CA2320687A1 - Multi-purpose model and analyzer for feed enzymes - Google Patents

Abstract

We hypothesized that a log-linear model could be used to predict and evaluate the response of chicks to a dietary enzyme supplementation and that an in vitro dietary viscosity assay could be used in conjunction with the model as the predictor or evaluator. The results demonstrated that the model was able to accurately predict the response of chicks fed diets containing the different amounts of an enzyme and different proportions of two cereals. The slope of the model was a measure of the efficacy of the feed enzyme. The efficacy, in turn, was able to correctly evaluate the effects of different feed enzymes when added to a diet and to identify the most suitable target cereal for an enzyme. No other model, as far as the authors are aware of, are able to achieve this accuracy. In addition, a Multi-purpose Enzyme Analyzer has been developed based on the model. The analyzer was able to determine the optimal amount of an enzyme and a substituted cereal that should be used in a diet for maximal profit, and to determine the amounts and the expected prices of the enzyme and cereal that will yield a given profit. Also, the effect of a feed enzyme could be evaluated using maximal profit as a criterion.
Therefore, the most profitable among several feed enzymes and the cereal that should be used for a given feed enzyme could be determined. Furthermore, a dietary viscosity assay has been developed. The results indicated that there was a linear relationship between the log of dietary viscosity change measured by the assay and the log of amount of enzyme added to a diet (r2 =
0.99, P < 0.005). The values from the assay were able to predict the response of chicks to a feed enzyme and also evaluate the efficacy of different feed enzymes, especially for those enzymes that hydrolyzed the viscous compounds in the diet. These studies demonstrated that the response of chicks to a feed enzyme and the efficacy of the enzyme could be accurately predicted and evaluated on the basis of a log-linear model using different criteria (performance and economic return), and different type of studies (in vivo and in vitro).
Key Words: Log-linear model, Enzymes, Poultry, Feeds Our previous studies demonstrated that a log linear equation could be used to accurately predict chick performance when a crude enzyme was added to a diet and that a single value, the slope of the log-linear equation, provided a measure of the efficacy of different feed enzymes. The objective of the current study was to determine if the model could also be used to establish a profit function for carrying out a least-cost analysis and to develop a software package, a Multi-purpose Enzyme Analyzer (MPEA), for evaluating and estimating the effect of enzymes when added to poultry feeds based on their profitability. The results demonstrated that there were high correlations between the efficacy of different feed enzymes (B
values, the slopes of the equations) and the maximal profits that were obtained when feed enzymes were added to a barley-based diet (r2 = 0.99, P < 0.2171). This suggested that the maximal profits as well as their B values could evaluate the effectiveness of different enzyme preparations. In contrast, there was a low correlation between the B values and the maximal profits when a feed enzyme was added to different cereal-based diets (r2 = 0.61, P = 0.2171). This suggested that there is not always a close association between efficacy of an enzyme when added to different cereals and the corresponding profitability. The MPEA was highly versatile as any combination of inputs such as the amounts of a feed enzyme and a substituted cereal required to yield a certain profit level could be determined. In addition, the results demonstrated that the price that should be paid for a feed enzyme when added to a given diet or for a cereal when used with a given feed enzyme to yield a maximal level profit could be also evaluated. In conclusion, the maximal profit that is obtained with a feed enzyme when added to a diet can become a useful standard to accurately evaluate different feed enzymes when added to a diet, to select the most profitable cereal for a given feed enzyme, to determine the optimal amounts of a feed enzyme and/or a cereal, and even to estimate the alternate price that could be paid for a feed enzyme and a cereal. Therefore, the MPEA provides a useful tool for the nutritionists in the enzyme and feed industry for evaluating the most economic use of feed enzymes and cereals in poultry diets.
(Key words: feed enzymes, maximal profit, profit functions, log linear model)

Description

'7 There has been increasing interest in quantitatively studying the effect of different levels of 8 feed enzymes (inputs) when added to a diet on the performance (outputs) of chickens (Friesen et 9 al., 1991; Bedford and Classen, 1992; Marquardt et al., 1994; and Zhang et al., 1996; 2000). The primary objectives of the former studies were ( 1 ) to estimate the optimal level of feed enzyme 11 addition required to obtain maximal chick performance (Friesen et al., 1991; Bedford and 12 Classen, 1992), and (2) to evaluate the efficacy of feed enzymes added to a diet (Rotter et al., 13 1989; Zhang et al., 1996; 2000). Frequently, the experimental designs and statistical procedures 14 have only provided trends on the effects of enzyme treatment but have not provided precise prediction values that can be obtained when a given enzyme is added to a given diet. Therefore, it 16 has been impossible to accurately estimate the relationship between inputs (enzyme or cereal) on 17 outputs (chick performance), or to establish the most profitable combination of inputs for a 18 specified output. In addition, researchers in nutrition have generally been concerned only with 19 biological rather than economic criteria to evaluate and make recommendations on the effects of feed enzymes. The criteria that have been used for the evaluation of performance often were the 21 treatments yielding the largest weight gain or the lowest feed to gain ratio per unit of enzyme 22 addition (Friesen et al., 1991; Bedford and Classen, 1992). However, these maxima or minima have seldom been utilized to estimate the most profitable output or optimal input. Even where

2 the objective was the prediction of the physical maxima or minima, the exact values could only

3 be accurately estimated by use of a prediction equation (Zhang et al., 1996).

4 Recently, we have developed a simple log-linear model to accurately predict the response of chickens to dietary enzymes (Zhang et al., 1996). The model equation was able to predict the 6 performance of chickens fed diets containing different amounts of an enzyme and different 7 proportions of two cereals. Simple but accurate log-linear equations were derived from many 8 previous dose response studies with feed enzymes, even though they were not designed for this 9 purpose. In addition, the efficacy of any enzyme preparation for a particular cereal or class of poultry with regards to any index of animal performance such as weight gain or feed to gain ratio 11 could be assayed from a single value of B, the slope of the model equation (Zhang et al., 1996;
12 Marquardt and Bedford, 1997). Therefore, it should be possible, using this equation along with 13 other analyses, to correctly estimate the maximum economic return obtained when a feed enzyme 14 is added to a diet. A requirement is that accurate input data be available.
The objective of this 1 S study was to develop a Multi-purpose Enzyme Analyzer (MPEA) for estimating the profitability 16 of using enzymes in poultry feeds. Three main applications of the Enzyme Analyzer were to: ( 1 ) 17 evaluate the effects of different enzyme preparations when they are added to a cereal-based diet 18 using maximal profit as a standard, (2) determine the amounts of an enzyme preparation and/or a 19 substituted cereal that should be used in a diet to obtain maximal profit, and (3) to establish the relationships among the price of an enzyme preparation, the price of the substituted cereal, and 21 the economic return. Therefore, the use of the modelling method in conjunction with nutrition 1 knowledge and computer technology should provide researchers and managers that use feed 2 enzymes a powerful new approach for the analysis and interpretation of their data.

Sources of Data 6 The data used in this study were obtained from four previous studies: Rotter et al. (1989), 7 Bedford and Classen (1992), Marquardt et al. (1994), Zhang et al. (1996).
The data for the first 8 study was obtained from Rotter et al. (1989) and Zhang et al. (1996). In experiment 3 of the study 9 from Rotter et al. (1996), one-day-old Single Comb White Leghorn chicks were fed a commercial starter crumble for a 7 d pre-experimental period. A barley-based diet was fed to 11 birds from 7 to 14 d of age in a completely randomized design. The diet consisted of the 12 following ingredients: 65.50% barley, 23.07% soybean meal, and 11.43% other ingredients. The 13 calculated metabolizable energy (MEn) of the diet was 12.20 MJ/kg. Five enzyme preparations 14 used in the study were: Cellulase Tv concentrate (T. viride)3, Celluclast (Trichoderma ressei)4, SP249 (Aspergillus niger)4, Finizym (A. niger)4, and Cereflo (Bacillus subtilis)4. The enzyme 16 activities as determined by manufacturer were: Cellulast, 1633 NCU/g;
SP249, 11240 PGU/g;
17 Finizym, 217 FBG/g; Cellulase Tv concentrate 23880 CU/g; and Cereflo, 67.5 KNU/g. All of the 18 enzymes at amounts of 0.003125, 0.00625, and 0.0125 % were added to the experimental diet for 19 the dose response study. Performance per chick was recorded at 14 d of age.
3 Miles Laboratories Inc.
4 Novo A/S Denmark.

5 1 Another data set used in the first study was obtained from Zhang et al.
(1996). In this 2 experiment, one-day-old Single Comb White Leghorn cockerels were fed a commercial starter 3 diet for a 7 d pre-experimental period. The experimental diets were fed to birds from 7 to 21 d of 4 age. The diet consisted of the following ingredients: 60% rye, 8.25% wheat, 24.5% soybean S meal, and 6.75% other ingredients. The calculated MEn of the diet was 12.34 MJ/kg. Rye grain

6 (Prima) was selected as the substituted cereal for wheat in the diet as it contains high levels of

7 viscous arabinoxylans. The arabinoxylans in rye grains are primarily responsible for its

8 antinutritive effects (Antoniou et al., 1981 ). They greatly reduce chick performance but are

9 efficiently hydrolysed by enzyme preparations containing xylanase activity (Fengler et al., 1988;
Fengler and Marquardt, 1988; Marquardt et al., 1994; Zhang et al., 1996, 1997). Two enzyme 11 preparations, RM1 (T. longibrachiatum)5 and NQ (T. ressei)6, were used in this study (Zhang et 12 al., 1996). The xylanase activity of RM1 and NQ was 389 and 778 U/g of enzyme preparation as 13 assayed by the azo-dye method (McCleary, 1992) using dye-labelled arabinoxylan as the 14 substrate. Different amounts of RM1 (0, 0.25, 0.75, 2.75, 6.75, 20.25 g/kg) and NQ (0, 0.1, 0.3, 0.9, 2.7, and 8.1 g/kg) were added to the diet, at the expense of rye, for a total 12 different 16 treatments. Bird weight and feed consumption based on six birds were recorded 4 h after removal 17 of feed at 21 d of age.
18 The data for the second study were obtained from experiment 2, Marquardt et al. ( 1994). In 19 this experiment, one-day-old Single Comb White Leghorn chicks were fed a commercial starter diet for a 7 d pre-experimental period. The experimental diets were fed to birds from 7 to 21 d of 5 Finnfeeds International Ltd., Wiltshire, UK.SN8 1XN.
6 Nutri-Quest, Chesterfield, MO, 63017.

1 age in a factorial arrangement of treatments: 4 (cereals) x 4 (enzyme doses). The cereals used in 2 four diets were 63% corn (unknown variety), 67% wheat (Katepwa), 66% hulless barley (Scout), 3 and 64 % rye (Prima), respectively. The calculated MEn of the four diets were 12.66, 13.37, 4 12.46, and 12.01 MJ/kg. The diets were supplemented with different concentrations (0, 0.5, 1, and 2 g/kg) of a crude enzyme preparation, Kyowa Cellulase (T. reesei)5. The xylanase and 6 cellulase activities as determined by the Japan Food Laboratory were 1500 and 1000 U/g, 7 respectively. The chick performances based on a bird basis were recorded at 21 d of age.
8 The data for the third study was obtained from Bedford and Classen (1992).
In this 9 experiment, one-day-old male broiler chicks were fed four diets supplemented with different amounts of a pentosanase preparation (experimental product6 from T.
longibrachiatum) in a 4 x 6 11 factorial arrangement of treatments from 1 to 19 d of age. The diets consisted of the following 12 proportions of rye (Musketeer) and wheat (unknown variety): 0:60, 20:40, 40:20, and 60:0 each 13 with 32.05% soybean meal, and 7.95% other ingredients. The calculated MEn of the four diets 14 were 12.85, 12.50, 12.15, and 11.80 MJ/kg, respectively. The enzyme preparation added to each 1 S of the four diets was 0, 1, 2, 4, 8, and 16 g/kg. The xylanase activity of this enzyme preparation 16 was 21 SO U/g as determined by the reducing sugar method when assayed on oat spelt xylan 17 (Seeta et al., 1989). Chick performances, based on six birds, were recorded at 19 d of age.
18 For demonstration purposes, the price range for enzyme preparations was assumed to be from 19 $ 3 to $ 7 per kg. The price for corn, wheat, barley, and rye was assumed to be $ 0.13, $ 0.12, $
0.08, $ 0.08 per kg, respectively. The barley and rye were used as substituted cereals for wheat in 21 the diet, therefore, their price was assumed to be less expensive than that of wheat. The average 1 price of other ingredients in a diet was $ 0.08 per kg and the price of chickens was $ 1.23 per kg.
2 Other prices can be inserted into the equations as desired as outlined below.
3 Outline of a Multi purpose Enzyme Analyzer (MPEA) 4 Recently, we have developed a log-linear model equation to predict the performance of chickens fed a cereal-based diet supplemented with different concentrations of a feed enzyme.
6 The model can estimate maximal economic return when a feed enzyme is added to a diet. Based 7 on the log-linear model, we have further developed a software package, a Multi-purpose Enzyme 8 analyzer (MPEA). The MPEA consists of two parts: a modelling and application part (Figure 1).
9 The modelling part has revenue, production cost, and profit functions. The MPEA has three applications. The first application evaluates the profitable efficacy of different enzyme 11 preparations added to a specific diet and determines the most profitable cereal for a specific 12 enzyme preparation based on maximal economic returns. The second is to determine the optimal 13 amount of a feed enzyme and a cereal used in a diet to obtain maximal profit. The third is to 14 determine the alternate price that should be paid for a given enzyme preparation and a cereal.
Principle of the MPEA: Maximal Profit with the Optimal Inputs 16 From the dose response of study with varying the levels of a feed enzyme added to a diet, the 17 log-linear model equation was selected to fit the data of the output or chick performance and the 18 input or amount of enzyme. The general model as proposed by Zhang et al.
(1996) for weight 19 gain (Equation 1 ) and feed intake (Equation 2) was:
Y=A+Blog(CX+1) [1~
21 F = a + b log (c X + 1 ) [2]

" CA 02320687 2000-09-21 ' 1 where, X was the amount of an enzyme (percentage of diet), Y and F were weight gain (g) and 2 feed intake (g), A, B, C and a, b, c were the corresponding coefficients of the two regression 3 equations, respectively. Based on the two equations, we have developed a profit function 4 (Equation 3) in general:
II=PrY'F~(P;X;) [3]
6 where, II is the profit, Py is the price of chickens, P; is the price of ingredients in a diet and X; is 7 the amount of the i-th variable such as rye, wheat, or enzyme preparation in a diet. The maximal 8 profit can, therefore, be calculated when the partial derivatives of Equation 3 are equal to zero 9 (Heady and Dillon, 1961 ). A more detailed profit equation can be deduced when other variables are utilized (Equation 4). For example, the optimal amounts of a feed enzyme and a substituted 11 cereal (rye or barley) for wheat or corn in a diet, that will yield maximal profits, can be 12 determined using parameters and equations outlined below.
13 Suppose: Y = weight gain (kg), Py = price of chicken per kg, 14 F = feed consumption (kg), (PF = price of feed per kg,) XE = % of diet (enzyme), PE = price of enzyme per kg, 16 XR = % of diet (rye or barley), PR = price of rye per kg, 1 ~ XW = % of diet (wheat), PW = price of wheat per kg, 18 Xo = % of diet (other ingredients), Po = price of other ingredients per 19 kg~
Constrains: XR + XW = 0.60 0 ~ XR s 0.60 21 XE + Xo = 0.40 0 s XE s 0.05 22 XR+XW+XE+Xo= 1.00 1 Then II = Py Y - F (PEXE + PRXR+ PWXW + Pte) (4]
2 Where Y = A + B log (C X + 1 ) 3 F = a + b log (c X + 1 ) 4 Since XW = 0.60 - XR
Xo=0.40-XE
6 When 8II ~ 8XE = 0 [5]
7 8II ~ 8XR = 0 [6]
8 The amounts of XE and XR that will yield the maximum profit can be calculated when the XE and 9 XR are inputted into Equation 4.
Analyses of Data 11 The coei~'icients (A, B, C or a, b, c) for the log-linear model for weight gain or feed 12 consumption for the data from the first and second study were calculated using a program 13 developed by Zhang et al. (2000). A multiple regression analysis was used for the data from the 14 third study to establish the response of chick performances, such as weight gain (Y) and feed intake (F), to the amount of enzyme (XE) and the proportion of rye (XR) in the diet. The general 16 regression equations are shown in the following equations (Equations 7 and 8).
17 Y = (Ao + A,XR + AZXRZ + A3 XR3) 18 + (Bo + B,XR + BzXR2 + B3 XR3) log (C X + 1 ) [7]
19 F - (ap + aIXR + a2XR2 + a3 XR3) + (bo + b,XR + b2XRZ + b3 XR3) log (C X + 1 ) [8]
21 These models were an extension of the models used in our previous research (Zhang et al., 1996).
22 The coefficients of the two regression equations, with the two variables such as the amounts of , CA 02320687 2000-09-21 1 enzyme and the amount of rye relative to wheat in the diet as the inputs of the equation, were 2 calculated by the stepwise regression method (SAS, 1994) where the C values of the log-linear 3 equation were assumed to be 2150. The data for the third study were also analyzed using Sigma 4 Plot (Kuo and Norby, 1992) to determine the level of profit that was obtained with different amounts of an enzyme and different proportions of a substituted cereal, such as rye substituted 6 for that of wheat, in a diet.
7 The standard error of means for all of the data are given in the original studies. The residual 8 standard deviations of regression for the log-linear model equations are listed in Table 1.

RESULTS AND DISCUSSION
11 Evaluating the Effect of Different Feed Enzymes 12 One of the problems encountered by nutritionists in the feed industry is how to select a feed 13 enzyme that would be most effective for a particular feed. The effect of different feed enzymes 14 are generally evaluated by biological criteria such as their effect on chick performance, digestibility of feed nutrients, and degree of reduction of the viscosity of digesta or the diet 16 (Bedford and Classen, 1992; Joroch et al, 1995; Zhang et al, 1996). In most studies, comparisons 17 among different enzyme preparations has been often carried out using the same amount of 18 different enzyme preparations in a cereal-based chick diet as determined by an enzyme activity 19 assay or the levels of inclusion in the diet as recommended by the manufacturers (Rotter et al., 1989; Guenter 1997; Boros et al., 1998; Zhang et al., 2000). However, it is difficult to correctly 21 evaluate different enzyme preparations based on their activities, since many enzyme preparations 22 are from different sources. Therefore, they often contain a different spectrum of enzymes with 1 different catalytic properties. In addition, the selection of the proper assay conditions such as pH, 2 especially when comparing the activity of different feed enzymes, is essential because the 3 selected pH will bias results in favour of an enzyme whose optimal pH is closest to the select 4 selected pH, which in turn may not be the optimal pH in vivo (Marquardt and Bedford, 1997;
Ziggers, 1999, Zhang et al, 2000). Recently, we have developed a new approach to accurately 6 evaluate the effects of different enzyme preparations. The approach uses a new concept for 7 estimating the efficacy of a feed enzyme, the slope of a log-linear model (Zhang et al., 1996).
8 This evaluation, although very useful, is only based on the biological data.
However, the goal of 9 many studies is often to select an enzyme preparation that will yield the greatest profit.
The objective of the first study was to determine if the effects of different feed enzyme 11 preparations on maximal profits could be evaluated using the MPEA. The profit functions (Table 12 1 ) were readily derived using Equation 4 from the production (Equation 1 ) and feed consumption 13 (Equation 2) functions. The maximal profit and the optimal amount of an enzyme that should be 14 added to a diet was calculated using Equations S and 6. The results in Table 2 indicated that the maximum profit per 1000 birds when given the optimal amount of each of the five enzyme 16 preparations, Cellulase Tv, Cellulast, Finizym, Cereflo, and SP249 were $
67.29, $ 61.27, $
17 51.91, $ 49.27, and $ 46.79, respectively. In this analysis, the assumed price of the enzymes were 18 the same. The sequence of these values also agrees with that of the B
values for the feed to gain 19 ratio as determined from the log-linear equation ( rz = 0.99, P < 0.0005).
The same trend was also observed in this study using data from Zhang et al. ( 1996). These results, in contrast to 21 subsequent results with different cereals or cereals plus enzymes, suggest that both the B values 22 and the maximal profit provided similar indices for the evaluation of different enzyme 1 preparations. This relationship, however, would not necessarily be the same if the price of the 2 different enzyme preparations was different. In addition, the advantage of the two methods, 3 especially for the method using maximal profit, is that they do not require a knowledge of 4 enzyme activity, the combination of enzymes used in a preparation, and the site of action of the enzymes in the gut. The information required for latter method (the maximal profit) is that (1) the 6 model equations be used to establish the influence of different concentrations of different enzyme 7 preparations on chick performance and (2) the price of the major ingredients used in a diet. The 8 method proposed in this study therefore provides a simple way to evaluate the collective effect of 9 different enzyme preparations when incorporated into chick diets based on maximal economic returns.
11 Identifying the Most Profitable Cereal When Used l~th a Feed Enzyme 12 On the basis of the proposed method (Zhang et al., 1996), the most suitable cereal for a target 13 enzyme preparation can be determined from the slope of a log-linear model.
In this study (study 14 2), the B values for the feed to gain ratio were calculated from the data of Marquardt et al.
(1994). The sequence of cereals producing the greatest response to an enzyme preparation in 16 decreasing order were rye, barley, wheat, and corn (negative control) (Table 3). However, the 17 sequence of the cereals that yielded the maximum profit following enzyme addition was 18 different. The maximal profits obtained when the enzyme preparation was added to a barley-, 19 corn-, wheat-, and rye-based diet were $ 135.00, $ 134.45, $ 133.55, and $
123.96 per 1000 birds, respectively when the price of all cereals were the same (Table 3). Therefore, under these 21 conditions, the relationship between the magnitude of the B values for feed to gain ratio and the 22 maximal profit was low ( rz = 0.61, P = 0.2171). This disagreement was also observed in the third 1 study ( rz = 0.59, P = 0.2340). The reason for this discrepancy is attributed to the fact that the B
2 values reflect the overall response of chicks to different amounts of an enzyme added to different 3 cereal-based diets while the maximal profits are not only affected by the efficacy of the enzyme 4 (B value) but also by the response of chick when fed different cereal-based diets without enzyme addition (A), and by the cost of the feed and the enzyme. The results therefore demonstrate that 6 the latter method (maximal profit) is more useful than the former procedure (B value) for the 7 feed or enzyme industry in determinating which cereal should be used with a given feed enzyme 8 to obtain the maximum profit. In addition, if the prices of wheat and corn were assumed to be $
9 0.12 and $ 0.13 per kg, wheat yielded a greater profit than corn and the rye grain at $ 0.08 per kg becomes a competitive cereal with wheat or corn ( $123.96 per 1000 birds for rye vs. $ 126.00 or 11 $ 126.73 per 1000 birds for corn or wheat). These results demonstrate that the price of a cereal 12 also influences profitability when a special feed enzyme is added to the cereal-based diet.
13 Therefore, an acceptable price for a substituted cereal such as rye, when used with an enzyme, 14 could be determined by comparing its maximal profit with that obtained by the use of the standard cereal such as wheat.
16 Optimal Amounts of Enzyme and Cereal That Should be Used in a Diet 17 One of the important applications of MPEA is to determine the amounts of an enzyme and a 18 cereal that should be used in the diet to obtain a maximum profit.
Generally, the performance 19 response of chicks fed a diet with increasing amounts of an enzyme is a hyperbolic saturated response pattern. It is well known that equal incremental amounts of enzyme when added to a 21 diet results in diminishing incremental changes in chick performance (Friesen et al., 1991;
22 Bedford and Classen, 1992; Marquardt et al., 1994, Zhang et al., 1996).
However, this study 1 demonstrates that the dose response of profit obtained with the addition of a feed enzyme yields a 2 quadratic rather than a hyperbolic pattern. The results, as shown in Figures 2 and 3, indicate that 3 the profit obtained with increasing amounts of a feed enzyme was increased to a certain point.
4 After that, the profit decreased with increasing amounts of the enzyme (Figures 2 and 3). This point can be readily calculated using the MPEA. The results demonstrated that the optimal 6 amounts of different enzyme preparations that should be added to a diet (Table 2) were 7 considerably different for a given feed enzyme when added to different cereal-based diets (Table 8 3), and for a feed enzyme when added to a diet with varying the proportions of two cereals (Table 9 4). These results, however, demonstrated that there was the high correlation between the values of B for feed to gain ratio and the optimal amount of an enzyme that should be used in a diet ( rz 11 = 0.99, P < 0.0005 for the first study, Table 2; rz = 0.92, P < 0.05 for the second study, Table 3; rz 12 = 0.89, P < 0.06 for the third study, Table 4). Therefore, the amount of an enzyme that should be 13 used in a diet to obtain maximal profit increases with an increasing B
value for the feed to gain 14 ratio. In addition, the optimal amounts of the two inputs to obtain maximum profit can also be determined by the MPEA. This is shown by the arrows indicated in Figure 4. The two variables 16 used in this study were variable amounts of enzyme and variable proportions of rye and wheat.
17 Profct Contours or Isoquants 18 The objective of obtaining maximal profit by enzyme addition to a given diet may not be the 19 only goal for a feed company or poultry farm. In some cases, the question that has to be asked is, does the enzyme and substituted cereal, used at various levels and in different combinations, give 21 the expected profit? The relationships among amounts of enzyme added to the diet, the relative 22 concentrations of two cereals (rye vs. wheat), the cost of the enzyme preparation, and the 1, resulting profit are illustrated in Figure 4. The two-dimensional figures on the right side of Figure 2 4 represents the contour of response associated with horizontal slices of the figure on the left.
3 These lines, called profit contours or isoquants, provide a useful tool to determine any 4 combination of inputs such as amounts of an enzyme and rye used in a diet for any fixed level of profit. For example, if the price of enzyme was $ 5 / kg (middle figure), it is possible to obtain $
6 65 (line labelled 65) of profit per 1000 birds with various combinations of rye (levels from 7 to 7 3 8 %) and an enzyme (levels from 0 to 1.6 %). The arrows ( 1 ) in the figures indicates the amount 8 of enzyme that should be used to yield maximal profits. For example, maximum profits of $
9 71.72, $ 71.27, or $ 70.98 per 1000 birds was obtained when the enzyme content was 0.27, 0.16, or 0.11 %, the rye content was 0, 0, or 0 %, and enzyme cost was $ 3, $ 5, or $ 7 per kg, 11 respectively. Different combinations of these inputs represent the optimal amounts of the enzyme 12 and the rye that should be used in the diet to obtain maximum profits.
13 Decision Maker for Price of Enzyme and Cereal Used 14 There are many factors that influence the profit obtained when a feed enzyme is added to a diet. They included the amount of enzyme added, the type and amount of cereals, the efficacy of 16 the feed enzyme, and the price of enzyme and cereals used. Once the profit function is 17 established, any variable in the equation can be calculated and analyzed provided other variables 18 are fixed. Therefore, the price that should be paid for an enzyme and a substituted cereal can be 19 determined. This can be illustrated by the comparison of two enzyme preparations, Cellulase Tv concentrate (CT) and Celluclast (CC). The results in Table 2 indicated that the maximal profits 21 per 1000 birds for CT and CC were $ 67.29 and $ 61.27 per 1000 birds when the price of both 22 enzyme preparations was $ S per kg. If the maximal profit of $ 67.29 per 1000 birds was the 1 target for both enzyme preparations, the price of CC should be reduced from $ 5 to $ 0.9 (Figure 2 2). The result suggest that the competitive price of CC can be determined by comparing its 3 maximal profit with that of CT. Let us assume that CC was an enzyme preparation being 4 developed to compete with CT for rye-based diets. Two possible methods could be used for CC
in order to obtain the same maximal profit as that of CT. The first would be to reduce its price 6 and the second would be to improve its efficacy (B value). The results indicated that an 82%
7 decrease in the price of CC ($ 5 to $ 0.9) would be required to yield the same maximal profit ($
8 67.29 /1000 birds) as obtained with CC at $ 5 / kg. However, the same results could be obtained 9 with a 17 % improvement in the efficacy of CC, an increase in its B value for the feed to gain ratio from -0.211 to -0.247. This suggests that an improvement in the ef~'icacy of an enzyme is a 11 much more effective means of increasing profitability than that obtained by reducing its price. In 12 some cases, it is not possible to obtain an equivalent maximal profit by changing the price of a 13 feed enzyme. For example, the only way that Finizym could yield the same maximal profit as 14 CT would be to improve its efficacy, i.e. improvement of its B value from -0.172 to -0.247 as shown in Table 2.
16 In addition, the maximal profit is also influenced by the price of the cereal used in a diet. As 17 indicated in Table 3, rye grain cannot compete with wheat when the price of these cereal are the 18 same. However, when a higher price of wheat was used, rye grain could yield a similar maximal 19 profit to that obtained with wheat. This strategy could also be used by a feed industry to determine the expected price of a target cereal in order to obtain a certain level of maximal profit.
21 In conclusion, the MPEA that was developed in this study can be used by the enzyme and feed 22 industries to evaluate different enzyme preparations based on their profitability, to determine the 1_ maximal economic return that can be obtained with the optimal inputs of feed ingredients such as 2 type and amounts of cereals and enzymes, and to analyze the relationship between the price of a 3 feed enzyme or a cereal and the economic return. This study demonstrates that a knowledge of 4 nutrition in combination with computer technology and the modelling method can provides nutritionists and managers in the enzyme and feed industry with useful information for their 6 research activities and business decisions.

19 The authors would like to thank the supports the Natural Science and Engineering Research Council of Canada, Ottawa, ON, Canada, K 1 G 1 FS and University of Manitoba, Winnipeg, MB, 21 Canada, R3T 2N2. The authors also thank M. Popp for his invaluable assistance.

2 Antoniou, T.C., R.R. Marquardt, and P. E. Cansfield, 1981. Isolation, partial characterization, 3 and antinutritional activity of a factor (pentosans) in rye grain. J. Agric.
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9 Bedford, M. R., and H. L. Classen, 1992. Reduction of intestinal viscosity through manipulation of dietary rye and pentosanase concentration is effected through changes in the 11 carbohydrate composition of the intestinal aqueous phase and results in improved growth 12 rate and food conversion e~ciency of broiler chicks J. Nutr. 122:560-569.
13 Boros, D., R.R. Marquardt, and W. Guenter, 1998. Site of exoenzyme action in gastrointestinal 14 tract of broiler chicks. Can. J. Anim. Sci. 78:599-602.
Fengler, A. L, and R.R. Marquardt, 1988. Water-soluble pentosans from rye: II
Effects on rate of 16 dialysis and on the retention of nutrients by the chick. Cereal Chem. 65:
298-302.
17 Fengler, A. L, J. R. Pawlik, and R. R. Marquardt, 1988. Improvements in nutrient retention and 18 changes in excreta viscosities in chicks fed rye-containing diets supplemented with fungal 19 enzymes, sodium taurocholate and penicillin. Can. J. Anim. Sci. 68:483-491.
Friesen, O.D., W. Guenter, B.A. Rotter, and R.R. Marquardt, 1991. The effects of enzyme 21 supplementation on the nutritive value of rye grain (Secale cereale) for the young broiler 22 chick. Poultry Sci. 70:2501-2508.

1 Guenter, W., 1997. Practical experience with the use of enzymes. Pages 53-62 in: Enzyme in 2 Poultry and Swine Nutrition. R.R. Marquardt, and Z. Han, ed. International Development 3 Research Centre, Ottawa, ON, Canada.
4 Heady, E. D., and J. L. Dillon, 1961. Economic applications. Pages 31-72 in:
Agricultural S production functions. E.O. Heady, and J. L. Dillon, ed. Iowa State University Press, 6 Ames, Iowa.
7 Kuo, J., and J. Norby, 1992. Sigma Plot~, Scientific Graphing Software, User's manual. Jandel 8 Scientific, San Rafael, CA.
9 Marquardt, R. R., 1997. Enzyme enhancement of the nutritional value of cereals: role of viscous, water-soluble, nonstarch polysaccharides in chick performance. Pages 5-17 in:
Enzyme in 11 Poultry and Swine Nutrition. R.R. Marquardt, and Z. Han, ed. International Development 12 Research Centre, Ottawa, ON, Canada 13 Marquardt, R. R., and M. Bedford, 1997. Recommendations for future research on the use of 14 enzymes in animal feeds. Pages 129-138 in: Enzyme in Poultry and Swine Nutrition. R.R.
Marquardt, and Z. Han, ed. International Development Research Centre, Ottawa, ON, 16 Canada.
17 Marquardt, R. R., D. Boros, W. Guenter, and G Crow, 1994. The nutritive value of barley, rye, 18 wheat and corn for young chicks as aRected by use of a Trichoderma reesei enzyme 19 preparation. Anim. Feed Sci. Technol. 45:363-378.
McCleary, B. V., 1992. Measurement of endo-1,4-~i-D-xylanase. Pages 161-170 in: Xylans and 21 xylanases. V. J. Beldman, G. Kusters- Van, M.A. Someren, and A.G.J.
Voragen, ed.
22 Elsevier Science Publishers, Amsterdam.

1 Rotter, B.A., M. Neskar, R.R. Marquardt, and W. Guenter, 1989b. Effects of different enzyme 2 preparations on the nutritional value of barley in chicken diets. Nutr. Rep.
Int. 39:107-3 120.
4 SAS., 1988. SAS/STAT'~ Users' Guide (Release 6.03). SAS Inst. Inc., Cary, NC.
Seeta, R., V Deshpande, and M. Rao, 1989. Role of (3-xylosidase in hemicellulose hydrolysis by 6 xylanase from Penicillium funiculosum. Biotechnol. Appl. Biochem. 11:128-132.
7 Zhang, Z., R. R. Marquardt, and W. Guenter, 2000. Evaluating the efficacy of enzyme 8 preparations and predicting the performance of Leghorn chicks fed rye-based diets using a 9 dietary viscosity assay. Poultry Sci. (accepted).
Zhang, Z., R. R. Marquardt, W. Guenter, and Z. Han, 1997. Effect of different enzyme 11 preparations supplemented in a rye-based diet on the performance of young broilers and 12 the viscosity of digesta and cloacal excreta. Chinese J. of Animal Sci. 34 (1): 3-6.
13 Zhang, Z., R. R. Marquardt, G Wang, W. Guenter, G H. Crow, Z. Han, and M.
R. Bedford, 14 1996. A simple model for predicting the response of chicks to dietary enzyme 1 S supplementation. J. Anim. Sci. 74: 394-402.
16 Ziggers, D. 1999. Enzymes: hidden catalysts come out of the dark. Feed Tech. 3(6):23-33.

FIGURE 1. Principle and Application of the Multi-purpose Enzyme Analyzer for Use of Enzymes in Poultry Feeds FIGURE 2. Estimated effect of price of enzymes and the amounts of enzymes added to a barley-based diet on the profit per 1000 birds in a one-week feeding study. The enzyme preparations used in this figure were CC (Celluclast ) from Novo A/S Demark and CT ( Cellulase Tv concentrate) from Miles Laboratories Inc. Data used for the calculations were from Rotter et al., 1989.
FIGURE 3. Profit as affected by cereal price and amounts of an enzyme added to the cereal-based diets. Different (A) and the same (B) price of cereals were used to calculate profit ($/bird). The assumed cost of the enzyme was $ 5 / kg. Data used for the calculations were from Marquardt, 1994. C, corn; W, wheat; B, barley; and R, rye.
FIGURE 4. Effect of different combination of two variables, amounts of enzyme (XE) and rye (XR) added to diets on the profit of chickens fed diets from 1 to 19 d of age.
Cereals in the diet were wheat plus rye (60 %). The profit function were: II = Py Y - F ~ ( Pi Xi ), where Y = (404 -2.04XR+ 5.25 X 1 O-3XRZ - 3.20X I O~XR3 ) + (9.78 + 3.49x 1 OXR - 1.29 x 1 O-'XRZ + 1.06X 10~ XR3) log (2150 X + 1 ), and F = (648 - 8.52 X 10-ZXRZ + 8.33 x 1 O~XR3) + (2.64 + 2.27 x I O-ZXRZ - 2.10 X 10~
XR3) log (2150 X + 1 ); II = profit ($/1000 birds), Y = weight gain (g), F =
feed consumption (g), Py and Pi represented the price of chickens and the price of the i-th ingredient (Xi) in a diet. The plots on the left gives the three-dimensional relationship for relative amount of rye in the diet (the balance is wheat), the amount of enzyme added to the diet, and the profits obtained assuming wheat and rye costs are $ 0.12 and 0.08 per kg, respectively, and that of enzyme is $ 3, S, or 7 per kg. The figures on the right are the profit contours of two-dimensional slices of that on the right for diets containing different amounts of enzyme and different percentage of rye in the diet. The number in each line represents the fixed profit that can be obtained by feeding different amounts (%) of rye and enzyme. The arrow indicated the amount of enzyme that should be used to obtain maximal profits. Data used for the calculations were from Bedford and Classen, 1992.

Table 1. The production and feed consumption functions established from a log-linear model for the data from Zhang et al. ( 1996, study 1 ), Rotter et al. ( 1989, study 1 ), Marquard et al.( 1994, study 2), and Bedford and Classen (1992, study 3) Cereal' Y = Weight gain (g)2 r SD3 F = Feed intake (g)Z r SD3 (Enryme) Barley 31.4 + 7.68 log 0.99 2.03 80.2 + 7.27 log 0.99 1.67 (CT)" ( 105 X +1 ) ( 105 X +1 ) Barley 31.0 + 6.79 log 0.99 0 80.1 + 7.72 log 0.99 0.66 (CC) ( 105 X +1 ) ( 1 OS X +1 ) Barley 30.8 + 4.99 log 0.99 1.06 79.9 + 5.75 log 0.99 0.28 (FZ) ( 105 X +1 ) ( 105 X +1 ) Barley 30.3 + 4.49 log 0.92 3.21 79.3 + 4.61 log 0.93 3.28 (CF) ( 105 X +I ) ( 105 X +I ) Barley 30.6 + 4.00 log 0.96 1.91 79.5 + 4.63 log 0.94 2.94 (SP) ( 105 X +1 ) ( 105 X +1 ) Rye(RM1)B536+45.61og(10'X+1)0.99 7.3 1309+45.61og(10~X+1)0.98 13.4 Rye (NQ)549 + 52.2 log 0.98 13.1 1317 + 59.6 log 0.94 26.2 ( 10' X +1 ) ( 10' X +1 ) Corn 135 - 1.67 log 0.96 0.9 275 - 1.16 log -0.83 4.3 (KC)~ (IOaX +1) (10'X +I) Wheat 125 + 0.81 log 0.98 0.8 248 + 0.43 log 0.9 1.1 (KC) (10' X +1) (10'X +1) Barley 113 + 2.26 log 0.99 2 220 + 4.87 log 0.99 0.3 (KC) ( 10' X +I ) ( 10~ X +1 ) Rye (KC)97 + $.76 log 0.99 0.3 220 + 9.09 log 0.99 2 ( 10 X +1 ) ( 10 X +I ) 0% rye (PP)° 399 + 3.55 log (10'°X +1) 0.81 11.4 664 + 13.1 log (l0 X +1) 0.52 10.7 20% rye (PP) 359 + 6.28 log (10' X +i) 0.99 2.5 622 + g.01 log (10° X
+1) 0.57 20.1 40% rye (PP) 306 + 21.6 log (105 X +i) 0.98 9.2 561 + 30.8 log (10° X
+I) 0.93 21 60% rye (PP) 232 + 54.4 log ( 10' X +1 ) 0.98 13.7 530 + 63.7 log ( 1 Oz X +I
) 0.94 20.6 ' Data from four studies were used to develop the prediction equation for weight gain, Y = A + B log (CX +1 ), and feed consumption, F = a + b log ( cX + 1 ), where Y and F are weight gain (g) and feed consumption (g), X is the amount of an enryme (%) added to a cereal-based diet, A, B, C and a, b, c are the coeffcients of the log-linear equations for weight gain and feed consumption, respectively. The performances of chicks predicted by the equations were the values per bird when Leghorns were fed from 7 to 14 d (A: Rotter et al., 1989) and from 7 to 21 d (C: Marquardt et al., 1994), and the values per 6 birds when Leghorns were fed from 7 to 21 d (B : Zhang et al., 1996), and when broilers were fed from 1 to 19 d (D: Bedford and Classen, 1992). The relative proportion of rye and wheat in the different diets were: 0, 60; 20, 40; 40, 20; and 60, 0.
2 The enzyme preparations used in the studies were RM1 and PP (a pentosanas preparation) from Finnfeed International Ltd; NQ and KC (Kyowa Cellulase) from Nutri-Quest; CT
(Cellulase Tv concentrate) from Miles Laboratories Inc.; and CC (Celluclast), FZ (Finizym), CF (Cereflo), and SP
(SP249) from Novo A/S Denmark.
' SD represents the residual standard deviation of regression for the log-linear equations.

TABLE 2. Effect of different enzyme preparations added to a barley- or rye-based diet on the efficacy of enzyme (B values), the optimal amounts of enzymes and the maximal profits obtained from Leghorn chicks in a one-week (Rotter et al., 1989) or two-week (Zhang et al., 1996) feed study (study 1 )' Source of Enzyme B Value3 Optimal Enzyme4 Maximal Profit Data Preparation2 (%) ($/1000 birds) Rotter et Cellulase -0.247 0.656 67.29 al., Tv 1989 Celluclast -0.211 0.56 61.27 Finizym -0.172 0.452 51.91 Cereflo -0.171 0.439 49.27 SP249 -0.139 0.3 85 46.79 Zhang et RM 1 -0.0943 0.31 S 1 O 1.19 al., 1996 NQ -0.0963 0.348 104.38 ' The assumed price for enzyme preparations used in the two studies was $ 5 per kg.
z The enzyme preparations used in the study of Rotter et al.( 1989) and Zhang et al. ( 1996) were Cellulase Tv concentrate (Trichoderma viride) from Miles Laboratories Inc. and Cellucast (T.
ressei) Finizym (Aspergillus niger), Cereflo (Bacillus subtilis), and SP249 (Aspergillus niger) from Novo A/S Demark; and RM1 (T. longibrachiatum) from Finnfeeds International Ltd. and NQ (T. reesei) from Nutri-Quest.
3 The B values were the slope of log-linear model equation calculated from the feed to gain ratio data. The values are the indexes of the efficacy of a feed enzyme added to a diet (Zhang et al., 1996; 2000).

4Amounts of enzyme to yield a maximum profit.

TABLE 3. Effect of cereal prices on optimal amounts of an enzyme added to different cereal-based diets and their maximal profits.
Value Same OptimalMaximal DifferentOptimalMaximal Cereal of Pricez Enzyme Profit Price2 Enzyme Profit B' ($/kg) 3 ($/1000 birds)($/kg) 3 ($/1000 birds) (%) (%) Corn 0.01 0.08 0 134.45 0.13 0 126 Wheat -0.03 0.08 0.0339 133.55 0.12 0.0335 126.73 Barley -0.04 0.08 0.0815 135 0.08 0.0815 135 Rye -0.0900.08 0.3419 123.96 0.08 0.3419 123.96 ' The B values are the slope of log-linear model equation calculated from the feed to gain ratio data (Zhang et al., 1996; 2000). The values are indices of the efficacy of a feed enzyme when added to different diets.
ZThese values represent the price of the cereals. The assumption was that the enzyme (Kyowa Cellulase, Finnfeeds International Ltd.) cost was $ 5 per kg.
3The optimal amount of enzyme calculated is that amount of enzyme that yield maximal profits.

TABLE 4. Effect of price of an enzyme and cereals on the maximal profits and the optimal amounts of an enzyme added to diets with different proportion of rye Price of Enzyme ($/kg) $ 3 $ 5 $ 7 Price Difference of Cereals $ 0.02 $ 0.04 $ 0.02 $ 0.04 $ 0.02 $ 0.04 ( o $ / kg)' Rye in B value' Optimal enzyme (%) diets2 0 % -0.0323 0.273 0.273 0.159 0.159 0.113 0.113 20 % -0.0482 0.461 0.462 0.27 0.271 0.191 0.192 40 % -0.0544 0.738 0.742 0.435 0.438 0.309 0.311 60 % -0.1867 1.262 1.272 0.748 0.754 0.537 0.537 Maximal profit ($/1000 birds) 0 % -0.0323 71.72 71.72 71.27 71.27 70.98 70.98 20 % -0.0482 68.15 68.59 67.4 67.83 66.91 67.34 40 % -0.0544 65.21 66.07 64.01 64.86 63.23 64.08 60 % -0.1867 63.27 64.58 61.19 62.48 59.85 61.13 ' This price presents the net difference between the price of wheat and the price of rye that was assumed as a cheap and substituted cereal for wheat in diets.
Z The corresponding amount of wheat in the four diets was 60, 40, 20, and 0 %, respectively.
3 The B values were the slope of log-linear model equation calculated from the data of feed to gain ratio. The values are indexes of the efficacies of a feed enzyme when added to a diet with different levels (Zhang et al., 1996; 2000).

'+ Introduction World feed production for industrialized farming currently tops 575 million tonnes 6 annually with about 57 % of the production being for pigs and poultry enterprises (Dunn, 1999, 7 Hofinan, 2000). However, only about 6% of manufactured animal feed contain enzymes. The 8 worldwide feed enzyme business is now estimated to be worth about $100 million, more than 20 9 times greater than the 1990 value. The potential is even greater (McCoy, 1998). Currently most of the enzymes that are used in feeds are xylanases for wheat- and rye-based diets and (3-11 glucanases for barley- and oat-based diets. The target of these enzymes are the non-starch 12 polysaccharides (NSPs) that are found in cereals; they include xylanases for xylans and ~i-13 glucanases for (3-glucans. Phytase is also widely used (Marquardt, 1997;
Ziggers, 1999). The use 14 of NSP enzymes in the animal feed industry has greatly expanded in the past ten years especially in countries like Canada that utilizes large quantities of cereals such as barley, wheat, triticale, 16 and rye in poultry and pig diets. As biological catalysts, NSP enzymes are able to neutralize the 17 negative effects produced by certain viscous NSP in these cereals. These enzymes when added to 18 diets, especially for poultry, have been shown to improve the efficiency of feed utilization, 19 increase the rate of growth, improve the health of the gastrointestinal tract, and reduce environmental pollution due to a decreased output of manure and gases such as ammonia 21 (Marquardt, 1997; Choct, 1997; Bedford, 1997b). However, many unseen benefits of exogenous 22 enzymes will gradually be explored in the future. The exogenous enzymes as feed additives has ~1 considerable potential since they are efficient in their catalytic functions and safe in applications.
2 Although feed enzymes have been proven to be highly beneficial, the use of enzymes has 3 many problems that must be solved before their full potential is reached.
One of the problems 4 that has to be solved is how to accurately determine the efficacy of a feed enzyme added to a diet.
S Most feed enzymes are primarily derived from different bacteria (e.g.
Bacillus spp) and fungi 6 (e.g. Aspergillus and Trichoderma spp). The major enzymes contained in many commercial 7 enzyme preparations (i.e., ~i-glucanases) are often intended for certain target-cereals (i.e., barley).
8 Although enzymes are labeled as if they all have the same effect on selected cereals, they often 9 have different pH optimums, substrate preferences, temperature optimums and thermal stabilities. In addition, the reaction conditions where exogenous enzymes act in the gut are 11 determined by the nature of condition in the intestine with very limited possibilities for 12 modification (Classen, 1996; van de Mierop and Ghesquiere, 1999). Also, the structure and 13 contents of the target substrates within and between cereals for enzymes are complex and vary in 14 nature. Consequently, the efficacy of most enzyme preparations varies considerably.
World markets are becoming less insular and subject to increasing international competition.
16 Faced with the rapid expansion of feed enzyme markets, nutritionists in the feed industry often 17 do not know how to select an enzyme preparation that is the most effective for their products.
18 Currently, comparison among different enzyme preparations has been often carried out on the 19 basis of the same amount of different enzyme preparations added to a diet.
The amount of enzyme preparations that are added to a cereal based diet is often determined on the basis of an 21 enzyme assay in a laboratory or by the level that is recommended by the manufacturer (Boros et 22 al., 1999; Guenter, 1997). However, it is difficult to correctly evaluate different enzyme ~1 preparations based on their activities, since many enzyme preparations are from different sources, 2 contain a different spectrum of enzymes with different catalytic properties.
The selection of the 3 correct assay conditions such pH, especially when comparing the activity of different feed 4 enzymes, is essential because the selected pH will bias results in favor of an enzyme whose optimal pH is closest to the selected pH. In addition, enzyme assay conditions vary considerably 6 among laboratories and they often do not reflect conditions at the site of action of exogenous 7 enzymes in the gastrointestinal tract. Therefore, the successful development of a method that 8 accurately evaluated the efficacy of a feed enzyme is highly important. This would not only 9 greatly assist the feed industry in the selection of an enzyme preparation having the highest efficacy, but would also establish a standard to evaluate the effect of a new generation of enzyme 11 preparations (a cocktail vs. a single type of enzyme), recombination DNA
enzymes (a 12 modification enzyme product vs. a natural enzyme preparation), and the processing of enzymes 13 (a dry mix vs. a liquid spray).
14 Another problem is how to accurately predict the response of a feed enzyme when added to a diet. There has been increasing interest in quantitatively studying the effect of the input into the 16 diet of different levels of feed enzymes on the outputs or the performance of chickens (Bedford 17 and Classen, 1992; Friesen et al., 1991; Marquardt et al., 1994; Rotter et al., 1989). The primary 18 objectives of these studies has been to estimate the optimal level of feed enzyme addition 19 required to obtain maximal performance in chickens (Bedford and Classen, 1992; Friesen et al., 1991 ). Frequently, the experimental designs and statistical procedures have only provided trends 21 on the effects of enzyme treatment but have not provided precise prediction values that can be 22 obtained when a given enzyme is added to a given diet. From this standpoint, it has been '1 impossible to conduct refined studies on the relationship between inputs (enzymes) on outputs 2 (chick performance), or to establish the most profitable combination of inputs for a specified 3 output. In addition, researchers in nutritional fields have generally been concerned only with 4 biological rather than economic criteria to evaluate the effects of feed enzymes and to make their recommendations. The largest weight gain or the lowest feed to gain ratio per unit of enzyme 6 addition have often been the criteria used for evaluation of performance(Bedford and Classen, 7 1992; Friesen et al., 1991). However, the most profitable output or optimal input has seldom 8 been the same as these maxima or minima. Even where the objective was prediction of physical 9 maxima or minima, the exact values can only be accurately estimated by a prediction equation where the experimental data are used to estimate this equation.
11 Recently, we have applied a log-linear model to predict the response of chickens to dietary 12 enzymes (Zhang et al., 1996). The model was able to accurately predict the performance of 13 chickens fed diets containing different amounts of an enzyme and different proportions of two 14 cereals. Data from many dose response studies of feed enzymes, although not designed for these purposes, confirmed that the simple log-linear equation was accurate. In addition, the efficacy of 16 any enzyme preparation for a particular cereal or class of poultry with regards to any index of 17 animal performance such as weight gain or feed to gain ratio can be determined from a single 18 value of B, the slope of the model equation (Marquardt and Bedford, 1997;
Zhang et al., 1996).
19 Therefore, it is possible to correctly evaluate the efficacy of a feed enzyme and to accurately predict the response of chickens to an enzyme when it is added to a diet using this new approach, 21 the log-linear model.
22 This review will mainly discuss our recent research on the use of the log-linear model to 1 evaluate and predict the response of chicks when a feed enzyme is added to the diet. It will cover 2 the following topics: hypothesis and the development of the log-linear model, evaluating the 3 efficacy of a feed enzyme using the model, predicting the response of chicks to a feed enzyme, 4 evaluating and predicting the profitable effect of a feed enzyme, and finally the use of an in vitro assay to predict in vivo response to an enzyme.

7 Hypothesis and the Log-linear Model 8 Dose Response Studies 9 Several dose response studies in our laboratory (Rotter et al., 1989;
Friesen et al., 1991;
Marquardt et al., 1994) have determined the level of a feed enzyme required to obtain maximal 11 growth performance in chicks fed cereal-based diets. In a study by Friesen et al. (1991), a crude 12 xylanase preparation with different levels of the enzyme was added to a 60%
rye-based diet. The 13 results indicated that the performance response of the growing chicks to increasing amounts of 14 enzyme was a typically hyperbolic pattern. The results from other studies also supported this observation (Bedford and Classen, 1992; Marquardt et al., 1994; Rotter et al., 1989; Zhang et al., 16 1996). In addition, the efficacy of different enzyme preparations, as determined by their effect on 17 the performance of Leghorn chicks when they were added to barley-based (Rotter et al., 1989) 18 and rye-based (Zhang et al., 1996) diets, was evaluated. Marquardt et al.
(1994) established the 19 dose response effect of a feed enzyme when added to different dietary cereals (such as corn, wheat, barley, and rye) on the performance of Leghorn chicks. Bedford and Classen ( 1992) also 21 studied the dose response effect on chick performance and viscosity of digesta of an enzyme 22 preparation when added to diets containing different proportional rye and wheat. Three basic 1 characteristics of the dose response were observed.: ( 1 ) the response pattern was typically a 2 hyperbolic curve, (2) each additional increment of enzymes that was added to the diet produced 3 diminishing incremental responses, and (3) different maximal improvements and diminishing 4 incremental responses were obtained with different enzyme preparations and different cereals.
The ability to accurately predict the effect that different amounts of an enzyme preparation have 6 on the performance of chickens would be of considerable value to the nutritional research 7 scientist and the livestock producer. This, however, is not a simple matter since there is not a 8 direct proportionality between the two factors, enhanced performance and amount of added 9 enzyme.
A Log Model and its Modification 11 The hyperbolic dose response curve reflects a common biological phenomenon, the "Law of 12 Diminishing Returns". The curve can be generated by several non-linear models, including 13 polynomial, exponential, or logarithmical models (Almquist, 1952; SAS, 1988), or other models 14 such as segmented or logistic models (Remmenga et al., 1997). However, for feed enzyme research, only a few authors have used these models to fit their data. For example, in the study of 16 Friesen et al. (' 1991 ), the exponential model was applied to estimate the maximal effective dose 17 of a feed enzyme when added to a 60% rye-based diet. In another study, Hesselman et al. (1982) 18 applied the polynomial model (linear and quadratic model) to predict the effect of different doses 19 of a (3-glucanase preparation on the productive response of chick s fed diets containing barley harvested at two stages of ripeness.
21 Recently, Zhang et al. (1996), based on the results of two dose response studies and some 22 published data, first applied the log model to predict the response of chicks fed diets containing 1 enzymes. The criteria for developing this model were: ( 1 ) there must be a good fit (high rz) 2 between the observed and predicted data (SAS, 1988), (2) the model should be simple to 3 interpret, and (3) the model should provide useful information. The general form of the log 4 model is written as follows:
Y=A+B logX [OJ
6 where, Y is the estimated performance value [for example, weight gain (g)], X is the 7 concentration of an enzyme (unit per kilogram of diet or percentage of diet), B is the slope of the 8 equation (performance change per log unit of an enzyme in the diet), A, the intercept (Y axis), 9 theoretically represents performance without an enzyme added to the diet.
However, this value is not readily obtained as there is no value for the log of zero (the value without enzyme 11 supplementation, i.e., when X = 0). In order to obtain an A value, Zhang et al. (1996) developed 12 a modified log model, Equation 1.
13 Y=A+Blog(X+E) [1J
14 In the model, an amount of enzyme (E) was selected which was very small and close to zero. The s value was shown to be essentially constant as it was not affected by the concentration of 16 enzyme for a given diet.
17 The intercept, A, in Equation 1 represents chick performance when a preselected and 18 substituted value for zero (s) is used. As such A = Y - B log g may not yield an accurate estimate 19 of chick performance for diets that do not contain an exogenous enzyme. In turn, the selected E
may also affect the slope B of Equation 1 [B = ( Y-A ) / log ( X + ~ )]. These are some of the 21 weaknesses of Equation 1. In addition, the introduction of an g value into Equation 1 not only 22 influences the accuracy of certain parameters, such as A and B, but its value is difficult to 1 calculate, therefore an arbitrary s value must be selected (Zhang et al., 1996). Therefore, the 2 model was further modified, as outlined below, to overcome these weakness.
In this approach s, 3 in Equation 1, was assigned a value of 1 ($ = 1) and X was amplified several fold by use of a 4 constant (C). Therefore, the new modified equation was as follows:
Y=A+Blog(CX+1) [2]
6 The intent of this modification was the same as that obtained with the s treatment in Equation 1;
7 that is, the value of 1 relative to CX should be very small as is E relative to X. Equation 2, when 8 X = 0 ( i.e., without enzyme addition), therefore became:
Y=A+Blog(C X 0+ 1 ) [3]
Since C x 0 = 0, and B log 1 = 0, then 11 yo = A [4]
12 The value of A in Equation 4 clearly indicated that it represents the predicted performance of 13 chicks without addition of an enzyme preparation (Yo). In addition, based on the same criteria for 14 selection of s (Zhang et al., 1996), a computer program using BASIC
language was developed based on a least squares procedure and a stepwise technique to calculate the different parameters 16 ( A, B, and C) of equation 2. In this program A, B and C values were selected when these values 17 yielded the highest coefficient of correlation (rz ).
18 The results from Zhang et al. (2000b) clearly demonstrated that in all cases, the A value as 19 determined by use of Equation 2 provided a better measure of observed performance values (Yo) than that of Equation 1. The results also indicated that Equation 2 in conjunction with the 21 developed computer program was a more suitable equation than Equation 1 as it not only 22 provided a more accurate estimate of the A value than Equation 1 as discussed above but also ~l overcame the main shortcoming of Equation 1 (i.e., an arbitrary s value used to calculate the log 2 zero value).
3 Efficacy of a Feed Enzyme and Hypothesis 4 One of the important characteristics of the log model is that the model is a non-linear model when X (the amount of enzymes added to a diet) is the input but is a simple linear model when 6 log X (log percentage of enzyme) is the input. These characteristics suggested that a hyperbolic 7 or non-linear relationship between the response of chicks (i.e., chick performance) and the 8 amount of enzyme added to a diet could be simply converted to a linear relationship by the log-9 linear model. In addition, Almquist ( 1952) in the study of vitamin metabolism in the gut demonstrated that a logarithmic method for evaluating data was extremely useful in many 11 diversified applications of biology since these relations were merely expressions of the Law of 12 Diminishing Returns, a common biological phenomenon. A particular valuable feature of the 13 logarithmic method of expressing the relationship between intake and biological response was 14 the fact that it provided a simple but accurate estimation of the slope of the response line. The slope of the line in the Almquist study was mainly associated with the magnitude of the 16 conversion rate constant for a provitamin to vitamin in the intestinal wall. The constant was 17 dependent upon many dietary and physiological factors in an absolute sense, but was relatively 18 constant within any one bioassay. Therefore, we hypothesized that the feed enzyme, in a manner 19 similar to the conversion of a provitamin into a vitamin, would convert a nutrient from an unavailable, because of anti-nutritive NSPs in the digesta, to an available nutrient through the 21 degradation of the anti-nutritive NSPs. The magnitude of the rate of conversion should be a 22 reflection of the ability of an enzyme to perform this task. Therefore, the B values can be used to 1 evaluate the efficacy of a feed enzyme when added to a diet.

3 Evaluating the Efficacy of a Feed Enzyme 4 Comparing the Efficacies of Different Feed Enzymes As hypothesized, the slope of the log-linear model can be used to evaluate the efficacy of a 6 feed enzyme. This in turn can be used to compare the effects of different enzyme preparations 7 when added to a diet, determine the suitable target cereal for a feed enzyme, evaluate the effect of 8 a newly developed enzyme preparation and even the effect of processing on the feed enzyme.
9 Zhang et al. (2000c) have recently tested the hypothesis using data from Zhang et al. (1996) and Rotter et al. ( 1989). In the study of Zhang et al.( 1996), two enzyme preparations, RM 1 and NQ, 11 with similar xylanase activity were used to compare their effect on the performance of chicks 12 when the enzyme was added to a rye-based diet. The results indicated that the B values of NQ
13 compared to RM1 in the first week for weight gain and the feed/gain ratio were 22.3 vs. 18.0 g 14 weight gain per log unit of enzyme added and -0.13 vs. -0.09 g gain/g feed intake/ log unit of enzyme added, which agrees with the trend seen for the corresponding overall net improvements 16 in chick performance (Ym - Yo, the maximal response related to the control) [i.e., 112 vs. 88 (g), 17 and -0.58 vs. -0.55 (g/g)) during the same period. Although the relationships between the B
18 values and the Ym - Yo values during wk 1 and wk 2 were high ( r = 0.99, P
< 0.001 ), they did 19 not change proportionately. Similar relationships were also obtained when the data from Rotter et al. (1989) were analyzed (Zhang et al., unpublished data). In their study of dose response, five 21 enzyme preparations, Cellulase Tv concentrate (CT), Celluclast (CC), Finizym (FZ), Cereflo 22 (CF), and SP249 (SP), were used to compare the efficacy of these enzymes on the performance 1 of Leghorn chicks fed a barley-based diet. The results indicated that the relative B values for 2 weight gain and feed to gain ratio from for chicks 7 to 14 d of age were 7.68, 6.79, 4.99, 4.49, 3 and 4.00 (g per log percentage of enzyme) and -0.2470, -0.2113, -0.1716, -0.1713, and -0.1386 4 (g/g per log percentage of enzyme), respectively. This trend agreed with that of the corresponding overall net improvements (Ym - Yo) that were obtained. The net improvements for the five 6 enzyme preparations, CT, CC, FZ, CF, and SP, were 22, 21, 16, 16, 14 in weight gain and -0.71, 7 -0.64, -0.54, -0.58, and -0.45 in feed to gain ratio. There were high correlation between the B
8 values and the net improvement in weight gain ( r2 = 0.98, P < 0.0016) and feed to gain ratio ( rz 9 = 0.96, P < 0.0041 ). These two studies clearly indicated that the B values accurately reflected the ability of a feed enzyme when added to a diet to improve the performance of chicks. Therefore, it 11 is a measure of the efficacy of an enzyme.
12 Evaluating the Suitable Target Cereal for a Feed Enryme 13 The structures and contents of NSPs varies in different cereals (Marquardt, 1997). Therefore, 14 the efficacy of a feed enzyme on different cereal-based diets was different and could also be evaluated by the slope of the log-linear model. The dose response study of Marquardt et al.
16 (1994) was used to test the hypothesis. In their study, different concentrations of a feed enzyme 17 (high in both xylanase and (3-glucanase activity) were added to corn-, wheat-, barley-, and rye-18 based diets. The effect of the enzyme on the different cereals was then evaluated to determine the 19 suitable target cereal for the enzyme. The results demonstrated that the effect of the enzyme on chick performance and the B value as calculated from Equation 2 were similar in trend. For 21 example, the observed weight gain values (Ym - Yo) for the corn, wheat, barley, and rye diets 22 were -6, 7, 22, and 29 g, respectively, while the B value calculated from Equation 2 were -1.67, 1 0.81, 2.26, and 8.76 g/log of percentage enzyme added to the diet, respectively. The correlation 2 between the two sets of data was high ( r = 0.90, P < 0.001 ). The results suggested that the B
3 values of the log-linear equation can be used to assess the efficacies of a feed enzyme when 4 added to different cereal-based diets. Part of the reason is the NSPs in these cereals are different.
These relationships were also supported by the data from Bedford and Classen (1992). In this 6 study, a dose response experiment of a feed enzyme was carried out using 4 different ratios of 7 two cereals (i.e., wheat to rye, 0:60, 20:40, 40:20, 60:0) and 6 doses of enzyme (0, 0.1, 0.2, 0.4, 8 0.8, and 1.6 %). Their results demonstrated that the net performance response of chicks to an 9 enzyme preparation that was high in xylanase activity increased dramatically as the proportion of rye was increased. The relevant B values for weight gain and feed to gain ratio during the two 11 week experimental period for diets containing 60, 40, 20 and 0 % rye as calculated by Equation 2 12 were 54.4, 26.1, 6.3, and 0.36; -0.103, -0.018, -0.016, and -0.013, respectively. The B values, as 13 were the improvements in observed performance values (Ym - Yo), were considerably higher for 14 diets containing a high compared to a low concentrations of rye which also reflects the overall efflcacies of an enzyme to degrade the different concentrations of its antinutritional substrate 16 (i.e., arabinoxylan) in the diet. Again, the B values and Ym - Yo were highly related ( r = 0.95, P <
17 0.001 ) but they did not change proportionality with the percentage of rye in the diet.
18 Therefore, the slope of the log-linear model, the B value, is an index of the efficacy of an 19 enzyme. This value not only provides the value which is a measure of the efficacy of different enzymes when the same diet is used but can also provide a measure of the efficacy of an enzyme 21 when added to different diets or when different amounts of their target substrates are present in 22 the diet.

2 Predicting the Response of Chicks 3 Accuracy of the Log-linear Model 4 Another important characteristic of the log-linear model is that the model accurately predicts the performance response of chicks (Zhang et al.,1996) and the viscosity reduction of digesta in 6 the gut. In the study of Zhang et al. ( 1996), two dose response experiments were conducted. The 7 data from Experiment 1 of the study were subjected to different types of regression analysis 8 (Table 2). The amount of enzyme added to the diet was generally not significantly correlated (P >
9 0.05) with chick performance during wk 1 when the data were subjected to linear, quadratic, or cubic regression analysis. However, when the dietary enzyme concentration data were converted 11 into their logarithmic values and subjected to linear regression analysis, all of the log-linear 12 values were significant (P s 0.005), with all rz values being greater than 0.88. The rz values for 13 the combined data of wk 1 and wk 2 for weight gain and feed to gain ratio were 0.99 (P < 0.001 ).
14 In addition, the data also were subjected to other models such as the polynomial, exponential, and saturation models (Michaelis and Menten model), their rz values were all less than that of the 16 log-linear model.
17 The predicted relationship between chick performance (data from Wk 1+2) and amount of 18 enzyme added to a rye based diet (solid lines, Figure 1 ) as determined by Equation 1 and actual 19 performance values (solid triangles or squares, Figure 1 ) demonstrate a very close fit ( rz = 0.99, P < 0.001 for weight gain and rz = 0.99, P < 0.001 for feed to gain ratio).
The inset of Figure 1 21 showed that there was a linear change in weight gain and feed to gain ratio when the 22 concentration of enzyme was plotted on a logarithmic scale.

l General Applicability of the Model 2 The general applicability of the model was tested using data from Experiment 2 of Zhang et 3 al. (1996) and those from the literature. The objective of these analyses was to determine whether 4 the log-linear model also yielded high rz values with these data when there was a significant S response to enzyme treatment. The results demonstrated that high r2 values (0.88 to 0.999) were 6 obtained during wk 1 and during wk 1+2 of the experiment. The slope of the lines (B) showed 7 that the response to enzyme was also higher in wk 1 and wk 1+2 but not in wk 2. Overall, the 8 data demonstrated that it is possible to predict the response to xylanase supplementation in chicks 9 at different ages.
Data from literatures were used to determine whether a similar relationship could also be 11 obtained between the log of the amount of enzyme added to the diet and chick performance.
12 Among the 13 comparisons, nine yield rz values for weight gain greater than 0.91, with all but 13 one comparison being greater than 0.77 (Equation 1 ). Regression analysis of the feed to gain ratio 14 also yielded similar trends. In addition, high rz values were obtained under different feed conditions [e.g., when enzyme was added to different cereals (rye, wheat, and barley) and a grain 16 legume (lupins)] with different types of enzymes ((i-galactosidase, [i-glucanase, and xylanase), 17 with different concentrations of two cereals in the diet (wheat and rye), and with different ages 18 and types of chickens (Leghorn and broiler).
19 Response Surface The model could be used not only to predict the response of a given diet to different amounts 21 of one enzyme, but also to determine the response to different amounts of any two dietary 22 components such as enzyme and the substituted cereal.1n order to achieve this goal an 1 experiment must be carried out where different amounts of an enzyme is added to diets 2 containing different proportions of two cereals. Such an experiment was conducted by Bedford 3 and Classen ( 1992). They fed four different concentrations of rye each with six different 4 concentrations of enzyme (xylanase) to broiler chicks from 1 to 19 days of age. The diets consisted of the following proportions of rye and wheat: 0:60, 20:40, 40:20, and 60:0. The 6 amounts of the enzyme added to each of the different diets were 0, 0.1, 0.2, 0.4, 0.8, and 1.6%.
7 Mutiple regression (SAS, 1988) was used to relate the response in chick gain (Y) to the 8 enzyme concentration (X) and the proportion of rye (Z) in the diet.
9 Y = Bo +B, log (X) + BZ Z + B3 Z log (X) [6]
This model was an extension of the models used previously in the sense that chick performance 11 is regressed on the logarithm of enzyme concentration. The response surface for the above model 12 is shown in Figure 2. Similar prediction equations can be generated for feed to gain ratio or any 13 other variable that fits the model. The results suggested that the response of chicks to an enzyme 14 supplementation can be accurately predicted not only the response to a given diet but also to any proportion of two cereals in diets supplemented with any given amount of an enzyme preparation 16 (Zhang et a.,1996).

18 Evaluating and Predicting Efficacy of Feed Enzymes Based on their Profitability 19 Development of a Multi purpose Enzyme Analyzer The log-linear model we have developed provides a basis to estimate the maximal economic 21 return when a feed enzyme is added to a diet. Based on the model, we have further developed a 22 software package, a Multi-purpose Enzyme Analysis (MPEA) (Figure 3) for predicting and l evaluating the profitable effect of an enzyme in poultry feeds. The enzyme analyzer has three 2 main applications: ( 1 ) to evaluate the effect of different enzyme preparations added to a cereal-3 based diet, (2) to determine the optimal amounts of an enzyme preparation and /or a substituted 4 cereal to be used in a diet, and (3) to analyze the relationships between the price of enzyme preparation, and the price of the substituted cereal, and the economic return.
6 Evaluating Efficacy of Different Feed Enrymes Based on their Profitability 7 As discussed in the previous section, the slope of the log-linear model is an index of the 8 efficacy of a feed enzyme. This evaluation, however, is only based on the biological criteria. The 9 goal of many studies is usually to select an enzyme preparation that will yield the greatest profit.
Zhang et al. (2000c) using the data selected from Rotter et al. (1989) and Zhang et al. (1996) 11 demonstrated that it was possible to select an enzyme preparation, among several different 12 enzyme preparations, that will yield a highest maximum profit when added to a diet at a certain 13 concentration. The maximal profit per 1000 birds for the five enzyme preparations when added to 14 the diet at the selected concentration would have been: Cellulase Tv, Celluclast, Finizym, Cereflo, and SP249 were $ 67.29, $ 61.27, $ 51.91, $ 49.27, and $ 46.79, respectively (Table 3).
16 The sequence of these values also agrees with that of the B values for feed to gain ratio from the 17 log-linear equation as indicated in Table 2 ( rz = 0.99, P < 0.0005). The same trend was observed 18 using data from Zhang et al. (1996). The results suggested that the B
values and the estimated 19 maximal profit provided similar indices for the evaluation of different enzyme preparations. In addition, the advantage of the two methods, especially for the method using maximal profit, is 21 that they do not require a knowledge of enzyme activity, the combination of enzymes in a 22 preparation, and the best site of action of the enzymes in the gut. The information required for the 1 method that estimates maximal profit is ( 1 ) the influence of different concentrations of different 2 enzyme preparations on chick performance as estimated from the model equations and (2) the 3 price of the major ingredients used in a diet.
4 Identifying the Most Profitable Cereal When Used With a Feed Enzyme On the basis of the method that we have proposed (Zhang et al., 1996), the most suitable 6 target-cereal for an enzyme preparation could be determined from the slope of a log-linear model.
7 The B values for the feed to gain ratio of were calculated from the data of Marquardt et al.
8 ( 1994). Based on the B values, the sequence of cereals producing the greatest response to an 9 enzyme preparation in decreasing order were rye, barley, wheat, and corn (negative control), respectively (Table 4). However, the sequence of the cereals that yielded the maximal profit 11 following enzyme addition was different. The maximal profit obtained by an enzyme preparation 12 added to a barley-, corn-, wheat-, and rye-based diet was $ 135.00, $
134.45, $ 133.55, and $
13 123.96 per 1000 birds, respectively when the same price of the used cereal was inputted (Table 14 4). The relationship between the magnitude of the B values for feed to gain ratio and the maximal profit values was low ( rz = 0.61, P = 0.217). This disagreement in the sequence was also be 16 observed in the study of the data from Bedford and Classen ( rz = 0.59, P =
0.234). The results 17 suggested that the method of the maximal profit could be more useful for the feed or enzyme 18 industry in determinating which cereal should be used with a given feed enzyme to obtain 19 maximal profit. In addition, if the prices of wheat and corn were assumed to be $ 0.12 and $ 0.13 per kg, wheat yielded a greater profit than corn and the rye grain at $ 0.08 per kg become a 21 competitive cereal with wheat or corn ( $123.96 per 1000 birds for rye vs.
$ 126.00 or $ 126.73 22 per 1000 birds for corn or wheat). These results suggested that the price of a cereal also influence 1 profitability when a special feed enzyme is added to the cereal-based diet.
2 Determining Optimal Amounts of Enryme and Cereal in a Diet 3 One of the important applications of MPEA is to determine the optimal amounts of a feed 4 enzyme and a cereal that should be used in a diet to obtain maximal profit.
Generally, the response pattern with increasing amounts of a feed enzyme on the performance of chicks fed a 6 diet is hyperbolic and not linear (Friesen et al., 1991; Bedford and Classen, 1992; Marquardt, 7 1994, Zhang et al., 1996). However, the dose response pattern obtained with the addition of a 8 feed enzyme yields a quadratic rather than a hyperbolic pattern of profit.
The results from the 9 study by Zhang et al. (2000c) indicated that the profit obtained with increasing amounts of a feed enzyme was increased to a certain point. After that, the profit decreased with increasing amounts 11 of the enzyme. This point can easily be calculated using the MPEA. The results demonstrated 12 that the optimal amounts of different enzyme preparations that should be added to a diet, of a 13 given feed enzyme that should be added to different cereal-based diets, and of a feed enzyme 14 added to a diet with varying the proportions of two cereals were considerably different.
Profit Contours or Isoquants 16 The objective of obtaining maximal profit by enzyme addition to a given diet may not bean 17 only business goal for a feed company or poultry farm. In some cases, the question that has to be 18 asked is, does the enzyme and substituted cereal, when used at various levels and in different 19 combinations, yield the expected profit? This question can be addressed by use of the MPEA.
The relationships among amounts of enzyme added to the diet, the relative concentrations of two 21 cereals (rye vs. wheat), the cost of the enzyme preparation, and the resulting profit are illustrated 22 in Figure 4. The two-dimensional figures on the right side of Figure 4 represents the contour of 1 the response associated with a individual horizontal slice of the figure on the left. The lines with 2 same numbers in the figure, called profit contours or isoquants, provide a useful tool to 3 determine any combination of inputs such as amounts of an enzyme and rye used in a diet for any 4 fixed level of profit. In there analyses, the assigned price of the enzyme were $ 3, $ 5, and $ 7 /
kg (top to bottom, Figure 4) and the price of rye and wheat were $ 0.08 and $
0.12 / kg, 6 respevtively.
7 Expected Price of Enzyme and Cereal 8 There are many factors that influence the profit obtained when a feed enzyme is added to a 9 diet. They include the amount of enzyme added, the type and amount of cereal, the efficacy of the feed enzyme, and the price of enzyme and cereals used. Once the profit function is established, 11 any variable in the equation can be calculated and analyzed when other factors are fixed.
12 Therefore, the price that should be paid for an enzyme and a substituted cereal can be 13 determined. This can be illustrated by the comparison of two enzyme preparations, Cellulase Tv 14 concentrate (CT) and Celluclast (CC). The results in Table 3 indicated that the maximal profits per 1000 birds for CT and CC were $ 67.29 and $ 61.27 per 1000 birds when the price of both 16 enzyme preparations was $ 5 per kg. If the maximal profit of $ 67.29 per 1000 birds was the 17 target for both enzyme preparations, the price of CC should be reduced from $ 5 to $ 0.9. The 18 result suggested that the competitive price of CC can be determined by comparing its maximal 19 profit with that of CT. Let us assume that CC was an enzyme preparation that was developed to compete with CT for rye-based diets. Two possible methods could be used for CC
in order to 21 obtain the same maximal profit as that of CT. The first would be to reduce its price and the 22 second was to improve its efficacy (B value). The results indicated that an 82% decrease in its 1 price ($ 5 to $ 0.9) would be required to yield the same maximal profit ($
67.290 /1000 birds) as 2 obtain with CC at $ 5 / kg. However, the same result could be obtained with a 17 % improvement 3 in the efficacy of CC, an increase in its B value for the feed to gain ratio from -0.2113 to -0.2470.
4 This suggests that an improvement in the efficacy of an enzyme is a much more effective means of increasing profitability than that obtained by reducing its price.
6 On the other hand, the maximal profit was also influenced by the price of cereal used in a diet.
7 As indicated in Table 4, rye grain cannot compete with wheat when the price of these cereal are 8 the same. However, when a higher price of wheat was used, the rye grain could yield a similar 9 maximal profit to that obtained with wheat. This strategy could be used by a feed company to determine the expected price of a target cereal in order to obtain a certain level of the maximal 11 profit.

13 From In Vivo Study to In Vitro Study 14 Background Feed enzymes have been evaluated using both in vivo and in vitro procedures.
Chick 16 performance, AME, digestibility of feed nutrients, digesta viscosity reduction for evaluating the 17 effect of a feed enzyme when added to a diet are generally classified as in vivo evaluations. Most 18 criteria used in in vivo assays are directly related to productivity, therefore, they are widely 19 accepted. The weaknesses of the in vivo assays are their high variation, low sensitivity, cost, and time requirements. On the other hand, in vitro methods for enzyme assays such as reducing sugar 21 and viscosity assays, the dietary viscosity assay, and digestibility as measured by various 22 incubation procedures, yielded low variation and high sensitivity, are inexpensive and relatively 1 rapid. Therefore, they are also widely used for the evaluation of a feed enzyme. However, there is 2 generally low correlation between the predicted values obtained from the in vitro methods and 3 the performance of chicks that is obtained when an enzyme is added to the diet.
4 Development of an In Vitro Dietary Enzyme Assay Zhang et al. (2000a) have recently developed an in vitro dietary enzyme assay to determine 6 the amount of feed enzymes that had been added to a rye-based diet and to evaluate the efficacy 7 of enzymes. Rye was selected as a model cereal, because it contains high concentrations of a 8 highly viscous NSP, arabinoxylans, that in turn can be effectively hydrolyzed by preparations 9 high in xylanase. The principle of the assay was to allow the enzyme in the diet to interact with the substrates in a buffered suspension of the diet for an appropriate time period followed by 11 centrifugation of the suspension and the measurement of the viscosity of the solution. Therefore, 12 both bound and free exogenous enzymes could react with the soluble, and insoluble NSPs of the 13 diet, similar to the condition in the gut. In this study, the relationship between dietary viscosity 14 change and the amount of enzyme added to the diet was established (Figure 5). Viscosity was expressed as its log value because this yields values that are equivalent to the amount of substrate 16 hydrolyzed (Boros et al., 1993). The results demonstrated that there was a linear relationship ( r >
17 0.99, P < 0.005) between log of the net viscosity change from the dietary extracts and log of the 18 concentration of enzyme added to the diet for all three incubation times (1, 2 and 8 h, 19 respectively). Using this relationship along with the appropriate references (enzyme and diet) as standards it should be possible to determine the amount of an enzyme in a diet using the in vitro 21 viscosity assay. Other assays have not been able to successfully monitor enzyme activity in the 22 diet.

1 Relationships Between Determined and Actual Enryme Activities in a Diet 2 Zhang et al. (1996) demonstrated that there was a linear relationship between chick 3 performance and the log amounts of enzyme added to a diet. The results of Bedford and Classen 4 (1992) indicated that there was a linear relationship between chick performance and the log of S intestinal viscosity. Therefore, we hypothesized that a linear relationship exists between the log 6 of viscosity change as determined by the in vitro assay and the log amounts of enzyme added to a 7 diet. Such a relationship was established in this study (Table 5, log CP vs.
log U/kg, r > 0.99, 8 Figure 5). The same trend was obtained for all of the different assay times (1 to 8, data not 9 shown). The results shown in Table 3 further demonstrate that the in vitro assay accurately estimated the amount of enzyme in the diet when viscosity was converted into its logarithmic 11 value but not when its arithmetic value was used ( r < 0.82, P > 0.05).
Collectively these results 12 demonstrate that when the viscosity values from the in vitro assay are converted into their log 13 values, they can accurately predict amount of enzyme in a diet with highly viscous compounds.
14 Prediction of Chick Performance by Use of the In Vitro Assay The objective of this comparison was to determine if data from the in vitro viscosity assay 16 could be used to accurately predict chick performance and to determine if its predicted value was 17 as accurate as that obtained using known amounts of enzyme that were added to the diet. The 18 data in Table 5 (chick performance vs. the enzyme activity added to the diet, or measured enzyme 19 activity by the in vitro assay) demonstrate that both the in vitro assay and the amount of enzyme added to the diet (the input, X ) were highly correlated ( r > 0.95) with animal performance (the 21 output, ~. In addition, the data in Figure 6 show that both amount of enzyme added to the diet 22 (C and D) and the amount of enzyme as determined by the log of the in vitro viscosity assay (A

1 and B) were linearly ( r > 0.99, P < 0.005) related to weight gain ( A and C
) and the feed to gain 2 ratio ( B and D). These data demonstrated that the degree of improvement obtained when a given 3 enzyme is added to the diet is a linear function of the log of enzyme activity which in turn is 4 directly related to the log of the net dietary viscosity change as determined by the in vitro assay.
Therefore, the log of dietary viscosity change not only was able to estimate the enzyme activity 6 added to the diet, but also was able to accurately predict the performance of chickens when used 7 in conjunction with the modified log-linear model.
8 Evaluate the Efficacy of Feed Enzymes by the Assay 9 The ability of two enzyme preparations (RM1 and NQ) to improve the performance of broiler chicks fed a rye-based diet and to reduce the viscosity of the diet as determined by the in vitro 11 assay were studied. The results showed that both enzyme preparations improved chick 12 performance and decreased the dietary viscosity in a concentration-dependent manner. Two 13 important trends were observed. First, the in vitro dietary viscosity assay appeared to be a more 14 sensitive index for evaluating the effect of enzyme response than that obtained from the feeding trial. Second, the improvements in chick performance when comparing the response of the two 16 enzyme preparations appeared to be more closely associated with the in vitro dietary viscosity 17 change than the amounts of enzyme added to the diet. This effect may be attributed to the 18 presence of different amounts of other viscosity reducing enzymes in the enzyme preparations or 19 to a difference in efficacy of xylanases (i.e., the nature of an enzyme) in the two preparations.
These data, therefore, suggest that the viscosity assay may provide a better index of the efficacy 21 of an enzyme preparation than a standard calorimetric activity assay.
22 On the basis of these observations it was hypothesized that the in vitro assay, when used with 1' the log-linear model, could also be used to accurately evaluate the efficacy of an enzyme added to 2 a diet. The efficacy of the two enzymes (i.e., their B values) were therefore calculated from the 3 model using the dietary viscosity changes as determined by the in vitro assay, and the amount of 4 enzyme added to the diet. The results in Table 5 showed that the B value of NQ was significantly greater than that of RM1 (0.265 vs. 0.124, P < 0.05) when they were calculated from log dietary 6 viscosity change as the output of the model and enzyme activity added to the diet as the input.
7 This difference indicates that the enzyme, NQ, more effectively hydrolyzed the viscous substrates 8 in the rye-based diet than RM1. However, there were no significant differences ( P < 0.05) 9 between the B values of the two enzyme preparations ( RM1 vs. NQ) calculated from the chick performance and the enzyme added to the diet (Table 5). The inability of chick performance data 11 to distinguish between the efficacy of the two enzymes in contrast with the in vitro assay may be 12 caused by several factors, including a difference in relative sensitivities or precision of the two 13 assays. In these studies, the relative standard error of means for the in vitro dietary viscosity 14 assay was much lower than that of performance of chickens, and as a result, it was a more precise 1 S indicator of the efficacy of the enzyme than chick performance.

1 ~ Implications 18 A log-linear model has been developed that it can be used to accurately predict and evaluate 19 the response of chicks to a feed enzyme in both in vivo and in vitro studies. The model and the concept of efficacy proposed in these studies can be readily used to predict and evaluate various 21 responses (i.e., performance, AME, digestibility of feed nutrients, or reducing viscosity of digesta 22 or diets) of different animals (poultry or swine) to different feed enzymes (xylanase, (3-glucanase, 1 ~i-galactosidase, or phytase) as well as other additives or nutrients (i.e., essential amino acids). In 2 addition, a refined level of output (chick performance) and inputs (feed enzyme and substituted 3 cereal), or the most profitable combination of inputs for a specific output can be evaluated by the 4 linear model when only two or three discrete enzyme dose treatments are used. These studies indicate the log-linear model when used in conjunction with a knowledge of nutrition and 6 computer technology can be a considerable assistance to nutritionists in their research activities 7 and business decisions.

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18 (accepted) 19 Zhang, Z., R. R. Marquardt, W. Guenter, and G. H. Crow. 2000c. Predicting and evaluating the profitable effect of enzyme in poultry feeds: use of a log-linear model in application.
21 Poult. Sci. (submitted).
22 Zhang, Z., R. R. Marquardt, G. Wang, W. Guenter, G. H. Crow, Z. Han, and M.
R. Bedford.

1 1996. A simple model for predicting the response of chicks to dietary enzyme 2 supplementation. J. Anim. Sci. 74: 394-402.
3 Ziggers, D. 1999. Enzymes: hidden catalysts come out of the dark. Feed Tech.
3(6):23-33.

1 Figure 1. The predicted relationship between chick performance during the 1 st plus 2nd wk of 2 experiment, and the amount of crude xylanase (RM 1 ) added to a rye-based diet as determined 3 from the equation Y= 517 + 45 IogX (rz = 1.00, residual SD = 3 g) or Y=2.46 -.09 logX (r2 =
4 0.99, residual SD = 0.01 g) where X = units of enzyme in the diet and Y =
weight gain (g) or the feed to gain ratio, respectively. Mean experiment values for weight gain (~) and feed to gain 6 ratio (1) are also shown. Inset figure represents the same data except the amounts of enzyme 7 have been transformed into their logarithmic values. (Source: Zhang et al., 1996).

9 Figure 2. Effect of enzyme concentration (X) and rye content of diet (Z) on chick gain (Y). Y =
436.11 + 7.58 log (X) - 0.63 Z + 0.75 Z log (X); all coefficents in the equation were significantly 11 different from zero ( p < 0.001) with the exception of the coefficient for log (X) (P < 0.1); rz =
12 0.94, residual SD = 12.56. (Source: Zhang et al., 1996).

14 Figure 3. Principle and application of the Multi-purpose Enzyme Analyzer for Use of Enzymes in 1 S Poultry Feeds. (Source: Zhang et al., 2000c).

17 Figure 4. Effect of different combination of two variables, amounts of enzyme (XE) and rye (XR) 18 added to diets on the profit of chickens fed diets from 1 to 19 d of age.
Cereals in the diet were 19 wheat plus rye (60 %). The profit function were: II = Py Y - F ~ ( Pi Xi ), where Y = (404 -2.04XR + S.2S X I O-3XR2 - 3.20X l0~XR3 ) + (9.78 + 3.49 X 1 OXR - 1.29 X I O-3XR2 + 1.06X 10'~ XR3) log 21 (2150 X + 1), and F = (648 - 8.52X 1 O-ZXRZ+ 8.33X 1 O~XR') + (2.64 + 2.27x

10-zXRZ- 2.l OX 10'~
22 XR3) log (2150 X + 1); II = profit ($/1000 birds), Y = weight gain (g), F =
feed consumption (g), 1 Py and Pi represented the price of chickens and the price of the i-th ingredient (Xi) in a diet. The 2 plots on the left gives the three-dimensional relationship for relative amount of rye in the diet 3 (the balance is wheat), the amount of enzyme added to the diet, and the profits obtained assuming 4 wheat and rye costs are $ 0.12 and 0.08 per kg, respectively, and that of enzyme is $ 3, 5, or 7 per kg. The figures on the right are the profit contours of two-dimensional slices of that on the right 6 for diets containing different amounts of enzyme and different percentage of rye in the diet. The 7 number in each line represents the fixed profit that can be obtained by feeding different amounts 8 (%) of rye and enzyme. Data used for the calculations were from Bedford and Classen, 1992.
9 (Source: Zhang et al., 2000c).

11 Figure 5. Log of viscosity changes [net log centipoises (log CP)] as affected by the concentration

12 of the enzyme (% NQ, Nutri-Quest, Chesterfield, MO) in extracts prepared from a rye diet

13 containing different concentrations of the enzyme. The extracts were incubated using the dietary

14 viscosity assay for different time intervals (-0-, 1 h, -1-, 2 h and -~-, 8 h) at 40 C, and viscosity values were converted to their logarithmic values and subtracted from the control values (diets 16 with no enzyme supplementation) to yield net viscosity values. Overall average standard errors 17 for thel, 2 and 8 h data were 0.009, 0.022, and 0.007 (log CP), respectively. (Source: Zhang et 18 al., 2000a).

Figure 6. Prediction of weight gain (A and C) or the feed to gain ratio (B and D) over a 7-d 21 period for Leghorn chicks fed a rye-based diet containing different concentrations of an enzyme 22 preparation (RMI, Finnfeed International Ltd., Wiltshire, UK) by a log-linear model equation 1 using either log of dietary viscosity change [log centipoise (log CP), A and B] determined by 2 incubation of the diet at 40 C, pH 5.0 for 4 h or log of enzyme activity (log U/kg, C and D) added 3 to the diet as the input of the equation. The linear regression equations were: YA 198 + 69.5 log 4 ( 10 X+1 ) for weight gain (A) and YB 2.65-0.24 log ( 1 Oz X+ 1 ) for feed to gain ratio (B) when the input (X) was dietary viscosity change (centipoises, CP), and Y~ 195+18.0 log (10 X+1) for 6 weight gain (C) and YD 2.64-0.091 log ( 10z X+1 ) for feed to gain ratio (D) when the input (X) 7 was enzyme activity added to the diet (IJ/kg); r > 0.99; P < 0.005. (Source:
Zhang et al., 2000a).

Table 1. Evaluation of the performance of Leghorn chicks fed a rye-based diet with different concentrations of enzyme using different parameters calculated in model Equations l and 2a Enzyme RM 1 NQ

preparation (U~g) (LJ/kg) (%

Wk Wk 2 2 wk Wk Wk 2 wk Wk Wk 2 1 2 2 wk WG (g)b (A,) 187 329 515 184 334 519 278 378 656 Yo 196 345 541 196 345 541 196 345 541 B 18 11 30 22 9.3 32 28 12 40 Ym Yo 88 60 149 112 38 160 112 38 160 rz 0.99 0.64 0.91 0.91 0.94 0.94 0.930.97 0.97 (r,2) 0.96 0.74 0.98 0.93 0.97 0.97 0.920.98 0.97 C 10 10 10 10 10 10 10 10' 10' F/G (g/g)b A 2.64 2.35 2.45 2.65 2.31 2.43 2.652.31 2.43 (A,) 2.67 2.37 2.48 2.67 2.31 2.45 2.152.23 2.2 Yo 2.64 2.31 2.43 2.64 2.31 2.43 2.642.31 2.43 BX 10-2 -9.1 -3.4 -6.3 -12.7 -2 -6.1 -12 -2 -6 Ym Yo -0.6 -0.19 -0.32 -0.58 -0.1 -0.27 -0.6-0.1 -0.3 rz 0.99 0.62 0.94 0.92 0.66 0.96 0.920.66 0.95 (r,z) 0.93 0.76 0.99 0.89 0.62 0.93 0.910.65 0.95 aSource: Zhang et al., 2000b.
bA, B, and C are the parameters calculated from Equation 2, Y = A + B log ( CX
+ 1 ), using the developed computer program, where Y is the chick performance [i.e., weight gain (g), feed to gain ratio (g/g)]; X is the enzyme preparation added to the diet (U/kg or %);
A, the intercept of the equation, represents the chick perfromance without addition of an enzyme preparation (g, g/g); B, the slope of the equation, provides an index fro evaluating the efficacy of an enzyme added to the diet (g or g/g per log U/kg; g or g/g per log %), and C is an adjusted factor used to correct the X value when enzyme is not added to the diet. X in Equations is the amount of enzyme (U/kg or %) added to the diet. A, which are the bracketed values are the A values as estimated from Equationl, Y = A + B log ( X + a ), which were originally reported by Zhang et al (1996). Ym and Yo represent the respective observed performance values of chicks [weight gain (g) or feed to gain ratio (g/g)J for the indicated periods when either the highest enzyme concentration or no enzyme is added to the different diet. rz is the correlation coefficient between the observed experimental values and predicted values when either equation 2 (r2) or equation 1 (r,2) was used. WG and F/G represent weight gain and feed to gain ratio, respectively.

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a~
o ~ "~., N t~~, o°°o, o°~,, o°y, ~ ~ ~' m 0 0 0 0 0 0 ~ o b °' o U ~~ ~ O O O O O O
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n Two d- o o c~ a~ ~ f~
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~ o, M ~ 00 00 d; ~n oo cv c, os ,~ ~ . ~b .o i a ~
e~~' ~ ~ 3 Q '~ .~ ~ ,~ ~ ~ v ~ T3 ar C" U
U p, U ~~ U ~ by dA dp G U
H ~' ~ a d v a a a '_ CA 02320687 2000-09-21 Table 3. Effect of different enzyme preparations added to a barley- or rye-based diet on the efficacy of enzyme (B values), the optimal amounts of enzymes and the maximal profits obtained from Leghorn chicks in a one-week (Rotter et al., 1989) or two-week (Zhang et al., 1996)a Source of Enzyme B Value' Optimal Enzyme Maximal Profit Data Preparationb (%) ($/ 1000 birds)d Rotter et Cellulase -0.247 0.656 67.29 al., Tv 1989 Celluclast -0.211 0.560 61.27 Finizym -0.172 0.452 51.91 Cereflo -0.171 0.439 49.27 SP249 -0.139 0.385 46.79 Zhang et RM1 -0.0943 0.315 101.19 al., 1996 NQ -0.0963 0.348 104.38 aSource: Zhang et al.(2000c).
bThe enzyme preparations used in the study of Rotter et al.(1989) and Zhang et al. (1996) were Cellulase Tv concentrate (Trichoderma viride) from Miles Laboratories Inc. and Cellucast (T.
ressei) Finizym (Aspergillus niger), Cereflo (Bacillus subtilis), and SP249 (Aspergillus niger) from Novo A/S Demark; and RM1 (T. longibrachiatum) from Finnfeeds International Ltd. and NQ (T. reesei) from Nutri-Quest.
'The B values were the slope of log-linear model equation calculated from the data of feed to gain ratio. The values are the indexes of the efl'lcacy of a feed enzyme added to a diet (Zhang et al., 1996; 2000).
dThe assumed price for enzyme preparations used in the two studies was $ 5 per kg.

Table 4. Effect of cereal prices on optimal amounts of an enzyme added to different cereal-based diets and their maximal profitsa Value Same Optimal Maximal DifferentOptimal Maximal Cereal of Price Enzyme Profit Price Enzyme Profit Bb ($/kg)(%) ($/1000 ($/kg) (%) ($/1000 birds) birds) Corn 0.005 0.08 0 134.45 0.13 0 126.00 Wheat -0.0280.08 0.0339 133.55 0.12 0.0335 126.73 Barley -0.0380.08 0.0815 135.00 0.08 0.0815 135.00 Rye -0.0900.08 0.3419 123.96 0.08 0.3419 123.96 aSource: Zhang et al. (2000c).
bThe B values were the slope of log-linear model equation calculated from the data of feed to gain ratio. The values are indexes of the efficacy of a feed enzyme added to different diets.
Therefore, the suitable cereal for a feed enzyme can be determined by the value (Zhang et al., 1996; 2000).

Table 5. Use of a log-linear model equation to evaluate the efficacy of enzymes added to the rye based diet by in vitro dietary viscosity assay and predict chick performance from the enzyme activity expressed as the amounts added to the diet (AEA) or the viscosity change determined by an in vitro dietary viscosity assay (MEA)e Outputb Input Parameters ed from obtain prediction equations (~ (X) A B4 C r P <

Viscosity vs.
AEA' MEA (log CP) RM1 (log -0.02 0.1248 10-2 0.99 0.005 U/kg) NQ (log U/kg)-0.03 0.265" 10 -2 0.99 0.005 Performance vs.
AEAd WG1 (g/6 birds) RM1 (log 195 18.08 10 0.99 0.005 U/kg) NQ (log U/kg)191 22.38 10 0.95 0.005 FG1 (g/g) RM1(log U/kg)2.64 -0.0918 10 2 -0.99 0.005 NQ (log U/kg)2.65 -0.1278 10 -0.95 0.005 Performance vs. MEA

WG1 (g/6 birds) RM1 (log 198 69.58 10 0.99 0.005 CP) NQ (log 198 72.28 10 0.97 0.005 CP) FG1 (g/g) RM1 (log 2.65 -0.248 10 2 -0.99 0.005 CP) NQ (log 2.65 -0.258 10 z -0.98 0.005 CP) aSource: Zhang et al. (2000a).
bWGI and FG1 were actual weight gain and feed to gain ratio over a 7-d period of a feeding trail for chicks fed a rye-based diet containing different amounts of added enzymes (RM1 or NQ). The relationship between the outputs such as chick performances (WGl and FG1) or log of dietary viscosity change (log CP) and the inputs such as the amount of enzyme in the diet (AEA
or MEA) was estimated from a prediction equation (Zhang et al., 1996; 2000b).
The equation is Y = A + B log (CX + 1), where Y = outputs (WG1 and FG1 or MEA), and X =
inputs, i.e., the amount of enzyme (xylanase) added to the diet (AEA) or its estimated activity value (MEA). The A is the intercept and represents performance without enzyme added to the diet. The B, the slope of the equation, represents the performance of chick per log unit of enzyme (weight gain or feed to gain ratio per log unit of enzyme for AEA, or weight gain or feed to gain ratio per log viscosity change for MEA, or log dietary viscosity change per log of enzyme activity added to the diet). The C is an adjusted factor that is required to calculate performance of chicks when fed diets without added enzyme. The data used to calculate the parameters of the equations were from Table 1.
°The outputs are log of dietary viscosity changes (log CP, centipoise) obtained using the in vitro viscosity assay during a 4-h incubation period and the inputs are the log of the amount of enzyme added to the diet (log U/kg).
dThe outputs are animal performances (Y) and the inputs are units of enzyme activity (X) added to the diet (AEA) or the enzyme activity as determined by in vitro dietary viscosity changes (MEA).
eB values for each comparison of the two enzymes not having the same superscript are significantly different (P < 0.05, t-tests).
fRMI (Finnfeed International Ltd., Wiltshire, UK) and NQ (Nutri-Quest, Chesterfield, MO) contained 389 and 778 U of xyalanase activity / g of original enzyme prepasration (stock enzyme), respectively, as determined at pH 4.7 by the colorimetric method of McCleary (1992).
The stock preparations were added to the diets to give the indicated activity values.

Claims