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Modeling stochasticity: Dealing with populations rather than individual pigs

C. Pomar^*,2, I. Kyriazakis, G. C. Emmans and P. W. Knap

^* Dairy and Swine Research and Development Centre, Agriculture and Agri-Food Canada, Lennoxville, Quebec, Canada J1M 1Z3; and Animal Nutrition and Health Department, Scottish Agricultural College, West Mains Road, Edinburgh, EH9 3JG, Scotland, UK; and and PIC International Group, Schleswig, Germany

	Abstract

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Pig production efficiency is the result of the responses of individual animals. However, experimental results are usually interpreted on the basis of mean animal responses with little emphasis given to variation around the means. Animals with different genetic potentials may respond differently to treatments, which makes it difficult to translate average population responses into either individual animal responses or across populations having different variation between animals. Nutritional theories that form the basis of current pig models are all at the level of individual animals. The problem of how to integrate across individuals to obtain population predictions is rarely addressed. To illustrate the effect of between-animal variation on population responses to dietary treatments, a pig growth model that predicts voluntary feed intake from parameters that predict the potential rates of protein and lipid retention was used. Feed intake is limited only by the ability of pigs to lose heat. Maximum heat production was set to always be that of a pig growing to its potential on a standard, balanced diet. An individual animal is defined by assigning values to three genetic parameters: protein weight at maturity, the ratio of body lipid-to-protein at maturity and a rate parameter. The model was made stochastic by assigning variation to these parameters. Population responses to increasing levels of available protein intake indicated that the linear-plateau model used to represent protein responses for an individual pig is compatible with the curvilinear response observed in experiments on populations. Increasing the time over which individual animal responses were measured also increases the curvilinearity of the response. Variation between animals has little effect on population feed intake, but it decreased population protein deposition rate, daily gain, and feed conversion ratio. It is concluded that mathematical models designed to simulate populations responses to treatments need to integrate the effect of population variation on growth and performance.

Key Words: Genetic Variation • Growth • Protein • Simulation Models

	Introduction

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The efficiency of pig production systems results from the efficiency of individual animals (Knap, 1995). However, reported research results give only rudimentary information about the variation observed between animals. Results are mainly interpreted as average responses to treatments with little emphasis given to the variation around means. This variation may be essential in the understanding of the biological mechanisms implicated in the response of populations to treatments. Examples of this are the impact of variation on population protein efficiencies and growth performance (Pomar, 1995; Ferguson et al., 1997), on thermoregulatory maintenance requirements (Knap, 1999, 2000a) and nutrient requirements (Pomar, 1995; Leclercq and Beaumont, 2000). Several mathematical models have been developed for a variety of applications and species, such as growing pigs (Whittemore and Fawcett, 1976; Black et al., 1986; Moughan et al., 1987; Pomar et al., 1991a; Ferguson et al., 1994; Knap, 2000a) among others. Model development evolves from empirical models to mechanistic ones in which biological principles are represented (France and Thornley, 1984). However, these principles are often derived from results obtained on populations of individuals that show phenotypic variation. Population means are then applied to single-animal models. Subsequently, such single animal models, perhaps representing some notional "average" animal, are used to model group-animal responses by assuming that all pigs have equal growth potentials and are at the same stage of growth. However, population responses may differ from individual responses as a result of between-animal variation (Curnow, 1973; Fisher et al., 1973; Pomar, 1995). The objective of this study was to use a pig growth model that predicts voluntary feed intake, performance, and protein and lipid deposition to deal with variation. The aim was to show the impact of between-animal variation on the interpretation of the biological principles represented within the model and the response of populations to various protein intakes.

Model Description
The model predicts voluntary feed intake, body weight, and composition of growing-finishing pigs during the growth period. Diet composition and pig genotype are inputs to the model. In addition, different assumptions about variation are studied. Animals are assumed to have free and continuous access to a single homogenous feed at any one time. The feed contains no toxins and is such that the rate of intake is not limited by the digestive capacity of the pig. The environment is thermally neutral at all times. Under these conditions, the pig is able to eat the amount of a balanced diet that is sufficient to satisfy its nutrient requirements. When the feed is unbalanced in terms of its protein-to-energy ratio, the amount of food eaten is limited by the amount of heat that the pig can lose. Maximum heat loss is set to what the pig would produce were it to be fed on a balanced standard diet. State model variables are actual body masses of protein (Pt) and lipid (Lt). The energy system used was that of Emmans (1994). Euler’s integration method was used to solve the differential equations with an integration step (dt) of 1 d. Rate variables are expressed in daily basis, energy is in megajoules, mass in kilograms, and concentrations in kilogram basis when not explicitly specified in the text.

Feeds are defined in terms of their contents of digestible energy (DEc), crude protein, apparent ileal digestibility, chemical score (ChSc) estimated as the amount of digestible amino acids of the diet that are in an ideal balance, digestible fat (DFc), and total indigestible organic matter content (IOMc). The digestible protein content of a diet (DPc) is calculated as the product of the crude protein content and its apparent ileal digestibility. Balanced digestible protein content (BPc) is calculated as the product of DPc and ChSc. Effective energy content (EEc) of the diet is the difference between DEc of the diet and losses resulting from the eaten diet (Emmans, 1994). In this energy system, energy losses from fermentation are considered negligible. The EEc of the feed is calculated from equations relating DEc and EEc to the chemical composition of the feed (see below). Although the net and effective energy systems are fundamentally different, both systems can be used successfully in mathematical models predicting the metabolic utilization of feed energy (Rivest et al., 1996). The model predicts, on a daily basis, body composition, protein and lipid deposition, and feed intake at any age and body condition. The model is based on that used by Knap (1999, 2000a), which includes some elements of the model of Moughan and Smith (1984), and uses the rules proposed by Emmans (1988, 1994, 1997) to predict feed intake, as well as the partitioning rules and other elements suggested by Kyriazakis and Emmans (1995, 1999). The basic rules driving protein and lipid deposition, simulating energy utilization, and predicting feed intake are similar to those used by Wellock et al. (2003).

A pig is genetically characterized by three parameters, which are the mature total body protein weight (Pm), its inherent fatness represented by the lipid-to-protein ratio at maturity (LPRm), and the maturing rate constant (B). Emmans (1988, 1997) and Ferguson et al. (1994) have presented the detailed theoretical description of this model. In this model, Pt and Lt define the actual state of the animal. Total body water and ash are quantified following Emmans and Kyriazakis (1999). Total body weight is the sum of the fill (gut and bladder) and the chemical constituents of the empty body, which are the protein, lipid, ash, and water masses.

The intrinsic potential for protein deposition rate (dPd) is assumed to follow the derivative of a Gompertz growth function (Emmans and Kyriazakis, 1999, 2001) as follows.

The potential rate of protein deposition is estimated from two parameters (B and Pm) that are assumed specific to each pig and from its current protein weight. An implication is that compensatory protein growth is not allowed. Any delay in protein retention alone will simply decrease the retention of the other body constituents (namely, lipid, ash, and water) and will delay the attainment of body’s mature size. The above framework is similar to the one used by Ferguson et al. (1994, 1997), Knap (2000a), and Wellock et al. (2003).

Associated with Pt is body lipid mass (Lt), which is predicted from LPRm and Pm. The value of the allometric coefficient b1 (Emmans, 1988) is calculated from LPRm only. The coefficient b1 and Lt are represented as follows.

To minimize integration errors, the desired lipid deposition rate (dLd) is then calculated by difference between Lt weights at times t + dt and t. The dPd and dLd are combined with estimations of protein and energy requirements to predict the unconstrained desired feed intake in a thermally neutral environment. Thus, under nonlimiting conditions, pigs will eat daily an unbalanced feed, until the requirement for the more-limiting nutrient is met. All nutrients other than the more-limiting one will be consumed at least to adequacy. The daily effective energy (EE_req) and ideal protein requirements (P_req) are calculated as follows.

where 50 and 56 are the effective energy costs (MJ/kg) of protein and lipid retention, respectively, and e_p is the efficiency of using ideally balanced protein for protein deposition. Here, EE_maint is the energy, and P_maint the ideal protein, requirements for maintenance calculated as suggested by Emmans (1994). Thus, when energy is the first-limiting nutrient, the desired feed intake (dFIe) is estimated as follows.

Similarly, when protein (or any essential amino acid) is the first limiting nutrient, dFIp will be that needed to meet its requirement:

A feed is balanced, by definition, when dFIe = dFIp. Otherwise, the desired feed intake (dFI) is the maximal value between dFIe and dFIp. Pigs are thus expected to eat extra protein on low-energy feeds and extra energy when feed protein content is the limiting factor. In the first case, pigs are assumed to deaminate any excess protein and to lose its nitrogen and part of its energy in the urine (Emmans, 1994). On low-protein feeds, the energy eaten above the requirement leads to additional lipid retention (Ferguson et al., 1994). On imbalanced feeds, the pig may be either fatter or leaner than it seeks to be. It is assumed that the pig will attempt to return instantly (i.e., within a day) to its normal fatness by reducing or increasing lipid deposition rate. Its desired rate of lipid deposition will then be either below or above the value calculated from its genetic potential (Kyriazakis and Emmans 1999). However, the ability of the pig to achieve its desired normal fatness will depend on the composition of the feed and its capacity to lose heat (see below). This compensatory lipid growth is in agreement with previous experimental results (Tullis et al., 1986; Kyriazakis et al., 1991).

The small number of parameters (Pm, LPRm, and B) used to characterize the animal’s genetic potentials for growth of protein and lipid, and the ability to predict voluntary feed intake, are attractive when the relationship between growth potentials and feed intake is of interest. The approach, also used in another form by Black et al. (1986), differs from those used in many other simulation models in which feed intake is either predicted from simple relationships or treated as input. In these latter models, the pig’s appetite needs to be characterized jointly with the genetic potential for protein deposition.

It is possible that the dFI needed to satisfy the requirement for the first-limiting nutrient (energy or the first-limiting amino acid in this model) cannot be achieved. This is due to constraints arising either from the feed that is offered or from the environment in which the animal is kept. In the first case, the feed constraint may be represented by its volume in terms of dry or organic matter intake (Black, et al., 1986; Ferguson et al., 1994; Pomar and Matte, 1995; Whittemore et al., 2001a) or feed bulkiness as measured by its water-holding capacity (Kyriazakis and Emmans, 1995; Whittemore et al., 2001c,d). For the purpose of present study, which is to investigate the effect of between-animal variation on pig population responses, the effect of feed bulkiness is avoided and no direct feed constraint is allowed.

In the model, pigs are assumed to be in thermoneutral conditions at all times and no thermoregulation mechanisms were incorporated into the model. The capacity to lose heat when unbalanced diets are offered is set to that predicted on a balanced feed. A balanced diet contains 12.6 MJ/kg of effective energy, a protein-to-energy ratio that meets the requirement and a protein balance and chemical composition similar to the one suggested by NRC (1998) for 20- to 50-kg BW pigs. The contents of IOMc and DFc are 0.12 and 0.03 kg/kg, respectively. The digestible energy content is 14.2 MJ/kg. The ratio between EE_req and P_req is the optimal ratio of the reference diet, from which optimal balanced protein content can be estimated as follows.

The relationship between DEc and EEc is

where 10.3 = 5.63 + 4.67. The value of 5.63 is the energy contained in the nitrogenous compounds excreted in the urine. The values of 3.8 and 4.67 are the heat productions associated with organic matter defecation and protein excretion, respectively (Emmans, 1994). It was assumed that 90% of DFc can be retained in the pig’s body as body lipid and 12 is the adjustment to account for the difference in heat increment of forming lipid from lipid and nonlipid dietary sources (Emmans, 1994). The ME dietary content (MEc), corrected to zero protein deposition, can then be estimated as

The amount of heat produced (H, MJ/d) by the reference pig, which is also the maximal amount of heat that any simulated pig can produce, is estimated as

where FI is the actual feed intake and hp and hl are the heat of combustion of the retained protein and lipid, respectively.

Heat loss will limit the voluntary feed intake of pigs on an unbalanced diet, or where body lipid needs to be increased following a previous energy deprivation. Heat loss is independent of the composition of the feed given and of the body fatness of the pig.

	Generating Populations

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As outlined above, a pig is described in this model in terms of only Pm, LPRm, and B; Gompertz functions are used to determine dPd and dLd. Between animals of the same population, there is likely to be a negative correlation between the values of B and Pm (Emmans 1988; Knap 2000b). Therefore, B and Pm cannot be simulated as being independent and their covariation needs to be estimated. To avoid this, Emmans and Fisher (1986) scaled the parameter B according to Taylor’s rule (Taylor, 1968, 1980) as follows.

where B* is the scaled value of B. The values of B*, Pm, and LPRm are then uncorrelated (Ferguson et al., 1997). Two genetic lines are used in the following simulations. The first, probably a traditional pig line, was that characterized by Ferguson and Gous (1993) and Ferguson et al. (1997). Average mean genetic parameters of this line are µPm = 38 kg, µLPRm = 2.5 kg/kg and µB* = 0.0294/d. The second line, which may represent a modern genotype, was characterized by Knap (2000b) from data of van Lunen (1994) collected from 60 female pigs of a synthetic sire line. This synthetic line was identified by Knap (2000b) as the most advanced meat-type pig genotype available in the early 1990s, which may represent pigs used today in well-managed piggeries. Mean genetic parameter values defining this line are µPm = 32 kg, µLPRm = 1.2 kg/kg, and µB* = 0.04079/d. Because data to estimate these parameters are scarce and it is difficult to determine their variability by experimentation, these authors estimated parameter variation by simulation as outlined by Knap (2000b) and Knap et al. (2002). Their results indicated that the genetic coefficients of variation for B*, Pm, and LPRm were 0.02, 0.10, and 0.15, respectively for the traditional line and 0.03, 0.07, and 0.15, respectively for the modern line. For each simulated pig within a population, values for B*, Pm, and LPRm are drawn at random, uncorrelated, and normally distributed (Emmans and Fisher, 1986; Ferguson et al., 1997; Knap, 2000a). The values that characterize the animals are drawn before each simulation and maintained throughout their simulated life. When comparing populations with different between-animal genetic variation, five populations are generated having 0, 0.5, 1, 1.5, and 2 times the estimated genetic variation of the above reference populations. The multiplier is 0 in the case of a single animal. Because the nutritional and the simplified thermal environment affects the expression of the genetic potential of the pig, generating genetic variation on B*, Pm, and LPRm simulates phenotypic variation. Therefore, pigs of the same genetic population but reared in different environments may show different growth curves and variances. Population values were obtained by simulating 2,500 pigs, ensuring that variances were stable between runs.

	Model Results and Discussion

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The model’s mathematical and logical properties were checked for consistency throughout development. The mathematical stability of the model was evaluated at different integration steps to ensure stability. Because the relationships driving protein and lipid accretion and predicting feed intake are similar to those used by Ferguson et al. (1994, 1997), Knap (2000a), Knap and Jorgensen (2000), and Kyriazakis and Emmans (1999), the model did not need to be validated in that respect. The main difference from previous models is the mechanism used to constrain feed intake when pigs are fed with unbalanced diets through setting a maximum to heat loss.

Voluntary Feed Intake
The proposed model predicts voluntary feed intake based on the animal’s energy and protein requirements and the composition of the offered diet. Depending on the pig’s fatness and the composition of the diet, feed intake may be limited by the amount of heat that the pig is able to dissipate into the environment.

Model predictions of feed intake were evaluated by comparing them to the predictions of several published relationships between feed intake and live body weight. Feed intake predictions based on the NRC (1998) and Patterson and Walker (1989) relationships are shown graphically (Figure 1) because most of the other published predictions lie between them (Whittemore et al. 2001a). The NRC (1998) relationship is proposed for a combination of barrows and gilts, which can be adjusted upward for castrates and downward for intact males and females. The model was set up to predict the voluntary feed intake of the traditional and the modern genetic lines, both fed successively on three feeds containing 14.23 MJ DEc/kg and having all other nutrients in excess, including lysine and protein. Feeds were formulated according to the NRC (1998) recommendations for the 30- to 90-kg BW interval. Model predictions were adjusted to account for 5% feed wastage.

View larger version (13K): [in this window] [in a new window]   Figure 1. Predicted voluntary feed intake over the 30- to 90-kg BW of the traditional (—•—) and modern(——) simulated pig genetic lines and according to Patterson and Walker (1989) (––) and NRC (1998)(––) prediction equations.

When predicting ADFI, most of the proposed relationships use weight or protein masses to predict the pig’s daily intake. Therefore, these equations need to be tailored to each genotype and periodically adjusted to account for genetic changes. However, the modeling framework proposed here is much more flexible than these empirical relationships because it can predict ADFI of pigs according to their genetic growth potentials and actual growth conditions.

The Effect of Variation Between Pigs on Protein Deposition
The amount of protein (amino acids) required to satisfy the total needs of a growing pig is the sum of the requirements for maintenance and retention, the latter corrected by the efficiency of utilization of the absorbed protein (or amino acids). The efficiency (e_p) with which the absorbed protein above maintenance is used for protein deposition is defined as the proportion of the additional ingested ideal protein, which is retained when protein is limiting and when energy is not limiting. Practically, e_p can be estimated by measuring the increase in protein deposition in pigs fed with increasing levels of protein in conditions under which this nutrient is always supplied below requirements. The relationship between protein retention and supply has been represented by a constant efficiency (Zhang et al., 1984), as two-phase linear (Taylor et al., 1979; Batterham et al., 1990), as curvilinear (ARC, 1981; Moughan, 1989; Fuller and Garthwaite, 1993), or by a linear plateau (Campbell et al., 1984). Furthermore, Bikker (1994) indicated that the goodness of fit of these models was quite similar, and, although the linear-plateau model tended to show a better fit, no firm conclusion could be drawn about the degree of curvature of the transition between the linear and plateau phases. Analogous linear-plateau models are also proposed to represent the responses between protein retention and energy supply (Black et al., 1986; NRC, 1998; Whittemore et al., 2001b).

The linear-plateau is frequently the preferred model (Whittemore et al. 2001b). This model was suggested by Black and Griffiths (1977) in sheep and Campbell et al. (1984) in pigs and applied to pigs by Whittemore and Fawcett (1976) and many other authors. However, other authors have suggested that e_p is not constant but decreases gradually as protein or energy intakes increase (ARC, 1981). However, the adequacy of the linear-plateau model is not always supported by experimental results and some concerns have been raised in relation to its appropriateness when representing pig populations (Baker, 1986; Moughan, 1999). Curnow (1973), Fisher et al. (1973), Fuller and Garthwaitte (1993), and Pomar (1995) suggested that a curvilinear response of protein deposition to protein intake, at the level of the population, might result from variation in individual animal responses. In this section, the effect that between-animal genetic variation may have on the evaluation of e_p when protein intake increases for populations with different degrees of heterogeneity was studied.

Populations of 50-kg BW modern pigs were fed for 1 d with 11 diets, all having 0.20 kg/kg dietary crude protein and the same ileal digestibility. The chemical score (ChSc) (i.e., protein quality) varied from 0.68 to 0.93. Varying ChSc allowed the pigs to eat the same amount of DPc, but amounts of ideal protein ranged from 212 to 290 g/d. Increases in ChSc may be obtained by adding lysine and other crystalline essential amino acids to give proportions closer to those of an ideal protein. In this exercise, pigs were restrictedly fed at 1.9 kg/d to facilitate the interpretation of the results. For a single 50-kg BW pig fed with the highest ChSc diet, ADG was of 997 g/d and ADPG and ADLG were 181 and 159 g/d, respectively. The pig growth model was constructed assuming that the response to limiting protein follows the linear-plateau model. The response of the population with zero variation is the direct outcome of this assumption (Figure 2). Maximal protein deposition rate is obtained for ChSc > 0.75. The slope of the response represents the marginal efficiency for protein utilization (e_p), whereas the intercept represents the protein requirements for maintenance.

View larger version (23K): [in this window] [in a new window]   Figure 2. Effect of between-animal variation (0 [––], 0.5 [––], 1 [––], 1.5 [–•–], and 2 [––] times the standard coefficient of variation of the population) and balanced protein intake on average daily protein deposition rate of 50-kg pig populations.

The Effect of the Duration of Data Collection Periods on Measurements of Protein Efficiency
Experimental error is a measure of the variation that exists among observations on experimental units treated alike. This variation comes from the inherent variability that exists in the experimental material to which treatments are applied and from the variation resulting from deficiencies in the experimental procedures used (Steel et al., 1997). In previous sections, the problem relating to the inherent variability of the experimental material (i.e., animals) was addressed. In this section, another source of variation that results from the experimental procedures used when measuring protein efficiency is considered. A fact often neglected is that an animal’s response to nutrient intake may change over the interval during which data are collected. In particular, when measuring protein deposition during a specific interval length, it should be noted that this variable might be changing over time.

The effect of length of the collection period can be illustrated by simulating the response of a single pig to increases in balanced protein intake. In this case, the modern genotype was fed with the 11 diets used in the previous section and data were collected for 1, 7, 14, 21 or 28 d. Pigs were restrictedly fed at 1.9 kg/d to simplify the interpretation of the results.

As in the previous section, maximal protein deposition was obtained for ChSc = 0.75. However, when the length of the period of data collection was increased from 1 to 28 d, the point at which protein deposition was maximal was greater, and a curvilinear transition zone appeared between the two linear phases with constant e_p (i.e., e_p = 0.82 and e_p = 0) (Figure 3). Values shown in this figure are average values for these collection periods. Because pigs are still increasing ADPG during these periods, maximal protein deposition also increases with the length of the collection period. Similarly, protein requirements for maintenance increases with time, and thus with the length of the collection period, which explains the fact that pigs fed with equal amounts of protein will decrease ADPG as the collection period increases. However, e_p remains unchanged as indicated by the fact that the initial slopes of the responses are similar. But what should be noted is that for the single simulated pig in this exercise, the transition zone between the two linear phases increases with the duration of the collection period.

View larger version (18K): [in this window] [in a new window]   Figure 3. Effect of data collection length (1 [––], 7[––], 14 [––], 21 [–•–], and 28 [––] d of collection) and balanced protein intake on average daily protein deposition rate on 50-kg BW pigs.

The Effect of Variation Between Animals on Growth Responses
From results presented in the previous sections, it should be expected that population responses to increases in ideal protein supply would be affected both by their genetic variation and by the length of the growing interval. To study the effect of between-animal variation on growth performance and intake, the 11 diets and the five modern pig populations used in the previous sections were fed ad libitum from 25 to 90 kg BW.

Average results across dietary treatments ranged from 1.94 to 1.89 for ADFI, from 965 to 906 g/d for ADG, from 175 to 159 g/d for ADPG, and from 171 to 156 g/d for ADLG. Dietary treatments had little effect on standard deviations (STD) for these variables, but they increased with the genetic population variation. The maximum simulated STD values for populations having genetic variations of 0.5, 1, 1.5, and 2 times the estimated mean between-animals genetic variation were estimated. They were as follows: 46, 91, 136, and 182 g/d for ADFI; 28, 56, 86, and 117 g/d for ADG; 4.6, 9.2, 13.9, and 19.6 g/d for ADPG; 9.3, 18.5, 28.4, and 37.0 g/d for ADLG. For most of these variables, maximal STD was obtained at the higher protein intakes.

On average, ADFI is little affected by dietary treatments although minimum values are obtained at low ChSc (results not shown). However, the effect of varying ChSc on ADPG and feed conversion ratio is more striking (Figures 4 and 5). Pigs were fed with a single feed throughout the growth period. For most of the pigs, this feed did not provide enough protein during the initial phase of growth but protein was oversupplied afterward. The extent of each of these two growth phases is determined by the genetic characteristics of the pig. For lean pigs, which have higher nutrient requirements, the initial growth phase is longer than for fatter pigs and increasing ChSc will reduce the length of this initial phase and increase the length of the latter. It is unusual and profitless to feed pigs to satisfy the maximal nutrient requirements of the overall growth period (Jean dit Bailleul et al., 2000), and, for most of the pigs of a herd, these two phases should be expected.

View larger version (20K): [in this window] [in a new window]   Figure 4. Effect of between-animal variation (0 [––], 0.5 [––], 1 [––], 1.5 [–•–], and 2 [––] times the standard coefficient of variation of the population) on average daily protein deposition rate of pigs (25- to 90-kg BW) fed with dietary protein of different chemical scores.

View larger version (20K): [in this window] [in a new window]   Figure 5. Effect of between-animal variation (0 [––], 0.5 [––], 1 [––], 1.5 [–•–], and 2 [––] times the standard coefficient of variation of the population) on average feed conversion ratio of pigs (25 to 90 kg BW) fed with dietary protein of different chemical scores.

The simulated phenotypic variation resulted from the interaction between the generated genetic variation and the nutritional and the simplified thermal environment of the pig. The responses of real populations to a given diet and environment are not only the result of variations in the genetic characteristics of the pig, but also the result of variations in nutrient composition, the environmental conditions in which animals are raised, and others. These other nongenetic sources of variation are difficult to simulate mechanistically in a proper way and have been avoided in this and previous stochastic models (Pomar et al., 1991b; Pomar, 1995; Ferguson et al., 1997; Knap, 2000a).

	Implications

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Results indicate that the linear-plateau model used to represent the response to protein supply in growing pigs is consistent with the curvilinear response that may be observed in experimental conditions. The curvilinear response may result from the variation between experimental animals and from limitations on the experimental procedures used. Models designed to simulate population responses need to integrate the effect of population variation on growth performance. The results show that the response of a population to treatments will differ in magnitude and shape from that assumed for an individual animal. Stochastic models that properly represent populations are therefore needed. Allowing for population variation is essential when models are to be used to predict nutrient requirements or to economically optimize swine production systems. For these applications, recommendations are particularly sensitive to the magnitude and shape of the model response as was found here.

	Footnotes

 
¹ The authors are grateful to C. T. Whittemore for his comments during the development of this project and to F. Sandberg for his assistance on manuscript preparation.

² Correspondence: P.O. Box 90, 2000, Route 108 East (phone: 819-565-9171; fax: 819-564-5507; E-mail: pomarc{at}agr.gc.ca).

Received for publication August 23, 2002. Accepted for publication April 24, 2003.

	Literature Cited

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ARC. 1981. The Nutrient Requirements of Pigs. Commonwealth Agricultural Bureaux, Farnham Royal, UK.

Baker, D. H. 1986. Problems and pitfalls in animal experiments designed to establish dietary requirements for essential nutrients. J. Nutr. 116:2339–2349.

Batterham, E. S., L. M. Andersen, D. R. Baigent, and E. White. 1990. Utilization of ileal digestible amino acids by growing pigs: effect of dietary lysine concentration on efficiency of lysine retention. Br. J. Nutr. 64:81–94.[Medline]

Bikker, P. 1994. Protein and lipid accretion in body components of growing pigs: effects of body weight and nutrient intake. Ph.D. Thesis, University of Wageningen, The Netherlands.

Black, J. L., R. G. Campbell, I. H. Williams, K. J. James, and G. T. Davies. 1986. Simulation of energy and amino acid utilisation in the pig. Res. Develop. Agric. 3:121–145.

Black, J. L., and D. A. Griffiths. 1975. Effects of live weight and energy intake on nitrogen balance and total N requirement of lambs. Br. J. Nutr. 33:399–413.[Medline]

Campbell, R. G., M. R. Taverner, and D. M. Curic. 1984. Effect of feeding level and dietary protein content on the growth, body composition and rate of protein deposition in pigs growing from 45 to 90 kg. Anim. Prod. 38:233–240.

Curnow, R. N. 1973. A smooth population response curve based on an abrupt threshold and plateau model for individuals. Biometrics 29:1–10.

Emmans, G. C. 1988. Genetic components of potential and actual growth. Pages 153–181 in Animal Breeding Opportunities. R. B. Land, G. Bulfield, and W. G. Hill, ed. Br. Soc. Anim. Prod. occasional publication 12, Br. Soc. Anim. Prod., Midlothian, Scotland, UK.

Emmans, G. C. 1994. Effective energy: a concept of energy utilisation applied across species. Br. J. Nutr. 71:801–821.[Medline]

Emmans, G. C. 1997. A method to predict the food intake of domestic animals from birth to maturity as a function of time. J. Theor. Biology 186:189–199.

Emmans, G. C., and C. Fisher. 1986. Problems in nutritional theory. Pages 9–39 in Nutrient Requirements of Poultry and Nutritional Research. C. Fisher, and K. N. Boorman, ed. Butterworths, London.

Emmans, G. C., and I. Kyriazakis. 1999. Growth and body composition. Pages 181–197 in a Quantitative Biology of the Pig. I. Kyriazakis, ed. CAB International, Wallingford, Oxon, UK.

Emmans, G. C., and I. Kyriazakis. 2001. Consequences of genetic change in farm animals on food intake and feeding behaviour. Proc. Nutr. Soc. 60:115–125.[Medline]

Ferguson, N. S., and R. M. Gous. 1993. Evaluation of pig genotypes. I. Theoretical aspects of measuring genetic parameters. Anim. Prod. 56:233–243.

Ferguson, N. S., R. M. Gous, and G. C. Emmans. 1994. Preferred components for the construction of a new simulation model of growth, feed intake and nutrient requirements of growing pigs. S. Afr. J. Anim. Sci. 24:10–17.

Ferguson, N. S., R. M. Gous, and G. C. Emmans. 1997. Predicting the effects of animal variation on growth and food intake in growing pigs using simulation modelling. Anim. Sci. 64:513–522.

Fisher, C., T. R. Morris, and R. C. Jennings. 1973. A model for the description and prediction of the response of laying hens to amino acid intake. Br. Poult. Sci. 14:469–484.[Medline]

France, J., and J. H. M. Thornley. 1984. Mathematical Models in Agriculture. Butterworths, London, UK.

Fuller, M. F., and P. Garthwaite. 1993. The form of response of body protein accretion to dietary amino acid supply. J. Nutr. 123:957–963.

Jean dit Bailleul, P., J. F. Bernier, J. van Milgen, D. Sauvant, and C. Pomar. 2000. The utilization of prediction models to optimize farm animal production systems: The case of a growing pig model. Pages 379–392 in Modelling Nutrient Utilization in Farm Animals. J. P. McNamara, J. France and D. Beever, ed. CAB International 2000, Wallingford, Oxon, UK.

Knap, P. W. 1995. Aspects of stochasticity: variation between animals. Pages 165–172 in Modelling Growth in the Pig. P. J. Moughan, M. W. A. Verstegen, and M. I. Visser-Reyneveld, ed. Wageningen Press, Wageningen, The Netherlands.

Knap, P. W. 1999. Simulation of growth in pigs: evaluation of a model to relate thermoregulation to body protein and lipid content and deposition. Anim. Sci. 68:655–679.

Knap, P. W. 2000a. Stochastic simulation of growth in pigs: Relations between body composition and maintenance requirements as mediated through protein turn-over and thermoregulation. Anim. Sci. 71:11–30.

Knap, P. W. 2000b. Time trends of Gompertz growth parameters in ‘meat-type’ pigs. Anim. Sci. 70:39–49.

Knap, P. W., and H. Jorgensen. 2000. Animal-intrinsic variation in the partitioning of body protein and lipid in growing pigs. Anim. Sci. 70:29–37.

Knap, P. W., R. Roche, K. Kolstad, P. Luiting, and C. Pomar. 2002. Characterization of pig genotypes. J. Anim. Sci. 80(Suppl. 1):174 (Abstr.).

Kyriazakis, I., and G. C. Emmans. 1995. The voluntary feed intake of pigs given feeds based on wheat bran, dried citrus pulp and grass meal, in relation to measurements of feed bulk. Br. J. Nutr. 73:191–207.[Medline]

Kyriazakis, I., and G. C. Emmans. 1999. Voluntary food intake and diet selection. Pages 229–248 in a Quantitative Biology of the Pig. I. Kyriazakis, ed. CAB International, Wallingford, Oxon, UK.

Kyriazakis, I., C. Stamataris, G. C. Emmans, and C. T. Whittemore. 1991. The effects of food protein on the performance of pigs previously given food with low or moderate protein contents. Anim. Prod. 52:165–173.

Leclercq, B., and C. Beaumont. 2000. Etude par simulation de la réponse des troupeaux de volailles aux apports d’acides aminés et de protéines. INRA Prod. Anim. 13:47–59.

Moughan, P. J. 1989. Simulation of the daily partitioning of lysine in the 50 kg liveweight pig: A factorial approach to estimating amino acid requirements for the growth and maintenence. Res. Develop. Agric. 6:7–14.

Moughan, P. J. 1999. Protein metabolism in the growing pig. Pages 299–331 in a Quantitative Biology of the Pig. I. Kyriazakis, ed. CAB International, Wallingford, Oxon, UK.

Moughan, P. J., and W. C. Smith. 1984. Prediction of dietary protein quality based on a model of the digestion and metabolism of nitrogen in the growing pig. N. Z. J. Agric. Res. 27:501–507.

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. 30:481–490.

NRC. 1998. Nutrient Requirements of Swine. (10th ed.). National Academy Press, Washington, DC.

Patterson, D. C., and Walker, N. 1989. Observations of voluntary food intake and wastage from various types of self-feed hopper. Pages 114–116 in the Voluntary Food Intake of Pigs. J. M. Forbes, M. A. Varley, and T. L. J. Lawrence, ed. Br. Soc. Anim. Prod. occasional publication no. 13. Br. Soc. Anim. Prod., Midlothian, Scotland, UK.

Pomar, C. 1995. A systematic approach to interpret the relationship between protein intake and deposition and to evaluate the role of variation on production efficiency in swine. Pages 361–375 in Proc. of the Symposium on Determinants of Production Efficiency in Swine. Can. Soc. Anim. Sci., Ottawa, Ont. Canada.

Pomar, C., D. L. Harris, and F. Minvielle. 1991a. Computer-simulation model of swine production systems. 1. Modeling the growth of young-pigs. J. Anim. Sci. 69:1468–1488.[Abstract]

Pomar, C., D. L. Harris, P. Savoie, and F. Minvielle. 1991b. Computer-simulation model of swine production systems. 3. A dynamic herd simulation-model including reproduction. J. Anim. Sci. 69:2822–2836.[Abstract]

Pomar, C., and J. J. Matte. 1995. Effet de l’incorporation d’écailles d’avoine dans l’aliment servi volonté sur le rationnement en nutriments, la prise alimentaire et les performances de croissance du porc en finition. Journ. Rech. Porcine Fr. 27:231–236.

Rivest, J., P. Jean dit Bailleul, and C. Pomar. 1996. Incorporation of a net energy system into a dynamic pig growth model. J. Anim. Sci. 74(Suppl. 1):196. (Abstr.).

Steel, R. G. D., J. H. Torrie, and D. A. Dickey. 1997. Principles and Procedures of Statistics: A Biometrical Approach. 3rd ed. McGraw-Hill, New York.

Taylor, S. C. S. 1968. Time taken to mature in relation to mature weight for sexes, strains and species of domesticates mammals and birds. Anim. Prod. 10:157–169.

Taylor, S. C. S. 1980. Genetic size-scaling rules in animal growth. Anim. Prod. 30:161–165.

Taylor, A. J., D. J. A. Cole, and D. Lewis. 1979. Amino acid requirements of growing pigs. 1. Effects of reducing protein level in diets containing high levels of lysine. Anim. Prod. 29:327–338.

Tullis, J. B., C. T. Whittemore, and P. Phillips. 1986. Compensatory nitrogen retention in growing pigs following a period of nitrogen deprivation. Br. J. Nutr. 56:259–267.[Medline]

van Lunen, T. A. 1994. A study of the growth and nutrient requirements of highly selected pigs. Ph.D. Thesis, University of Nottingham, UK.

Wellock, I. J., G. C. Emmans, and I. Kyriazakis. 2003. Modelling the effects of the thermal environment and dietary composition on pig performance: Model logic and concepts. Anim. Sci. (in press).

Whittemore, C. T., and R. H. Fawcett. 1976. Theoretical aspects of a flexible model to simulate protein and lipid growth in pigs. Anim. Prod. 22:87–96.

Whittemore, C. T., D. M. Green, and P. W. Knap. 2001a. Technical review of the energy and protein requirements of growing pigs: food intake. Anim. Sci. 73:3–17.

Whittemore, C. T., D. M. Green, and P. W. Knap. 2001b. Technical review of the energy and protein requirements of growing pigs: protein. Anim. Sci. 73:363–373.

Whittemore, E. C., G. C. Emmans, B. J. Tolkamp, and I. Kyriazakis. 2001c. Tests of two theories of food intake using growing pigs. 2. The effect of a period of reduced growth rate on the subsequent intake of foods of differing bulk content. Anim. Sci. 72:361–373.

Whittemore, E. C., I. Kyriazakis, G. C. Emmans, and B. J. Tolkamp. 2001d. Tests of two theories of food intake using growing pigs 1. The effect of ambient temperature on the intake of foods of differing bulk content. Anim. Sci. 72:351–360.

Zhang, Y., I. G. Partridge, H. D. Keal, and K. G. Mitchell. 1984. Dietary amino acid balance and requirements for pigs weaned at 3 weeks of age. Anim. Prod. 39:441–448.

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