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3
Models for Estimating Energy and Amino Acid Requirements
Quantitative nutrient requirements are not the same for all pigs but vary with changes in genetic strain, gender, health, temperature, stocking density, and other factors. This fact was acknowledged in the previous edition of this publication (National Research Council, 1988), but information available at that time was judged inadequate to estimate nutrient requirements for specific situations. This edition uses a mathematical modeling method to help the user derive situation-specific estimates of nutrient requirements.
Fortunately, the variations in nutrient requirements are not random or mysterious. They are related in logical patterns to variations in a small number of variables. For growing pigs, these variables are rate of protein accretion, energy intake, and dietary energy density. In this edition, our understanding of those patterns is used to estimate, by use of mathematical models, the different nutrient requirements for different pigs.
Overview Of The Models
The following five principles guided the development of the models:
Ease of Use. Any method of estimating situation-specific nutrient requirements will be more difficult to use than were those in previous editions of this publication. However, the models in this edition were developed to be easy to use by people with varying levels of nutritional expertise and with limited information about the specific situation.
Continued Relevance. The models should be flexible enough to adapt to continued changes in genetics and production systems that will occur during the life of this edition (until it is replaced by its successor). Many of these changes cannot be predicted at present.
Simplicity. The models should not only be easy to use, but also structurally simple, so they can be understood readily by users.
Transparency. The user must be able to understand how the models work (all equations are provided in Appendix 1) and be able to evaluate the information used to develop them.
Anchored to Empirical Data. Where possible, quantitative relationships built into the models are based on measurements at near the whole-animal level rather than on theoretical values.
It is recognized that the emphasis on ease of use and simplicity has a cost. More complex models requiring more data inputs by the user might be able to produce more accurate estimates of requirements over a wider range of conditions.
The models are not traditional simulation models. They do not predict pig performance and carcass composition from nutrient intake and other information. They do not move through time, predicting the changes in body weight and composition at each time step (e.g., one day). Rather, these models are simply a structured method for developing factorial estimates of nutrient requirements. They estimate the amount of a nutrient used for each major function of the body (e.g., maintenance, protein accretion, milk production) and sum them to estimate a total daily requirement.
In the interest of simplicity, the models address only energy and amino acid intake. For growing-finishing pigs, the model estimates only amino acid requirements, presuming that the pigs are allowed ad libitum consumption of feed. Both energy and amino acid requirements are estimated for the gestating and lactating sow.
The models estimate the amounts of nutrients needed to support the level of performance currently found in the herd of interest (e.g., lean growth rate of finishing pigs or litter growth rate of lactating sows). The current level of performance is a result of many factors—genetic, nutritional, health, and environmental—and the models do not attempt to identify those factors that limit the current level of performance. In some cases, current performance may
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be limited by the amounts of amino acids consumed. In those cases, the models would be expected to predict amino acid requirements near the amounts currently provided, but performance may be improved by increasing those levels. Therefore, when the predicted requirements are near, or above, the levels currently fed, it would be prudent to repeat the measurements of performance with higher dietary amino acid levels, and use the new estimate of performance level in estimating requirements with the model.
Growing-Finishing Pigs
Requirement for Lysine
The daily lysine requirement is the sum of the requirements for maintenance and for protein accretion.
Maintenance
The daily true ileal digestible lysine requirement for maintenance is assumed to be 36 mg/kg of metabolic body weight (BW0.75), based on the data of Wang and Fuller (1989).
Protein Accretion
The daily amount of lysine needed to support protein accretion is the product of two numbers: (1) the daily amount of protein accreted, and (2) the amount of true digestible lysine needed for each gram of protein accreted. These components are estimated separately.
Protein Accretion Rate
The protein accretion rate is estimated in two steps. First, the potential rate is estimated; then, if necessary, the rate is decreased, to be consistent with the amount of energy consumed.
The potential protein accretion rate varies in different situations as well as within a situation as the pig grows. It is necessary to have an equation that describes for a given situation the potential protein accretion rate (g/day) at each stage of growth, an example of which is shown in Figure 3-1. That equation can be obtained in either of two ways, at the option of the user:
It can be provided by the user. Information provided by the user can determine both the overall rate of accretion and the shape of the accretion curve. This is the preferred method of obtaining the equation, but the user should use reliable data measured in the situation of interest. It is not useful to provide assumed data.
The other way is to use a default equation provided in the model. To do so, the user must provide an estimate of the mean fat-free carcass lean accretion rate over the growing-finishing period. This mean accretion rate can be
FIGURE 3-1
Potential whole body protein accretion rate of pigs of high–medium lean growth rate with a carcass fat-free lean gain averaging 325 g/d from 20 to 120 kg body weight (default equation of the model). The lean growth rate of 325 g/day is converted to a mean whole body protein accretion rate of 127.5 g/day (325/2.55 = 127.5).
calculated easily from four items of information that should be readily available to most users:
Carcass weight at slaughter;
Percent fat-free lean in the carcass at slaughter;
Assumed fat-free lean in the carcass at the beginning of the growing period;
Number of days in the growth period.
Detailed instructions in Appendix 2 will help the user calculate the mean fat-free carcass lean accretion rate in grams/day for the growing-finishing period. The model assumes the mean lean accretion rate is measured over the period of 20 to 120 kg body weight. If the beginning or ending weights are different from 20 or 120 kg, the mean lean accretion rate must be adjusted; these adjustments are also provided in Appendix Table 2-1.
The default equation describing potential protein accretion rate versus body weight is derived from the mean carcass fat-free lean accretion rate in two steps:
First, the mean carcass fat-free lean accretion rate is converted to mean whole body protein accretion rate. This is a two-stage conversion, from fat-free lean tissue to protein and from carcass to whole body. The conversion factor is taken as 2.55 g of carcass fat-free lean tissue per gram of whole body protein, a value derived from several reports cited by Susenbeth and Keitel (1988), plus more recent data reported by Bikker et al. (1996a,b).
Second, an equation is used to provide estimates of the potential protein accretion rate at any body weight, expressed relative to the overall mean, as follows:
where Factor is the proportion of the overall mean, and BW is the body weight in kg (the overall mean of the factor
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is 1.0). The potential protein accretion rate at a given body weight is then determined by multiplying the overall mean for protein accretion rate by the factor. Similarly, the lean gain at a given body weight can also be determined by multiplying the overall mean lean growth rate by the factor.
This equation was proposed as a compromise between widely varying shapes of protein accretion curves versus body weight. When the performance of the entire model in estimating lysine requirements was subsequently evaluated, this equation proved to be satisfactory and was clearly superior to the others tested, at least as a component of this model. This is the equation shown in graphic form in Figure 3-1. This approach simply moves the regression curves up or down with variation in overall lean accretion rate, keeping the shape of the curves constant, as shown in Figure 3-2.
As discussed previously, the user may provide an accretion curve for carcass lean or whole body protein, which is different than the model's default curve. An aid for developing different curves is shown in the Appendix (Appendix 3).
To this point, an equation describing protein accretion rate versus body weight is provided, either by the user or by the default equation within the model using the mean carcass fat-free lean accretion rate provided by the user. Then the user simply enters the weight of the pigs whose requirements are to be estimated. The model calculates from the equation the potential protein accretion rate at the body weight indicated.
The model tests whether the energy intake is adequate to support the potential rate of protein accretion. The amount of energy (or feed) consumed in the specific situation and at the body weight of interest is determined in either of two ways:
It can be provided by the user. This is the preferred method, but the energy (or feed) intake data should be
FIGURE 3-2
Potential whole body protein accretion rates of pigs of medium, high–medium, and high lean growth rates with carcass fat-free lean gains averaging 300, 325, and 350 g/day from 20 to 120 kg body weight (default equation of the model).
derived in the situation of interest. It is not useful to provide assumed or desired rates of intake.
A default equation describing DE intake at each body weight is provided in the model. It is patterned after the equation presented by National Research Council (1986), but modified to account for recent empirical data suggesting greater feed intake during the early growth period and slightly decreased feed intake during late finishing. The modified equation produces estimates of total dietary lysine requirements, on a percentage basis, that are in general agreement with recent empirical data summarized in Table 2-2 assuming a mean fat-free carcass lean growth rate of 325 g/day. The equation for a combination of barrows and gilts is:
This equation is modified for either barrows or gilts by applying the following adjustment, which is added to the DE intake for barrows or subtracted for gilts:
where DEI is DE intake (kcal/day) calculated from Equation 3-2. Equation 3-3, a modification of a National Research Council (1986) equation, results in a difference of approximately 0.1 percentage point in the total lysine requirement between finishing barrows and gilts (see Chapter 10, Table 10-3), as suggested by the studies of Cromwell et al. (1993) and Hahn et al. (1995). The shape of the DE intake curves for barrows, gilts, and a 1:1 ratio for the two genders is shown in Figure 3-3.
There are also adjustments in predicted DE intake for variations in ambient temperature and in stocking density (space/pig), as in the system presented originally by National Research Council (1986).
FIGURE 3-3
Estimated daily digestible energy (DE) intakes of barrows, gilts, and a 1:1 ratio of barrows to gilts consuming feed on an ad libitum basis from 20 to 120 kg body weight (default equation of the model).
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The incremental amount of protein accretion supported by an increment of 1 Mcal of DE intake above the intercept of 55 percent of maintenance is calculated by the following equation, which is a modification of the equation of Black et al. (1986):
where protein accretion is for a given day expressed in g/Mcal DE intake above 55 percent of maintenance; BW is body weight in kg; MPAR is the mean protein accretion rate over the range of 20 to 120 kg BW expressed in g/day; and T is the effective ambient temperature in °C. This equation estimates protein accretion only when accretion is limited by energy intake. In many situations, energy intake is not limiting and further increments in energy intake do not change protein accretion. The relationship is shown graphically in Figure 3-4 for several body weights. Equation 3-4 estimates the slopes of the ascending lines in Figure 3-4.
The first term in the right side of the equation is the same as in the original equation of Black et al. (1986) but expressed in units consistent with the rest of the model. It changes the slope of the relationship of protein accretion to energy intake, causing the slope to gradually flatten as the pig increases in body weight. Results of studies conducted since the publication of the original equation are inconclusive but can be interpreted to suggest that the slope should be flatter for larger pigs than for smaller ones (Quiniou et al., 1995), in agreement with the new equation.
The second term is an adjustment of the slope for differences in mean potential protein accretion rate, causing the slope to be steeper for pigs with a greater potential protein accretion rate. There is no compelling reason to believe that the two factors must always be closely related, but the evidence available to date (Campbell and Taverner, 1988; Quiniou et al., 1995) suggests that such a relationship occurs, at least in some situations. In the absence of further
FIGURE 3-4
Relationship of whole body protein gain and digestible energy intake in pigs from 5 to 150 kg body weight.
information, it is judged prudent to make an adjustment consistent with the current empirical data.
The final term in the equation is an adjustment of the slope for ambient temperature. It is based on the report of Close and Mount (1978), which showed clearly that the slope of protein accretion on energy intake becomes flatter as ambient temperature increases.
The model solves the equation to determine the amount of protein accretion that can be supported by the amount of DE consumed. It then compares this value with the potential protein accretion rate defined above and takes the lower value as the amount of protein actually accreted if amino acid intake is adequate.
Lysine Required per Gram of Protein Accreted
This parameter was deduced from recent experiments reported in the literature that estimated the lysine requirement of pigs between 20 and 120 kg body weight. The data set was restricted to those experiments in which (1) lysine was clearly the first-limiting amino acid, and (2) whole (empty)-body protein accretion was measured, or carcass lean accretion was measured from which whole body protein accretion could be calculated by dividing by 2.55 (see earlier discussion). There were eight requirement estimates from three publications (Batterham et al., 1990; Bikker et al., 1994b; Hahn et al., 1995). For each estimate, the amount (g/day) of true ileal digestible lysine above maintenance consumed at the requirement was divided by the protein accretion rate (g/day) at that level of lysine intake. This approach does not require the assumption that the relationship of protein accretion to lysine intake is linear. The eight values ranged from 0.094 to 0.157, with a mean of 0.122.
As a further check on this value, whole body protein accretion (g/day) was plotted (Figure 3-5) against true ileal
FIGURE 3-5 Relationship of daily whole body protein deposition and daily intake of true ileal digestible lysine above maintenance. Based on data from 18 experiments and adapted from a summary by Kerr (1993).
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digestible lysine intake above maintenance (g/day), using data from a wider range of experiments (Campbell et al., 1984, 1985, 1988, 1990; Batterham et al., 1990; Chiba et al., 1991; Bikker, 1994b; Friesen et al., 1994; Hahn et al., 1995). The data set included the experiments mentioned in the previous paragraph, and also (1) experiments in which it is not clear that lysine was the first-limiting amino acid, and (2) experiments for which it was necessary to make further assumptions in order to estimate whole body protein accretion. All treatments except those above the requirement are plotted. The slope of the regression line suggests that an increment of approximately 0.123 g of true ileal digestible lysine was consumed for each additional gram of protein accreted. The agreement of this number with the one in the previous paragraph (0.122) lends confidence.
Therefore, the relationship of lysine required above maintenance to whole body protein accretion rate in the model is as follows:
where Lysine is the daily requirement for true ileal digestible lysine intake above maintenance in grams, and PD is daily protein deposition in the whole body in grams.
This equation can be considered to encompass two relationships. The first is the lysine content of whole body protein, a value that varies with protein intake (Bikker et al., 1994a) but is usually within the range of 6.5 to 7.5 g lysine/100 g body protein. The second relationship is the marginal efficiency of use of absorbed lysine for deposition in protein. The regression coefficient in the equation (0.12), when considered along with the lysine content of whole body protein, reflects a marginal lysine efficiency of 54 to 62 percent.
In summary, the lysine requirement for protein accretion is determined from the equation above and is added to the maintenance requirement for lysine to obtain the total daily lysine requirement. All lysine values are in grams of true ileal digestible lysine. An example is shown in Figure 3-6.
FIGURE 3-6
Daily lysine requirement (true ileal digestible basis) of pigs with a mean lean growth rate (carcass fat-free basis) of 325 g/day from 20 to 120 kg body weight as estimated by the model using default equations.
Note that the whole body protein accretion rate is a single adjustment for variations in genetic strain, gender, health, stocking density, as well as interactions among these and other factors. In fact, it is not necessary or possible to enter other descriptions of these variables. The user does not provide a qualitative description of the breed, commercial genetic line, or strain of the pigs. Even if such a description were quantitatively meaningful at the time the model was developed, future genetic progress would diminish the accuracy and usefulness of such a description. Similarly, attempts might be made to define health status by describing the production system employed (e.g., all in/all out animal flow, segregated early weaning, multi-site production), but variations in health status within the type of production system and future development of superior systems would limit the value of such a definition for deriving quantitative estimates of whole body protein accretion.
Requirements for Other Amino Acids
Requirements for the essential amino acids other than lysine are also considered to consist of separate components for maintenance and protein deposition. Calculations are based upon the ideal protein system in which requirements for each of the other amino acids are expressed relative to the lysine requirement. The model uses two patterns of ideal protein, one for maintenance and one for protein accretion, as described in Chapter 2. The final blend of the two patterns depends on the relative proportion of lysine needed for maintenance and whole body protein accretion. The patterns are on a true ileal digestible basis.
Expression of Amino Acid Requirements
The procedures described above produce estimates of amino acid requirements (true ileal digestible basis) expressed in g/day. The daily DE (or ME) intake is either provided by the user or estimated within the model, so amino acid requirements are easily expressed as g/Mcal DE. The user provides the energy density of the diet (Mcal DE/kg), which allows the calculation of the amount of feed consumed (kg/day). Then the amino acid requirements are calculated as a percentage of the diet, on a true ileal digestible basis (Figure 3-7). The percentage requirements of true ileal digestible amino acids are also expressed as percentage requirements of apparent ileal digestible amino acids and percentage requirements of total amino acids by using the equations given in Table 3-1. The equations in Table 3-1 were derived by calculating the percentages of true and apparent ileal digestible amino acids and total amino acids in diets formulated with varying ratios of corn and soybean meal, using the true and apparent ileal digestibility coefficients reported in Chapter 11, Tables 11-5 and 11-6. It is recognized that these conversions only apply
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FIGURE 3-7
Dietary lysine requirement (%, true ileal digestible basis) of pigs with a mean lean growth rate (carcass fat-free basis) of 325 g/day from 20 to 120 kg body weight as estimated by the model using default equations.
to corn–soybean meal diets, which emphasize the need to formulate on a true ileal digestible basis for diets that contain other ingredients.
The total lysine requirements, expressed as a percent of the diet, generated by the model for pigs with average, medium–high, and high lean growth rates (carcass fat-free lean accretion rates of 300, 325, and 350 g/day, respectively) over the range of 20 to 120 kg body weight are shown in Figure 3-8.
Gestating Sows
Nutrient restriction is used to control weight gain in sows (see discussion in Chapter 1). The model for gestating
TABLE 3-1 Equations for Converting Percentages of Amino Acids from a True Ileal Digestible Basis to an Apparent Ileal Digestible Basis, from an Apparent Ileal Digestible Basis to a True Ileal Digestible Basis, and from a True or Apparent Ileal Digestible Basis to a Total Basis in a Corn–Soybean Meal Dieta
True to Apparentb
Apparent to Truec
a
b
a
b
Arginine
-0.0089
0.9602
0.0092
1.0414
Histidine
-0.0006
0.9456
0.0006
1.0576
Isoleucine
-0.0097
0.9490
0.0103
1.0537
Leucine
0.0157
0.9389
-0.0167
1.0651
Lysine
-0.0210
0.9524
0.0221
1.0500
Methionine
0.0021
0.9415
-0.0022
1.0621
Cystine
-0.0002
0.9084
0.0003
1.1008
Methionine + Cystine
0.0018
0.9246
-0.0020
1.0816
Phenylalanine
-0.0089
0.9481
0.0093
1.0548
Tyrosine
-0.0030
0.9463
0.0031
1.0567
Phenylalanine + Tyrosine
-0.0118
0.9473
0.0124
1.0556
Threonine
-0.0150
0.9061
0.0165
1.1036
Tryptophan
-0.0074
0.9130
0.0081
1.0953
Valine
-0.0049
0.9230
0.0054
1.0834
True to Totald
Apparent to Totale
a
b
a
b
Arginine
0.0213
1.0571
0.0311
1.1009
Histidine
0.0119
1.0884
0.0126
1.1511
Isoleucine
0.0070
1.1198
0.0180
1.1800
Leucine
-0.0452
1.1378
-0.0641
1.2119
Lysine
0.0365
1.0973
0.0607
1.1522
Methionine
0.0024
1.0948
0.0000
1.1628
Cystine
0.0029
1.1447
0.0031
1.2603
Methionine + Cystine
0.0053
1.1205
0.0031
1.2119
Phenylalanine
-0.0051
1.1261
0.0054
1.1877
Tyrosine
0.0031
1.1091
0.0066
1.1721
Phenylalanine + Tyrosine
-0.0015
1.1186
0.0124
1.1808
Threonine
0.0191
1.1373
0.0379
1.2551
Tryptophan
0.0043
1.1036
0.0132
1.2088
Valine
0.0052
1.1337
0.0113
1.2283
aAlthough linear relationships are indicated, the actual relationships are more complex.
bFrom true to apparent ileal digestible amino acids: apparent, % = a + (b × true, %).
cFrom apparent to true ileal digestible amino acids: true, % = a + (b × apparent, %).
dFrom true ileal digestible amino acids to total amino acids: total, % = a + (b × true, %).
eFrom apparent ill digestible amino acids to total amino acids: total, % = a + (b × apparent, %).
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FIGURE 3-8
Dietary lysine requirements (%) of pigs of medium, high–medium, and high lean growth rates with carcass fat-free lean gains averaging 300, 325, and 350 g/day from 20 to 120 kg body weight as estimated by the model using default equations. The requirements are for total lysine, assuming a corn–soybean meal mixture.
sows approaches the issue of restriction in either of two ways. First, the user can provide the amount of DE consumed daily as input data, along with the sow's body weight at breeding and the estimated litter size. The model will then calculate the estimated weight gain (and the composition of that gain) and the amount of each amino acid needed to achieve that gain. Second, the user can provide the desired amount of weight gain as input data, along with the sow's body weight at breeding and the litter size. The model will then calculate the amount of DE and amino acids needed to achieve that desired gain. The two approaches to the calculations are based on the same quantitative relationships, described below.
Composition of Weight Gain
Based on the data of Beyer et al. (1994), the products of conception associated with each fetus are assumed to total 2.28 kg in weight and contain 246 g of protein. The remainder of the weight gain of the gestating sow is in the maternal body and includes both lean and adipose tissues. The proportion of the maternal gain that is fat tissue is estimated based on the following equation from the data of Beyer et al. (1994):
where MG is maternal weight gain (kg). Note that the regression coefficient (0.638 in Equation 3-6) will likely vary among animals. The choice of this relationship reflects the assumption that when amino acid requirements are met and energy intake is restricted, it is the amount of energy that sets the limit of fat tissue accretion. The amount of lean tissue that is accreted is the difference between fat tissue accretion and total maternal weight gain.
When the user provides the DE intake, maternal weight gain is determined from the amount of energy available, assuming that the daily energy requirement for growth of the products of conception is 35.8 kcal of ME/pig. The maintenance requirement is 106 kcal of ME/kg0.75. The energy available for maternal gain is the difference between DE intake converted to ME by the factor of 0.96 and the sum of the energy required for maintenance and the products of conception. The energy (ME) for maternal gain (MEG) is converted to weight gain by the following relationship derived from the data of Beyer et al. (1994):
The daily weight gain is the sum of the maternal weight gain and the daily weight gain of the products of conception (19.8 g/day times the number of pigs). The total weight gain for gestation can then be calculated and partitioned to fat and lean as noted above.
Requirement for Energy
The daily energy requirement is the sum of the requirements for maintenance, for protein and fat accretion, and for thermoregulation. Tissue accretion is the sum of that in the maternal body and the products of conception.
Maintenance
The daily maintenance requirement of the gestating sow is considered to be 106 kcal ME/kg BW0.75 (or 110 kcal DE/kg BW0.75) (National Research Council, 1988).
Protein And Fat Accretion
The amounts of protein and fat accreted daily are calculated as described above, and assuming the gestation length is 115 days. The energy cost of protein accretion is assumed to be 10.6 kcal of ME/g and that of fat accretion to be 12.5 kcal of ME/g.
Products Of Conception
The daily energy requirement for the products of conception is 35.8 kcal of ME for each fetus.
Thermoregulation
Additional energy is required when sows are maintained in a cold environment. In the model, an average 24-hour temperature of 20°C is considered as ideal. The model predicts that a sow with an average gestation weight of 200 kg will need approximately 240 additional kcal of ME (250
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kcal of DE) per day for each 1°C below 20°C. No adjustment is made for temperatures above 20°C.
The total daily requirement for ME is the sum of the requirements for maintenance, for tissue accretion, for the products of conception, and for thermoregulation. The requirement for DE is the requirement for ME/0.96.
Requirement for Lysine
Maintenance
The daily maintenance requirement for true ileal digestible lysine is considered to be 36 mg/kg BW0.75, as for growing pigs.
Protein Accretion
The daily nitrogen retention is calculated as the sum of maternal protein gain divided by 6.25, and the nitrogen accretion in the products of conception. Regression analysis of the data of King and Brown (1993) shows the true digestible requirement above maintenance for gestating sows to be 0.807 g of lysine/g of nitrogen retained, assuming the true digestibility values shown in Table 11-6 for the ingredients used in the experimental diets (wheat, skim milk powder, and soybean meal). If this parameter is expressed as grams of true ileal digestible lysine above maintenance per gram of accreted protein, the value is 0.129 (0.807/6.25 = 0.129). This value is similar to the corresponding value of 0.12 used in the growth model (see Equation 3-5). The good agreement lends confidence in both parameters. It was suggested in an earlier review (Pettigrew, 1993), based largely on requirement estimates of the National Research Council (1988), that threonine was likely the first-limiting amino acid in the diets used by King and Brown (1993). However, more recent calculations of the Pettigrew (1993) data produced estimates that suggest lysine and threonine are virtually co-limiting in these diets. Thus, it is considered appropriate to treat the response as though lysine were limiting.
The total daily requirement for lysine is the sum of the requirements for maintenance and for protein accretion.
Requirements for Other Amino Acids
Daily requirements for the other essential amino acids are estimated by a method analogous to the one used for growing pigs. There is a set of requirement ratios for maintenance and another set for protein accretion (Chapter 2). The final blend of the two patterns depends on the relative proportion of lysine needed for maintenance and accretion. The patterns are on a true ileal digestible basis.
Expression of Amino Acid Requirements
The procedures described above produce estimates of amino acid requirements (true ileal digestible basis) expressed in g/day. The daily DE intake is either provided by the user or estimated within the model, so amino acid requirements are easily expressed as g/Mcal DE. The user provides the energy density of the diet (Mcal DE/kg), which allows the calculation of the amount of feed consumed (kg/day). Then, the amino acid requirements are calculated as a percentage of the diet, on a true ileal digestible basis. The percentage requirements are also expressed on an apparent ileal digestible basis and a total basis (in a corn–soybean meal diet) by means of the equations given in Table 3-1.
Lactating Sows
Estimation of nutrient requirements for lactating sows is complicated by the sow's propensity to contribute energy and amino acids retrieved from her own body to help support her milk production. Many sows will not consume enough feed to provide fully the enormous amount of nutrients needed for milk production, and therefore they lose weight. The amount of body reserves used for milk production appears to vary widely.
Milk production potential also varies widely among sows, which causes large variations in nutrient requirements. Therefore, the user must describe the pertinent situation by providing information on the number of suckling pigs per litter and the average daily body weight gain of the suckling pigs.
The model approaches the calculations in either of two ways. First, the user can provide the amount of energy consumed daily as input, along with litter size and rate of growth of the suckling pigs. The model will then calculate the estimated weight gain or loss, as well as the amino acid requirements to meet the target level of milk production. Second, the user can provide the weight gain or loss of the sow during lactation as input, along with data on litter size and growth rate of the suckling pigs. The model will then calculate the amount of DE and amino acids needed.
The model is designed to calculate amino acid requirements for observed levels of milk production. It is tentatively assumed, in the absence of convincing data, that these nutrient levels will also maximize subsequent reproductive performance. This assumption, however, requires further testing.
The two approaches to the calculations are based on the quantitative relationships described below.
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Requirement for Energy
The daily energy requirement is the sum of the requirements for maintenance, milk production, and thermoregulation.
Maintenance
The daily maintenance requirement of the lactating sow is considered to be 106 kcal of ME/kg BW0.75 (or 110 kcal of DE/kg BW0.75), the same as for the gestating sow.
Milk Production
The amount of energy transferred from the sow to the suckling litter in milk is estimated by a rearrangement of the equation of Noblet and Etienne (1989):
where Milk energy is expressed in kcal GE/day and Litter gain is in g/day.
The amount of dietary ME required to produce this amount of milk energy is calculated by dividing the milk energy by 0.72, assuming that the marginal efficiency of use of ME for milk production is 72 percent (Noblet and Etienne, 1987).
Thermoregulation
Lactating sows kept in a cold or hot farrowing house will adjust their energy intake accordingly. The model considers an average 24-hour temperature of 20°C as ideal and it predicts that an additional 310 kcal of dietary ME (323 kcal of DE) will be consumed per day by sows for every 1° below 20°C. Similarly, 310 fewer kcal of ME (323 kcal of DE) will be consumed per day by sows for every 1° above 20°C.
Energy From The Sow's Body
The total energy requirement is modified by the energy associated with changes in body weight during lactation. Regression analysis of the data of Beyer et al. (1994) produced the following relationship:
where protein gain is in g/day and ADG is the sow's average daily gain of body weight in grams. Note that both protein gain and ADG are often negative, reflecting weight loss in the lactating sow. The composition of body weight gain or loss in the lactating sow may vary with several factors, including energy and amino acid intake. However, a constant relationship is used in the model for simplicity.
This relationship is used directly for calculation of energy balance when the user provides body weight change as an input. Each gram of protein retrieved from the sow's body is assumed to provide 5.6 kcal of GE toward meeting the energy requirement. The amount of protein is divided by 0.23 to estimate the amount of lean tissue mobilized (assuming lean tissue is 23 percent protein). Subtracting the amount of lean tissue mobilized from the total amount of body weight lost gives an estimate of the amount of adipose mobilized. This adipose tissue is considered to be 90 percent fat, and it is assumed that 9.4 kcal of GE per gram of fat mobilized is available to be applied toward the energy requirement. The total energy from mobilized tissue is used with an efficiency of 0.88 to meet the energy demands of lactation.
The regression equation given above indicates that marginal weight loss is 9.42 percent protein by weight. Further calculations from this number show that 9.55 percent of the energy in the mobilized tissues is from protein (using the assumptions described in the previous paragraph). This relationship is used in estimating the amount of protein, fat, and body weight lost when the DE intake (provided as an input) is less than the energy demand.
Requirement for Lysine
The daily requirement for lysine is the sum of the requirements for maintenance and for milk production, with a reduction to account for the use of the sow's body protein to provide part of the lysine needed for milk production.
Maintenance
The daily maintenance requirement for true ileal digestible lysine is considered to be 36 mg/kg BW0.75, as for growing pigs.
Milk Production
The requirement is taken to be 22 g of apparent ileal digestible lysine/kg of litter weight gain. This factor was derived from a review of the literature patterned after that of Pettigrew (1993). From several empirical estimates of the lysine requirement to maximize milk production, the requirement and the litter growth rate at the requirement were recorded. The original diet formulations were used to calculate the apparent ileal digestible lysine levels. Reports included in the summary were those used by Pettigrew (1993) in his review (Boomgaardt et al., 1972; Lewis and Speer, 1973; O'Grady and Hanrahan, 1975; Chen et al., 1978; Stahly et al., 1990; Johnston et al., 1993) and one more recent one (Monegue et al., 1993). A total of eight requirement estimates were included. The lysine require-
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ments were regressed on the litter growth rates (Figure 3-9), to produce the following equation:
where Lysine is the apparent ileal digestible lysine requirement in g/day, and Litter gain is in g/day. The coefficient, 0.022, is the factor introduced above. The requirement estimate is then converted from apparent to true ileal digestible lysine.
From The Sow's Body
The intercept in Equation 3-10 suggests that the sows in these studies were contributing 6.39 g of lysine/day from their body tissues to support milk production. To this number is added the amount of lysine lost unavoidably from the body (the maintenance requirement). The maintenance requirement for the sows in these experiments is estimated to be 1.67 g/day, so the total amount of lysine contributed from the sow's body is estimated to be the sum of these two numbers, 8.06 g/day.
There are alternate methods for the use of the information described above in estimating lysine requirements. The first method is to simply add the maintenance requirement to the total amount of lysine needed to support milk production (0.022 g of lysine/g of litter weight gain). This sum is conceptually the amount needed to prevent mobilization of the sow's body protein for providing amino acids for milk production. The second method is to subtract from that number the 8.06 g/day described above as the amount that the sow will contribute from her body without reducing milk yield. That smaller number is conceptually the amount needed to maximize milk production while accepting protein loss from the sow's body. The model uses a third, intermediate method. It subtracts only the 6.39 g/day that is the intercept in Equation 3-9. Note that this estimate of body tissue mobilization is completely independent of the estimates of tissue mobilization that
FIGURE 3-9
Relation of litter growth rate to dietary apparent ileal digestible lysine intake by lactating sows.
were used in estimating energy requirements and/or weight loss.
Requirements for Other Amino Acids
The requirements for the other essential amino acids are calculated from the ratios of amino acid requirements for maintenance (same as in the growth model), the ratios of amino acids required for milk production (taken as the ratios in milk [Pettigrew, 1993], with one modification), and the ratios of amino acids contributed by body protein (Pettigrew, 1993). The data reported by Pettigrew (1993) were generated from a survey of the literature.
The ratios of amino acids needed for milk production were modified from those offered by Pettigrew (1993) only in the case of valine. There is now evidence at both the whole-animal level (Richert et al., 1996) and the tissue level (Boyd et al., 1995) that the valine requirement of lactating sows is higher than would be predicted from the amount secreted in milk. Therefore, the ratio of valine to lysine for milk production is increased from the value of 0.73 (Pettigrew, 1993) to a value of 0.85. Setting valine at 85 percent of lysine for milk production was based on the assumption that lysine is first-limiting in corn–soybean meal diets containing up to 1.0 percent total lysine. This ratio of 0.85 results in requirement estimations suggesting that lysine and valine are co-limiting in corn–soybean meal diets containing about 1.0 percent lysine, and that valine is first-limiting at higher amino acid concentrations.
Expression of Amino Acid Requirements
The procedures described above produce estimates of amino acid requirements (true ileal digestible basis) expressed in g/day. The daily DE intake is either provided by the user or estimated within the model, so amino acid requirements are easily expressed as g/Mcal DE. The user provides the energy density of the diet (Mcal DE/kg), which allows the calculation of the amount of feed consumed (kg/day). Then the amino acid requirements are calculated as a percentage of the diet, on a true ileal digestible basis. The percentage requirements are also expressed on an apparent ileal digestible basis and a total basis (in a corn–soybean meal diet) by using the equations given in Table 3-1.
Weanling Pigs
The growth model does not estimate energy or amino acid requirements for weanling pigs weighing less than 20 kg body weight, because of insufficient information on biological relationships at this early stage of growth. However, a mathematical equation was used to estimate the
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percentage of total dietary lysine required at a given weight between 3 and 20 kg. The regression equation represents the best-fitting line through the following estimated requirements based on empirical data (see Chapter 2): 1.45% lysine at 5 kg, 1.25% lysine at 10 kg, 1.15% lysine at 15 kg, and 1.05% lysine at 20 kg body weight. The equation (shown in Figure 3-10) is:
The apparent and true ileal digestible percentages of lysine were calculated by rearranging the equation involving the coefficients in Table 3-1. It is recognized that these coefficients apply to corn-soybean meal mixes and do not take into account other ingredients (milk and/or blood byproducts) that likely will be in diets for young pigs. The percentage true ileal digestible lysine is converted to grams per day and the lysine requirement for protein accretion is calculated by subtracting the lysine requirement for maintenance. The ratios of other amino acids to lysine for maintenance and accretion are used to calculate the true ileal digestible requirement for each of the other amino acids. The total requirements (maintenance plus accretion) are expressed as a percentage of intake and can then be converted to apparent and total by the equations in Table 3-1.
The user should be aware that although this method of estimating the other amino acid requirements based on their ratio to lysine seems logical, there is no experimental evidence to support such a method.
DE intake is estimated by a modification of the National Research Council (1986) equation for pigs weighing less than 20 kg body weight, as follows:
Feed intake is then determined by dividing DE intake by the DE concentration of the diet. Figure 3-11 illustrates
FIGURE 3-10
Dietary lysine requirement (%) of pigs from 3 to 20 kg body weight using the default equation of the model (total basis, assuming a corn-soybean meal diet).
FIGURE 3-11
Estimated daily feed intake of pigs from 3 to 20 kg and from 20 to 120 kg body weight based on the default equations for digestible energy intake in the model divided by the digestible energy concentration of the diet (3,400 kcal/kg).
the estimated feed intake of pigs from 3 to 20 kg and from 20 to 120 kg based on the default equations of the model. The daily amino acid requirements (true, apparent, total) are calculated by multiplying the percentage estimates by the daily feed intakes.
The equations estimating amino acids do not take into account differences in genetic potential for lean growth rate or differences in health status, both of which likely have a large impact on the requirements of weanling pigs. Also, gender is not considered. Temperature and space per pig, however, can be entered by the user, and they impact the DE intake estimates.
The user should be aware that the growth model does not always allow a smooth transition in the amino acid requirements from the end of the starting phase (19.9 kg body weight) to the beginning of the growing phase (20 kg body weight). This is due to the fact that the model estimates amino acid requirements at 20 kg based on the lean growth rate of the pigs, whereas lean growth rate is not taken into account by the model during the starting phase.
Mineral And Vitamin Requirements
Traditional modeling procedures were not used to estimate the requirements for minerals and vitamins. Instead, estimates were made from empirical experiments.
Estimates were made on a dietary concentration basis for six weight ranges of pigs (3 to 5, 5 to 10, 10 to 20, 20 to 50, 50 to 80, and 80 to 120 kg body weight) and for gestating and lactating sows. Exponential equations were then used to fit the midpoints of these weight ranges for starting, growing, and finishing pigs, by means of the following equation.
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Two examples of how the equation gives the requirement for a mineral (calcium) and a vitamin (riboflavin) compared with the estimated requirements for the various weight categories of pigs from 3 to 120 kg body weight are shown in Figures 3-12 and 3-13, respectively. Note that the equation gives a requirement value that intersects the estimated requirement at approximately the midpoint of the body weight range. The individual coefficients for the prediction equations for the minerals and vitamins are shown in Table 3-2. The daily requirements were calculated by multiplying the predicted dietary concentrations by the daily feed intake.
Exponential equations were not used to estimate mineral and vitamin requirements for gestating or lactating sows. Daily requirements of minerals and vitamins for sows were calculated by multiplying the estimated dietary concentrations by the daily feed intake.
Evaluation Of The Models
The models were evaluated in three ways (Black, 1995): (1) simulation of experiments reported in the literature,
FIGURE 3-12
Estimated dietary calcium requirement (%) of pigs from 3 to 120 kg body weight using the generalized exponential equation in the model.
FIGURE 3-13
Estimated dietary riboflavin requirement (mg/kg) of pigs from 3 to 120 kg body weight using the generalized exponential equation in the model.
and comparison of simulated to measured requirements; (2) subjective evaluation of the response of model predictions to changes in input values (behavioral analysis); (3) tests of the sensitivity of model predictions to changes in selected model parameters.
Growth Model
Experimental estimates of lysine requirements listed in Table 2-2 were simulated with the model, and the predicted requirements compared to the requirements estimated directly from the experimental data. Inputs to the model included the mean growth rate of carcass fat-free lean tissue and the feed intake recorded in the experiment. Several reports did not provide adequate information to support a reliable simulation, and these were excluded from the process. The default lean accretion curve was used in all cases. Studies included were reports by Rao and McCracken (1990), Friesen et al. (1994), and Coma et al. (1995a,b).
There is a systematic error in this approach that causes the model to underestimate the requirement determined experimentally. Most experimental estimates of the lysine requirement under a given set of conditions are conducted over a significant time period, as the pigs grow several kilograms. During the experimental period, the lysine requirement presumably changes. The pigs would be expected to respond to higher dietary lysine concentrations during the early part of the experiment than later, and this early response would be reflected in the requirement estimate. Therefore, the experimentally determined requirement, expressed as percentage of the diet, is appropriate for pigs near the initial weight. However, the feed intake reported for the experiment is usually for the entire period, so it is necessary when using the model to estimate the requirement of pigs at the midpoint of the experiment. This requirement, as percent of the diet, should be lower than the experimental estimate of the requirement at the beginning of the experiment. In order to minimize this bias, experiments that covered more than 25 kg growth were arbitrarily excluded from the evaluation process. However, some bias remains.
The results are summarized in Table 3-3. Overall, the model underestimated the requirement by 2.0 g/day. Examination of the difference in three stages of growth showed a mean difference of -0.8 g/day from 20 to 50 kg body weight, an overestimate of 0.1 g/day from 50 to 80 kg, and an underestimate of 4.4 g/day from 80 to 120 kg. On a percentage of the diet basis, the model underestimated the requirements by 0.08 percentage units. The percentage estimates of the model were close to the measured requirements for the two lighter weight groups, but the model estimates were 0.15 percentage points less than the measured requirement for the heaviest weight class.
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TABLE 3-2 Coefficients Used in the Growth Model to Predict Mineral and Vitamin Requirements (percentage or amount/kg of diet) for Pigs of Various Body Weightsa
Coefficients
a
b
c
R2
Minerals
Calcium (%)
0.0658
-0.1023
-0.0185
0.99
Phosphorus, total (%)
-0.2735
-0.0262
-0.0244
0.99
Phosphorus, available (%)
-0.0557
-0.4160
0.0050
0.99
Sodium (%)
-0.3897
-0.7984
0.0815
0.97
Chlorine (%)
-0.3010
-0.8317
0.0724
0.95
Magnesium (%)
—
—
—
—
Potassium (%)
-1.2375
0.0736
-0.0412
0.99
Copper (mg)
1.8799
0.0097
-0.0391
0.99
Iodine (mg)
—
—
—
—
Iron (mg)
4.6600
0.0642
-0.0597
0.99
Manganese (mg)
2.0364
-0.4508
0.0317
0.91
Selenium (mg)
-0.6910
-0.3236
0.0097
0.89
Zinc (mg)
4.9230
-0.1716
-0.0134
0.96
Vitamins
Vitamin A (IU)
8.2033
-0.3548
0.0262
0.92
Vitamin D3 (IU)
5.6700
-0.1722
0.0042
0.89
Vitamin E (IU)
3.4095
-0.5082
0.0628
0.83
Vitamin K (menadione) (mg)
—
—
—
—
Biotin (mg)
—
—
—
—
Choline (g)
0.2659
-0.6297
0.0664
0.98
Folacin (mg)
—
—
—
—
Niacin, available (mg)
3.4970
-0.3884
0.0094
0.98
Pantothenic acid (mg)
2.8651
-0.3171
0.0250
0.99
Riboflavin (mg)
1.7129
-0.2314
0.0005
0.99
Thiamin (mg)
—
—
—
—
Vitamin B6 (mg)
1.3009
-0.5088
0.0477
0.93
Vitamin B12 (µg)
2.9577
0.1840
-0.1092
0.96
a Estimated requirements = ea+b(lnBW)+c(lnBW)2, where BW is body weight. Body weights used in the derivation of the equations represented the midpoints of the weight ranges of 3 to 5, 5 to 10, 10 to 20, 20 to 50, 50 to 80, and 80 to 120 kg. These equations will give values that approximate the mineral and vitamin requirements for pigs of these weight ranges shown in Table 10-5.
TABLE 3-3 Evaluation of Growth Modela
Total dietary lysine
(grams/day)
(% of diet)
Author
Gender
Regimen
Mean BW (kg)
Carcass fat-free lean gain (g/day)
Meas req
Pred req
Diff
% Meas
Meas req
Pred req
Diff
% Meas
Coma et al. (1995a)
Barrows
Ad lib
31.3
292
18.3
15.4
-2.9
84.2
0.97
0.81
-0.16
83.5
Coma et al. (1995a)
Barrows
Restrict
31.3
292
13.1
11.3
-1.8
86.3
1.01
0.87
-0.14
86.1
Rao and McCracken (1990)
Boars
Ad lib
44.0
412
21.2
23.1
1.9
109.0
1.12
1.26
0.14
112.5
Friesen et al. (1994)
Gilts
Ad lib
44.5
376
21.5
21.2
-0.3
98.6
1.28
1.24
-0.04
96.9
Friesen et al. (1994)
Gilts
Ad lib
63.8
376
22.2
22.3
0.1
100.5
1.03
1.06
0.03
102.9
Coma et al. (1995a)
Barrows
Ad lib
98.3
292
21.9
17.2
-4.7
78.5
0.61
0.48
-0.13
78.7
Coma et al. (1995a)
Barrows
Restrict
98.3
292
22.8
16.8
-6.0
73.7
0.85
0.63
-0.22
74.1
Coma et al. (1995b)
Gilts
Ad lib
105.5
292
19.1
16.5
-2.6
86.4
0.66
0.57
-0.09
86.4
Overall mean
-2.0
89.6
-0.08
90.1
Period means
20 to 50 kg BW
-0.8
94.5
-0.05
94.8
50 to 80 kg BW
0.1
100.5
0.03
102.9
80 to 120 kg BW
-4.4
79.5
-0.15
79.8
a Column headings: Meas req = measured lysine requirement; Pred req = predicted lysine requirement from the model; Diff = difference in the measured and predicted requirement; % Meas = predicted requirement as a percentage of the measured requirement.
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TABLE 3-4 Evaluation of the Lactation Modela,b
DE Intake Entered
Weight Change Entered
Author
Meas req
Pred req
Diff
% Meas
Pred req
Diff
% Meas
Total Dietary Lysine (g/day)
Touchette et al. (1996)
49.7
38.4
-11.3
77.3
42.3
-7.4
85.1
Stahly et al. (1992)
47.0
52.2
5.2
111.1
56.8
9.8
120.9
Coma et al. (1996)
55.3
54.9
-0.4
99.3
49.6
-5.7
89.7
Sauber, low-lean, (1996)
42.0
46.6
4.6
111.0
45.8
3.8
109.0
Sauber, high lean, (1996)
51.0
48.1
-2.9
94.3
42.2
-8.8
82.7
King et al. (1993)
41.0
40.9
-0.1
99.8
40.8
-0.2
99.5
Knabe et al. (1996)
42.0
41.8
-0.2
99.5
37.2
-4.8
88.6
Mean
46.9
46.1
-0.7
98.9
45.0
-1.9
96.5
Total Dietary Lysine (% of diet)
Touchette et al. (1996)
1.28
0.99
-0.29
77.3
0.89
-0.39
69.5
Stahly et al. (1992)
0.90
1.00
0.10
111.1
0.92
0.02
102.2
Coma et al. (1996)
0.83
0.82
-0.01
98.8
0.89
0.06
107.2
Sauber, low-lean, (1996)
1.15
1.10
-0.05
95.7
1.15
0.00
100.0
Sauber, high lean, (1996)
1.15
0.92
-0.23
80.0
1.11
-0.04
96.5
King et al. (1993)
1.08
1.08
0.00
100.0
1.08
0.00
100.0
Knabe et al. (1996)
0.75
0.74
-0.01
98.7
0.80
0.05
106.7
Mean
1.02
0.95
-0.07
94.5
0.98
-0.04
97.5
a The evaluation is based on the measured and predicted requirements of total dietary lysine. Two conditions were tested—either DE intake was entered in the model or sow lactation weight change was entered.
b Column headings: Means req = measured lysine requirement; Pred req = predicted lysine requirement from the model; Diff = differences in the measured and predicted requirement; % Meas = predicted requirement as a percentage of the measured requirement.
Behavioral analysis showed the model to perform qualitatively as expected and consistent with current nutritional concepts. Sensitivity analysis showed the model to be very sensitive to the parameter that relates the lysine requirement to whole body protein accretion (0.12 g true ileal digestible lysine/g protein accreted).
Gestation Model
No reports were identified that provided all of the information needed to appropriately test the gestation model by comparison of simulated to measured requirements.
Lactation Model
Experimental estimates of lysine requirements were simulated with the model, and the predicted requirements compared to the requirements estimated directly from the experimental data. Inputs to the model were DE density, body weight after farrowing, lactation length, number of pigs in the litter, daily pig weight gain, environmental temperature, and either DE intake or sow weight change during lactation. A total of seven requirement estimates from six reports (Stahly et al., 1992; King et al., 1993; Knabe et al., 1996; Coma et al., 1996; Sauber, 1996; Touchette et al., 1996) were simulated, including studies with both high lean and low-lean genotypes by Sauber (1996). In several of these experiments, performance improved as the dietary lysine level increased all the way to the highest level. In those cases, the measured requirement was taken to be the highest level fed, even though the requirement for maximum performance may have been higher. This approach is appropriate in evaluation of this model because the model estimates the amount of lysine needed to reach the level of performance attained in the experiment.
The results are summarized in Table 3-4. When DE intake was provided as an input, the predicted daily lysine requirement averaged 46.1 g, which is 0.7 g less than the measured requirement (range of -11.3 to 5.2 g). The average of the predicted requirements expressed as percentage of the diet was also slightly less than the average measured requirement, and individual cases ranged from an underestimate of 0.29 percent of the diet to an overestimate of 0.10 percent. When sow weight change during lactation was provided as an input rather than DE intake, the predicted daily requirement averaged 1.9 g less than the measured requirement (range of -8.8 to 9.8 g). When the requirement was expressed as percentage of the diet, the model underestimated the requirement by 0.04 percent relative to the measured values, with a range of -0.39 to 0.06 percent.
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Representative terms from entire chapter:
body weight