Response Surface Models to Predict Broiler Performance and Applications for Economic Analysis

A study was carried out to elaborate response surface models using broiler performance data recovered from literature in order to predict performance and elaborate economic analyses. Nineteen studies published between 1995 and 2005 were retrieved using the systematic literature review method. Weight gain and feed conversion data were collected from eight studies that fulfilled the pre-established inclusion criteria, and a response surface model was adjusted using crude protein, environmental temperature, and age as independent variables. The models produced for weight gain (r = 0.93) and feed conversion (r = 0.85) were accurate, precise, and not biased. Protein levels, environmental temperature and age showed linear and quadratic effects on weight gain and feed conversion. There was no interaction between protein level and environmental temperature. Age and crude protein showed interaction for weight gain and feed conversion, whereas interaction between age and temperature was detected only for weight gain. It was possible to perform economic analyses to determine maximum profit as a function of the variables that were included in the model. It was concluded that the response surface models are effective to predict the performance of broiler chickens and allow the elaboration of economic analyses to optimize profit.


INTRODUCTION
The precise determination of the cost/benefit ratio in broiler rearing depends on the development of mathematical models capable of predicting growth and feed intake as a function of the factors that affect such variables (Oviedo-Rondón & Waldroup, 2002).Dietary protein (Kidd et al., 2005), environmental temperature (Faria Filho, 2003), and slaughter age (Zuidhof, 2005) are known to affect performance, carcass characteristics, and economic viability of broiler chicken production.Consequently, mathematical models that include such variables may help decision-making on which nutritional and management procedures should be used to optimize profit.Mathematical modeling is thus an important tool to the poultry industry, and has generated a large number of studies on this issue (Eits et al., 2005 a,b;Sakomura et al., 2005;Sklan & Noy, 2005;Zuidhof, 2005).
Among the available mathematical tools, response surface models are of great practical applicability, as they allow analyzing more than one factor simultaneously by means of first and second order polynomials, and are also able to assess the interaction between the factors involved in the study (Freund & Littell, 2000).Eits et al. (2005a) emphasized that the models should be practical (to include variables that are known by nutritionists), flexible (to involve variables such as sex, nutritional levels, environmental temperature, among others), and precise (derived from many databases).In such context, models have been developed based on literature results in order to predict performance, carcass characteristics (Eits et al., 2005 a) and profit (Eits et al., 2005 b) of broiler rearing as a function of the crude protein levels and have shown satisfactory adjustments.
A consistent retrieval of already published research may be accomplished by using the method of systematic literature review, also known as systematic review (Castro et al., 2002).Such review is the scientific technique of screening literature through specific methods to identify, select, and critically evaluate the relevant studies.Therefore, many factors must be previously defined and mentioned in the text, such as the search strategy, the databases, the time frame, and the criteria for including the studies.The studies that are not included must be cited, and their exclusion must be justified.Therefore, systematic reviews are reproducible and generally not biased.
The objective of this study was to elaborate response surface models based on literature data that include the independent variables crude protein, environmental temperature and slaughter age in order to predict performance and elaborate economic analyses.

Study screening
A systematic review was performed according to Castro et al. (2002); by means of electronic search of the key words environmental temperature, dietary protein and broiler chickens in the databases Biological Abstracts, Cab Abstracts, Medline, and Scielo in the period between 1995 and 2005.Afterwards, the references of the retrieved studies were also searched.The non-published results of research studies carried out by our group were also included (Departamento de Morfologia e Fisiologia from Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista -Jaboticabal / São Paulo / Brazil).

Inclusion criteria
The studies included in the analysis fulfilled the following criteria: 1) the studies evaluated the effects of temperature in environment controlled rooms and the levels of crude protein on the broiler chickens performance of commercial strains; 2) the studies presented number of repetitions, number of birds per repetition, nutritional levels, and performance results in tables; 3) the trials started between 20 and 23 days of age and lasted more than one week; 4) during the initial period, the broilers were reared under thermoneutral conditions.

Data collection
Means of weight gain (g/bird/d) and feed conversion (g/g) were collected from the studies that fulfilled the inclusion criteria.Such data were entered in Microsoft Excel ® spreadsheets together with information on temperature (ºC), dietary protein levels (%), mean age in days ([initial age+slaughter age] / 2), number of replicates, and number of birds per replicate.

Statistical analysis
Surface response models were adjusted (Freund & Littell, 2000).The following model has been proposed: body weight gain (g/bird/day) or feed conversion (g/g) in the i th observation; X i0 = 1 (intercept); X i1 = mean age (days) in the i th observation; [mean age = (initial age + final age) / 2] X i2 = X i1 2 ; X i3 = environmental temperature (ºC) in the i th observation; X i4 = X i3 2 ; X i5 = dietary crude protein (%) in the i th observation; X i6 = X i5 2 .β 0 , β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , β 7 , β 8 e β 9 = parameters estimated by the weighted least square method, considering as a weighting factor the total number of birds used to obtain the mean (number of repetitions*number of birds per repetition), expressed as a percentage of the total number of birds in the database.Therefore, means obtained using a higher number of birds had greater weight when parameters were estimated.ε i = random error associated to the i th observation.
Data were analyzed for the presence of outliers, homogeneity of variance, and normality of studentized errors of residuals (Freund & Littell, 2000).Parameters showing probabilities lower than 5% were kept in the model.

Model validation
The developed models were tested for their and Applications for Economic Analysis and Applications for Economic Analysis and Applications for Economic Analysis and Applications for Economic Analysis and Applications for Economic Analysis 133 accuracy, precision, and bias (Harlow & Ivey, 1994).Accuracy identifies if there are differences between the model-predicted values and the observed values.Accuracy was assessed using a T test in order to test the hypothesis that the sum of the differences between observed and predicted values was null.Precision verifies if the model predicts the distribution around the mean.It was assessed by plotting a graph with the studentized errors and the observed values.Bias represents systematic failures that the model may have and was verified by plotting the predicted values against the observed values.

Economic analysis
A program was elaborated in a Microsoft Excel ® spreadsheet to determine which protein level, rearing temperature, and slaughter age promoted maximum profit according to market changes (the diet and the live bird prices).The resulting equations for weight gain and feed conversion were used to calculate income, cost, and profit, which were defined by: Income live bird = live weight x price per kg of live bird; Cost = [(feed intake x diet price) / 0.70].Therefore, feeding costs were considered to be 70% of the total cost.Feed intake was determined as the product between weight gain and feed conversion; Profit = Income live bird -cost.
Live weights at 1 and 21 days of age, feed intake from 1 to 21 days of age, diet prices, and live bird were established as input variables to be defined by the program user.Microsoft Excel ® Solver was then used to define which protein level, temperature, and slaughter age resulted in maximum profit.
A simulation of profit maximization was performed; the values considered as normal market scenario were the cost of R$ 0.531/kg diet for the diet fed from 21 days to slaughter age and the income of R$ 1.40/ per kg of live bird.Three unfavorable market situations were simulated: (A) diet cost 20% higher; (B) price paid for the live bird 20% lower; (A+B) both situations occurring simultaneously.Such market situations were applied to optimize the slaughter age that promoted maximum profit for broilers reared at different temperatures and to optimize the levels of crude protein that resulted in maximum profit when slaughter age was changed.Additionally, weight gain and feed conversion were optimized for the situations already described.

Systematic literature review
The systematic review retrieved 19 studies, out of which 11 did not fulfill the inclusion criteria: the trial was not carried out in rooms with controlled environment (Rahman et al., 2002;Zarate et al., 2003 a,b); the trial did not start between 20 and 23 days of age (Cahaner et al., 1995;Faria Filho et al., 2005, 2006;Temim et al., 1999Temim et al., , 2000 a,b) a,b); the trial did not use a commercial broiler strain and lasted less than one week (Gonzalez-Esquerra & Lesson, 2005); the performance results were not presented (Hruby et al., 1995).
The eight studies that fulfilled the criteria were Alleman & Leclercq (1997), Cheng et al. (1997 a,b), Cheng et al. (1999), and four studies from our group (Faria Filho, 2003, 2006).Such studies involved only Arbor Acres & Ross, Cobb and Ross male broiler chickens reared on litter or in cages, and the age varied between 21 and 49 days old.Rearing temperatures varied from 20 to 35ºC, crude protein levels from 16 to 24%, and initial weights from 784 to 899g.

Surface response
The weight gain and feed conversion estimated parameters of the response surface model are shown in Table 1.
The linear and quadratic terms of the polynomials for crude protein levels, broiler mean age, and environmental temperature were significant for weight gain and feed conversion (Table 1).These results are shown in Figure 1 for a hypothetical situation (45-dayold broilers reared at 25ºC and fed with 20% protein), in which one of the three factors was changed and the others were kept constant.
Protein levels that optimized weight gain and feed conversion were 20.5 and 21.3%, respectively (Figure 1-A).Such values are higher than those recommended by Rostagno et al. (2005), of 19.7% CP for the period between 22 and 33 days of age and 18.3% CP from 34 to 42 days of age.Nevertheless, the values are similar to the NRC (1994) recommendations, of 20% protein for broilers in the grower phase.
Slaughter ages that optimized weight gain and feed conversion were 45.5 and 36.6 days, respectively (Figure 1-B).Sakomura et al. (2005) determined growing parameters of Ross ® broilers from 1 to 70 days of age and observed that the growth rate (g/day) for males is maximum at 42 days, which is close to the 45.5 days of age in the present study.Besides, feed conversion gradually worsens with age (Cobb, 2001), and the slaughter age that minimizes feed conversion is younger than the age that maximizes weight gain.
As to rearing temperature, better weight gain and feed conversion were obtained at 22.1 and 25.4ºC, respectively (Figure 1-C).These results evidence that the optimal rearing temperature depends on the characteristic to be optimized.Faria Filho et al. (2005) observed that cold-exposed broilers during the starter phase showed higher weight gain than birds reared in a thermoneutral environment, but feed conversion was worse.The mean rearing temperature recommended by Cobb (2001) for birds from 21 days of age until slaughter is 22.5ºC, which is similar to that obtained for body weight gain optimization.
There was no significant interaction between environmental temperature and crude protein levels for weight gain and feed conversion (Table 1).The independence between the two factors on weight gain and feed conversion indicates that the effect of a particular protein level is the same for broilers reared either at thermoneutral or high temperatures.Nutritionists oppose to the increase in the dietary protein levels when broilers are submitted to heat because of the high caloric increment of protein (Musharaf & Latshaw, 1999).Nevertheless, Temim et al. (2000b) verified that high-protein diets (25%) had no effect on the turnover of the muscles Pectoralis major, Sartorius, and Gastrocnemius of broilers reared at 22 or 32ºC.Such results indicate that high-protein diets do not increase heat production, since muscle turnover is highly associated to heat production (Macleod, 1997).The lack of heat production in broilers fed high protein levels was also found by Faria Filho (2006).These findings support the utilization of diets with high protein levels even in hot environments.
There was a significant interaction between age and crude protein levels for weight gain and feed conversion (Table 1).In Figure 2-A, the response surface graph shows the behavior of such interaction for feed conversion.It is observed that 35-day-old broilers improved feed conversion when high protein levels were fed; on the other hand, the effect gradually disappeared with age.The result for weight gain was similar (graph not shown).
Age and environmental temperature showed a significant interaction for weight gain (Table 1).The results presented in Figure 2-B show that weight gain decreased as age increased when birds were heatexposed.Such results occurred because broilers become very susceptible to heat during the grower phase (after 21 days of age).During growth, feathering is completed and the area/volume ratio of the birds decreases; these are the main reasons why older birds have difficulty to maintain thermal homeostasis during heat exposure.May & Lott (2001) elaborated response surface models and observed that the birds became more sensitive to heat as body weight (age) Increased.

Model validation
Table 1 shows the coefficient of determination (r 2 ) values for weight gain (r 2 = 0.93) and feed conversion (r 2 = 0.85), indicating that the developed models satisfactorily explained the data variation.The fitted models did not explain only 7% of the variations in weight gain and 15% of the variations in feed conversion.This lack of fitting might be explained by factors that were not included in the model, such as dietary energy levels, amino acid supplementation, and stocking density, in addition to factors that were not controlled.Accuracy was measured using a T test in order to verify the hypothesis that the sum of the differences between the values predicted by the model and the observed values was zero.The hypothesis has not been refuted for weight gain (p=0.61),nor for feed conversion (p=0.34), which indicates the good accuracy of the model.
The models also adequately predicted the distribution around the mean (precision).Figures 3-A and 3-C show that the studentized errors are well distributed around the mean for weight gain and feed conversion, respectively, indicating the good precision of the models.
The graph of predicted versus observed values allows verifying the presence of biases.For a nonbiased model, the graph must have the aspect of a straight line.In Figures 3-B and 3-D, the dotted line represents the ideal situation, whereas the full line is the curve estimated by the least square method.Both for weight gain (Figure 3-B) and for feed conversion (Figure 3-D), there was good proximity between the two curves, indicating the absence of biases.
It is worth noting that the data used for the accuracy, precision, and bias tests were the same as those used to elaborate the model, which is not the ideal situation.Therefore, it is suggested that the models are tested with other databases, preferably with field data, for a complete validation of the model.

Economic analysis
Figure 4-A shows the optimization of the slaughter age that promoted better profit or performance as a function of rearing temperature and market conditions.
In all simulated market scenarios, it was seen that broilers reared at 32ºC should be slaughtered earlier to optimize profit or performance as compared to birds reared at 22 or 27ºC.In addition, in unfavorable market scenarios (high price of the diet, A; low price of the live bird, B; or both conditions simultaneously, A+B), it was more profitable to slaughter the birds earlier, particularly under the situation A+B.It is interesting to note that the slaughter age that promotes maximum weight gain was considerably higher than the age that optimizes profit or feed conversion.
Figure 4-B shows the optimization of protein levels that promoted greater profit or performance as a function of slaughter age and market scenarios.It was seen that protein requirements decreased with increasing slaughter age in any market situation.Furthermore, the imposed market scenarios (normal, A, B, and A+B) did not change protein requirements for maximum profit.Protein requirements for optimizing weight gain and feed conversion were higher than

Figure 1 -Figure 2 -
Figure1-Feed intake, weight gain, and feed conversion predicted as a function of the dietary crude protein level (A), age (B), and rearing temperature (C) in which one of the three factors was changed whereas the other two were kept constant.

Figure 3 -
Figure3-Evaluation of precision (A and C) and bias (B and D; the dotted line represents the optimal situation, whereas the full line is the curve estimated by the least square method) of the response surface models elaborated for weight gain and feed conversion.

Figure 4 -
Figure 4 -Slaughter age optimization as a function of rearing temperature (A), and protein levels as a function of slaughter age (B) and market conditions.Normal = normal market scenario; A = diet price 20% higher; B = live bird price 20% lower; A+B = both A and B occurring simultaneously; GP = optimization for weight gain; CA = optimization for feed conversion.

Table 1 -
Estimate parameters, standard error of the mean (SEM), and probability (P) for weight gain and feed conversion of 21 to 49day-old broiler chickens as a function of environmental temperature (temperature; °C), dietary crude protein (protein; %), mean age (age; days; [ (initial age + final age) / 2]).