Models of pig growth: problems and proposed solutions

LIVESTOCK pREiEEFN

ELSEVIER

Livestock Production

Science 5 1 (1997) 119- 129

Models of pig growth: problems and proposed solutions G.C. Emmans

*,

’

I. Kyriazakis

Genetics and Behauioural Sciences Department, Scottish Agricultural College, Edinburgh, West Mains Road, Edinburgh, EH9 3JG, UK Accepted

17 April 1997

Abstract A system to predict the growth and body composition of a pig from a knowledge of its genotype and diet is one of both scientific and practical interest and concern. Three of the major problems that need to be solved in order to produce such a predictive system are considered here: (i) the prediction of the potential rate of protein retention from a description of the pig and its state; (ii) the prediction of the rates of retention of the two other components of the lipid-free body which are ash and water; (iii) the prediction of the actual rates of retention of protein and lipid from a knowledge of the rate of intake of food and its composition. The existing proposed answers to these problems are described and criticised. We then present what, in our view, are the best solutions currently available. The first problem is solved by the use of the Gompertz growth equation. The second problem is dealt with by allometry but with a better theoretical underpinning. It is proposed that the third problem, i.e., that of predicting the actual rates of retention of protein and lipid, when the rate of protein retention is below the potential rate because of the limiting food supply, can be solved by using a simple rule. The rule is that the marginal material efficiency of using the ideal protein supply above maintenance for growth, is directly proportional to the energy: protein ratio of the food up to a maximum value. Thus the amount of extra protein gained per unit of extra food energy depends only on the amount of extra (ideal) protein supplied with it and is independent of liveweight and of pig genotype. The solutions to the three problems constitute a framework which can be applied to predict the response of a pig to its diet at a time and over time. Given the small number of parameters that need to be evaluated, the framework can be extended to predict the responses of different kinds of pigs to the same diet. Providing that the distributions of the values of the parameters are known, the approach can be adopted to predict the responses of the individuals which comprise a population of pigs to their diet. 0 1997 Elsevier Science B.V. Keywords: Growth;

Pigs; Protein retention;

Protein utilisation;

Simulation

1. Introduction In papers published about twenty years ago, Whittemore (Whittemore and Fawcett, 1974, 1976; Whittemore, 1976) raised a series of problems that needed

* Corresponding author. ’ Originally presented as a meeting paper at the 46th EAAP Annual Meeting-Prague

1995 (P1.2,’ 1.4).

0301-6226/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO301-6226(97)00061-4

models; Growing

pigs

to be solved to construct a pig growth model. These were related to the upper limit to protein retention and to energy use where food intake was known. The problems have turned out to be important ones; Whittemore (1983) and Black et al. (1986) have proposed possible solutions to them. In this paper we deal with three of the major problems that were raised. We will present existing answers, criticise these, and then present, what seem to us to be the

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Livestock Production Science 51 (1997) 119-129

best solutions currently available. The proposed answers are general across genotypes and degrees of maturity. This is appropriate given that Whittemore (1995) has reviewed the history of the problem of constructing pig growth simulation models, and has concluded that “limitations to understanding (of potential tissue accretion and potential nutrient utilisation) are particularly evident in the case of the young growing pig and simulation models are especially limited in their use at this time.” As well as being of practical importance, the field of predicting pig growth and composition raises important scientific problems. The three scientific problems that are dealt with in this paper are: (i) the prediction of the potential rate of protein retention as some function of a description of the pig; (ii> the prediction of the rates of retention of the two other components of the lipid-free body which are ash and water; (iii) the prediction of the actual rates of retention of protein and lipid from a knowledge of the rate of intake of food and its composition. Given that the empty body can be seen as comprising the four components viz. protein, lipid, ash and water (Emmans and Fisher, 1986), all of the three problems can be seen as being needed to be solved in order to solve that of predicting the response of a pig, in terms of the rate of gain of the empty body, and its composition, to its diet. As is characteristic of animal science at its best, the scientific and practical problems turn out to be different aspects of the same thing.

2. Problem 1: the upper limit to protein retention Whittemore and Fawcett (1974), following Kielanowski (1966), pointed out that a pig would probably have some inherent upper limit to the rate at which it could grow protein, and that this needed to be known in order to have a useful model. It was emphasised that pig genotypes would differ in their inherent rate of protein growth and in order to run the model for a particular kind of pig, that kind of pig would need to be sufficiently described. Thorbek (1975) published the results of a large number of N balance experiments made on the pigs in Denmark at that time over a wide range in

liveweight. A polynomial function in metabolic body weight was used to describe the data. She proposed that an upper limit to the rate of protein retention, PR g/d, could be predicted from pig liveweight, W kg, by the function shown in Eq. (l), which is a quadratic in W o.75 as WI.50 = (WO.75)2: PR = 9.25W”.75 - 0.166W’,50

g/d

(1)

While it is not particularly elegant, Eq. (1) does have some of the properties expected of a growth function: (i) PR tends to zero as W tends to zero; (ii) PR has a maximum value, one of 129 g/d, when W = 85 kg; (iii) PR tends to zero as W tends to some upper limit, in this case a value of 213 kg. Whittemore and Fawcett (1976) also chose a polynomial form of function and, from the same data, derived the quadratic in W which is Eq. (2): PR = 60 + 1.63W - 0.0094W 2 g/d

(2)

Eq. (2) is not only inelegant but makes PR tend to 60 g/d as W tends to zero. It shares with Eq. (1) the desirable properties that PR has a maximum value, and that it goes to zero as W reaches some value, in this case, 205 kg. Whittemore (19761, in an attempt to simplify the necessary description of the pig, proposed that PR could be treated as a constant for the liveweight range of 20 to 120 kg which is the commercially interesting range. Different kinds of pigs could then be described by giving them different values for this single number. The apparent simplicity of using a single number as a sufficient description of the pig is much more than offset by its unpleasant consequences for a growth function. It is surprising that even now this notion continues to have its followers (de Lange, 1995; Moughan, 1995). Quiniou et al. (1995) found maximum rates of protein retention of 169, 184, 194 and 179 g/d at liveweights of 45, 65, 80 and 94 kg respectively but, perversely, concluded that “no effect of stage of growth was found” on the rate of protein retention. While the numbers may not have been significantly different they are consistent with the idea that there is an intermediate liveweight at which the rate of protein retention is at a maximum.

G.C. Emmans, 1. Kyriazakis/Liuestock

In another attempt to relate PR to W, Carr et al. (1975) summarised experimental data into a system: PR = (6.25W”.75)

. (3.324 - O.O98W+ O.OOlZ) g/d (3)

where Z=

W2forW<45andZ=45(2W-45)forW>45(

The expressions are unhelpful and lead to the rather strange predictions shown in Fig. 1 where the predictions of Eqs. (1) and (2) are also shown. Black et al. (1986) proposed the function: PR=a.Wk.((P,,,-P)/P,)g/d

(5)

to predict the potential rate of protein retention. Without the rather unpleasant W k, term PR is made to depend only on mature protein weight, Pm, and current protein weight, P, with just one other parameter, a. This can be seen as a step forward. In Eq. (5), the Wk term, when k is positive, has the effect of causing an increase in the value of PR at a given protein weight if the pig simply has more fat in its body. This does not seem sensible and the justification for the term is not clear. The equation has since been modified (Black et al., 1995) to become: PR=k.((P,,,-P)/Pm).(W+Ws)ag/d

(5a)

where k, a and w, are ‘constants’ and dependent on pig genotype. The equation “has considerable flexibility” (Black et al., 1995). With four parameters (the values of all of which have to be estimated to

140

Protein retention (g/d)

1

25

50

75

100

125

150

175

200

Liveweight (kg)

Fig. I. The prediction of the upper limit to the rate of protein retention (PR, g/d) from pig liveweight (W, kg) according to the equations of Carr et al. (1975). (- * -1, Thorbek (197%. c---j and Whittemore and Fawcett (1976) (- - -1.

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Production Science 51 (1997) 119-129

describe a pig genotype), and two state variables (P and W > it is not surprising that it “has considerable flexibility”. More important issues are whether it is a sensible answer to the problem and, if so, how the values of the four parameters are to be estimated for a given kind of pig. In marked contrast to the various equations proposed above is a growth function with just two parameters:

PR = B. P,,, log,( P,,,/P)

g/d

which makes the potential rate of protein retention depend only on the protein weights currently, P, and at maturity, P,,,, through the only other parameter, B. Eq. (6) is the derivative of the Gompertz growth function. This traditional function (Gompertz, 1825) appears to have been used specifically for the protein growth curve firstly for poultry (Emmans, 1981a,b), before being proposed as part of a more general animal growth model (En-mans, 1988). Ferguson and Gous (1993a,b) showed how the values of the parameters of the function (B and Pm) could be estimated from suitable measurements on pigs. They also showed that data from experiments on pigs were consistent with the functional form. Subsequently Ferguson et al. (1994) used the function in a model for pigs. Others have successfully used the function to describe the growth of other species of domestic animals (Emmans, 1989, for turkeys; Knizetova et al., 1991b, for ducks; Knizetova et al., 1991a, and Hancock et al., 1995, for chickens; Knizetova et al., 1994, for geese). Whittemore has also adopted the Gompertz growth function for pigs, (Whittemore et al., 1988; Whittemore, 1994, 1995). Eq. (6) is proposed for use because of its advantages, which are economy of parameters with clear biological meaning, its generality and its application to all stages of growth. Real data on actual growth, where this is not the potential, may not be well described by Eq. (6), but this is not its purpose, nor is it the purpose of the other equations presented. Its purpose, and theirs, is to describe the potential rate of protein retention; this will be the actual rate only in conditions which allow it to be attained. While it may be difficult to test whether this is the case for any single data set, the distinction remains an important one.

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3. Problem 2: the prediction of the rates of retention of ash and water The second problem is important for models where liveweight, W, plays an important part as water weight, WA, is usually the major component of the body, and the accurate prediction of W therefore rests on the accurate prediction of WA. Whittemore and Fawcett (1974) originally proposed that WA in the empty or lipid-free body depends in part on lipid weight, but subsequently (Whittemore, 1983) made it depend only on protein weight as others have done (ARC, 1981). Ash weight, ASH, has usually been made to depend on protein weight only. The usual relationships used are those of simple power (allometric) functions: ASH=k,.P” WA=k,.Pb

kg kg

(7) (8)

For ash the value of the exponent, a, is often assumed to be unity and recent work (Kyriazakis and Emmans, 1992a,b; Kyriazakis et al., 1994) has shown that there is no need to change this assumption, at least for potential growth. The value of the scalar, k,, is agreed to be close to 0.2 in potential growth across pig genotypes. It is, however, possible to change the ash: protein ratio by severe under-feeding with protein whilst minerals are provided in relative abundance (Kyriazakis et al., 1991). In the latter case the value of k, was increased to 0.24, i.e., pigs contained more ash in relation to protein than in potential growth. However, even considerable errors in estimating ASH have relatively trivial effects on the estimation of body weight. The exponent for water, b, is usually assumed to be less than unity. This has the consequence that the water:protein ratio in the empty body will decrease steadily as the pig grows. The assumption that the value of the exponent b is constant across genotypes and sexes, and is not affected by feeding, has recently been supported by Emmans and Kyriazakis (1995). It was concluded that the value of b at 0.855 was not different between Large White X Landrace male and female pigs, and neither was it different between male Chinese Meishan and male Large White X Landrace pigs. The value of 0.855 was originally proposed by Kotarbinska (1969) and adopted

Production Science 51 (1997) 119-129

by ARC (1981). It has, however, been proposed by Emmans and Kyriazakis (1995) that the value of the water scalar k, will vary systematically between pig genotypes depending on their mature size, measured as mature protein weight P,,,. This follows from the expectation of an essentially constant composition of the mature lipid-free body (Emmans, 1988). The value of k, is made a function of P,,, through the assumption that the water: protein ratio at maturity is uncorrelated with mature protein weight. This assumption makes for consistency with the growth function in Eq. (6) proposed above. With this change the current expressions used for the composition of the lipid-free body are satisfactory. The simple power function chosen to describe the relationship between water and protein has a theoretical basis and does not rely simply on fitting some particular set of data (Emmans, 1988). Where (i) the weights of two body components are both Gompertz functions of time and, (ii) the value of the rate parameter B is the same for both, then it can be shown algebraically that their weights will be related by a simple power function as above (Emmans, 1988).

4. Problem 3: the prediction of the actual rates of

retention of protein and lipid The problem of predicting the actual rates of both protein and lipid retention can be approached in two steps. If the rate of protein retention can be found then the rate of lipid retention can be predicted from the rate of protein retention, the rate of energy supply and an ‘energy system’ (ARC, 1981; Emmans, 1994). The solution proposed by Whittemore and Fawcett (1974) was that the rate of protein retention depended only on the (ideal) protein supply above maintenance until a maximum rate of protein retention, PR,,, g/d, was achieved. The material efficiency with which ideal protein was utilised above maintenance, now called er, was implicitly assumed to be constant across genotypes and degrees of maturity and to be equal to unity. This suggestion is represented in Fig. 2 and by the equation: PR=e,((FZ*FCPC.d,;u) when PR < PR,,,

-MP)

g/d, (9)

G.C. Emmans, I. Kyriazakis/Livestock protein retention ( PR, g/d)

Ideal protein supply (IPS, g/d)

Fig. 2. The relationship between protein retention and ideal protein supply as seen by Whittemore and Fawcett (1974). The net efficiency of ideal protein utilization above maintenance, ep, was assumed to be constant and to have the value of unity.

where FZ g/d, is the rate of intake on a limiting food with a crude protein content of FCPC g/g, the dietary crude protein has a digestibility of d,, g/g, the digested protein a value in relation to ideal protein (ARC, 1981) of u, and MP g/d is the ideal protein needed for maintenance. The simplicity of the function makes it attractive but it was not able to predict the rate of protein retention in many circumstances-in particular in the case of small pigs and larger pigs on energy-limiting diets. Alternative solutions to the problem, and their consequences, are presented below. 4.1. Solution 1: the assumption 1ipid:protein ratio in the gain

of a minimum

Whittemore and Fawcett (1976) attempted to overcome the problem by introducing the rule that there had to be a minimum ratio of lipid to protein in the gain. The new parameter was (LR: PR),,,in, where PR and LR are the rates of retention of protein and lipid respectively. Providing that this ratio was been attained then the rate of protein retention depended only on the rate of protein supply according to Eq. (1). The value of (LR:PR),,, was initially set to 1, following the suggestion of Kielanowski (1966) that even a drastic feed intake limitation was unlikely to result in a lower value. A consequence of the above rule was that Whittemore and Fawcett (1976) were able to predict the observed protein retentions of both young pigs and

Production Science 51 (1997) 119-129

123

of those on low energy allowances. Later Whittemore (1983) suggested that (LR: PRjmin was genetically determined and hence that its value would vary between different kinds of pigs; it was expected to be lower for genetically improved pigs. The rule, as judged by its consequences for prediction, was useful. Unfortunately it is not consistent with the biology of the pig. There are instances where pigs are able to lose lipid and yet retain protein in their bodies (Fowler, 1978; Kyriazakis and Emmans, 1992a,b). Despite the fragility of the concept the rule has been incorporated into several subsequent pig growth models (e.g. Moughan et al., 1990; Pomar et al., 1991; TMV, 1991; Walker and Young, 1993; de Lange, 1995). 4.2. Solution 2: the assumption that there is a minimum value for the marginal ratio of extra 1ipid:extra protein retained It took almost 20 yr for Solution 1 to be challenged by de Greef (1992) and de Greef and Verstegen (1995) who recognised the difficulties that it raised. Their solution was to introduce a different constraint on the rate of protein retention when energy was in short supply. They pointed out that data from experiments (e.g., that of Campbell et al., 1983) suggested that there were linear relationships between the rates of retention of both protein, PD, and lipid, LD, and energy intake, DEI. The equations, where PD < PDmax, given by de Greef and Verstegen (1995), were: PD=a+b.DElg/d

(‘0)

LD=c+d.DEIg/d

(11)

The meaning of the equations is shown in Fig. 3. According to de Greef and Verstegen (1995): “The [values of the] parameters a, b, c and d varied between sexes and weight ranges.. . When the equation describing lipid deposition is divided by the equation describing protein deposition the ratio between lipid and protein deposition as dependent on digestible energy intake (DEI) is described”. They proposed that “each extra MJ of energy intake is partitioned to protein and lipid deposition according to a constant ratio. This constant ratio between extra protein and extra lipid deposition provides an alter-

124

G.C. Emmans, I. Kyriazakis/Livestock Retention rate

I

5 i Lipid

i P

z

:

Energy intake rate

Fig. 3. The relationship between energy intake rate, and protein and lipid retention rates as seen by de Greef (1992). Protein and lipid retention rates increase by b and d g/MJ respectively as energy intake increases. The ratio d/b is called the ‘marginal ratio’ of extra lipid to extra protein retained.

native parameter. . . to describe this constancy. . . [which] is called the marginal ratio.” The use of the ‘marginal ratio’, which is d/b from Eq. (10) and Eq. (1 l), is a solution which can be seen as a definite improvement over Solution 1 with a clearer biological basis. For ‘protein adequate’ foods PR (or PD) is calculated from the rate of energy intake using the value of the ‘marginal ratio’ which is made to depend on pig genotype and liveweight. A difficulty is that the term ‘protein adequate’ is not clearly defined for different genotypes at different liveweights. A disadvantage of the solution is it has a high information requirement; the values of at least four parameters (a, b, c and d in Eq. (10) and Eq. (11)) for each genotype at each liveweight are needed. de Greef and Verstegen (1995) reported that the value of the ‘marginal ratio’ in the literature varied between 1.7 and 6.2 in different experiments on pigs of different weights, sexes and genotypes.

Production Science 51 (1997) 119-129

Fig. 4). The marginal efficiency of using dietary N for N retention was assumed to be constant across different liveweights and, by implication, for different genotypes. (This proposal is taken forward in the next solution). Where N retention was not limited by N supply it was proposed that there would be a response to extra energy intake as indicated in Fig. 4. Black et al. (1986) followed Black and Griffiths (1975) in making N retention on ‘protein adequate’ diets a linear function of the energy supply. It was proposed that the rate of response to energy would decline as liveweight increased and that, at a given liveweight, it would differ between genotypes. No solution was proposed to the problem of defining a ‘protein adequate’ diet for a given genotype at a given liveweight. The proposals that the rate of response of N retention to energy supply would (i) decline as liveweight increased and (ii) would differ between genotypes at a given liveweight are made in the model ‘Auspig’ which is available on a restricted basis (Black et al., 1995). While it is not straightforward to show where these two proposals are wrong it can be shown that the amount of information to implement them is high. The coefficient describing the rate at which N retention increases per unit of extra energy intake needs to be known for all genotypes of interest, at all liveweights of interest.

4.3. Solution 3: the assumption that there is a rate of response in protein retention to unit increase in the energy supply characteristic of a pig at a liueweight Black that the the rate limiting

and Griffiths (1975) proposed, for lambs, rate of N retention was a linear function of of N supply as long as energy was not (their figure 6 which is reproduced here as

Fig. 4. The fitted relationship between N balance and N intake for liquid-fed lambs of different liveweight (p, 5 kg; --15 kg: ---, 25 kg) and metabolisable energy (ME) intake (mJ/d). The figure is reproduced from Black and Griffiths (1975).

G. C. Emmans, I. Kyriazakis / Lioestock Production Science 51 f 19971119-l 2,0 Protein Retention (PR,g/d) c

125

29

existed. They found no evidence that the two extremely different genotypes differed from each other. This finding needs further appropriate tests but it does suggest no genetic variation at this level. 4.4. Solution 4: the assumption that the material efficiency of using ideal protein for growth varies with the energy:protein ratio of the food

11

13

15

ME Intake (YJW)

Fig. 5. The relationship between protein retention, PR g/d, and energy above maintenance, mJ/d, for pigs of 45 (-0 -1, 65 (- 0 -1, 80 (- n -) and 94 (- 0 -1 kg liveweight, derived from the data of Quiniou et al. (1995).

There is experimental evidence that the N retention response to extra food energy does not change with liveweight. Quiniou et al. (1995) found essentially no change. At liveweights of 45, 65, 80 and 94 kg the relationship between protein retention and ‘energy intake above maintenance’ was as illustrated in their Fig. 1, with no data shown, and Fig. 5 here, where the 16 data points are shown. At the successive liveweights the slopes, for the treatments where protein retention was limited, were 9.1, 10.6, 12.1 and 9.5 g/MJ; the authors report that the differences between these were not significant. The unweighted mean slope is 10.3 g/MJ and it is this slope that is drawn in Fig. 5 for all four of the liveweights. The assumption that the rate of change of protein retention with energy intake does not change with liveweight is clearly not rejected by these data. It is probably relevant that Quiniou et al. (1995) used the same food at all liveweights, i.e., the energy:protein ratio of the food was constant; in other experiments the energy:protein ratio is often higher for the heavier pigs. These figures are supported by the experiment of Emmans and Kyriazakis (1996) who found no difference between pigs of 12 and 72 kg liveweight. Kyriazakis and Emmans (1992a,b), Kyriazakis et al. (1994), and Kyriazakis and Emmans (1995) used two extremely different pig genotypes, viz. Chinese Meishan and commercial modem genotypes to see if differences in the response of N retention to energy

Kyriazakis and Emmans (1992a,b) abandoned the use of any constraint on the 1ipid:protein ratio in the gain. Instead they proposed that the net material efficiency (i.e., the slope of protein retention on protein supply above maintenance) of using ideal protein for protein retention, et,, is directly proportional to the ratio of metabolisable energy to digestible crude protein of the food, up to a critical value at which it attains its maximum value called ep*. Beyond this critical value, ep* remains constant and at its maximum as indicated in Fig. 6: ep = I_L.(MEC/DCPC),

when ep < e,*

(12)

where MEC is the metabolisable energy content of the feed, kJ/g, and DCPC its digestible crude pro-

, o. Efficiency of protein utilisation (3

Energy:Protein

ratio (MECIDCPC,

kJ/g)

Fig. 6. The relationship between the net efficiency of the use of ideal protein above maintenance, er, and the metabolisable energy: digestible crude protein ratio of the food (MEC/DCPC, kJ/gJ as proposed by Kyriazakis and Emmans (1992b). The maximum value of ep is called ei Foods cannot have a value of MEC/DCPC of less than 18 kJ/g.

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G.C. Emmans, I. Kyriazakis/Liuestock

tein content, g/g. The current estimates of the values of the two parameters ,U and el are 0.0112 and 0.81 respectively (Kyriazakis and Emmans, 1992a,b; Kyriazakis et al., 1994). The values are assumed to be constant across genotypes and across degrees of maturity (liveweights) for any particular genotype. The implications of Solution 4 are, (i) that the amount of extra protein gained depends only on the amount of extra protein supplied and on the (MEC/DCPC) ratio of the food, providing that the potential rate of PR has not been attained and, (ii) that the amount of extra lipid retained follows from the extra energy intake and that part of it needed for the retention of the extra protein. It follows that the ratio of extra lipid retention to extra protein retention, the ‘marginal ratio’ of de Greef and Verstegen (1995) can be predicted as a function of the food protein content (at a constant food energy content) as shown in Fig. 7. The ratio is predicted to attain a minimum value of approximately 0.90 for DCPC = 0.165 g/g and above when MEC = 12 k.I/g. The calculated minimum value for the ‘marginal ratio’ is

,,M) ALW APR r

o~78.:o 0’120.i.l o.;a a;*IA

Il.;* 0.L

Production Science 51 (1997) 119-129

significantly lower than that proposed by de Greef (1992) in Solution 2. Two consequences of Solution 4 are (i) that two new parameters, ,u and e; are introduced and, (ii) that the partitioning of energy and protein intakes by the pig appear to be correctly predicted as shown by Kyriazakis and Emmans (1992b). The proposal that the values of /A and ei are the same for different pig genotypes, and for different degrees of maturity of a given pig genotype, is supported by the results of the experiments of Kyriazakis et al. (1994) and Kyriazakis and Emmans (1995) on Large White X Landrace and Chinese Meishan pigs. It was found that the values of both p and ep* did not differ between these two very different pig genotypes. It would appear, therefore, to be a safe assumption that they are constant across pig genotypes in general, although tests of this assumption for other genotypes are justified. The results of the experiment of Emmans and Kyriazakis (1996) at initial liveweights of 12 and 72 kg, and of Quiniou et al. (1995) over a range of liveweights are also consistent with this. Further tests of this important proposal at different liveweights are to be encouraged. There are, however, experiments whose results suggest a difference in e; between different pig genotypes (e.g., Campbell and Taverner, 1988). These experiments, however, do not constitute strong tests of the above proposition, since there is some doubt as to whether the treatments applied were limiting in protein supply for all genotypes at all times during the experiments. This is a condition that must be met if the net material efficiency is to be measured (Kyriazakis and Emmans (1995)). Solution 4 is preferred over the other three mainly because of the fewer parameters that need to be estimated for a given kind of pig. Recently Whittemore (1995) has recognised its merits and has discussed its consequences on the prediction of protein and lipid deposition in the pig.

Digestible CP content of food (g/g)

Fig. 7. The predicted relationship between the ratio of extra lipid to extra protein retention (ALRAPR) and the digestible crude protein (CP) content of the food, from the assumption that the material effkiency of ideal protein utilization above maintenance varies with the energy: protein ratio of the food. The ALRAPR ratio attains its minimum value of approximately 0.9 when the digestible CP value exceeds 0.165 g/g for a food with an MFZC of 12 kJ/g.

5. Discussion and conclusions Solutions have been proposed here to the three problems raised by Whittemore and Fawcett (1974, 1976) and presented at the start of the paper. It is

G.C. Emmans, I. Kyriazakis/Licestock

proposed that the first problem, which is that of predicting the potential rate of protein retention as some function of the pig, is solved by the use of the Gompertz function (Emmans, 1981a,b, 1988; Ferguson and Gous, 1993a,b; Ferguson et al., 1994). Whittemore (1994, 1995) seems now to have come to the same view, although others (de Lange, 1995; Moughan, 1995; Quiniou et al., 1995) still quote the earlier position of Whittemore (1983). The second problem, that of predicting the rates of retention of ash and water, is dealt with by allometry but with a better theoretical underpinning. A considerable advantage to using the Gompertz form of growth equation is that, under one crucial assumption, chemical allometry can be algebraically deduced (Emmans, 1988). The use of mature composition as a part of the description of the pig also allows for more general quantitative functions to be used for different pig genotypes (Emmans, 1988; Emmans and Kyriazakis, 1995). It is proposed that the third problem, i.e., that of predicting the rates of retention of protein and lipid, when the rate of protein retention is below the potential rate because of the limiting food supply, can be solved by using a simple rule. The rule is that the net material efficiency of using ideal protein for growth is directly proportional to the energy to protein ratio of the food up to a maximum value. Thus the amount of extra protein gained per unit of extra food energy depends only on the amount of extra (ideal) protein supplied with it. The amount of extra lipid retained per unit of extra energy supplied follows from the difference between extra energy supplied and that needed for the extra protein retention. The advantage of the proposed rule is that the values of its two parameters are assumed to be independent of pig genotype and liveweight. This simple position is supported by recent experimental evidence (Kyriazakis and Emmans, 1992a,b, 1995; Kyriazakis et al., 1994; Quiniou et al., 1995; Emmans and Kyriazakis, 1996) as already described. The preferred solutions to the three problems presented here constitute a framework which can be applied to predict the response of a pig to its diet at a time and over time. The variables of the framework are those associated with the Gompertz function which are the Gompertz rate parameter, B, and the mature protein weight, P,,,. Given that the values of

Production Science 51 (1997) 119-129

127

both of these variables can be measured in pigs (Ferguson and Gous, 1993a,b) then the framework can be extended to predict easily the responses of different kinds of pigs to the same diet. Furthermore, given that the values of only two pig variables are needed, the approach can be adapted to predict the responses of the individuals which comprise a population of pigs to their diet, providing that the distributions of these variables are known, i.e., their variances and covariances. A requirement is that the pig breeders become interested in collecting the information that is needed &nap, 1995). The approach advocated here can readily be extended to predict the rate of lipid retention on nonlimiting and balanced diets given the value of the mature fatness of the pig (see Emmans, 1988). Once this additional descriptor is available the approach can then be extended to deal with the problem of predicting food intake (Emmans and Kyriazakis, 1989; Emmans, 1995, 1997).

Acknowledgements

This paper combines parts of the papers on ‘Descriptions of pig growth and food intake using empirical regression models’ and ‘The necessary and adequate variables required for the prediction of the responses of a growing pig to its diet’, presented respectively by the two authors at the 46th Annual Meeting of the European Association for Animal Production.

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