibrous content of second sorghum, the ash and fibre values did not differ markedly between the two foods.
The higher fibre content in wheat brans resulted in lower values of AME compared to corn and sorghum (Table 3).The presence of higher fibre content in food can reduce the energy use of dietary nutrients, due to the low degradation of indigestible carbohydrates in the large intestine, especially in the lower body weight pigs (NRC, 2012) 1993).
The AME:ADE ratio ranged from 0.94 to 0.97, for corn and sorghum, and 0.88 to 0.90 for wheat brans (Table 3).Except for the corn had the highest value (0.97), the other corn had lower AME:ADE ratio (0.94 and 0.95), less than 0.98 (FERREIRA et al., 1997) and 0.96 and 0 .97 (CASTILHA et al., 2011).The smallest values of AME: ADE ratio for wheat brans (Table 3) indicated that the energy losses in the urine were important, possibly resulting from increased catabolism of protein and increased energy demand (NRC, 2012), as wheat brans had higher protein content than corn and sorghum (Table 2).
There was no statistical difference (p>0.05) between the DCGE and MCGE of the corn and sorghum (Table 3), confirming the finding of no apparent justification, based on chemical compositions, for the differences between ADE and AME values between the two foods.These results showed that corn and sorghum cultivars formed a homogeneous group of food on the digestibility and metabolizability, suggesting the possibility of replacing corn with sorghum in pig diets.
In this study, the average values of DCGE and MCGE of corn ranged from 85.55 to 90.61% and from 80.98 to 84.93%, respectively (Table 3), and were similar to those described by Castilha et al. (2011), who found DCGE between 87.42 and 89.37% and MCGE between 84.01 and 86.00%. The DCGE (92.19 and 88.78%) and the MCGE (87.61 and 83.91%) of sorghum were discrepant between both cultivars, but the AME:ADE ratio was next (0.95 and 0,94) and remained similar to that obtained for corn (Table 3).
For wheat brans, the average DCGE (78.43 and 78.98%) and MCGE (69.18 and 70.35%) were lower (p<0.05) to those obtained for corn and sorghum (Table 3), indicating the formation of a heterogeneous group of lower digestibility and metabolizability energy, due to the higher fibre content (Table 2), confirming the low digestibility of the fibre content in the gastrointestinal tract of pigs (NRC, 2012).
In the graphical analysis of the single validation AME 1a test model (Figure 1), confirmed the similarity between observed and predicted values of AME, in which the straight linear model of 1 st degree presented angle with the horizontal axis of 47.77º.This value is close (p>0.05) to the ideal condition of straight angle (y = x), which is 45º, indicating that the AME 1a model can be used as a tool to obtain AME values of corn and sorghum national for growing pigs.The single validation test for the hypothesis β 0 = 0 and β 1 = 1 associated with the model AME 1b = 39.33 + 0.969ADE presented descriptive level value (p) equal to 0.0298 (Table 4), indicating that the observed values and estimated AME of the corn and sorghum international were close, but not enough, with the error (α = 0.05) used in this study.
The rejection of the joint hypothesis β 0 = 0 and β 1 = 1 observed in single validation tests for EMA 1c and EMA 1d models, adjusted with the ADE as regressor, and AME 2 , AME 3 , AME 4 and AME 5 models, adjusted with chemical and energy composition as regressor, can be explained by the lower observed AME values obtained in the experiment regarding AME values found in scientific articles.In addition, the estimates of the model parameters were based upon the chemical composition values and energy feeds available in the scientific literature, which were distinct from food composition values used in the assay, analysed in a laboratory, which values were used to obtain AME estimated by the models.
The validation results by bootstrap simulation revealed that the model AME 1a = 2.547 + 0.969ADE, related to national corn and sorghum cultivars, had the highest percentage validation (68%) in 200 bootstrap samples (Table 4).The model AME 1b = 39.33 + 0.969ADE, referring to corn and sorghum international, presented the second largest validation index (29.5%),however, this percentage was not satisfactory, given that corresponded to only 59 validations in 200 tests.We found no references in the scientific literature validation tests, through bootstrap simulation, of AME prediction models of energy foods from different sources for pigs.
Models that have the ADE as regressor are not the most suitable for use in feed formulation in practical situations, because they require to carry out the experiment.However, the use of these reduces the need for hand labour in the collection and storage of urine, and allows reduction in time and cost of research.
Although it is recommended the use of models with independent variables of chemical composition, being easily applied in zootechnical practice, models that had the CP , CF, EE, ash and GE as regressive showed unsatisfactory percentage of cross-validation (0 to 11.5%), showing a low reliability for the prediction of AME.The criteria to be adopted for a model to be classified as suitable for the validation of independent data is subjective, depending on the requirement of the researcher and the research objectives.In the conditions of work and considering the lack of information related to the use of bootstrap simulation in zootechnical area, 68% validation index (136 validations in 200 samples) presented by the AME 1a model for national corn and sorghum cultivars can be considered satisfactory, with intermediate reliability.
Other studies on the use of bootstrap simulation in assessing the validation of AME prediction models for pigs should be performed, in order to provide more information related to the predictive ability of models.

CONCLUSIONS
The apparent metabolizable energy values of food energy for growing pigs on the basis of feed ranged from 3161-3275 kcal kg -1 for corn cultivars, 3317-3457 kcal kg -1 for sorghum cultivars and 2767-2842 kcal kg -1 for wheat bran.The AME 1a = 2.547 + 0.969ADE model is valid for the estimation of AME of national corn and sorghum cultivars and can be used as a tool for formulating diets for pigs.

Castilla
et al. (2011) did not find a significant Spearman correlation (p>0.05) between average observed values of AME for cultivars of corn and estimated values of AME obtained by the model (AME = 989.76+ 0.86ADE, R 2 = 0.79); however, the authors found that the AME = 1.00ADE -0.68CP (R 2 = 0.99) and AME = 0.997ADE -0.68CP + 0.23EE (R 2 = 0.99) models, proposed by Noblet and Perez (1993), who used ADE and CP as regressors, provided estimates of AME with significant correlation (p<0.05) with the observed AME values.

Figure 1 -
Figure 1 -Graphical analysis of the single validation test of AME 1A model for corn and sorghum national: Straight of the ideal condition (solid line) and model of 1 st degree of the observed values as a function of the predicted AME (longdash line)

Table 1 -
Centesimal and calculated composition of the reference diet as a feed basis . the AME 2B = 2306.26+ 0.39GE -123.95CF+ 33.05EE -49.63ash model.These models were used jointly to estimate the AME of corn, sorghum and wheat brans.The models were fitted without the use of regressive ADE, ADE*SD, ADE*FD 1 and ADE*FD 2 N. T. E.Oliveira et al.yielded

Table 2 -
Chemical composition (%) of food as a feed basis 1 . The CF can reduce dietary fat and protein

Table 3 -
Gross energy (GE), apparent digestible energy (ADE) and apparent metabolizable energy (AME), expressed in kcal kg -1 , digestibility (DCGE) and metabolizability coefficients (MCGE) of the GE, expressed in %, and the AME:ADE ratio of corn, sorghum and wheat brans for growing pigs as a feed basis Metabolizable energy in energy food for growing pigs and cross-validation regression models digestion enhancing endogenous secretion.Additionally, the fermentation of the fibre produces volatile fatty acids, which is lower metabolic efficiency (NOBLET; PEREZ,

Table 4 -
Linear regression models of apparent metabolizable energy (AME) as a function of chemical and energy composition of corn (C), sorghum (S) and wheat bran (WB) for pigs, estimated from national (N) and international (I) data, significance probability (p) to the joint null hypothesis and percentage of validation of the models in 200 bootstrap samples (PVB) N. T. E.Oliveira et al.