until slaughter in well-managed commercial facilities, weight loss is not ...... wealth Agricultural Bureaux, Slough, UK. Baldwin, R L. 1976. Principles of mode-.
Computer simulation model of swine production systems: I. Modeling the growth of young pigs C. Pomar, D. L. Harris and F. Minvielle J ANIM SCI 1991, 69:1468-1488.
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COMPUTER SIMULATION MODEL OF SWINE PRODUCTION SYSTEMS: 1. MODELING THE GROWTH OF YOUNG PIGS' Chdido P o m d , Dewey L. Harris3 and Francis Minvielle4 Universitd Lava15, Qudbec, Canada, GlK-7P4 and
U.S. Department of Agriculture, A R S , Clay Center, NE 68933-0166 ABSTRACT
Theoretical concepts and relationships were used to develop a deterministic pig growth model. The model predicts, in a continuous form, growth and body composition of boars, barrows, and gilts according to genotype, diet, and management conditions. The model is aggregated at the whole-animal level with three main elements of body composition: total body DNA, total body protein mass 0, and total body mass of lipids, with PT determining the secondary elements of ash and moisture. The primary factors regulating growth were associated with cellular hyperplasia and hypertrophy in agreement with the basic concepts described by Baldwin and Black (1979). Differential equations representing DNA accretion and protein synthesis and degradation were adapted from Oltjen et al. (1985). Normal pig protein growth was characterized from published data. Body PT was used to reflect several metabolic activities related to animal size and age, as in some prior models. Dietary energy and protein were used in sequence until requirements are satisfied, first for maintenance, then for protein growth, and finally for fat deposition. A comparison between experimental and simulated results illustrates that the model may simulate growth and body composition of young pigs adequately. Key Words: Growth Models, Simulation, Pigs J. Anim. Sci. 1991. 69:146%1488
bly the most prevalent is the empirical approach, in which growth is described by the Various approaches have been used to use of a single or a few equations, often as a predict animal growth. The earkst and possi- function of age. Such an empirical approach can provide valid predictions for a n m w range of situations closely related to experimental conditions under which the data were 'The authors wish to acknowledge the many suggestions concerning model elements from numerous discus- collected. However, the empirical approach sions with scientists at the Roman L. Hruska U.S. Meat collapses when it is used to extrapolate results Anim. Res. Center at Clay Center, NE. These include G. beyond the original experimental conditions. L. Bennett, R. K. Christenson, J. J. Ford, K. E. Gregory, Therefore, to increase flexibility and effective K. A. Leymaster, M. D. -Neil, R R Maura, W. G. prediction in a wide range of situations, animal Pond, L. D. Young, plus Philippe Savoie from Agric. Canada at Lemoxville (Qukbec) Canada. The efforts of I. models should be more mechanistic (deducM. Dzakuma in developing the figures and Sherry Kluver tive) rather than empirical in their components for typing the manuscript are also appreciated. This study (Baldwin, 1976; Whittemore, 1986). The conwas partly supported by a grant fiom CORPAQ- cepts of cellular hyperplasia and hypertrophy Agriculture, Q u h . 2Present address: Station de Recherche, Agriculture (Winick and Noble, 1966) have been applied Canada, C.P. 90,Lennoxville, Qukbec, Canada, JIM-1Z3. successfully to represent the fundamental proc3R0man L. Hruska U. S. Meat Anim. Rw. Center. esses regulating growth in mammalian tissues Author to whom reprint requests should be addressed. (Baldwin and Black, 1979; Burleigh, 1980). 4preSent address: INRA-CNRZ, Labomtoire de GQlB Oltjen et al. (1985, 1986a.b) used the basic tique Factorielle, 78350, Jouya-Josas, France. premises proposed by Baldwin and Black 5Dept. of Zootechnie, FSAA. (1979) and applied them at the whole-animal Received October 16, 1989. level to simulate postweaning growth and Accepted June 14, 1990. Introduction
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PIG GROWTH MODEL
composition in rats and steers of different frame sizes. The aggregation at the wholeanimal level made by Oltjen et al. (1985) resulted in a simple model having wider applicability and accuracy than models derived empirically. Several models have been developed that simulate growth in the pig (Whittemore and Fawcett, 1976; Tess et al., 1983; Whittemore, 1983; Moughan and Smith, 1984; Black et al., 1986; Moughan et al., 1987). However, these models either are empirical or they include a limited number of factors determining protein accretion and growth efficiency. The main objective of the present study was to develop a swine growth model incorporating fundamental biological processes regulating the accretion of body protein as well as energy and protein metabolism. This model was to include additional factors that are known to affect these processes. Fundamental among these factors were genotypic and nutritional effects and their interactions with growth and body composition. Theoretical concepts and relationships presented herein constitute the basic framework for a complete reproducing gilt/sow model (Pomar et al., 1991). Only genetic and nutritional factors were included at this stage of model development in order to better evaluate their impact on swine growth performance while avoiding model overparameterization. strategy
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ses had to be included when lack of knowledge necessitated use of reasonable intuition about the concerned mechanisms. In other cases, empirical equations had to be developed. Data from the scientific literature were the primary source of information used to estimate model parameters. Reasonable values were assumed when the necessary data were unavailable. The model is detenninistic, dynamic, and aggregated at the whole-animal level with three primary composition elements: total body protein precursor (PP) as a mathematical approximation of total body deoxyribonucleic acid (DNA), total body protein mass (PT), and total body mass of lipids (LT). Rate variables are expressed on a daily basis, energy is in megajoules 0 and mass is in kilograms when not explicitly specified in the text. These and other abbreviations are shown in Table 1. Animal Body Composition
Empty body weight is defiied in the model as the algebraic sum of the main chemical components of the empty animal. These are the total body mass of protein 0, lipid (LT), water (HT), and ash (AT). Rather than choosing body components that result from dissection or any other physical measurements, chemical constituents of the body were chosen to represent pig body composition because of their fundamental nature. physical body components are numerous and their development during growth and the reproductive cycle is not well studied. However, these main chemical body components can be reduced to two parameters (PTand LT) and their development can be described independently of the tissues in which they are accumulated. This simplifcation is supported by results of Kotarbinska (1969). According to their results, body water and fat are statistically independent and body protein 0can be used to predict body water and ash with little loss of accuracy. The following equation developed by Kotarbinska (1969) is used in our model to predict HT mass:
The growth simulation model was written in FORTRAN; it predicts body composition and weight of boars, barrows, and female pigs during the growth period, Pig genotype, diet amount, and composition and management alternatives are input parameters specified by the user according to the desired strategy for the simulation. It is assumed in the model that the diet is adequately balanced and palatable for all known nutrients (including minerals and vitamins and all amino acids except lysine) during all stages of growth. Euler's integration method is used to solve the differential equations with an integration step no greater HT = 4.889 pY.s55,R2 = .955. than 1 d To overcome the limitations of the empirical relationships, known causal relationships A mass equivalent to 21% of the protein have been included in the model with the gain is assumed to be retained in the body as accuracy required to represent the observed body ash, as proposed by Whittemore (1983), biological phenomena. In some cases, hypothe- and in close agreement with the estimates of
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Kotarbinska (1969). Also, as estimated by literature to modify the predictions of the Whittemore, empty body weight is assumed to physical body composition of pigs for each of be 95% of total body weight (WT) at all these factors. The following transformations weights. The net amount of protein (PTr) and are, therefore, only empirical, and comparisons lipid (LTr) retained is calculated at each between model alternatives, genotypes, or real integration step and total PT and LT mass data in physical body composition form should be done with caution. subsequently are updated. Dissected lean carcass (MD) can be estiTransformation of chemical composition into physical composition is not required mated according to the sex of the pig by the during the fundamental simulation process. following equations of Tullis 1982): However, transformation is performed in order MDe (intact males) = 2.16 FT to obtain more traditional measures close to MDf(females) = 2.24PT those observed in the practices of pork MDc(barrows) = 2.29FT. production. The relationship between chemical and physical composition is Likely to differ Carcass dissected fat (FD) can be estimated between sexes, genotypes, and even strains. Nutrients, management, and other factors also by the following equation m s , 1982): can affect these relationships (ARC, 1981; F D = .98 LT -.14. Whittemore, 1983; Rook et al., 1987). Not enough data are available presently in the From Whittemore et al. (1981), total bone dissected from the pig carcass (BD) can be evaluated as follows: TABLE 1. ABBREVIATIONS AND ACRONYMS USED IN THE TEXT Symbol
Meaning
Ai
Live body weight at maturity (as defiied by Taylor, 1980) Average daily gain Average daily feed intake Total body ash mass Dissectible carcass bone mass Digestible daily energy intake Total body deoxyribonucleic acid constant Energy protein requirements Peed conversionratio (AFI/ADG) Daily feed intake Dissectible carcass fat mass Total body mass of water Ideal protein intake Ideal protein used for maintenance Intrinsic potential rate of protein accretion constants constant Total body mass of lipids Body lipid accretion Dissectible carcass lean mass Backfat thickness Total body protein precursor approximiitionfor DNA Maximal protein precursor mass at maturity Protein precursor rate of accretion Total body protein mass Rate of body protein degradation Maximal protein mass at maturity Body protein accretion Rate of body protein synthesis Simulation time or pig's age Live body weight
ADG
AFI AT BD DE DNA
Ei
EM FCR
m
Fn HT
rm lPM IPTr
3 LTr MD p2 PP
PPMX PPr
Fr
m
PTMX PTr PTSr t
WT
BD = 2.57 AT.
Tullis (1982) also estimated backfat thickness (Pz>at 65 mm from the mid-line at the region of the last rib by the following q u ation :
These and other relationships are described in more detail by Whittemore (1983). Extrapolation of these relationships to adult animals is done cautiously even though some equivalencies have been found between adult and young pigs (whitternore et al., 1980). Intrinsic Potential for Protein Accretion The intrinsic potential of protein accretion (IPTr) is defined as the maximal amount of protein that an animal can retain in a day when there is no external (mainly nutritional) limitation. In the present context, our objective is to provide a mechanism that considers the underlying causative factors involved in protein growth. Thus, equation forms used in this model to evaluate IPTr have been adapted from Oltjen et al. (1985, 1986b), who based their model on the structure and concepts developed by Baldwin and Black (1979).
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PIG GROWTH MODEL
Because published data are insufficient to estimate the initial and fiial DNA content in the pig body accurately, and because protein retention occurs in tissues other than muscle, the term PP (protein precursor) is presented in this paper as an approximation of the total DNA body content for curve-fitting purposes, PPr being the rate of PP retained or lost and PPMX the PP mass at maturity. For the same reasons, muscle DNA/protein ratio is assumed equivalent to the total body PP/protein ratio. The equations used to estimate IPTr in the present model are as follows: (1) PTSr(t) (2)PTw) (3) lPTr(t) (4)PPr(t)
= K2 PP(t)E2 = K3PT(t>E3
= PTSr(t) - PTDr(t)
= K1 (PPMX - PP(t)) PPWE1
where IPTr and PPr represent, respectively, the rates of IFT and PP accretion, t is the animal age, Ki and E; are constants, €TSr(t) and FTDr(t) are, respectively, the rates of body protein synthesis and of degradation, and PT is the total body protein mass. Equation 4 was chosen to drive PP accretion because of the better data fit obtained when growth is simulated from an early age with other equations suggested by Oltjen et al. (1985). Values for the constants El, I%, and E3 are 3 2 , .73, and .73, respectively, as proposed by Oltjen et al. (1985, 1986b). Muscle development is accompanied by increase of both total nucleic acid (DNA or ribonucleic acid, RNA) and protein accumulated per unit of nucleic acid (Burleigh, 1980). Differences between breeds have been observed for total muscle DNA and DNNprotein ratio (Burleigh, 1980), but results are not consistent (Powell and Aberle, 1975). According to Ezkwe and in (1975), m w a r d et al. (1975), and Waterlow et al. (1978), PP/ protein ratio in muscle tissues at maturity is assumed to be 2.5 mg/g. The former intrinsic potential model for protein accretion shows more sensitivity for the difference &tween initial and final PP/protein ratio than for the absolute values alone. Consequently, initial (21 d of age) PP/protein ratio (11.25 mg/g) is assumed to be 4.5 times the ratio at maturity, which is close to the findings of Powell and Aberle (1975), Stickland et al. (1975), and Gilbreath and Trout (1973). Because protein mass at 21 d of age usuaUy is lolown and PT at
maturity (PTMX) is assumed to be genetically determined, and because it can be supplied by the user, initial and mature PP masses are calculated by multiplying the corresponding PP/protein ratios by the initial and fiial PT masses. Because estimates of the synthesis constant K2 and of the degradation constant K3 are highly correlated, Oltjen et al. (1985) proposed to estimate K3 with an independent measurement of total protein degradation rate in order to obtain a better fit for the model that estimates the intrinsic potential of protein accretion. Few of these measurements are available in the literature. However, because of the correlation between K2 and K3, K3 can be directly obtained from K2 without important loss of prediction accuracy. The small variation of PT mass observed in adult empty sows given ad libitum access to feed (Walstra, 1980; K. A. hymaster, personal communication) is the result of an equivalent rate for body protein synthesis and degradation. Therefore, K2 and K3 can be related as follows: K3 = K z P P M X . ~ ~ P T M X - . ~ ~ = K2 (2.5 prprzx).73PI'MX-.73 = 1.952K2.
I
data
birth until
maturity for males, females, and barrows (Walstra, 1980) were used to characterize normal protein growth in pigs. Thus, dissected lean carcass measurements were transformed to total body protein mass (PT) with the (1982)9 but with Propsed equations Of the dissected lean as an because the standard deviation for MD and for are equivalent (ROOk et 1987). PT mass is in close agreement with the one available in the literature for Young animals cwhittemore et al., 1978; Tullis and Whittemore, 1986) and the one of K. A. h ~ m s t e r (Personal COm~CatiOn)for mature SOWSCalculated PTMX are: 43.5, 35.5, and 34.9 for males, females, and barrows, respectively. The constants K1 and K2 were estimated from transformed data using a nonlinear, weighted least squares minimization procedure (SAS, 1985). Residuals were weighted by multiplying them by the inverse of the observed PT values. Weighted residuals were used to ensure the same proportional deviation between the
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m)
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POMAR ET AL. TABLE 2. PROTEIN MASS AT MA0, PROTEIN PRECCTRSOR (Ki), AND PROTEIN SYNTHESIS (Kz) RATE CONSTANTS AND U"J3GHTED RESIDUAL S U M OF SQUARES (RSS) OBTAINED FOR THE BASE GENOTYPE
Gender
PTMX
Ki
K?
RSS
43.5 35.5 34.9
BO1127 .om146 .002073
.011175
6.6499
.OD7358
5.6443 1.6248
~
Males Females Barrows
observed and predicted data throughout the pig's life. Only data from pigs given ad libitum access to feed were used, and protein accretion was assumed not to be limited by any extrinsic factor. Fitted Ki values and residuals are shown in Table 2. Standard patterns for PP and PT growth for males, females, and barrows are shown in Figures 1 and 2. Along with the curves for I T mass in the upper part of Figure 2, the mean data points of Walstra (1980) are plotted. Patterns of IPTr (the intrinsic limit of PTr) are dependent not only on age and weight or some measurement of physiological and nutritional status of the pig (PP, PT, and PPMX in the present model), but also on sex, breed, or strain (Camet al., 1977). Sex effects on IPTr are modeled herein by using specific Ki parameter values as documented previously (see Table 2). However, a similar procedure cannot be performed to model the genotypic effects on IPTr because literature data are not sufficient to estimate the specific Ki values for each breed or strain. Nevertheless, Taylor (1980) proposed two genetic size-scaling rules to summarize the observed similarities that exist during the growth process between different mammalian genotypes. The Taylor rules are based on the principle that several biological growth processes show remarkable uniformity in their relationship to mature body weight when examined over a range of different genotypes. According to the basic assumptions made in the present model, body protein mass at maturity 0 would be genetically determined through PPMX (the body protein precursor mass at maturity). Therefore, Taylor's rules can be used assuming FTIi4X and PPMX as driver variables instead of mature body weight. Thus, applying Taylor's rules to the model proposed formerly, K1 is modified as follows:
.OM968
where the variables and constants with "w" superscript indicate the values obtained with the Walstra (1980) data. These data represent the base genotype in this model. The set of equations presented above describes accretion of whole-body protein in pigs under conditions of normal growth. Adaptation of the Oltjen et al. (1985) model under varied nutritional regimens was carried out in various stages, all of them normally requiring appropriate data. Because appropriate data on pigs are scarce or nonexistent, the following mechanism was implemented in this model to accommodate the effect of extrinsic factors on protein growth: when extrinsic factors, such as nutrition, limit protein retention (PTr), PPr is restricted in the same proportion as PTr. It is assumed that growing pigs are not fed under severe restrictions that would require the use of body protein reserves for maintenance. The present protein accretion sub-model is a simplification of mechanisms regulating protein accretion. In this respect, the present model can be considered more mechanistic than some previous swine models, although it is more empirical than other models with more detailed representation. Protein and Fat Accretion The factorial method is used in the model to estimate energy and protein requirements in pigs. Dietary energy and protein are employed first for maintenance, then for protein growth, and fiially for fat deposition. Lysine is generally accepted to be the first limiting amino acid in cereal-based diets for growing pigs (ARC,1981). For this reason, lysine concentration in the diet is used to calculate the ideal protein intake @PI) as proposed by Whittemore (1983) for growing pigs. Protein requirements for maintenance represent the obligatoq protein losses (ARC,1981)
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PIG GROWTH MODEL
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excreted, mainly via urine and feces. The However, to ensure appropriate comparisons of apparent digestibility coefficient takes into genotypes while assuming that fat and ash account intestinal excretions. Obligatory pro- masses are not involved in the obligatory tein losses in urine might be related to protein losses, FT was chosen to drive IPM. metabolic weight, as stated by Carr et al. For this reason, the predicted values of the (1977).The following equation of Whittemore former equation were used to estimate an et aL (1978) is used as a basis for predictions equivalent relationship with PT as the driver of IPM because it yields reasonable estima- variable. The data set of Walstra (1980)from 21 d of age until maturity was used for this tions throughout the life of the pig: purpose. Because sex differences were small, all the data were pooled and a new set of IPM = 1.32 WT.75.
PP mass lgl
120 r
Age of the pigs (days] Figure 1. Protein precursor (PP) and accretion (PPr) relative to the age of the pig.
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parameters was calculated. The resulting q u a tion is as follows:
IPM = -00595 PT-74, R2 = .98.
This vation was not to h€'rove the prediction accuracy of the relationship of Whittemore et al. (1978), but it allows comp~sonsof genotypes with divergent carcass compositions. The ideal dietary protein available for growth is obtained by subtracting the amount
of ideal protein used for maintenance from the ingested ideal protein (PI).This assumes that an ideal amino acid balance for maintenance is also ideal for growth. The efficiency of use of available IPI for protein retention has not been adequately studied. Nevertheless, an efficiency of 95% is assumed in the model. This value is consistent with the views of ARC (1981) and Whittemore (1983). For animals fed for ad libitum intake or for which feed is slightly restricted, body protein
PT mass Ikgl
50 -
i
,Or
2o
I
t
lo
O-
0 0
200
400
600
800
Age of the pigs [days]
1000
Figure 2. Protein mass (PT) and accretion @Tr) relative to the age of the pig.
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PIG GROWTH MODEL
accretion (FTr) generally is independent of the total body mass of lipids (LT), the latter being a function of the energy surplus given to the animals (Kielanowski, 1976). Therefore, the minimum value between net ideal protein I - IPM) intake available for growth (.95 x P and the intrinsic potential for protein accretion (FI’r) represents the final retention of protein that is PTr, if there is not any other intrinsic limitation. A similar approach was used by Whittemore and Fawcett (1976) and Whittemore (1983) to model pig growth. Energy requirements for maintenance are estimated in the present model by the following equation (Tess et al., 1983):
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simulated animals. Because energy and protein requirements are independently accounted for in the model, the LTr/PTr ratio is evaluated at each integration step. When energy available for lipid retention does not satisfy this minimum ratio, a fraction of IPI available for protein retention is deaminated, decreasing PTr and increasing LTr until a satisfactory ratio is attained Because healthy young pigs do not lose weight from a few days after weaning until slaughter in well-managed commercial facilities, weight loss is not incorporated into the growth model. However, a later extension of the model will incorporate weight loss for conditions in which nutrient requirements exceed intake.
EM (MJ/d) = 2.3364 PT.74. This reIationship yields reasonable predicted values from early age until maturity and uses PT as the independent variable. It seems reasonable to use PT to predict EM in this model to allow a fair comparison between genotypes with different body composition, particularly at high levels of feeding cress et al., 1983, 1984). A similar EM predictor has been proposed by Whittemore (1983). Metabolizable energy efficiency is assumed to be 54% for protein and 74% for fat deposition (ARC, 1981). The energy content of the retained body protein and fat are 23.7 and 39.6 MJ/kg, respectively. Therefore, total energy expenditures for protein and fat retention are 43.9 and 53.5 MJ/kg, respectively, including the retained energy itself. Urine losses are calculated by assuming that, for each kilogram of protein deaminated, urine energy content is 7.2 MJ and 4.9 MJ/kg are spent for urea synthesis (Whittemore, 1983). It also was assumed that gaseous losses of energy from gut digestion are not significant for cerealbased diets (Fuller and Boyne, 1972; Whitte more, 1983). These efficiencies are considered constant throughout the pig’s life. It is unlikely that normal growth can be achieved without lipid retention. Kielanowski (1966) suggested that even a drastic feed intake limitation will not result in a lipid to protein accretion ratio (LTr/PTr) lower than 1. Recently, Whitternore (1983) has given possible values and indicated that modem strains of pigs are rapidly diminishing this ratio to values lower than 1. In this model, the minimum LTrhTr ratio is supplied by the user according to the sex and genotype of the
Ad Libitum Feed Intake Pigs eat discrete meals that usually are taken during the day in association with water drinking (Houpt, 1986). Volunkuy feed intake increases with the weight and age of the animal (NRC,1987). To model the control of feed intake in pigs, as in other species, is a laborious task because of the complexity of the mechanisms implicated in the determination of meal size and frequency. Furthermore, the mechanisms that are controlling feed intake can act at different time intervals (from shortterm to long-term) and are influenced by environment, diet characteristics, and other factors. Two approaches traditionally are used to simplify the estimation of the amount of daily food intake of pigs. The frrst one assumes that voluntary feed intake (FI) is primarily determined by the capacity of the animal to utilize nutrients or, equivalently, to satisfy maintenance, growth, and production needs. Although it is not evident whether needs or metabolic capacity determine the final amount of consumed food, this approach has been used successfully by Tess et al. (1983) and Black et al. (1986) in their swine models. An alternative approach would use total live body weight (WT) or metabolic weight or age to drive FI, based on the fact that an important relationship exists between voluntary feed intake and several of these variables (NRC, 1987). Nevertheless, both approaches are mathematically equivalent when pigs’ requirements are related to some measurement of age or weight. Consequently, we assumed that, within a wide range of dietary energy concentrations, pigs of
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the same body composition tend to consume equal amounts of digestible energy (DE). Considering voluntary feed intake as a maximum, levels of limit feeding can be modeled readily. Not addressed in the current model is the influence of nonnutritional environment (ambient temperature, etc.) on voluntary feed and energy cost for thermogenesis intake. In the present model, fat accretion (LTr) is a function of the energy surplus consumed by the animal and is not limited directly by any intrinsic factor. Therefore, FI is the final determinant of LTr under normal dietary conditions. To be consistent with this assumption, total mass of lipids (LT) should not be involved in the determination of meal sue because it usually is independent of age and gut or metabolic capacity. Thus, when body weight (of which LT is a component) is used to predict FI, there is a potential feedback effect leading to aberrant LT growth. Thus, a third alternative using total body protein mass (PT) as the driver of Fl overcomes these difficulties. The ad libitum feed intake was derived in the present model from the following relationship proposed by NRC (1987) for pigs from 4.5 to 117 kg of WT:
The formula for DE intake can be extended to incorporate the concepts of appetite and palatability. Multiplicative constants (FIK) representing relative voluntary intakes for specific genotypes or for the palatability of the diet are introduced with values greater than 1 representing increases in either of these. Due to the nature of the model for protein and fat accretion, increases in intake, due to either, will lead to increased growth, which predominantly will be fat. This manner of representing the relationship between increased intake and increased fatness is different from the model of Tess et al. (1983), who regressed ad libitum energy intake on maintenance requirements, protein gain, and fat gain. Calibration of the appetite and palatability multiplication factors for specific genotypes and diets promises some difficulties, but it seems necessary to make the model fully represent fatness differences. Evaluation of the Young Pig Growth Model
Setting of criteria for model evaluation is a very important, but debatable, process; it may not always be feasible (Baldwin, 1976). The model user has to be the ultimate judge of its validity (Dent and Blackie, 1979). Although none of the tests presently existing is sufficient DE (MJ/d) = 55.07 (1 d K j B W ) , to ensure an accurate, wide representation of the real system, model evaluation can be where Kj = .0176. An equivalent equation was divided into two processes: model testing (or proposed by ARC (1981). If the proportion of verification) and validation (Dent and Blackie, protein content in the body is supposed to have 1979). small variations in growing pigs, as suggested Mathematical and logical consistencies by Kotarbinska (1969), the former equation were checked throughout the whole model can be directly transformed in order to be development. Also, parameter values and the driven by PT. Thus, from the data of Walstra model structure were discussed critically with (1980), it was estimated that normally grown qualified scientists and modified until results male pigs fed for ad libitum intake have were reasonable and consistent. A preliminary approximately 14.77% PT. This value is in validation exercise was performed by comparclose agreement with estimations of Kotar- ing perfonnanw of this model (predicted) binska (1969) and Whittemore et al. (1980). against experimental results (actual) obtained Therefore, Kj can be replaced by .1192 (.0176/ by Giles et al. (1986) (Evaluation Exercise 1). .1477) in the former equation when PT In addition, performance of the present model replaces BW as the independent variable. The is compared to the Edinburgh pig model output predicted intake for nursery pigs seems appro- reported by Whitternore (1981) (Evaluation priate according to Tullis and Whittemore Exercise 2). In both cases, detailed simulation (1986) and is close to other proposed predic- results are shown in order to better evaluate tors (NRC,1987) for pigs weighing between 5 the ability of the model to simulate pig growth. and 20 kg. The same transformation made for Genotypic definitions are difficult to establish feed intake is used to adjust the predicted FI because protein mass at maturity of the values according to the sex of the pig (NRC, represented breeds is not known. Nevertheless, 1987). for this exercise, protein mass at maturity was
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TABLE 3. EXPERIMENTAL AND SIMULATED GROWTH PERFORMANCE OF PIGS FED FOR AD LIBITUIVl INTAKE FROM 20 TO 50 IULOGRAMS -OD 1) AND FROM 50 TO 85 IUL0GRAM.S
LNE BODY WEIGHT PERIOD 2)' Simulatedresults
Experimental resultsb
PeriodC
ADG
API
FCR
1 2 1&2
762 784 770
1.73 2.33 2.02
2.28 3.00 2.64
1
719 712 708
1.77 2.35 2.06
2.5 1 3.33 2.92
2
1&2
p2
Boars 12.9 16.0
13.4 17.4
-
ADG
AFI
FCR
p2
67 1 882 77 1
1.72 2.68 2.17
2.55 3.04 2.8 1
13.4 21.9
680 846 760
1.72 2.68 2.19
2.53 3.17 2.88
13.4 22.4
652 810 729
1.71 2.65 2.17
2.62 328 2.97
13.7 23.1
-
-
Castrates
-
-
-
2
-
-
1&2
-
-
-
-
1
-
-
-
'ADG = average daily gain (g), AFI = average feed intake (kg/d), FCR = feed conversion d o , P2 = experimental and simulated backfat thickness (mm) at the region of the last rib at 65 mm from the mid-line. Experimental results were determined by ultrasonic probe at 50 kg and by direct carcass measurement at 85 kg live body weight. %-om Giles et al. (1986). 'Diet B replaced diet A in the second growth period.
specified to be 52.6, 43.3, and 41.5 kg for intact males, females, and castrates, respectively, to characterize the genotype of improved animals. Ambient temperature effects are not accounted for in this model, although they can influence feed intake and pig performance. In all cases, model calibration to experimental results was not performed, and, therefore, trends and magnitude differences observed in these exercises are basic criteria to evaluate performance of the model. Performance variables used in this analysis were average daily gain (ADG,in grams), average daily feed intake (AFI, in kilograms/ day), feed conversion ratio ( F a total AFT/ ADG for the period) and backfat thickness (P2). In both exercises, dietary crude protein digestibility was set at 75%. Evaluation Exercise 1. Giles et al. (1986) studied the response of growing Large White pigs to dietary lysine concentration (eight levels) as influenced by feed intake (restricted and ad libitum), sex (intact males and females), and live weight (from 20 to 50 kg live body weight IWT] in the first growth period and from 50 to 85 kg WT in the second one). Two basal diets (A and B) were formulated with barley and soybean meal to contain 178 and 153 g CP/kg, 14.2 and 13.9 MI DE/kg and 8.0 and 6.4 g lysinekg, respectively. Free
lysine was added to both diets to produce 16 diets with dietary lysine concentrations ranging from 8.0 to 12.2 g/kg in the first growth period and from 6.4 to 9.8 g/kg in the second one. Other essential amino acids also were added in the free amino acid form to maintain their balance relative to lysine as recommended by ARC (1981). Diet A was fed to the pigs in the first growth period and diet B in the second one. Diet protein concentration was similar in all treatments, whereas lysine concentration of protein ranged from 44.9 to 68.5 g/kg and from 41.8 to 64.1 g k g for the first and second growth periods, respectively. Because the differences in dietary lysine concentration on pig performance were small and because nutritional requirements were met when pigs are fed for ad libitum intake, only mean results are shown in Table 3. Detailed simulated results at the lowest dietary lysine concentration level are shown in Figures 3 and 4. Simulated male and female pigs fed for ad libitum intake had lower ADG during the first growth period than the trial ones, although these differences were reversed during the second period. Simulated pigs fed for ad libitum intake had, on average, ADG similar for males but higher (+7%) for females, higher AFI (+7% for males and +6% for females), and higher FCR for males (+6%) but not for
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FQMAR ET AL.
females (-1%). Differences in feed intake libitum access to feed. Similar results were between simulated sexes result mainly from obtained in simulated pigs of any sex, because differences in total body protein mass. Protein the amount of ideal protein available for tissue mass is, in turn, affected by the adult protein growth was sufficient even at the lowest mass attributed to each sex. Differences in feed experimental lysine concentration level. Acintake between trial and simulated pigs proba- cordingly, protein accretion rates shown in bly are the basis for most of the observed Figure 3B are equal to the intrinsic potential differences in ADG.Lysine concentration in for protein accretion. As a result of the genetic the diet had little effect on ADG and FCR for parameters attributed to each sex in this both trial male and female pigs given ad exercise, gilts at an early age have higher body
1
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m
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Simulated Age of Pig (days) Figure 3. Simulated daily feed iutake (A), protein (B) and fat Q accretion rates of pigs with ad libitum feed intake plotted relative to their age.
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PIG GROWTH MODEL
protein accretion rate than males of similar age during the first growth period. However, castrated pigs retained less protein than the other pigs over the whole simulated interval (Figures 3B and 4B). Also, weight gain of females was slightly faster than that of males and castrates during the first growth period (Figure 4A). However, during the second period, rate of weight gain by females was
intermediate between gain of males and castrates (Figure 4A). Simulated pigs increased their feed intake slightly after 50 kg body weight to compensate for the lower energy concentration of the new diet. This change did not affect protein growth because these pigs still were at their maximal potential. However, fat accretion increased slightly (Figure 3C) because energy efficiency is higher in diet B
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Figure 4. Simulated protein (€3) and fat (C) body mass and live body weight (A) of pigs fed for ad libitum intake plotted relative to their age.
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POMAR ET AL.
than in A because there is less protein surplus being deaminated. Experimental and simulated results for restricted pigs are shown in Table 4. Detailed simulated results for the highest (12.2 and 9.8 g/kg) and lowest (8.0 and 6.4) lysine mncen-
tration level in both growth periods are shown in Figures 5 and 6. Differences between trial and simulated pigs during the overall experiment are small. However, simulated pigs tended to grow slightly faster (+1% for males and +lo% for females) than trial ones during
TABLE 4. EXPERIMENTAL AND SIMULATED EPFECTS OF DIETARY LYSINE CONCENTRATION ON GROWTH PEFWORMANCE OF FEED-RESTRIC'IED BOARS AND PEMALE PIGS FROM 20 TO 50 I(LL0GRAMS (PERIOD 1) AND FROM 50 TO 85 KILOGRAMS OF LIVE BODY WEIGHT (PERIOD2)a Treatments
-ental
Period'
Lysine
ADG
Am
1
8.O 8.6 9.2 9.8 10.4 11.0 11.6 12.2 Mean 6.4 6.9 7.4 7.8 8.3 8.8 9.3 9.8 Mean Mean
499 514 536 557 575 580 614 602 560
1.18 1.14 1.17 1.19 1.21 1.18 1.20 1.21 1.16
653 687 704 707 723 683 730 718 701 621
1.90 1.90 1.90 1.90 1.90 1.91 1.87 1.90 1.90
8.0 8.6 9.2 9.8 10.4 11.0 11.6 12.2 Mean 6.4 6.9 7.4 7.8 8.3 8.8 9.3 9.8
496 493 508 488 52 1 502 561 561 516 620 643 648 632
2
1&2 1
2
1&2
Meall Mean
150
resultsb pz
A D G A m
FCR
p2
2.36 2.23 2.19 2.14 2.10 2.10 1.99 2.01 2.13
12.3 11.4 12.0 11.9 10.5 11.4 10.3 9.3
531 555 570 574 574 574 574 574 566
1.31 1.31 1.32 1.32 1.32 1.32 1.32 1.32 1.32
11.1
2.91 2.77 2.70 2.70 2.63 2.80 2.58 2.65 2.72 2.42
15.3 16.3 14.8 155 12.8 13.0 125 12.2 14.0
584 614 647 674 686 686 686 686 658 612
1.97 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.65
2.46 2.37 2.31 2.30 2.30 2.30 2.30 2.30 2.33 3.38 3.22 3.05 2.93 2.88 2.88 2.88 2.88 3.01 2.70
2.44 2.46 2.41 2.43 2.33 2.42 2.17 2.17 2.35 3.09
11.3 11.3 11.4 10.9 11.4 12.4 11.3 11.0 11.3 14.8 14.5 14.5 11.3 15.5 14.3 16.0 13.8
530 552 568 577 578 578 578 578 567 584 614 633 633 633 633 633 633 625 597
1.31 1.31 1.32 1.32 1.33 1.33 1.33 1.33 1.32 1.98 1.98 1.98 1.98 1.98 1.98 1.98 1.98
2.47 2.38 2.32 2.30 2.29 2.29 2.29 2.29 2.33 3.38 3.22 3.13 3.12 3.12 3.12 3.12 3.12
1.98 1.66
3.17 2.78
646
1.20 1.21 122 1.18 1.20 1.20 1.22 1.22 1.21 1.91 1.90 1.90 1.91 1.91 1.89 1.91 1.91
2.94 3.03 2.97 2.97 2.96 2.95
641 571
1.90 1.52
2.99 2.67
644 639 652
simulated results
3.00
11.1
-
14.3
-
10.7 10.4 10.4 10.4 10.4 10.4 10.4 10.5 17.8 16.8 16.0 155 15.3 15.3 15.3 15.3 15.9
-
11.1
10.7 10.5 10.3 10.3 10.3 10.3 10.3 105 17.8 16.8 16.2 16.1 16.0 16.0 16.0 16.0 16.4
-
'ADG = average daily gain (g), Am = avemge feed intake (kg/d), FCR = feed conversion ratio, Lysine = dietary lysine concentration in gkg,P2 = experimental and simulated backfat thiclmess (mm)at the region of the last rib at 65 IIIf ~ ro~ m the mid-line. Experimental results were determined by ultrasonic probe at 50 kg and by direct carcass measurement at 86 kg live body weight. %om Giles et al. (1986). %et B replaced diet A in the second growth period.
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the first growth period and slightly slower (-6% for males and -2% for females) during the second one. For all pigs with restricted intakes, simulated FCR was higher (+S%) than observed in the experiment, partly due to higher AFI (+lo%).Genetic effects also can contribute to these differences. Under restriction and according to sex and growth period, increasing dietary lysine concentration increased ADG and decreased FCR and P2 until a plateau was reached in all cases. However, t h i s effect was not obvious in trial pigs. Both trial and simulated results indicate that lysine concentration in the diet should be higher for pigs with restricted intake than for pigs given ad libitum access to feed. Simulated females had lower lysine requirements than males, at least during the second growth period, because their protein retention decreased faster than in males. Simulated feed-restricted male and female pigs raised with the lowest level of lysine had similar feed intake and body weight gain with both diets (Figures 5A and 6A). At the lowest levels of lysine, protein and fat growth rates were limited by the availability of dietary nutrients rather than by the genetic potential for growth, therefore, no differences were observed between sexes. Only during the last days of the first growth period did simulated males and females, fed with the lowest dietary lysine level, reach their maximum potential for protein growth; only then did protein accretion rate differ between males and females (Figure 5B). Because this difference was small and occurred over a short period of time, body protein and fat mass of these pigs remained similar throughout the experiment (Figure 6B). The decline in protein accretion rate in both male and female pigs fed at the lowest lysine level resulted from the decline of protein intake after the diet was changed at 50 kg WT. On the other hand, pigs fed the highest dietary lysine level during growth were at their maximal protein growth potential throughout the experiment. Because lysine concentration was inadequate at the lowest level, these pigs gained less protein (Figures 5B and 6B) and more fat (Figures 5C and 6C) than those fed at the highest lysine level. Simulated females with high lysine level gained slightly more body protein (Figure 6B) and weight (Figure 6A) than males during the first growth period but less during the second, as observed in pigs with ad libitum intake. During the second
growth period, female pigs fed at a high lysine level had a higher lipid accretion rate than males did because their growth of body protein was decreased The shift to a lower energy and protein content of the diet for the second growth period resulted in a decline of the fat accretion rate of all animals Figure 5C)and of the protein accretion rate of the pigs fed at the lowest lysine level (Figure 5B). Evaluation Exercise 2. In this exercise, model growth performance is compared to the growth performance derived from the Edinburgh pig model reported by Mittemore (1981). For this purpose, two diets differing in energy and digestible protein and two feeding alternatives were used (Table 5). Results from both models are shown in Table 5. Detailed results of our model only are shown in Figures 7 and 8. Compared with the Edinburgh model, on the average our model predicted lower ADG (-8%), higher AFI (+14%), higher FCR (+24%), that pigs need more days (+8 d) to reach 90 kg of live body weight, and that they had more backfat ( 4 . 8
TABLE 5. EDINBURGH AND PROPOSED SWINE MODEL PERFORMANCE FOR THREE DIETARY REGIMENS'
Run
1
Dietary alternatives Diet Digestible crude protein, g k g 130 13.0 Digestible energy, WAcg Ration 1.0 Initial, kgld 20 Increase, kghvk 2.6 Maximum, kg/d output Edinburghpig modelb 791 ADG,g 2.03 m,kg/d 2.57 FCR 89 Days (from 20 to 90kg WT) 17.6 P2. mm Present pig model 744 ADG, g 2.37 Am,W d 3.18 FCR 94.5 Days (from20 to 90kg WT) 22.9 P7,
-
2
3
130 170 13.0 14.0 1.0 .15 2.2
1.o .15
2.2
725 747 1.81 1.80 2.50 2.41 97 94 15.0 15.8 657 681 2.05 2.04 3.11 2.99 106.5 103.0 19.4 20.5
= average daily gain, AFI = average feed intake, FCR = feed conversion ratio, P2 = simulated backfat thickness (mm) at the region of the last rib at 65 ram from the mid-line. whittemore (1981).
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1.15
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Simulated Age of Pig (days) Figure 5. Simulated effects of dietary lysine concentration on daily feed intake (A) and protein (B) and fat (C) accretion rates of feed-restricted pigs relative to their ages.
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PIG GROWTH MODEL
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POMAR ET AL.
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Simulated Age of Pig (days) Figure 7. Simulated effects of three dietary regimens on daily feed intake (A) and protein (B) and fat (c)accretion rates relative to the age of the pigs (see Table 5 for description of the dietary regimens for each run).
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1485
PIG GROWTH MODEL
95 'I
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Simulated Age of Pig (days) Pigure 8. Simulated effects of three dietary reghens on live body weight (A) and protein (El) and fat (C) body mass relative to the age of the pigs (see Table 5 for description of the dietary regimens for each run).
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POMAR ET AL.
mm). Differences between models probably result from differences in AFI and in retained protein, the latter likely resulting from differences in simulating genotypic potential for protein accretion. Nevertheless, response differences in these two models to the dietary alternatives quantitatively were very similar in direction and magnitude. In this exercise, simulated pigs reached their maximal protein growth potential in all cases, which resulted in equivalent masses of body protein (Figure 7B). Thus, only the accretion and mass of body lipids (Figures 7C and 8C) were affected by restricting feed intake. The effect of the amount of feed intake and of diet composition on growth efficiency can be studied by comparing runs 1 to 2 and 2 to 3, respectively. Because the optimal protein accretion rate was reached in all cases, treatment effects were observed only on body fat accretion rates, which in tum were related to the daily ingestion of energy. At early ages, fat accretion rate increased as daily feed intake increased. However, after feed intake reached a plateau, fat accretion rate decreased slowly both because protein accretion rate continued to increase and because of the increasing energy demand for maintenance that resulted from the growth of the pig’s body protein mass. Discussion
A deterministic model based on theoretical concepts and relationships regulating protein accretion and nutrient partitioning in young pigs has been described. The model was designed to be flexible, and the effect of genotype, diet, and management strategy can be simulated in a wide range of circumstances. Although simulation models are a simplification of the real system, the initial validation exercises indicate that this model adequately simulates growth and body composition of growing pigs, even though it requires further calibration. Mathematical characterization of the expected body protein mass at maturity for specific genetic populations has not been achieved at the present stage of model development. Most of the discrepancies observed between predicted and observed data seem to be related to this aspect of the model. Appropriate data describing body protein growth for each specific swine population are
needed to characterize this parameter accurately. Environmental factors that have not been included in this model also are likely to be responsible for some of these differences. Because of the complexity of the model, more validation and sensitivity analyses are needed to identify model components that require closer calibration or further mathematical representation. In addition, nonnutritional factors such as climate, season, and housing influences need to be incorporated into expanded versions of this model. In practice, model building is an iterative process and, in this sense, model improvement never is complete. The swine simulation model proposed herein is, in part, more mechanistic than other models previously developed; it is the first that uses theoretical concepts to simulate the growth of protein in young pigs. This mechanistic approach seems to be an advance in the mathematical representation of growth and body composition of pigs, whatever their age or physiological status. Because of their universal nature, incorporating these mechanisms should result in accurate simulation of the effects of nutritional, genetic, and other factors on efficiency of growth. The model of Black et al. (1986) includes a large number of factors that determine swine efficiency, so calibration may be prohibitively difficult at this time. The proposed growth model includes the three most important factors involved in the performance of confined growing pigs: sex, genotype, and nutrition. This simplification has been made to better evaluate their impact on swine growth performance while avoiding over-parameterization. Nevertheless, model development is inherently an iterative-learning process in which accuracy and generalization result from doing and redoing. Further model developments will include a more specific estimation of wholesale cuts and organs from body chemical composition, the evaluation of protein quality from the dietary amino acids composition, a more mechanistic estimation of voluntary feed intake, the effects of climate and housing on feed intake and growth efficiency, and so on. Excluding Black’s model, other published pig models simulate growth within the weight interval of 20 to 100 kg. Like the proposed model, these models target many important aspects related to the physiological use of feed
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PIG GROWTH MODEL
resources for maintenance and growth of body lean and fat. The main assumption of these related models is centered on the fact that potential protein accretion in pigs is constant within the modeled interval. However, the model described herein simulates pig growth over a larger time interval and provides a mechanistic approach to simulate protein growth. The interest in protein growth and its characteristics is fundamental for evaluating swine production systems. In fact, protein is the principal contributor to carcass lean, which is the most valuable component of the pig's body. Implications
A computer simulation model was developed to predict growth and body composition of growing pigs. The prediction equations incorporate the interaction of performance potentials, due to genetics and other factors, with the amounts and characteristics of nutrients in the growing and finishing diets. This model facilitates synchronizing one's feeding program with the performance potential of pigs to maximize lean growth perfonnance by controlling diet input. Therefore, it should help reduce costs due either to excessive dietary nutrients or to excessive fat deposition. Literature Cited ARC. 1981. The Nutrient Requirements of Pigs. Commonwealth Agricultural Bureaux, Slough, UK. Baldwin, R L. 1976. Principles of modeanimal systems. Proc. N.Z. Soc. Anim. Prod. 36:128. Baldwin, R. L. and J. L. Black. 1979. Simulation of the effects of nutritional and physiological status on the ''an tissues: description and evaluagrowth of tion of a computer program. CSIRO Aust. Anim. Res. Lab. Tech. Paper No. 6. p 1. Bladc, J. L., R. G. Campbell, I. H. Williams, K. J. James and G. T. Davies. 1986. Simulation of energy and amino acid utilization in the pig. Res. Dev. Agric. 3:121. Burleigh, I. G. 1980. Growth curves in muscle nucleic acid and protein: problems of interpretation at the level of the muscle cell. In: T. J. Lawrence (Ed.) Growth in Animals. p 101. Butterworths, London. Cam, J. R,K.N. Boorman and D J A . Cole. 1977. Nitrogen retention in the pig. Br. J. Nutr. 37143. Dent, J. B. and M. J. Blaclde. 1979. Systems Simulation in Agriculture. Applied Science Publishers, London. Ezekwe, M.0. and R J. Martin. 1975. Cellular characteristics of skeletal muscle in selected strains of pigs and mice and the unselected conmls. Growth 39:95. Fuller, M. F. and A. W. Boyne. 1972. The effects of environmentaltemperatureon the growth and m e t a h lism of pigs given different amounts of feed. 2. Energy
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metabolism. Br. I. Nutr. 28:373. Gilbreatb, R L. and J. R. Trout. 1973. Effects of early postnatal dietary protein reshiction and repletion on porcine muscle growth and composition. J. Nutr. 103: 1637. Giles,L. R., E. S. Batterham and E. B. Dettmana 1986. Amino acid and energy interactions in growingpigs. 2. Effects of food intake, sex and live weight on responsesto lysine concentrationin barley-based diets. Anim. Prod. 42:133. Houpt, T. R. 1986. Physiologic controls of ingestive behavior in pigs. In: M. E. Tumbleson (Fkl.) Swine in BiomedicalResearch. p 943. Plenum Press, New York Kielanowski, J. 1966. Energy and protein metabolism in growing pigs. In: 9th Int. Cong. Anim. Rod., Edinburgh. p 85 (Abstr.). Oliver and Boyd, Edinburgh. Kielanowski, J. 1976. The chemical composition of the liveweight gain and the performance of growing pigs. Livest. Prod. Sci. 3:257. Kotarbinska, M. 1969. Bad& and Pnemiana Energii u Rosnacych Swin. Instytut Zootechniki, Krakow, Wydawnictwa Wlasne, No. 238, Wroclaw. p 68. Millward, D. J., P. J. Garlick, R.J.C. Stewart, D. 0. Nnanyelugo and J. C. Waterlow. 1975. Skeletalmuscle growth and protein turnover. Biochem. J. 150 235. Moughaq P. J. and W. C. Smith. 1984. Predictionof dietary protein quality based on a model of the digestion and metabolism of nitrogen in the growing pig. N.Z. J. Agric. Res. 27501. Moughan, P. J., W. C. Smith and G. Pearson. 1987. Description and validation of a model simulating growth in the pig (20-90 kg liveweight). N.Z. J. Agric. Res. 30481. NRC. 1987. Predicting Feed Intake of Food-Producing Animals. National Academy Press, Washington, DC. Oltjen, J. W., A. C. Bywater and R L. Baldwin 1985. Simulationof normal protein accretion in rats. I. Nutr. 11545. Oltjeq J. W., A. C. Bywater and R. L. Baldwin. 1986a Evaluation of a model of beef cattle growth and composition. J. Anim. Sci. 62:98. Oltjen, J. W., A. C. Bywater, R. L. Baldwin and W. N. Garrett. 1986b. Development of a dynamic model of beef cattle growth and composition. J. Anim. Sci. 62: 86. Pomar. C., D. L. Harris and F. Minvielle. 1991. Computer Simulation Model of Swine Production Systems: II. ModeBody Composition and Weight of Female Pigs, Fetal Development, MilkProductionand Growth of Suckling Pigs. J. Anim. Sci. 69:1489. Powell, S. E. and E. D. Aberle. 1975. Cellular growth of skeletal muscle in swine differing in muscularity. J. Anim. Sci. 40:476. Rook, A. J., M. Ellis, C. T. Whittemoreand P. Phillips. 1987. Relationships betweenwhole-body chemical composition, physically dissected carcass parts and backfat measurements in pigs. Anim. Rod. 44:263. SAS. 1985. SAS User's Guide: Statistics. SAS Inst., Inc., Gary, NC. Stickland,N. C.,E. M. WiddowsonandG. Goldspink. 1975. Effects of severe. energy and protein deficiencies on the fibres and nuclei in skeletal muscle of pigs. Br. J. Nutr. 34421. Taylor, St. C. S. 1980. Genetic size-scahg rules in animal growth. Anim. Rod. 30161. Tess, M. W., G. L. Bennett and G. E. Dickerson. 1983.
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