- Email: [email protected]
Accuracy, Precision, and Commercial Benefits of Growth Modelling for Broilers1
01994 Applied Poultry Science, Inc
ACCURACY, PRECISION, AND COMMERCIAL BENEFITS OF GROWTH MODELLING FOR BROILERS' H. B. HARLOW2 and F. J. N E Y Novus International,Inc., #20 Research Park Drive, St. Charles, MO 63304 Phone: (314) 926-7440 F M : (314) 926-7405
Primary Audience: Nutritionists, Live Production Managers, Broiler Integrators
lows many of these decisions to be assisted by DESCRIPTION OF PROBLEM the enhanced information provided by compuIn any broiler operation, everyday decisions impact the profitability of the business. Examples of these decisions include selection of feed ingredients, specification of the feeding program, feed manufacturing, drug programs, breed selection, and mechanical housing equipment such as house style, ventilation, feeders, and waterers. Today many of these decisions are made using intuition, industry experience, or word-of-mouth recommendations. However, over the past decade the technology has become available that al-
terized growth models. The purpose of this paper is to outline a procedure that can be used to select and evaluate a growth model for use in a particular commercial operation. The first step in evaluatingagrowth model is to determine how the model will be used. Commercially, growth models can be used for a variety of applications. These range from estimating how a change in feeding program will impact feed conversion to determining if nutrition is a probable cause for an observed performance problem. Questions involving
Presented at the 1994 Poultry Science Association Informal Nutrition Conference Symposium: Poultry Modelling - Theoretical and Practical Evaluations 2 To whom correspondence should be addressed 1
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feed utilization can be evaluated according to economics - how a change in feeding program will impact unit bird cost. Figure 1 illustrates the impact of changing dietary energy and protein on unit bird cost. The cost per bird is given using a typical U.S.diet and 1992 feed prices, revealing that the best economics under these conditions occurred at a moderately low feed density. In examining Figure l it is important to keep in mind that modifications to a cornmercial feeding program can have unintended effects. For example, increasing early diet density can have a negative impact on early survivability due to leg and heart problems aggravated by higher growth rates. One commercially important application of growth modelling would be to determine whether or not an observed field problem is the result of a change in nutrition. In this case a model would determine if the observed growth would have been expected given the delivered feed amounts and composition, based on the variation observed in past performance. Any growth estimate of this type should be qualified with a confidence interval for the desired level of confidence, usually
95%. Thus, if the actual production falls within the expected range, the observed performance can be attributed to the nutritional factor. If the production falls outside the expected range, the cause can be categorized as the result of some non-nutritional factor. The size of the confidence interval, which is related to the live growout variation, can be used to determine if production is "under control" according to the statistical definition. Thus, growout variation has a significant cost associated with it and should be kept as small as is feasible [l]. The selection of a growth model should be based upon commercial goals. Over the last decade a number of broiler models have been available commercially [2,3,4,5,6,7,8]. A few of these are summarized in Table 1. These models evaluate broiler growth using a wide variety of approaches ranging from the straightforward (attaching an economic optimizer to a Gompertz growth curve) to more sophisticatedrule-based systems (information about growth is compiled into an "expert"system). The different programs also vary in the amount and type of input data required and
Cost per Kg.
:u.s.cents)
.tal l/K -IGURE 1. Impact of changing energyand protein on unit live weight cost. The base feeding program consisted )f four diets with energy, protein, and feed weight defined as (3200,23, 0.82),(3200,21, 1.05), (3250, 19.5, ).87),and (3275, 16, 0.21) for diets 1 through 4, respectively.
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MODEL NAME Chickopt"
BRIEF DESCRIPTION
DATE AVAILABLE
I
Economic optimizer tied to a Gompertz style compartmental model
I
Late 1994
Walla Model
Enterprise model providing economic modelling for an entire operation
Announced 1993
Fortell" Broiler [9]
Commercial version of the Edinburgh broiler model with u m i f i e d imDrovements
1991
Hurwitz Broiler
IEconomic model, earty predecessor to Chickopt"
IGM"
I
Pesti/Brill Model
I
Edinburgh Broiler
Statistical model based upon a large series of feeding trials, tied to an oDtimizer
I1990
I
1989
Quadratic response surface model which determined the least cost finishing ration
Late 1980's
A rule-based compartmental model based upon daily growth partitioned according to growth potential and available nutrients
Early 1980's
how they are adjusted or calibrated to represent commercial production. While there are a number of different approaches that can be used to evaluate growth models, the procedure described in this paper is the one developed by the authors as a tool to guide the development of the IGM" [lo]. In order to describe the evaluation process of models it is necessary to define some terminology, including "calibration," ''accuracy,""precision," and "bias." CALIBRATION Calibration is the process of adjusting model parameters to allow a growth model to estimate the growth of commercialbroilers. Of the currently available models, each uses a different calibrationmethod. For example, the Edinburgh growth model [q requires the coefficients for a Gompertz [ll]growth curve and the sensible temperature profile for the growout. The Chickopt" [12] model requires live weight data, taken weekly, so that the coefficients for a Gompertz equation can be estimated by the program. The IGM" program requires a minimum of twenty flocks of production data so that a statistical model can be adjusted to reflect the observed broiler growth. Each of these methods has strengths and weaknesses. The important point is that following the calibration step, each model should be able to predict commercial production accurately.
ACCURACY Accuracy can be defined as how closely a model estimates production data. That is, if feed conversion is the estimate required, the model should closely estimate the feed conversion observed in the field. Accuracy can be expressed in a number of ways. One way is to express it as a percentage within a range. For example, if a model were accurate to one point of feed conversion (0.01) and if an operation has an average feed conversion of 1.90 and a range of feed conversions of 1.70-2.10, the relative accuracy could be expressed as: Error Relative Accuracy = -= 0'01 x 100 = 2.5% Range (1.90 - 1.70)
Thus, the model would have a relative accuracy of 2.5%. A second method to define the accuracy would be to use a t-statistic. A t-statistic determines if a collection of estimates is significantly different from the actual values. For example, if a model were used to estimate the feed conversion for the production of a complex on a flock-by-flock basis, a t-statistic could be computed on the collection of estimates. The t-statistic would be given as: average (delta) 6 t-statistic = where:
SD (delta) n = number of flocks predicted average = simple average operator SD = standard deviation delta = actual -predicted
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This equation makes the assumption that the actual and predicted variances are equal, in most cases a reasonable assumption. However, since a model cannot reasonably account for all of the sources of variation, the formula for the t-statistic with unequal variance may be more appropriate in situations where the variances of the actual and predicted production parameters are significantly different. In either case, once a t-statistic has been calculated, a table of critical t-values can be used to determine whether or not the model predictions are significantly different from the actual data. The smaller and hence less significant the t-value is, the better the accuracy. PRECISION The precision of a model can be assessed according to the distribution of the prediction errors. That is, a precise model not only correctly predicts the average value but also predicts the distribution of the data. This achievement would be reflected in the standard deviation of the residuals or the difference between the actual and predicted values. BIAS Bias can be defined as a systematicfailure of a model. For example, a model with a bias may consistently over or under predict live weight for birds which are lighter or heavier than the average. An example of bias appears in Figure 2. A model and calibration without bias would have the cigar-shaped region of data points oriented along the dashed line. However, in this example the model failed to account for the observed variation and is biased, resulting in the data lying along the solid line instead. A model can be accurate and precise and still not predict the response of broilers to changes in a feeding program because different breeds have different growth curves, efficiency of feed utilization, and resistance to stress. Figure 3 shows an example of two breeds grown using the same feeding program and feed ingredients. Examination of this figure shows that a model that is accurate for one breed will be inaccurate or biased for the other. It is important to note here that not only are the general shapes of the surfaces (i.e., response of the birds to nutrients) differ-
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2.8
1
2
12
2.2
,
I
I
2.4
2.6
2.8
Actual Live Weight (Kg.) FIGURE 2. Data from 200 commercial flocks plotted as a scatter graph to demonstrate bias.
ent, but the relative weights of the birds are significantly different. Regions with the same surface shading correspond to diets that provide similar weight gain. The width of the shaded regions corresponds to the 95% confidence level for the mean from the data set from which these surfaces were generated. A bicubic spline smoothing algorithm was used to smooth the plotted surfaces. Obviously, an accounting for breed must be considered in any commercial setting. Additionally, the genetics of broilers changes to such an extent that the life expectancy of a breed adjustment is only two to four years. Bias can also occur due to differences in feed ingredients. That is, the feed manufactured does not always contain the energy and protein levels intended. If the error in feed content occurs in a systematic way, a bias in model estimates results. Model bias can occur in two ways. The most common sources of bias in the rule-based models are inaccurate or incorrectly applied rules. In a mathematical or statistical model, the rule is the equation that describes the growth of the animal. If this equation has the wrong shape or characteristics, it results in bias or "lack of fit" as the statisticians describe it. However, even when the rules are correct, bias can still be a problem because the data used to calibrate the model has a pattern of errors leading to a poor or incorrect calibration. The more sensitive a model is to the pattern of variation or the error structure of a set of calibration data, the more likely a model
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Strain A 21 dav
395
I
Strain B 21 day
KcalKg.
Protein
:IGURE 3. These two graphs illustrate the difference in growth pattern between two common commercial ]reeds. The breeds are characterized as: A) a slowgrowing strain and B) a fast-growing strain.
will be biased and the poorer the precision becomes. An ideal model would be insensitive to the distribution of errors in the calibration data. However, the sensitivity to variation is a function of the mathematics used in the model, and all models are susceptible to bias to some extent. When all of these factors are considered, the modern crafter of growth models has a significant challenge. Given the necessities of modern business and the narrow profit margins of the broiler industry, it is critical that a growth model be selected carefully. The rest of this paper will describe the techniques applied by the group to evaluate two different growth models: the IGM" program version 4.02.2 and Chickopt" program version 1.0.
The second problem is the micro evaluation or the application of a model to commercial data. Since most flocks in a commercial setting are fed identical diets in slightlyvarying amounts for similar periods of time, the micro evaluation looks at how well the model predicts the distribution of the live weight or feed conversion in the field. Together, the macro and micro evaluations can provide an excellent evaluation of the accuracy and precision of the model. THE IGM" GROWTH MODEL The IGM" program is a semi-empirical model, the culmination of a large number of research trials run at the Novus International, Inc. Poultry Research Facility. The basic premise of the model makes no assumptions about the growth of broilers. Instead, the program captures the growth pattern expressed by the birds grown in large numbers on different feeding programs at the research facility. To date 288 different feeding programs have been investigated.The feeding programs were carefully selected using experimental design technology so that the impact of energyand protein in the diet on production parameters could be accuratelydetermined as a function of age. A mathematical model, constructed to fit this data, is called the "base model'' and describes the growth response of broilers to energy and protein. It is accurate and precise over the range of feeding programs included in the experimentaldesign and accounts for most of the variation observed in
MATERIALS AND METHODS In understanding the applicability of a growth model to a commercial operation researchers must face two distinct problems. The first problem that must be addressed is a macro evaluation of how well a growth model predicts changes in performance from changes in energy and protein over a wide range of feeding programs. This evaluation is typically accomplished using a feeding study, which provides information about the relative accuracy of a model with regard to dietary changes. As an example,one might look at how well a model accounts for the change in feed conversion that accompanies a change in dietary protein or energy content.
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performance, with model R2values up to 0.99. To date over twenty separate feeding trials have been conducted for growth modelling. The studies used to generate the base model for the IGM" program covered a number of diets. They also covered the energy range from 2920 to 3420 kcaVkg and protein between 13 and 27%. Since protein is only part of the story for a growing bird, the feeds used in these studies were formulated using amino acids in constant ratio. The constant ratio followed the 1986 Maryland Recommendation [13] and was keyed to the amount of total sulfur amino acids (TSAA) in the diet. All diets were formulated using corn, soybean meal, supplementalamino acids, and a vitamin and mineral premix. The premix was added to a level so that essential vitamins, minerals, and choline were equal to, or slightly in excess of, the NRC recommendations [14].Amino acid supplementation,when necessary, was accomplished using commercially available sources. Additionally, if the density of the diet was so low as not to be feasible to formulate using corn and soybean meal, rice hulls were used as a diluent. From each experiment, feed intake, individual and pen live weights, feed conversion, mortality, culls, and carcass composition data were collected. This data was taken at predetermined ages ranging from 5 to 77 days and collected for a number of different breeds, including most of the breeds used commercially in the U.S. The data were assembled into data sets analyzed using SAS [15]. A base model was generated as specified accordingto the experimental design. The carcass composition measurements were taken by dissection and included chilled carcass yield, breast muscle (pectoral major and minor), breast frame, wings, leg quarters, and feet. Over the range of experiments the model explained over 80% of the variation in carcass composition. The capabilities of the IGM" program fall into four areas: the estimation of production parameters, optimization of the feeding program, evaluation of flock performance, and evaluation of the sources of performance variation. In each case a calibration is necessary before the model can be applied to a particular commercial facility.The calibration process for the IGM" program is accomplished by collectingcommercial performance data, consisting of information about the feed
manufactured during the period, the amount of feed delivered, live production data, and processing information. These data were used to adjust the base model to reflect production at the commercial site. The adjustment of the N o w International, Inc. base surface to match the commercial data allows an accounting to be made for the differences in average performance, response of the birds to energy and protein, and rate of growthcalibration will generally be successful so long as the birds in the field are responding to the nutrients in the diet. In some cases, factors other than nutrition interfere with the performance of the commercial flocks. In these cases a calibration cannot be successful. But given a successful calibration, the model can be used productively. The IGM" program could be used to determine the impact of dietary changes on the performance of birds in the field. Characteristics that can be modelled would include live weight, feed conversion, age, and carcass composition. For example, if the feed allocation is changed between the diets which make up the feeding program, the model can assess what impact that will have on feed conversion. Others might ask, "What would the impact be of adding or removing energy or protein from the diet both on cost and performance?"From a commercial standpoint, one of the more valuable applicationsof a model is to minimize feed cost or feed conversion or maximize the value of the produced bird. This ability is directly related to the profitability of an operation since feed accounts for a major portion of the cost of producing a broiler. The factors that the IGMN growth model can currently optimize include least cost per unit live weight and unit carcass value. Since the calibration process uses individual flock information to adjust the base model to accurately represent the commercial production, the actual and predicted data are readily available. Predicted data can evaluate how particular flocks are doing in light of the nutrients contained in the feed consumed by the buds. On average, the difference will be zero for a calibrated model. However, some flocks will perform better or worse than the average. Since a growth model accounts for nutrition, it is possible to compare these flocks with the impact of differing ages and feed amounts corrected.
Poultry Modelling Symposium HARLOW and IVEY CHICKOPT" The Chickopt" program was written over a number of years by two Israeli scientists, Shmuel HunVitz and Hovav Talpaz. It is an extension of the Israeli growth model that is well documented in the Literature [16, 17, 18,191 and will only be briefly described here. The Chickopt" program consists of an optimizer tied to a compartmental growth model based upon a Gompertz growth curve. The growth of each compartment (protein, feathers, and fat) leads to an amino acid and energy requirement. These requirements are then used to determine the feed cost, which is computed using a built-in linear feed formulation program (LP) to determine the cost of a particular feeding program. The Chickopt" program ties energy and protein together accordingto a predefined protein:energy ratio determined experimentally at the Israeli Agricultural Research Organization (-0). The inputs into the Chickopt"' program include weekly growth data, the desired live weight, information about feed component cost, and nutritional limits for the LP portion of the program. The output is the dailygrowth and feed cost. Additionally, the program provides feed composition and cost. The outputs predicted by the Chickopt" program include daily gain, potential daily gain, feed intake, feed conversion, and economic analysis ($/ft2, $/lb, $/bird, and $/ft2/day). Additionally, the program computes the feed formulation and nutrient composition of the predicted diet on an individual diet basis. The program allows the user to choose between weekly, biweekly, or specified dietary periods. The program also provides a calculation so that the economic impact of early feed restriction can be estimated or optimized. The concept behind feed restriction is that by restricting feed early, tissue mahtenance is reduced. There is some evidence that birds restricted early will exhibit compensatory growth in the time period following the restriction [20]. DATA REQUIREMENTS nKo sets of data were used in the evaluation of the growth models given here. The first set of data is a subset of one of the research trials used to test the base surface for the IGM" program. This data was used for the macro evaluation of the models. The second
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set of data is performance data from the field, selected from the large amount of commercial data accumulated in the implementationof the IGM" program at many complexes around the world. This data set was selected from a typical producer to represent flock performance in the U.S.
RESULTS AND DISCUSSION The research trial was conducted at the N o m Dardenne Research Facility using 128 battery cages with five birds per cage. The feed was prepared as described in the IGM" model description (above). The birds in each pen received the same diet ad libitum for 21 days. At weekly intervals the birds and the feed were weighed. Mortalities were corrected by computing the pen feed conversion, determining the amount of feed necessary to account for the weight increase in the dead birds, subtracting this feed amount from the pen feed amount, and recomputing a"corrected" feed conversion. The design used was a 4 x 4 x 2 full factorial with variables being energy, protein, and bird sex. Similar data was available at weekly intervals for female and male birds. Table 2 gives the results of this study. Data from the male and female treatments at the same energy and protein level were combined to estimate the performance of mixed sex birds. Data from all sixteen energy and protein treatments was then used to calibrate the IGM" program. This calibration predicted the live weight and feed conversion for those diets along the diagonal. While it is not considered statistically valid to evaluate a mathematical model by estimating data points included in the calibration set, here it determined a lack of fit of the model for comparative purposes. It should also be noted that the calibration used all of the data while the comparison used only a subset of the data. The results of this comparison appear in Table 3. The weekly data from the combined male and female treatment containing 3085 kcaVkg energy and 21% protein were used to calibrate the Chickopt" program. Again the diagonal elements of Table 2 were estimated. Since the Chickopt" program uses a fxed protein:energy ratio, the diagonal elements seemed to give the fairest comparison. The results from this comparison also appear in Table 3.
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TABLE 2. Female live weiahts (feed to aainl of two broiler strains showinn the response to eneray and proteinA
ENERGY LEVEL
*Data are the average of four pens per treatment B~ = a slow-growingstrain, B = a fast-growing strain
In examining Table 3 it is clear that both models performed an adequate job of estimating the 21-day live weight and feed conversion with the largest live weight error being 41 g or 6.3% with a relative error of 47% for the IGM" program. The largest feed conversion error was produced by Chickopt: 14points (0.145)or 10.3% with a relative error of 55%. In each case the largest error occurred on an extreme diet that would be unlikely to be employed in the field. Both programs faired much better regarding live weight for diets more typical of those employed in the field (center two columns), with relative errors of around 15%. However, for feed conversion the IGM" program outperformed Chickopt"
I with a relative error
of 8.4% (compared to . . 44.3% for Chickopt". Perhaps most of the difference in feed conversion accuracy can be linked to the futed energy:protein ratio employed by this version of the Chickopt" program. The Chickopt" program was formulated with a protein:energy ratio that closely matches commercial formulas, while the data used in this test spans a particularly wide range of protein:energy ratios. COMMERCIAL COMPARISON The micro evaluation of the two programs involved two sets of commercial data selected to provide a fair evaluation of each program in real world settings. The set of data selected for
TABLE 3. IGM'" and Chickopt" program estimations of experimental data following calibrationA
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Chickopt" came from a producer that produced buds where a set of weekly live weight data was available that could be used for calibration purposes. Due to the requirement for weekly live weights for calibration, the commercial data used to evaluate Chickopt"' is approximately four years old. Data of this age would be expected to have poorer feed conversion and average daily gain due to the constant improvements in genetics made by commercial breeders. These advances can readily be seen by observing the feed conversions in Tables 4 and 5. For the IGM" program a more current calibration data set was selected with birds of a comparable age located in the same geographical part of the country. Because of the volume of data used by the IGM" program, only a sample of the predicted flock data is given. The original data set contained 265 flocks from a four-month period. The calibration of Chickopt" used weekly live weight data. Once the program was calibrated, the flock data was estimated using actual feed intakes. The Chickopt" program estimates to the nearest whole day, so feed was added to the last diet to insure that the program output extended at least one day beyond that to which the birds were grown. The estimates for live weight given the consumed feed were adjusted using h e a r extrapolation over the last day in which the feed
should have been consumed. The results of this comparison for twelve flocks appear in Table 4. Table 5 offers a similar set from the IGM" program. Since only a portion of the data from the IGM" program could be presented, the first twelve flocks in the calibration set were selected. Examination of Tables 4 and 5 shows that both programs are able to do a reasonably good job of estimating the resultant live weights. The relative accuracy of the IGM" program using the twelve flocksin Table 4 was 16.5%, where the standard deviation of the residual live weight was used as the estimate for the error. If the standard deviation from the entire data set of 265 observations was used (0.021), the relative error was 13.4%.The t-value (Equation 2) was calculated to be -0.573, with the critical value for the t-test at the 95% confidence level being 2.179. The t-value for the entire set of 265 flocks was -0.101. The data set in Table 4 contains one outlier, the third observation down. This data point was determined to be an outlier using the Grubbs test at the 99% confidence level [21]. The Grubbs statistic was 0.29 with a critical value of 0.3554. Correcting for the outlier, the relative accuracy is 8.9% (Table 4). For the Chickopt" program the relative accuracy of the data given in Table 5 was 14.7% with a t-value of 1.805, which is well below the critical value of 2.179. This level of
TABLE 4. A subset of the actual commercial data used to determine the accuracy and precision of the I G M " program AGE
NUMBER FEED OFBIRDS CONVERSION
ACTUAL
LIVE WEIGHT (kg)
42
31600
1.830
1.898
42
39600
1.772
1.855
41
50300
1.857
1.775
42
29600
1.789
1.807
42
33200
43
36400
1.791 1.765
1.904 1.880
41
38300
1.782
1.932
42
48000
1.793
1.870
43
37900
1.794
1.863
42
28700
1.774
1.856
45
39200
1.789
1.876
42
39300
1.793
1.877
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;ion of the Chickopt" program
NUMBER FEED OF BIRDS CONVERSION
AGE
ulooo
42 44
21300
2.000 1.999
42
19200
1.900
42 42 42 42
44 42 43 42 45
I
21300 21200 22000 21000 21300 21000 21600 21300 19200
I
1.990 1.890 1.900
1.910 2.009 1.940 1.980 2.040 2.080
I
ACLZlAL
PREDICTED
LIVE W I G H T (kg)
LIVE WEIGHT (kg) Starter
Grower
Finisher
1.656
1.690
0.998
1.802
0512
1.679
1.713
0.939
1.857
0.561
1.724
1.671
1.041
1.783
0.451
1.740 1.676 1.702 1.705
0.937
1.890
0.622
0.939 0.913
1.857 1574
0.850
1.733 1.738 1.756 1.no 1.806
I
ACTUAL FEED WEIGHTS (kg)
1.810 1.765
0.937
1.824 1.842 1.865
1.819 1.854
0.923 0.939
1.910
1.914
accuracy is quite good considering the small calibration data set required. Another method to perform the micro evaluation of a growth model is to determine the amount of variation explained by the model. The easiest and most informative method is to plot a scatter graph of the actual versus the predicted production parameter. Figure 4 records this procedure for the live weight of commercial broilers (Note that this is not the same data set as was used in the calibration work described previously). In Figure 4, actual vs. predicted live weights are plotted. An ellipse was drawn that contained approximately 95% of the data points. The variance not accounted for in the model is the ratio of the minor to the major axis. If the model accounted for all of the variation in live weight, all of the points would fall on the diagonal line. However, there are always sources of variation not captured by a model. These result in unexplained variations and in a deviation of the points from the diagonal line. If an ellipse is drawn that contains 95% of the data points, the ratio of the minor axis to the major axis provides an excellent estimate for the variation not explained by the model. Conversely, one minus this quantity is the variation explained by the model. This result is the same as the correlation coefficient between the actual and predicted quantities squared. When the percent of variation was determined for the example data given in Tables 4
c.,
I
0.951
I I I
0.952
1.506 1.890 1.774 1.970
0.488
I I
I
1
0.923
0.802 0.812 0.754
2.04
.,-l
I
1.70
1.81
1.93
2.04
Actual Live Weight (Kg) FIGURE 4. Illustration of the use of a scatter graph to estimate the amount of variance not accounted for in the model.
and 5, the Chickopt" program explained 78% of the variation in live weight, while the IGM" program explained 81% of the variation if the outlier is removed. When this value was determined for all 265 flocks in the IGM" calibration data set, it was found to be 92.6%. In either case both models explain a majority of the variation in the commercial data sets. Experience with this procedure over time has shown that a model can account for between 50 and 95% of the observed variation in live weight for most commercial operations.
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Each of the models tested here demonstrated both strengths and weaknesses. For example, some of the strengths of the Chickopt" program are that it is easy to use, provides reasonable estimates of the amino acid needs for the bird, provides a selfcontained LP program, and requires a small calibration data set. Some of the weaknesses of this program include the use of a fixed protekenergy ratio which leads to errors in estimates for feed conversion and that the individual flock estimates needed for the analysis of variance have to be computed manually. On the other hand, the strengths of the IGM" program include relatively higher precision and accuracy, an approach that makes no assumptions about broiler growth, and the ability to estimate carcass com-
position. Additionally, the program provides individual flock estimates as part of the calibration process. Some of the weaknesses of the IGM" program include the requirement for large calibration data sets, program complexity, and lack of an integral LP program requiring several passes between the user's LP program and the IGM" optimizer to reach the correct solution. Additionally, the program as it exists today requires substantial computational resources to operate, both in terms of program size and memory requirements that preclude ready implementation of the program on a desktop PC. Overall, the IGM" and Chickopt" programs complement one another because the weaknesses of one are the strengths of the other.
CONCLUSIONS AND APPLICATIONS 1. In developing and applying growth models over the last six years, it has become evident that broiler production is a science with capable professionals involved in all aspects of production. Consequently, any model must be quite good if it is to contribute in the competitive environment of a modern broiler complex. 2. The techniques described in this paper can be used to evaluate the effectivenessof a growth modelling program for a particular commercial organization or goal. It is important to understand the strengths and weaknesses of any model in order to obtain the maximum commercial benefit. 3. Growth models have provided a much needed tool to understand the cost variable environment under which a modern broiler complex operates. Growth models are rapidly moving away from being a tool used as a competitive advantage by a privileged few and toward a resource required by any organization desiring to remain profitable in the cost variable environment of a global market place. 4. Growth models provide a tool to diagnose problems that have been very difficult to address previously. In the past when a producer desired to evaluate new technology or different feeding programs, small trials were conducted in research facilities. However, there was never a guarantee that these results could be directly applied in the field because of differences in field stresses. Models provide a scientific approach to evaluating new concepts and ideas in the field by removing the variation attributable to the feed consumed by the bird. This method allows for better decisions to be made in a timely and efficient manner. 5. Growth modelling remains a rapidly developing field. The field is becoming more and more competitive with new entries entering the market on a regular basis. While the current models are not perfect, they represent a valuable tool for the modern broiler producer.
REFERENCES AND NOTES 1. Harlow, H.B. and F.J. Ivey, 1993. Consequences of variation on rofitability in commercial broiler production. Poultryh. n : ~ . 2. Pcsli, G.M., RA Arraes, and B.R Miller, 1986.Use of the auadratic erowth resmnse to dietan, Drotein and energy 'concentr&ons in feast-cost feed 'fknulation. Poultry Sci. 65:104&1051.
3. Rhone-Poulenc advertisement in November 1993 issue of Poultry Digest which provides a brief description of the Wala Group agricultural growth model, p. 3A. 4. Muirhead, S., 1991. Simulation modeling provides new insight into nutritional problems. Feedstuffs 63:14.
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402 5. Emmans, C.C., 1981.A model of the growth and animals,particularlypoultry. feed intakeof &-fed Pa es 103-110 in: Computers in Animal Production. G.h. Hillyer, C.T. Whittemore,and RG.Gunn, eds. Occ. Publ. No.5, Br. Soc. h i m . Prod. 5:103-110. 6. Emmpns, G.C., 1987.Growth, body com and feed intake. World’s Poultry Sci. Assn. J. 43:%2
7.Harlow, H.B. and FJ. Ivey, 1994a. Growth models: Window on bottom-line costs. Broiler Industry 573&34. 8. Harlow, H.B. and FJ. Ivey, 1994b. Improvements in broiler production throu the use of the Novus lvey Gmwth Model (IGM’).&es 21-31 in: P m . Nutr. and Tech. Symposium, St. Louis, MO. 9. Fortrell‘ is a registered trademark of Heartland Lysine, Inc.
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10.IGMn is a registered trademark of Nons International, Inc. 11.Parks, J.R, 1982.ATheo of Feeding and Growth of Animals. Springer-Verlang, x w York, NY. 12. ChickoptN is a registered trademark of the Israel Agricultural Research Organization (ARO). 13. Thomas, O.P., 1986. Amino Acid Requirements for Broilers. Page 79 in: P a . Maryland Nutr. Conf., Baltimore, MD.
14. Nalional Research Council, 19M. Nutrient Reuirements of Poultry. 8th Edition. Natl. Acad. Sci., ashington, DC.
&
15.SAS Insitutc, 1992.SAS User’s Guide. Version 6. SAS Institute, Inc., Cary, NC. 16.Talpaq H., S.Hunvitz, and J.R de la Torre, 1988. Economic optimization of a wth trajectory for broilers. h e r . J. ~ g r&on. . 70E390.
17. Talpaz, H., S. Humitr, J.R de la Torre, P.J.H. Sharpe, 1986.Dynamic optimization model for feeding of broilers. J. Agr. Systems 20121-132. 18.Hurwilz, S, and H. Talpaq 1994.Operation manual for Chicko tm program. A cultural Research Organization, The eolcani Ccnter,%-Dagan, Israel.
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19. Unikd Slales Israel Binational Agricultural Research and Developmenl Fund, 1990.Optimization of growth trajectov, feed composition, and carcass quality of broiler chickens. Final Report. BARD, Bet-Dagan, Israel. 20. Talpaz, H., 1991. Modeling of the dynamics of accelerated growth following feed restriction in chicks. Agr. Systems 36:125-135. 21. Crubbs, F.E, 1950. Sam le criteria for testing outlying observations. Annals of Lath. Stat. 21:27-58.
ACCURACY, PRECISION, AND COMMERCIAL BENEFITS OF GROWTH MODELLING FOR BROILERS' H. B. HARLOW2 and F. J. N E Y Novus International,Inc., #20 Research Park Drive, St. Charles, MO 63304 Phone: (314) 926-7440 F M : (314) 926-7405
Primary Audience: Nutritionists, Live Production Managers, Broiler Integrators
lows many of these decisions to be assisted by DESCRIPTION OF PROBLEM the enhanced information provided by compuIn any broiler operation, everyday decisions impact the profitability of the business. Examples of these decisions include selection of feed ingredients, specification of the feeding program, feed manufacturing, drug programs, breed selection, and mechanical housing equipment such as house style, ventilation, feeders, and waterers. Today many of these decisions are made using intuition, industry experience, or word-of-mouth recommendations. However, over the past decade the technology has become available that al-
terized growth models. The purpose of this paper is to outline a procedure that can be used to select and evaluate a growth model for use in a particular commercial operation. The first step in evaluatingagrowth model is to determine how the model will be used. Commercially, growth models can be used for a variety of applications. These range from estimating how a change in feeding program will impact feed conversion to determining if nutrition is a probable cause for an observed performance problem. Questions involving
Presented at the 1994 Poultry Science Association Informal Nutrition Conference Symposium: Poultry Modelling - Theoretical and Practical Evaluations 2 To whom correspondence should be addressed 1
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feed utilization can be evaluated according to economics - how a change in feeding program will impact unit bird cost. Figure 1 illustrates the impact of changing dietary energy and protein on unit bird cost. The cost per bird is given using a typical U.S.diet and 1992 feed prices, revealing that the best economics under these conditions occurred at a moderately low feed density. In examining Figure l it is important to keep in mind that modifications to a cornmercial feeding program can have unintended effects. For example, increasing early diet density can have a negative impact on early survivability due to leg and heart problems aggravated by higher growth rates. One commercially important application of growth modelling would be to determine whether or not an observed field problem is the result of a change in nutrition. In this case a model would determine if the observed growth would have been expected given the delivered feed amounts and composition, based on the variation observed in past performance. Any growth estimate of this type should be qualified with a confidence interval for the desired level of confidence, usually
95%. Thus, if the actual production falls within the expected range, the observed performance can be attributed to the nutritional factor. If the production falls outside the expected range, the cause can be categorized as the result of some non-nutritional factor. The size of the confidence interval, which is related to the live growout variation, can be used to determine if production is "under control" according to the statistical definition. Thus, growout variation has a significant cost associated with it and should be kept as small as is feasible [l]. The selection of a growth model should be based upon commercial goals. Over the last decade a number of broiler models have been available commercially [2,3,4,5,6,7,8]. A few of these are summarized in Table 1. These models evaluate broiler growth using a wide variety of approaches ranging from the straightforward (attaching an economic optimizer to a Gompertz growth curve) to more sophisticatedrule-based systems (information about growth is compiled into an "expert"system). The different programs also vary in the amount and type of input data required and
Cost per Kg.
:u.s.cents)
.tal l/K -IGURE 1. Impact of changing energyand protein on unit live weight cost. The base feeding program consisted )f four diets with energy, protein, and feed weight defined as (3200,23, 0.82),(3200,21, 1.05), (3250, 19.5, ).87),and (3275, 16, 0.21) for diets 1 through 4, respectively.
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MODEL NAME Chickopt"
BRIEF DESCRIPTION
DATE AVAILABLE
I
Economic optimizer tied to a Gompertz style compartmental model
I
Late 1994
Walla Model
Enterprise model providing economic modelling for an entire operation
Announced 1993
Fortell" Broiler [9]
Commercial version of the Edinburgh broiler model with u m i f i e d imDrovements
1991
Hurwitz Broiler
IEconomic model, earty predecessor to Chickopt"
IGM"
I
Pesti/Brill Model
I
Edinburgh Broiler
Statistical model based upon a large series of feeding trials, tied to an oDtimizer
I1990
I
1989
Quadratic response surface model which determined the least cost finishing ration
Late 1980's
A rule-based compartmental model based upon daily growth partitioned according to growth potential and available nutrients
Early 1980's
how they are adjusted or calibrated to represent commercial production. While there are a number of different approaches that can be used to evaluate growth models, the procedure described in this paper is the one developed by the authors as a tool to guide the development of the IGM" [lo]. In order to describe the evaluation process of models it is necessary to define some terminology, including "calibration," ''accuracy,""precision," and "bias." CALIBRATION Calibration is the process of adjusting model parameters to allow a growth model to estimate the growth of commercialbroilers. Of the currently available models, each uses a different calibrationmethod. For example, the Edinburgh growth model [q requires the coefficients for a Gompertz [ll]growth curve and the sensible temperature profile for the growout. The Chickopt" [12] model requires live weight data, taken weekly, so that the coefficients for a Gompertz equation can be estimated by the program. The IGM" program requires a minimum of twenty flocks of production data so that a statistical model can be adjusted to reflect the observed broiler growth. Each of these methods has strengths and weaknesses. The important point is that following the calibration step, each model should be able to predict commercial production accurately.
ACCURACY Accuracy can be defined as how closely a model estimates production data. That is, if feed conversion is the estimate required, the model should closely estimate the feed conversion observed in the field. Accuracy can be expressed in a number of ways. One way is to express it as a percentage within a range. For example, if a model were accurate to one point of feed conversion (0.01) and if an operation has an average feed conversion of 1.90 and a range of feed conversions of 1.70-2.10, the relative accuracy could be expressed as: Error Relative Accuracy = -= 0'01 x 100 = 2.5% Range (1.90 - 1.70)
Thus, the model would have a relative accuracy of 2.5%. A second method to define the accuracy would be to use a t-statistic. A t-statistic determines if a collection of estimates is significantly different from the actual values. For example, if a model were used to estimate the feed conversion for the production of a complex on a flock-by-flock basis, a t-statistic could be computed on the collection of estimates. The t-statistic would be given as: average (delta) 6 t-statistic = where:
SD (delta) n = number of flocks predicted average = simple average operator SD = standard deviation delta = actual -predicted
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This equation makes the assumption that the actual and predicted variances are equal, in most cases a reasonable assumption. However, since a model cannot reasonably account for all of the sources of variation, the formula for the t-statistic with unequal variance may be more appropriate in situations where the variances of the actual and predicted production parameters are significantly different. In either case, once a t-statistic has been calculated, a table of critical t-values can be used to determine whether or not the model predictions are significantly different from the actual data. The smaller and hence less significant the t-value is, the better the accuracy. PRECISION The precision of a model can be assessed according to the distribution of the prediction errors. That is, a precise model not only correctly predicts the average value but also predicts the distribution of the data. This achievement would be reflected in the standard deviation of the residuals or the difference between the actual and predicted values. BIAS Bias can be defined as a systematicfailure of a model. For example, a model with a bias may consistently over or under predict live weight for birds which are lighter or heavier than the average. An example of bias appears in Figure 2. A model and calibration without bias would have the cigar-shaped region of data points oriented along the dashed line. However, in this example the model failed to account for the observed variation and is biased, resulting in the data lying along the solid line instead. A model can be accurate and precise and still not predict the response of broilers to changes in a feeding program because different breeds have different growth curves, efficiency of feed utilization, and resistance to stress. Figure 3 shows an example of two breeds grown using the same feeding program and feed ingredients. Examination of this figure shows that a model that is accurate for one breed will be inaccurate or biased for the other. It is important to note here that not only are the general shapes of the surfaces (i.e., response of the birds to nutrients) differ-
COMMERCLAL GROWTH MODELLING
2.8
1
2
12
2.2
,
I
I
2.4
2.6
2.8
Actual Live Weight (Kg.) FIGURE 2. Data from 200 commercial flocks plotted as a scatter graph to demonstrate bias.
ent, but the relative weights of the birds are significantly different. Regions with the same surface shading correspond to diets that provide similar weight gain. The width of the shaded regions corresponds to the 95% confidence level for the mean from the data set from which these surfaces were generated. A bicubic spline smoothing algorithm was used to smooth the plotted surfaces. Obviously, an accounting for breed must be considered in any commercial setting. Additionally, the genetics of broilers changes to such an extent that the life expectancy of a breed adjustment is only two to four years. Bias can also occur due to differences in feed ingredients. That is, the feed manufactured does not always contain the energy and protein levels intended. If the error in feed content occurs in a systematic way, a bias in model estimates results. Model bias can occur in two ways. The most common sources of bias in the rule-based models are inaccurate or incorrectly applied rules. In a mathematical or statistical model, the rule is the equation that describes the growth of the animal. If this equation has the wrong shape or characteristics, it results in bias or "lack of fit" as the statisticians describe it. However, even when the rules are correct, bias can still be a problem because the data used to calibrate the model has a pattern of errors leading to a poor or incorrect calibration. The more sensitive a model is to the pattern of variation or the error structure of a set of calibration data, the more likely a model
Poultry Modelling Symposium HARLOW and IVEY
Strain A 21 dav
395
I
Strain B 21 day
KcalKg.
Protein
:IGURE 3. These two graphs illustrate the difference in growth pattern between two common commercial ]reeds. The breeds are characterized as: A) a slowgrowing strain and B) a fast-growing strain.
will be biased and the poorer the precision becomes. An ideal model would be insensitive to the distribution of errors in the calibration data. However, the sensitivity to variation is a function of the mathematics used in the model, and all models are susceptible to bias to some extent. When all of these factors are considered, the modern crafter of growth models has a significant challenge. Given the necessities of modern business and the narrow profit margins of the broiler industry, it is critical that a growth model be selected carefully. The rest of this paper will describe the techniques applied by the group to evaluate two different growth models: the IGM" program version 4.02.2 and Chickopt" program version 1.0.
The second problem is the micro evaluation or the application of a model to commercial data. Since most flocks in a commercial setting are fed identical diets in slightlyvarying amounts for similar periods of time, the micro evaluation looks at how well the model predicts the distribution of the live weight or feed conversion in the field. Together, the macro and micro evaluations can provide an excellent evaluation of the accuracy and precision of the model. THE IGM" GROWTH MODEL The IGM" program is a semi-empirical model, the culmination of a large number of research trials run at the Novus International, Inc. Poultry Research Facility. The basic premise of the model makes no assumptions about the growth of broilers. Instead, the program captures the growth pattern expressed by the birds grown in large numbers on different feeding programs at the research facility. To date 288 different feeding programs have been investigated.The feeding programs were carefully selected using experimental design technology so that the impact of energyand protein in the diet on production parameters could be accuratelydetermined as a function of age. A mathematical model, constructed to fit this data, is called the "base model'' and describes the growth response of broilers to energy and protein. It is accurate and precise over the range of feeding programs included in the experimentaldesign and accounts for most of the variation observed in
MATERIALS AND METHODS In understanding the applicability of a growth model to a commercial operation researchers must face two distinct problems. The first problem that must be addressed is a macro evaluation of how well a growth model predicts changes in performance from changes in energy and protein over a wide range of feeding programs. This evaluation is typically accomplished using a feeding study, which provides information about the relative accuracy of a model with regard to dietary changes. As an example,one might look at how well a model accounts for the change in feed conversion that accompanies a change in dietary protein or energy content.
396
COMMERCIAL GROWTH MODELLING
performance, with model R2values up to 0.99. To date over twenty separate feeding trials have been conducted for growth modelling. The studies used to generate the base model for the IGM" program covered a number of diets. They also covered the energy range from 2920 to 3420 kcaVkg and protein between 13 and 27%. Since protein is only part of the story for a growing bird, the feeds used in these studies were formulated using amino acids in constant ratio. The constant ratio followed the 1986 Maryland Recommendation [13] and was keyed to the amount of total sulfur amino acids (TSAA) in the diet. All diets were formulated using corn, soybean meal, supplementalamino acids, and a vitamin and mineral premix. The premix was added to a level so that essential vitamins, minerals, and choline were equal to, or slightly in excess of, the NRC recommendations [14].Amino acid supplementation,when necessary, was accomplished using commercially available sources. Additionally, if the density of the diet was so low as not to be feasible to formulate using corn and soybean meal, rice hulls were used as a diluent. From each experiment, feed intake, individual and pen live weights, feed conversion, mortality, culls, and carcass composition data were collected. This data was taken at predetermined ages ranging from 5 to 77 days and collected for a number of different breeds, including most of the breeds used commercially in the U.S. The data were assembled into data sets analyzed using SAS [15]. A base model was generated as specified accordingto the experimental design. The carcass composition measurements were taken by dissection and included chilled carcass yield, breast muscle (pectoral major and minor), breast frame, wings, leg quarters, and feet. Over the range of experiments the model explained over 80% of the variation in carcass composition. The capabilities of the IGM" program fall into four areas: the estimation of production parameters, optimization of the feeding program, evaluation of flock performance, and evaluation of the sources of performance variation. In each case a calibration is necessary before the model can be applied to a particular commercial facility.The calibration process for the IGM" program is accomplished by collectingcommercial performance data, consisting of information about the feed
manufactured during the period, the amount of feed delivered, live production data, and processing information. These data were used to adjust the base model to reflect production at the commercial site. The adjustment of the N o w International, Inc. base surface to match the commercial data allows an accounting to be made for the differences in average performance, response of the birds to energy and protein, and rate of growthcalibration will generally be successful so long as the birds in the field are responding to the nutrients in the diet. In some cases, factors other than nutrition interfere with the performance of the commercial flocks. In these cases a calibration cannot be successful. But given a successful calibration, the model can be used productively. The IGM" program could be used to determine the impact of dietary changes on the performance of birds in the field. Characteristics that can be modelled would include live weight, feed conversion, age, and carcass composition. For example, if the feed allocation is changed between the diets which make up the feeding program, the model can assess what impact that will have on feed conversion. Others might ask, "What would the impact be of adding or removing energy or protein from the diet both on cost and performance?"From a commercial standpoint, one of the more valuable applicationsof a model is to minimize feed cost or feed conversion or maximize the value of the produced bird. This ability is directly related to the profitability of an operation since feed accounts for a major portion of the cost of producing a broiler. The factors that the IGMN growth model can currently optimize include least cost per unit live weight and unit carcass value. Since the calibration process uses individual flock information to adjust the base model to accurately represent the commercial production, the actual and predicted data are readily available. Predicted data can evaluate how particular flocks are doing in light of the nutrients contained in the feed consumed by the buds. On average, the difference will be zero for a calibrated model. However, some flocks will perform better or worse than the average. Since a growth model accounts for nutrition, it is possible to compare these flocks with the impact of differing ages and feed amounts corrected.
Poultry Modelling Symposium HARLOW and IVEY CHICKOPT" The Chickopt" program was written over a number of years by two Israeli scientists, Shmuel HunVitz and Hovav Talpaz. It is an extension of the Israeli growth model that is well documented in the Literature [16, 17, 18,191 and will only be briefly described here. The Chickopt" program consists of an optimizer tied to a compartmental growth model based upon a Gompertz growth curve. The growth of each compartment (protein, feathers, and fat) leads to an amino acid and energy requirement. These requirements are then used to determine the feed cost, which is computed using a built-in linear feed formulation program (LP) to determine the cost of a particular feeding program. The Chickopt" program ties energy and protein together accordingto a predefined protein:energy ratio determined experimentally at the Israeli Agricultural Research Organization (-0). The inputs into the Chickopt"' program include weekly growth data, the desired live weight, information about feed component cost, and nutritional limits for the LP portion of the program. The output is the dailygrowth and feed cost. Additionally, the program provides feed composition and cost. The outputs predicted by the Chickopt" program include daily gain, potential daily gain, feed intake, feed conversion, and economic analysis ($/ft2, $/lb, $/bird, and $/ft2/day). Additionally, the program computes the feed formulation and nutrient composition of the predicted diet on an individual diet basis. The program allows the user to choose between weekly, biweekly, or specified dietary periods. The program also provides a calculation so that the economic impact of early feed restriction can be estimated or optimized. The concept behind feed restriction is that by restricting feed early, tissue mahtenance is reduced. There is some evidence that birds restricted early will exhibit compensatory growth in the time period following the restriction [20]. DATA REQUIREMENTS nKo sets of data were used in the evaluation of the growth models given here. The first set of data is a subset of one of the research trials used to test the base surface for the IGM" program. This data was used for the macro evaluation of the models. The second
397
set of data is performance data from the field, selected from the large amount of commercial data accumulated in the implementationof the IGM" program at many complexes around the world. This data set was selected from a typical producer to represent flock performance in the U.S.
RESULTS AND DISCUSSION The research trial was conducted at the N o m Dardenne Research Facility using 128 battery cages with five birds per cage. The feed was prepared as described in the IGM" model description (above). The birds in each pen received the same diet ad libitum for 21 days. At weekly intervals the birds and the feed were weighed. Mortalities were corrected by computing the pen feed conversion, determining the amount of feed necessary to account for the weight increase in the dead birds, subtracting this feed amount from the pen feed amount, and recomputing a"corrected" feed conversion. The design used was a 4 x 4 x 2 full factorial with variables being energy, protein, and bird sex. Similar data was available at weekly intervals for female and male birds. Table 2 gives the results of this study. Data from the male and female treatments at the same energy and protein level were combined to estimate the performance of mixed sex birds. Data from all sixteen energy and protein treatments was then used to calibrate the IGM" program. This calibration predicted the live weight and feed conversion for those diets along the diagonal. While it is not considered statistically valid to evaluate a mathematical model by estimating data points included in the calibration set, here it determined a lack of fit of the model for comparative purposes. It should also be noted that the calibration used all of the data while the comparison used only a subset of the data. The results of this comparison appear in Table 3. The weekly data from the combined male and female treatment containing 3085 kcaVkg energy and 21% protein were used to calibrate the Chickopt" program. Again the diagonal elements of Table 2 were estimated. Since the Chickopt" program uses a fxed protein:energy ratio, the diagonal elements seemed to give the fairest comparison. The results from this comparison also appear in Table 3.
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TABLE 2. Female live weiahts (feed to aainl of two broiler strains showinn the response to eneray and proteinA
ENERGY LEVEL
*Data are the average of four pens per treatment B~ = a slow-growingstrain, B = a fast-growing strain
In examining Table 3 it is clear that both models performed an adequate job of estimating the 21-day live weight and feed conversion with the largest live weight error being 41 g or 6.3% with a relative error of 47% for the IGM" program. The largest feed conversion error was produced by Chickopt: 14points (0.145)or 10.3% with a relative error of 55%. In each case the largest error occurred on an extreme diet that would be unlikely to be employed in the field. Both programs faired much better regarding live weight for diets more typical of those employed in the field (center two columns), with relative errors of around 15%. However, for feed conversion the IGM" program outperformed Chickopt"
I with a relative error
of 8.4% (compared to . . 44.3% for Chickopt". Perhaps most of the difference in feed conversion accuracy can be linked to the futed energy:protein ratio employed by this version of the Chickopt" program. The Chickopt" program was formulated with a protein:energy ratio that closely matches commercial formulas, while the data used in this test spans a particularly wide range of protein:energy ratios. COMMERCIAL COMPARISON The micro evaluation of the two programs involved two sets of commercial data selected to provide a fair evaluation of each program in real world settings. The set of data selected for
TABLE 3. IGM'" and Chickopt" program estimations of experimental data following calibrationA
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Chickopt" came from a producer that produced buds where a set of weekly live weight data was available that could be used for calibration purposes. Due to the requirement for weekly live weights for calibration, the commercial data used to evaluate Chickopt"' is approximately four years old. Data of this age would be expected to have poorer feed conversion and average daily gain due to the constant improvements in genetics made by commercial breeders. These advances can readily be seen by observing the feed conversions in Tables 4 and 5. For the IGM" program a more current calibration data set was selected with birds of a comparable age located in the same geographical part of the country. Because of the volume of data used by the IGM" program, only a sample of the predicted flock data is given. The original data set contained 265 flocks from a four-month period. The calibration of Chickopt" used weekly live weight data. Once the program was calibrated, the flock data was estimated using actual feed intakes. The Chickopt" program estimates to the nearest whole day, so feed was added to the last diet to insure that the program output extended at least one day beyond that to which the birds were grown. The estimates for live weight given the consumed feed were adjusted using h e a r extrapolation over the last day in which the feed
should have been consumed. The results of this comparison for twelve flocks appear in Table 4. Table 5 offers a similar set from the IGM" program. Since only a portion of the data from the IGM" program could be presented, the first twelve flocks in the calibration set were selected. Examination of Tables 4 and 5 shows that both programs are able to do a reasonably good job of estimating the resultant live weights. The relative accuracy of the IGM" program using the twelve flocksin Table 4 was 16.5%, where the standard deviation of the residual live weight was used as the estimate for the error. If the standard deviation from the entire data set of 265 observations was used (0.021), the relative error was 13.4%.The t-value (Equation 2) was calculated to be -0.573, with the critical value for the t-test at the 95% confidence level being 2.179. The t-value for the entire set of 265 flocks was -0.101. The data set in Table 4 contains one outlier, the third observation down. This data point was determined to be an outlier using the Grubbs test at the 99% confidence level [21]. The Grubbs statistic was 0.29 with a critical value of 0.3554. Correcting for the outlier, the relative accuracy is 8.9% (Table 4). For the Chickopt" program the relative accuracy of the data given in Table 5 was 14.7% with a t-value of 1.805, which is well below the critical value of 2.179. This level of
TABLE 4. A subset of the actual commercial data used to determine the accuracy and precision of the I G M " program AGE
NUMBER FEED OFBIRDS CONVERSION
ACTUAL
LIVE WEIGHT (kg)
42
31600
1.830
1.898
42
39600
1.772
1.855
41
50300
1.857
1.775
42
29600
1.789
1.807
42
33200
43
36400
1.791 1.765
1.904 1.880
41
38300
1.782
1.932
42
48000
1.793
1.870
43
37900
1.794
1.863
42
28700
1.774
1.856
45
39200
1.789
1.876
42
39300
1.793
1.877
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;ion of the Chickopt" program
NUMBER FEED OF BIRDS CONVERSION
AGE
ulooo
42 44
21300
2.000 1.999
42
19200
1.900
42 42 42 42
44 42 43 42 45
I
21300 21200 22000 21000 21300 21000 21600 21300 19200
I
1.990 1.890 1.900
1.910 2.009 1.940 1.980 2.040 2.080
I
ACLZlAL
PREDICTED
LIVE W I G H T (kg)
LIVE WEIGHT (kg) Starter
Grower
Finisher
1.656
1.690
0.998
1.802
0512
1.679
1.713
0.939
1.857
0.561
1.724
1.671
1.041
1.783
0.451
1.740 1.676 1.702 1.705
0.937
1.890
0.622
0.939 0.913
1.857 1574
0.850
1.733 1.738 1.756 1.no 1.806
I
ACTUAL FEED WEIGHTS (kg)
1.810 1.765
0.937
1.824 1.842 1.865
1.819 1.854
0.923 0.939
1.910
1.914
accuracy is quite good considering the small calibration data set required. Another method to perform the micro evaluation of a growth model is to determine the amount of variation explained by the model. The easiest and most informative method is to plot a scatter graph of the actual versus the predicted production parameter. Figure 4 records this procedure for the live weight of commercial broilers (Note that this is not the same data set as was used in the calibration work described previously). In Figure 4, actual vs. predicted live weights are plotted. An ellipse was drawn that contained approximately 95% of the data points. The variance not accounted for in the model is the ratio of the minor to the major axis. If the model accounted for all of the variation in live weight, all of the points would fall on the diagonal line. However, there are always sources of variation not captured by a model. These result in unexplained variations and in a deviation of the points from the diagonal line. If an ellipse is drawn that contains 95% of the data points, the ratio of the minor axis to the major axis provides an excellent estimate for the variation not explained by the model. Conversely, one minus this quantity is the variation explained by the model. This result is the same as the correlation coefficient between the actual and predicted quantities squared. When the percent of variation was determined for the example data given in Tables 4
c.,
I
0.951
I I I
0.952
1.506 1.890 1.774 1.970
0.488
I I
I
1
0.923
0.802 0.812 0.754
2.04
.,-l
I
1.70
1.81
1.93
2.04
Actual Live Weight (Kg) FIGURE 4. Illustration of the use of a scatter graph to estimate the amount of variance not accounted for in the model.
and 5, the Chickopt" program explained 78% of the variation in live weight, while the IGM" program explained 81% of the variation if the outlier is removed. When this value was determined for all 265 flocks in the IGM" calibration data set, it was found to be 92.6%. In either case both models explain a majority of the variation in the commercial data sets. Experience with this procedure over time has shown that a model can account for between 50 and 95% of the observed variation in live weight for most commercial operations.
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Each of the models tested here demonstrated both strengths and weaknesses. For example, some of the strengths of the Chickopt" program are that it is easy to use, provides reasonable estimates of the amino acid needs for the bird, provides a selfcontained LP program, and requires a small calibration data set. Some of the weaknesses of this program include the use of a fixed protekenergy ratio which leads to errors in estimates for feed conversion and that the individual flock estimates needed for the analysis of variance have to be computed manually. On the other hand, the strengths of the IGM" program include relatively higher precision and accuracy, an approach that makes no assumptions about broiler growth, and the ability to estimate carcass com-
position. Additionally, the program provides individual flock estimates as part of the calibration process. Some of the weaknesses of the IGM" program include the requirement for large calibration data sets, program complexity, and lack of an integral LP program requiring several passes between the user's LP program and the IGM" optimizer to reach the correct solution. Additionally, the program as it exists today requires substantial computational resources to operate, both in terms of program size and memory requirements that preclude ready implementation of the program on a desktop PC. Overall, the IGM" and Chickopt" programs complement one another because the weaknesses of one are the strengths of the other.
CONCLUSIONS AND APPLICATIONS 1. In developing and applying growth models over the last six years, it has become evident that broiler production is a science with capable professionals involved in all aspects of production. Consequently, any model must be quite good if it is to contribute in the competitive environment of a modern broiler complex. 2. The techniques described in this paper can be used to evaluate the effectivenessof a growth modelling program for a particular commercial organization or goal. It is important to understand the strengths and weaknesses of any model in order to obtain the maximum commercial benefit. 3. Growth models have provided a much needed tool to understand the cost variable environment under which a modern broiler complex operates. Growth models are rapidly moving away from being a tool used as a competitive advantage by a privileged few and toward a resource required by any organization desiring to remain profitable in the cost variable environment of a global market place. 4. Growth models provide a tool to diagnose problems that have been very difficult to address previously. In the past when a producer desired to evaluate new technology or different feeding programs, small trials were conducted in research facilities. However, there was never a guarantee that these results could be directly applied in the field because of differences in field stresses. Models provide a scientific approach to evaluating new concepts and ideas in the field by removing the variation attributable to the feed consumed by the bird. This method allows for better decisions to be made in a timely and efficient manner. 5. Growth modelling remains a rapidly developing field. The field is becoming more and more competitive with new entries entering the market on a regular basis. While the current models are not perfect, they represent a valuable tool for the modern broiler producer.
REFERENCES AND NOTES 1. Harlow, H.B. and F.J. Ivey, 1993. Consequences of variation on rofitability in commercial broiler production. Poultryh. n : ~ . 2. Pcsli, G.M., RA Arraes, and B.R Miller, 1986.Use of the auadratic erowth resmnse to dietan, Drotein and energy 'concentr&ons in feast-cost feed 'fknulation. Poultry Sci. 65:104&1051.
3. Rhone-Poulenc advertisement in November 1993 issue of Poultry Digest which provides a brief description of the Wala Group agricultural growth model, p. 3A. 4. Muirhead, S., 1991. Simulation modeling provides new insight into nutritional problems. Feedstuffs 63:14.
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402 5. Emmans, C.C., 1981.A model of the growth and animals,particularlypoultry. feed intakeof &-fed Pa es 103-110 in: Computers in Animal Production. G.h. Hillyer, C.T. Whittemore,and RG.Gunn, eds. Occ. Publ. No.5, Br. Soc. h i m . Prod. 5:103-110. 6. Emmpns, G.C., 1987.Growth, body com and feed intake. World’s Poultry Sci. Assn. J. 43:%2
7.Harlow, H.B. and FJ. Ivey, 1994a. Growth models: Window on bottom-line costs. Broiler Industry 573&34. 8. Harlow, H.B. and FJ. Ivey, 1994b. Improvements in broiler production throu the use of the Novus lvey Gmwth Model (IGM’).&es 21-31 in: P m . Nutr. and Tech. Symposium, St. Louis, MO. 9. Fortrell‘ is a registered trademark of Heartland Lysine, Inc.
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10.IGMn is a registered trademark of Nons International, Inc. 11.Parks, J.R, 1982.ATheo of Feeding and Growth of Animals. Springer-Verlang, x w York, NY. 12. ChickoptN is a registered trademark of the Israel Agricultural Research Organization (ARO). 13. Thomas, O.P., 1986. Amino Acid Requirements for Broilers. Page 79 in: P a . Maryland Nutr. Conf., Baltimore, MD.
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19. Unikd Slales Israel Binational Agricultural Research and Developmenl Fund, 1990.Optimization of growth trajectov, feed composition, and carcass quality of broiler chickens. Final Report. BARD, Bet-Dagan, Israel. 20. Talpaz, H., 1991. Modeling of the dynamics of accelerated growth following feed restriction in chicks. Agr. Systems 36:125-135. 21. Crubbs, F.E, 1950. Sam le criteria for testing outlying observations. Annals of Lath. Stat. 21:27-58.