A meta-analysis of dry matter intake in Nellore and Zebu-crosses cattle

The study was carried out to develop and to evaluate new equations to predict dry matter intake (DMI) of Nellore and Zebu-crosses cattle using meta-analysis procedure. The data used to estimate the parameters were collected from independent performance experiments using growing and fattening Nellore and Zebu-crosses cattle, and they were compiled from 561 experimental units. Before proposing an equation to predict DMI, it was observed that the genetic group was a source of statisticaly significant variation. Therefore, equations to predict dry matter intake in the Zebu-Crosses and Nellore cattle were independently developed. The regression equations for Zebu-crosses cattle were: DMI = -2.6098 + 0.08844BW0.75 + 4.4672ADG – 1.3579ADG2 and DMI = -1.0094 + 0.01608BW + 4.4363ADG -1.2548ADG2. The regression equations for Nellore cattle were: DMI = -2.7878 + 0.08789BW0.75 + 5.0487ADG – 1.6835ADG2 and DMI = -1.3559 + 0.0159BW + 5.6397ADG – 1.8494ADG2. In order to evaluate fitted equations, it was utilized data from independent experiments published from 2005 to 2008 in the Revista Brasileira de Zootecnia. The equations (DMI) for Nellore overpredicted dry matter intake for estimates lower than 7 and higher than 10 kg·d-1. For Zebu-crosses cattle, dispersions of 3 kg d-1 were observed when extreme intakes were evaluated, however, when the equation included BW 0.75, the intercept did not differ from zero and the slope did not differ from 1. It is not possible to fit only one equation for preditcting DMI for beef cattle in tropical conditions, because there are differences between Zebu and Zebu-crosses. Fitted equations that include ADG and BW 0.75 should be used as an alternative method to predict dry matter intake of Zebu-crosses and Nellore beef cattle in tropical conditions.


Introduction
Numerous quantitative intake prediction models have been developed, nevertheless, none has achieved widespread acceptance and none uses a universally applicable and robust prediction model (Pittroff & Kothmann, 2001).Optimally, beef cattle producers should develop intake prediction equations that are specific to give production situations; such equations should account for a greater percentage of the variation in intake than would be possible with a generalized equation (NRC, 2000).
The National Research Council guidelines for beef cattle production (NRC, 2000) have been used in Brazil to formulate diets and evaluate feeding programs.However, these equations were developed mostly with Bos taurus cattle, with a size scaling procedure that is used to adjust differences in mature animal size.In addition, although anabolic stimulants are prohibited in Brazil, they were used in some of the cattle in the database employed to generate the dry matter intake model proposed by the NRC (2000).
When the main purpose of predictive models of dry matter intake is to p redict the concentration of each nutrient in total dry matter intake, the concentration of net energy for maintenance (NEm) in the diet should not be an input variable of model.In order to estimate the content of energy and other nutrients in the diet, it is necessary to initially predict the DMI.Moreover, the nutritional requirements of the animal are primarily determined by the body weight (BW; Plegge et al., 1984), and this, in turn, is dependent on its performance (NRC, 1987).Thus, the residual feed intake, used in the genetic improvement of feed efficiency, is used to predict the feed intake of each animal using an equation with BW 0.75 and average daily gain (ADG) (Kolath et al., 2006).
Researchers have gathered data from multiple published studies and attempted to formulate a quantitative model that best explains the reported observations.Generally, there are significant differences among studies; if these differences are not taken into account, they can result in a bias in the estimation of parameters (slopes and intercept) of regression models.Therefore, a meta-analysis, which incorporates the Study effect and its interaction as random components of a mixed model, must be used.This should result in better prediction equations of biological systems and a more accurate description of their prediction errors (St-Pierre, 2001).
This study was carried out to develop and evaluate new equations for dry matter intake prediction in Nellore cattle and Zebu-crosses using a meta-analysis procedure.

Material and Methods
The data used to estimate the parameter were collected from independent performance experiments that evaluated growing and fattening Nellore and Zebu-crosses (Nellore × Bos taurus) cattle.The data recorded for each observation included sex (SEX), initial body weight (iBW), final body weight, days on feeding (DOF), dry matter intake, and average daily gain (ADG).All data were obtained from feedlot Nellore and Zebu-crosses cattle that were individually fed ad libitum.Only data of bulls and steers were used.
The initial dataset had 32 theses (studies) with 845 experimental units (n, individual cattle).Five thesis (study) with 284 observations were rejected due to data duplication or because they did not meet the initially criteria for selection established for the meta-analyses.This dataset that met the criteria for inclusion in this study was compiled from 27 theses (Table 1) and resulted in 561 observations.
Initially, the significance of the effects of genetic group (GG) and its interactions were calculated and tested statistically by ANOVA, using either body weight (BW) and metabolic body weight (BW 0.75 ) as dependent variable of dry matter intake.The model used included terms for body weight (BW and BW 0.75 ), average daily gain (ADG) and average daily gain quadratic (ADG 2 ) and the interactions with genetic group.The effects of independent variables were considered significant (P<0.15).
An equation development was conducted in PROC MIXED by using mixed-model regression techniques (St-Pierre, 2001).The study was defined as the subject of the random effect term.Independent variables were initially fitted to a model that included a fixed intercept and slopes and random effects of study in the intercepts and slopes, using an unstructured variance-(co)variance matrix (UN option).When the random slope-intercept covariance term was not significant (P>0.10) or when the models that included slope-intercept covariance did not converge, option VC (variance components structure) in PROC MIXED was used.Akaike's information criteria (AIC) and Bayesian information criteria (BIC) were used to define the best variance-(co)variance matrix.
The independent datasets used to evaluate the DMI prediction equations for Nellore and Zebu-crosses were provided by eight and twenty-two studies, respectively, from articles published between 2005 and 2008 in the Revista Brasileira de Zootecnia and Boletim de Indústria Animal, both Brazilian publications.The selected experiments were those reporting treatment means for all variables considered in the model selection process.
The evaluation of the model was performed by linear regression analysis between the observed and the predicted values of dry matter intake, which is a statistical test widely used in model evaluation, and through the analysis of residual or prediction errors (difference between observed dry matter intake and predicted dry matter intake) vs. dry matter intake observed plots (Draper & Smith, 1981).Mayer & Butler (1993) recommended to plot observed vs. predicted data, since they can be directly and easily visualized from the graph.Therefore, both types of plots were used for visual evaluation.
The observed data was used as the ordinate and model predictions as the abscissa.In addition, the intercept and the slope were calculated by regression of residues (observed -predicted DMI) on mean-centered predicted DMI.For this evaluation purpose, the tested null hypothesis was the one in which the intercept and the slope, simultaneously, did not differ from zero and unity, respectively (Mayer et al., 1994).In the models, when slope and intercept values were equal to unity and zero, respectively, the model was deemed statistically similar to the data observed (P<10).
Mean proportional bias was calculated as the slope of the regression of the predicted data on the observed data with a zero intercept (Shah & Murphy, 2006).A mean proportional bias <1 indicates an under-prediction across the range of observed values, and a value > 1 indicates overprediction (Roseler et al., 1997).
To evaluate model precision, a number of commonly used deviance measures were employed, including root mean square error (RMSE), mean absolute error (MAE) and mean square prediction error (MSPE), as proposed by Picard & Cook (1984).
The concordance correlation coefficient (CCC; Lin, 1989), also known as the reproducibility index, was used because it has been suggested to simultaneously account for accuracy and precision.It can be expanded into two components, the first one is the correlation coefficient estimate (r), which measures precision, and the second (Cb) is the bias correction factor, which indicates how far the regression

Results and Discussion
The results of the ANOVA indicated that the GG was a significant source of variation for all of the traits of interest (Table 2).Therefore, different equations to predict DMI for Zebu-crosses and Nellore cattle should increase the accuracy.In addition to possible breed-specific effects, NRC (1987) reported that genetic selection for feed efficiency could produce animals with increased feed intake potential, suggesting that genetic potential for growth may affect feed intake.
Over the years, research in Brazil has suggested that Zebu-Crosses have greater DMI than Nellore cattle (Menezes & Restle, 2005).Furthermore, it is well established that Holstein steers have a greater DMI than beef steers of similar initial weight; therefore, the NRC (2000) recommended that DMI would be increased 4% for Holstein vs. beef crosses, and 8% for Holsteins relative to other beef breeds.The higher DMI by Holstein steers compared to beef breeding steers may be due to a high maintenance energy demand.Holstein cattle have a higher proportion of organ and gut, which increases its metabolic rate (Jones, 1985).
All data used (Table 3) were from experiments that had a minimum duration of 50 days; an adaptation period was insured to minimize the impact of compensatory growth on DMI.Fox et al. (1972) found that compensating steers consumed 16% more feed than continuous growth steers when re-fed on a corn-based diet.
All the fitted equations exhibited a negative coefficient for the variable ADG 2 (kg•d -1 ); this indicates that the DMI reaches a plateau (Table 4), which might be directly related to the energy concentration of the diet.Starting from the gains that occur at maximum DMI, the energy demand will be supplied by a low fiber/high energy diet which will reduce the DMI, as it was suggested by the theory of intake regulation for the energy demand (Mertens, 1994).Because of the importance of this effect, NRC (2000) included the variables NEm and NEm 2 for the adjustment of equations for DMI.
However, because of the inherent difficulty in accurately determining the net energy content of the diet, Thornton et al. (1985) developed an equation to predict dry matter intake throughout the feeding period, which includes initial body weight and days on feeding.The dry matter intake predicted  Figure 1 -Simulation of the prediction of dry matter intake for steers with average body weight of 200 (above) and 400 kg (down), and different average daily gain (kg•d -1 ), using the adjusted equations 1.1 and 2.1 (Table 4).
by this equation accounts for 50% of the variation observed in dry matter intake.The feed intake is typically represented in the overall shape of a dry matter delivery curve for a feedlot pen, with dry matter intake initially increasing to a peak and then decreasing as days on feeding increases due to the increase in body fat content of animals in the feedlot pen.
A simulation of dry matter intake behavior based on the fitted equations was performed (Figure 1), and the relationship of average daily gain and dry matter intake (g/kg PV 0.75 ) can be observed.When dry matter intake is expressed in g/kg BW 0.75 , the fitted equations with respect to average daily gain exhibit a dry matter intake curve with three distinct segments: adaptation; plateau; and decline phases, which correspond to adaptation to the feedlot environment, increasing body weight, and increasing body fat content.
However, given the shape of the dry matter intake curve, nutrient requirements during different phases of the finishing period may differ greatly for cattle in tropical conditions.The intake plateau was predicted by the equations 1.1 and 2.1, when average daily gain was in the range from 1.64 to 1.50 kg•d -1 , corresponding to 108.4 e 100.3 g/kg BW 0.75 (equation 1.1) and 106.64 e 99.04 g/kg BW 0.75 (equation 2.1) for steer of 200 and 400 kg, respectively.
The three phases of dry matter intake (Figure 1) support the concept that quadratic equations allow better fitting of dry matter intake prediction.When dry matter intake reaches plateau, it is likely that the demanded level of energy in the diet results in metabolic mechanisms that inhibit additional dry matter intake.
Residual feed intake is an index that can be used to calculate the efficiency of an animal (Archer et al., 1999).The residual feed intake value for each animal was calculated as the difference between the actual and the expected intake.The expected feed intake used by several researchers was calculated by the regression of the actual intake on average daily gain and metabolic weight (Kolath et al., 2006).Therefore, when the energy concentration of the diet is not available for dry matter intake prediction, it could be replaced by the average daily gain.Despite of being a characteristic of the animal that affects the dry matter intake, the average  daily gain accounts for direct effects of diet that can limit intake by simplifying the model and avoiding the use of variables with practical difficulties and with cumulative mistakes in its determination such as NEm.
Including body weight and average daily gain in the equations could account for several factors that are related to the voluntary intake, thus this method can be used to simplify dry matter intake predictions in practical conditions.
To evaluate the equations to dry matter intake prediction proposed in this study, it was used an independent dataset obtained from experiments conducted with Zebu-crosses and Nellore cattle (Table 5).
The analysis of residuals (Figure 2) is important in order to identify data points that cause departures of the assumptions considered in linear regression (Tedeschi, 2006).The predictions for Nellore cattle overestimated dry matter intake when it was smaller than 7 or greater than 10 kg•d -1 ; nonetheless, the predicted dry matter intake for both equations were close to the equality line (Figure 2).For Zebu-crosses cattle, dispersions of 3 kg•d -1 were observed when extreme intakes were considered.Yungblut et al. (1981) suggested that overestimation of dry matter intake has more serious consequences for ration formulation than does underestimation.If beef cattle eat less than what was predicted, their total nutrient intake could be lesser than the amount required to reach its potential performance.However, dry matter intake underestimation could be worse when feed costs are considered by decision support models; this is because feed costs would be underestimated, and predictions for profitability would be erroneously high.In contrast, overestimation of feed cost could result in more conservative decisions, and alternatives evaluated as profitable could be more favorable than expected.
The slope and intercept of the regression of observed and predicted by the equation that does not include metabolic body weight were significantly different than   unity and zero, respectively (P>.10), indicating that these equations are not appropriate to predict dry matter intake in tropical conditions.However, for the equation that included metabolic body weight, the intercept did not differ from zero and the slope did not differ from 1 (Table 6).
All equations resulted in an overprediction of dry matter intake mean due to negative mean bias and location shift (u).For both Zebu-Crosses and Nellore cattle, the prediction equations that included metabolic body weight were more precise.These equations had a slight advantage over the equation using body weight if mean square prediction error, mean absolute error, and mean bias were evaluated.
The partition of mean square prediction error into threecomponents revealed that random errors appear to be the major cause of inaccuracy in the dry matter intake prediction.Additionally, equation 2.2 for Nellore cattle, which did not include metabolic body weight, had a mean bias value larger than 37% of the observed dry matter intake mean .Yungblut et al. (1981) considered a mean bias smaller than 10% of the actual dry matter intake mean as acceptable; this condition was in agreement for equations 1.1; 1.2 and 2.1, which had values of, 0.003; 4.745 and 9.096% respectively.
When the correlation concordance coefficient (r, u and Cb), which consists of a measure of precision and accuracy, was analyzed, the best fitting equation to dry matter intake prediction was those including metabolic body weight in the model.The equation used for dry matter intake prediction of Zebu-crosses beef cattle had a location shift (u) close to zero, and a bias correction (Cb) very close to 1, as well as a high r, indicating that this was the most precise and accurate model.

Conclusions
A single equation should not be used to predict dry matter intake for beef cattle in tropical conditions, because there are differences between Zebu and Zebu-crosses.Equations that include average daily gain and metabolic body weight should be used as an alternative method to predict dry matter intake of Zebu-crosses and Nellore beef cattle in tropical conditions.

Figure 2 -
Figure 2 -The relationship between actual dry matter intake and error (predicted minus observed DMI) using fitting equations.

Table 1 -
Summary of the thesis data for meta-analysis used in the development dry matter intake equation line deviates from the slope of unity.The location shift (u) relative to the scale is the squared difference of the means relative to the product of two standard deviations.All statistical analyses were carried out by using SAS (version 9.1, SAS).

Table 2 -
Summary of ANOVA: significance of the variables and the interaction effects of genetic group (GG)

Table 3 -
Descriptive statistics of the dataset used on the development of dry matter intake prediction equations to Zebu-crosses (n = 201) and Nellore (n = 360)

Table 4 -
Solution of the fixed effects of the regression equations obtained to Nellore cattle, purebred and Zebu-crosses AIC = Akaike information criterion; BIC = Bayesian information criterion.

Table 6 -
Statistics from regression of observed dry matter intake on dry matter intake predicted by developed equations in the evaluation data set