BODY PROTEIN GROWTH' NON-LINEAR AND LINEAR FUNCTIONS IN

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1 81996 Applied Poultry Scimce, Inc NON-LINEAR AND LINEAR FUNCTIONS IN BODY PROTEIN GROWTH' MILAN HRUBII, MELVIN L. HAMRE, and CRAIG N. COON2 Depamnent of Animal Science, University of Minnesota, St. Paul, MN Phone: (612) FM: (612) Primary Audience: Nutritionists, Production Managers, Poultry Producers, Researchers DESCRIPTION OF PROBLEM Function of body weight (or body component weight) related to age can describe growth of broilers [l]. The term "growth function" denotes an analytical function written as a single equation: W = f (t), where W is organic mass (e.g., weight) and t is time [2]. Talpaz et al. [3] used the non-linear Gompertz function to describe the growth of broilers and developed an algorithm to help optimize a broiler operation. The researchers reported that the use of a growth model led to an 8-10% savings in production cost. Successful adjustment of nutrient levels in poultry rations and to increase the profit of an enterprise through growth modelling requires a good prediction of the genetic potential of birds using one of the many available growth functions. There is limited information on fitting the growth functions to data obtained from restricted growth studies, such as feed and high temperature restriction. Ricklefs [4] described growth modification and development using selected and unselected lines of broilers and Japanese quail. The author showed how altering one of the Gompertz function variables affected the growth curve. Research suggests that body protein instead of average body weight should be used in growth modelling [q. Body protein is a more reliable indicator of growth because of variation in water content of the body and the effect of nutrition and environmental temper- 1 Published as Paper Number 22085, Scientific Journal Series, Minnesota Agricultural Experiment Station. 2 To whom correspondence should be addressed

2 110 GROWTH FUNCTIONS ature on carcass fat content. Summers and Leeson [6] have shown that an increase in percent carcass fat corresponds to a decrease in percent protein. To evaluate the effect of environmental temperature on fitting a broiler growth function, we elected to: First, estimate parameters of the mathematical linear and non-linear functions of growth that fit the body protein weight curve of broilers grown under three temperature treatments from hatching through 19 wk of age; second, compare the non-linear Gompertz and logistic and linear polynomial equations and their acceptability for a description of restricted growth; and third, measure the levels of protein and fat in dry matter of bled, plucked broiler carcasses up to 19 wk of age. MATERIALSAND METHODS Sets of three pens of 50 broiler chicks (Peterson x Peterson) of each sex were reared under three temperature treatments: 32.2"C, 26.7"C, and 21.1"C as described by Hruby et al. [q. Performance data and carcasses obtained as described in the previous paper were fiuther analyzed in this report. The frozen carcasses from broilers up to 10 wk of age were quartered and ground in a food processor [8]. Because of their larger size, the carcasses from broilers older than 10 wk were cut up using a band saw [9] and ground in a grinder [lo]. Moisture, ether extract, and crude protein content of carcasses were determined using methods of the Association of Official Analytical Chemists [ll]. Total body protein and lipid weights were calculated for broilers by multiplying the percentages of protein and lipid, respectively, by the body weight. We used these data for modelling growth of broiler body protein weights. Statistical analysis was completed on all data as described in References and Notes [12]. Since the shape of the growth curves calculated from data collected under 267 C and 32.2"C was quite similar, we have included only figures for the 322 C treatment to illustrate the effect of high environmental temperature. RESULTS AND DISCUSSION The high coefficients of determination (R2) suggest that all three models tested are of similar value (Tables 1 and 2). Rogers et al. [ 131 fitted growth data from a broiler feed restriction study to three non-linear growth functions. They concluded that all three models (Gompertz, logistic, and saturation kinetics) accurately described growth of broilers. TABLE 1. Coefficient estimates and determinations for models fitted to male broiler Drotein weiahts 1 MODEL I PARAMETER* I TEMPERATURE I Gompertz A-maximal response (g) 1085f72 958k68 819f125 k-rate constant 0.212f f f t*-time at POI (Wk) R f0.460 I 7.411k0.504 I f

3 HRUBY et al. Research Report 111 TABLE 2. Coefficient estimates and determinations for models fitted to female broiler protein weights 4th degree polynomial R Constant a (42.04) (33.45) (31.09) a (29.03) (22.98) (21.81) a (5.95) (4.69) (4.54) a (0.46) (0.36) (0.35) a (0.01) (0.01) (0.01) R The Gompertz growth function described the protein weight of broilers at different ages more precisely up to 5 wk of age (Figure 1) than the logistic function. The Gompertz model could serve to describe the growth of broilers reared up to the usual slaughtering age. Knizetovfi et al. [14] also found the Gompertz function preferable for describing the growth of poultry up to 26 wk of age. At higher environmental temperatures none of the functions tested fit body protein data well. The difference between estimated body protein weights using the Gompertz function and real observations was higher during the first 6 wk of age for broilers reared at 32.2"C than for the 21.1"C group. The differences were, however, smaller than when the logistic function was used to fit these M 800 W FIGURE 1. Total protein weight of bled, plucked male broilers from 21.1% treatment fitted to three growth functions

4 112 GROWTH FUNCTIONS observations (Figure 2). That both the nonlinear Gompertz and non-linear logistic functions were not able to fit data obtained from broilers under higher environmental temperature treatments suggests that both functions describe growth reliably only under thermoneutral conditions. The linear 4th degree polynomial function follows observed data very closely throughout the experiment. The polynomial function underestimated fitted values from 1 day to 1 wk of age. This function employs coefficients that have no biological meaning or logical explanation, as opposed to the coefficients in non-linear functions. Since the polynomial function follows closely a pooled average of observations at every point in time, fluctuations occur in predicted values. Such fluctuations are obvious in Figure 3, where male broiler body protein weights from the 32.2"C treatment are fitted to linear and nonlinear functions. As Parks [2] explains, extrapolation of polynomials yields nonsense, and this model should be used only within the range of the experimental data. Thus the polynomial function could not reliably predict body protein weight at 25 wk of age if its coefficients were derived from body protein weight data up to 19 wk of age. High environmental temperature decreases body protein growth rate for both males and females (Figure 4) and decreases time required to reach the point of inflection (POI) for both sexes. The POI is the highest point (the highest protein weight gain) on the curve of growth rate prediction. Thus, broilers reared at higher temperatures reach the end of the asymptote (the inclining part of curve) sooner, although at a lower growth rate. The growth rate of male broilers was affected more negatively by high environmental temperature than the growth rate of the female broilers. Female broilers at 21.1"C and 267 C have almost identical growth rates. However, comparing the growth rate of male broilers from the 21.1"C treatment to that of male broilers from the 26.7"C treatment makes the difference due to higher environmental temperature apparent (Figure 4). The larger negative effect of high environmental temperature on growth of male broilers than female broilers evidently results from the higher protein growth of males, as well as male broilers' higher sensitivity to restrictive factors of growth introduced during the rearing. There was a significantly (P1.05) higher percentage of protein in dry matter of male broilers than in female broilers from 10 wk of age (Figure 5). The level of protein decreased with age. Decrease in percentage of protein in broiler carcasses corre ^M 400 v.i-,/ / XGompertz ---- Logistic -Linear " FIGURE 2. Total protein weight of bled, plucked female broilers from 322 C treatment fitted to three growth functions

5 HRUBY et al. Research Report 113 sponds to an increase in percentage of carcass fat [5]. Indeed, the percent ether extract on a dry matter basis was significantly higher for females than males in all three temperature treatments from 10 wk of age (Figure 6). Males showed significantly lower fat levels in broilers reared under 32.2"C in the finishing period of growth (10 to 19 wk of age) than in broilers from 21.1"C. Hurwitz et al. [15] mentioned that decline of fat deposition in broilers is possibly due to higher maintenance requirements for energy beyond 27 C. v FIGURE 3. Total protein weight of bled, plucked male broilers from 32.2"C treatment fitted to three growth functions *male 21.1"C Elfemale 21.1"C +male 26.7"C *female 26.7"C fmale 32.2"C *female 32.2"C E 8 ' 6 E 4 0' PROPORTION OF MATURITY FIGURE4. Body protein growth rate for male and female broilers reared under three temperatures by proportion of mature body protein

6 114 JAPR GROWTH FUNCTIONS 50 fmale 32.2"C Xfemale 32 2 C n & E E Y h g b *male 21.1"C Qfemale 21.1'C +male 26.7OC *female 26.7" fmale 32.2OC Xfemale 32.2' 30 FIGURE 6. Percent of fat in dry matter of feather free, blood free broiler carcasses

7 HRUBYetal. Research Report 115 CONCLUSIONS AND APPLICATIONS 1. The non-linear Gompertz and logistic functions and the linear polynomial function are all suitable for describing the growth of a broiler in a thermoneutral environment on the basis of the coefficient of determination. 2. The non-linear Gompertz and logistic functions are able to predict the shape of the growth function more logically than the linear function. 3. High environmental temperature decreases the protein growth of a broiler and the time required to reach the highest point on the weight gain curve (the point of inflection). The genetic potential of broilers for mature protein weight and rate of protein gain will need to be determined under thermoneutral conditions. 4. From 10 wk of age, males had higher levels of protein on a dry matter basis than females. Females had higher levels of fat in dry matter than males. 1. Parks, J.R, A TheoIy of Feedin and Growth of Animals. Springer-Verlag, New York, A. 2. Thornley, J.H.M.and1.R Johnson, 1990.Plant and Crop Modelling. A Mathematical Approach to Plant and Crop Physiology. 1st Edition. Oxford Sci. Pub., Oxford, England. 3. Talpaz, H., S. Hnrwitz, J.R De La Tom, and PJ.H. Sharpe, Economic optimization of a growth trajectory for broilers. Amer. J. Agr. Eon Ricklefs, RE, Modification of growth and development of muscles of poultry. Poultry Sci. 64:156? Gous, RM., Future research goals in broiler nutrition identified by means of computer simulation modelling. Pa es 1 23 in: Proc. Arkansas Nutr. Conf., Little Rock, Ak Summers, J.D. and S. Leeson, Composition of poultry meat as affected by nutritional factors. Poultry Sci Hruby, M., M.L. Hamre, and C.N. Coon, Free-choice feeding and three temperature treatments. J. AppI. Poultxy Res. 4: R 800, Robot Coupe S. A., Montceau Les Mines, France. 9. H 5012, The Hobart Mfg. Co., Troy, OH, USA. 10. H 600, The Hobart Mfg. Co., Troy, OH, USA. 11. Association of Official Analytical Chemists, Official Methods of Analysis. 15th Edition. Assn. Off. Anal. Chem., Washington, DC. 12. Non-linear (NLIN) models were computed using the NLIN option of SAS/STAT@! [16] with the DUD REFERENCES AND NOTES algorithm. All beginnin values of the parameters were estimated. Linear (LIP$ re ession analyses were run on the LIN option of SAS/&AT. Fitted values for body protein were obtained and residuals calculated to evaluate the best possible fit. The e uations used were: Body protein weight at week (?) is equal to 1 Aexp(-exp(-k(t-t*))) e, Gompertz function [l; 2 A/(l+exp(-kit-t*))) + e, Logistic function,171; I 3 a0 + ait + a2t + a3t3 + a4t4 + e, Polynomial func- tion; where A is a final (mature) protein body weight, k stands for growth rate constant, t* is time at point of inflection, a is a constant, t is an age in weeks, and e is an error. The data were also subjected to two-way analysis of variance and calculated means were compared using LSD method. 13. Rogers, S.R., G.M. Pesli, and H.L Marks, Comparison of three nonlinear regression models for describing broiler growth curves. Growth 51: Knizetovi. H.. J. Hvinek. B. Knize. and.i. Roubicek, Ana$s 0'. gro&h curves 'of fowl. I. Chickens. Br. Poultry Sci Hluwitz, S., M. Weiselberg, U. Eisner, I. Bartov, G. Riesenfeld, M. Sharvit, A. Niv, and S. Bornstein, The energy requirements and performance of growing chickens and turkeys as affected by environmental temperature. Poultry Sci SAS Institute, SAS@ User's Guide: Statistics. Version 6.03 Edition. SAS Institute, Inc., Cary, NC. 17. Robertson, T.B., On the normal rate of growth of an individual and its biochemical significance. Arch. Entwicklungsmech Org ACKNOWLEDGEMENT The authors would like to thank Gold'n Plump Poultry, Inc., St. Cloud, MN for supporting this study.