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Appendix 1
Equations Used to Model the Biological Basis for Predicting Nutrient Requirements
Growth Model
Assumptions
There are a number of constants or assumptions that are used in the model, and these are as follows.
Rate of carcass fat-free lean (FFL) gain is a function of body weight (BW) and is the same for barrows, gilts, and boars
Lysine required per unit of protein accretion is 0.12 g of true digestible lysine/g of protein accretion
Maintenance lysine requirement is 0.036 g/kg of BW raised to 0.75 power (BW0.75)
ME is 0.96 × DE
Conversion of carcass FFL to whole body protein: whole body protein = FFL/2.55
Protein concentration in FFL tissue is 23%
Fat concentration in fat tissue is 90%
ME required for maintenance is 106 kcal/kg of BW0.75
ME required for protein synthesis is 10.6 kcal/g
ME required for fat synthesis is 12.5 kcal/g
Input Data
These include the dietary energy concentration (kcal of DE or ME/kg), daily DE or ME intake (Mcal; note that this value is optional, and if a value is entered it is used in subsequent calculations), pig weight (kg), the number of gilts and the potential FFL gain of gilts (g/day), the number of barrows and the potential FFL gain of barrows (g/day), the number of boars and the potential FFL gain of boars (g/day), space per pig in square meters (m2), and temperature in °C. The effects of space per pig are minimized at 0.41 m2 up to 20 kg BW, at 1.06 m2 from 20 to 50 kg BW, and at 1.10 m2 above 50 kg BW.
Calculations
Average FFL gain for the group of pigs is calculated from the number of barrows, gilts, and boars times the respective FFL gain rate divided by the total number of pigs in the group.
Carcass FFL gain, g/day. The fractional FFL gain based on the BW is calculated from the following relationship.
The result is multiplied by the average FFL gain to give the carcass FFL gain for the simulation.
DE intake, Mcal/d—The predicted intake uses the following equations with adjustments for temperature, space per pig, and gender. Note: if feed intake is specified, the predicted feed intake is not used and the specified intake is used.
For pigs less than 20 kg BW:
For pigs from 20 to 120 kg BW:
Adjustments to DE intake.
Gender: between 30 and 120 kg BW, an adjustment for gender distribution is calculated from the following relationship.
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The adjustment is added for barrows and subtracted for gilts and boars. A weighting factor is calculated for mixed groups by subtracting the number of gilts and boars from the number of barrows and dividing by the total number of pigs. The adjustment is multiplied by the weighting factor to obtain the final adjustment to be added to DE intake.
b.
Space allowance (SP). The adjustment is calculated and the negative result is added to DE intake.
Pigs 20 kg BW or less: for space allowance less than 0.41 m2
Pigs from 20 to 50 kg BW: for space allowance less than 1.059 m2
Pigs 50 kg BW or greater: for space allowance less than 1.095 m2
Note: Caution should be used in making adjustments for crowding because the adjustments are not precise. Adjustments may be too great at the lower end of each weight range category.
Temperature (T). The adjustment is calculated and added to DE intake.
Potential whole body protein gain based on energy intake. Whole body protein gain based on the following equation.
Carcass FFL gain (step 2) to whole body protein gain, g/day. Conversion of FFL gain to whole body protein gain by a factor of 2.55.
Whole body protein gain (g/day) is the value that is used in the following calculations and is the smaller of the protein gain from step 5 and from the lean gain accretion curve (step 6).
True ileal digestible lysine required for maintenance (g/day).
True ileal digestible lysine required for protein gain (g/day).
For pigs from 20 to 120 kg BW:
For pigs 20 kg BW or less:
True ileal digestible lysine, % = (Total lysine - 0.0365)/1.0973 Feed consumed, g = DE intake/DE concentration True ileal digestible lysine (g/day) = True ileal digestible lysine (%) × Feed consumed (g/day) × 0.01 True ileal digestible lysine for gain (g/day) = True ileal digestible lysine (g/day) - Lysine required for maintenance (step 8)
True ileal digestible amino acid requirements (g/day). The true ileal digestible lysine required for maintenance (step 8) is multiplied by the ratio of each amino acid to lysine for maintenance (Chapter 2, Table 2-1). The true ileal digestible lysine for gain (step 9) is multiplied by the ratio of each amino acid to lysine for gain (Chapter 2, Table 2-1). The sum of the requirement for maintenance and gain for each amino acid is the daily total true ileal digestible requirement.
True ileal digestible requirements (g/day) are converted to requirements as a percentage using the DE intake/day and the DE concentration of the diet. The true ileal digestible requirements as a percentage are converted to apparent or total using the equations in Chapter 3, Table 3-1.
Estimating potential performance
ME intake ME intake = DE intake × 0.96
ME required for protein synthesis Whole body protein gain (step 7) × 10.6
ME for maintenance 106 × BW0.75
Thermoregulatory energy Step 4c
Energy available for fat synthesis ME intake - step b - step c - step d
Fat synthesized (g/day) Step e/12.5
Fat tissue (g/day) Step f/0.9
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Protein tissue (g/day) Whole body protein gain/0.23
Daily BW gain (g/day) (step g + step h)/0.94
Feed-to-gain ratio Daily feed intake/Daily BW gain
Crude protein (corn–soybean meal diet) Crude protein (%) = 5.22 + (15.51 × True digestible lysine, %)
Gestation Model
Assumptions
A number of constants or assumptions have been made and are as follows.
Gestation length is 115 days
Gestation weight gain in the products of conception is 2.28 kg/pig (19.8 g/day for each pig)
Protein gain in the products of conception is 245 g/pig (2.13 g/day for each pig)
Nitrogen gain in the products of conception is 39.2 g/pig (0.34 g/day for each pig)
Body weight (BW) is the weight at breeding plus one-half of the total gestation weight gain
Metabolic body weight is BW0.75
ME required for maintenance is 106 kcal/kg of BW0.75
ME required for protein synthesis is 10.6 kcal/g
ME required for fat synthesis is 12.5 kcal/g
ME required for daily gain of the products of conception is 35.8 kcal/pig
Lean tissue contains 23% protein
Fat tissue contains 90% fat
True ileal digestible lysine requirement for maintenance is 0.036 g/kg of BW0.75
Input Data
These include the DE or ME concentration (kcal/kg), daily DE or ME intake (optional) (kcal/day), sow weight at breeding (kg), the expected number of pigs born, the desired weight gain during gestation (kg) and temperature (°C).
Note: Daily energy intake is an optional input. If daily energy intake is not provided, the energy required for the desired weight gain is calculated. If a value is entered for daily energy intake, weight gain is calculated using the input energy intake and then the amino acid requirements are calculated to support that level of performance.
Calculations
Maternal weight gain
If DE or ME intake is not input, then: Maternal weight gain = Gestation weight gain - (2.28 × No. of pigs) Maternal fat gain = (Maternal weight gain × 0.638) - 9.08 Maternal lean tissue gain = Maternal weight gain - Maternal fat gain
If daily DE or ME intake is input then: ME in the products of conception = No. of pigs × 35.8 kcal/pig Maintenance ME requirement = 106 × BW0.75 ME for maternal weight gain = ME intake - ME in the products of conception - maintenance ME Maternal weight gain = 87 + (ME for maternal weight gain - 0.12171) Daily gestation weight gain = (Maternal weight gain) + (No. of pigs × 19.8 g) Gestation weight gain = Daily gestation weight gain × 115
Because the maintenance requirement is dependent on gestation weight gain, these relationships are solved by iteration. Gestation weight gain is then partitioned into protein and fat gain by the same relationships as are used when daily DE intake is not provided.
Average daily nitrogen retention is the sum of maternal nitrogen retention and nitrogen in the products of conception.
Maternal nitrogen retention
Nitrogen in the products of conception
True ileal digestible lysine requirement for gain is calculated from N retention.
True ileal digestible lysine requirement for maintenance.
Total true ileal digestible lysine requirement is the sum of the requirement for gain and maintenance.
True ileal digestible amino acid requirement (g/day). The true ileal digestible lysine required for maintenance (step 4) is multiplied by the ratio of each amino acid to lysine for maintenance (see Chapter 2, Table 2-1). The true ileal digestible lysine required for gain (step 3) is multiplied by the ratio of each amino acid to lysine for protein accretion (Chapter 2, Table 2-1). The total require-
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ment is the sum of the requirements for maintenance and gain.
True ileal digestible requirements (g/day) are converted to a percentage using the DE intake/day and the DE concentration of the diet. The true ileal digestible requirements as a percentage are converted to apparent or total using the equations in Chapter 3, Table 3-1.
Estimation of energy requirements
ME for protein synthesis (Total N retained/0.16) × 10.5 kcal/g
ME for maternal fat synthesis Maternal fat gain × 12.5 kcal/g
ME for the products of conception No. of pigs × 35.8 kcal/pig
ME for thermoregulation. Because gestating sows are limit fed, only energy required to maintain body temperature is considered: (20 - T) × BW0.75 × 4.5.
ME for maintenance 106 × BW0.75
The total ME required is the sum of a through e.
Estimating potential performance
Weight gain of the products of conception No. of pigs × 19.8 g × 115 days
Maternal weight gain Gestation weight gain - (2.28 kg × No. of pigs)
Maternal fat tissue gain ((Daily maternal weight gain × 0.638) - 9.08) × 115
Maternal lean tissue gain Maternal weight gain - maternal fat gain
Crude protein (corn–soybean meal diet) Crude protein (%) = 5.22 + (15.51 × True digestible lysine, %)
Lactation Model
Assumptions
A number of constants or assumptions have been made and are as follows:
Body weight (BW) is the postfarrowing weight plus one-half of the total lactation weight change
Metabolic body weight is BW0.75
ME required for maintenance is 106 kcal/kg of BW0.75
ME required for protein synthesis is 10.6 kcal/g
ME required for fat synthesis is 12.5 kcal/g
Lean tissue contains 23% protein
Fat tissue contains 90% fat
True ileal digestible lysine requirement for maintenance is 0.036 g/kg of BW0.75
Input Data
These include the dietary DE or ME concentration (kcal/kg), daily DE or ME intake (optional) (mcal/day), sow weight after farrowing (kg), expected weight change during lactation (kg) (Note: weight loss is entered as a negative value), daily pig weight gain (g/day), lactation length (days), the number of pigs in the litter, and farrowing house temperature (°C).
Note: Daily energy intake is an optional input value. If energy intake is entered, the weight change is calculated and any entered expected weight change is not used.
Calculations
Lactation weight change is calculated if DE intake is an input.
ME intake = DE intake × 0.96 (or input ME)
ME required for milk = ((Daily weight gain/pig × No. pigs nursed × 4.92) - (90 × No. pigs nursed))/0.72
Maintenance ME requirement = 106 × BW0.75
Thermoregulatory ME requirement = (20 - T) × 310
Total ME required = Sum of steps b, c, and d
ME available for maternal weight change = ME intake - Total required ME
Protein weight change (g/day) = (((step f/0.88) × 0.0942)/5.6) - 1.47
Fat weight change (g/day) = ((step f/0.88) - ((step f/0.88) × 0.0942))/9.4
Average daily weight change = (step g/0.23) + (step h/0.9)
Lactation weight change = Average daily weight change × Lactation length
Because the lactation weight change affects the metabolic body weight, and therefore the maintenance requirement, the series of equations are solved by iteration.
If DE or ME intake is not an input, the lactation weight change is calculated from the following steps:
Average daily gain (ADG, g) = Lactation weight change (g)/Lactation length
Protein in the weight change (g) = (ADG × 0.0942) + 1.47
Fat in the weight change (g) = ADG - (Protein in the weight change/0.23)
Energy in the weight change = (Protein in the weight change × 5.6) + (Fat in the weight change × 0.9 × 9.4)
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Lysine required
Apparent digestible lysine for milk production (g) = (Daily pig weight gain × Pigs in litter × 0.022) - 6.39
Apparent digestible lysine for milk production (g/day) is converted to a percentage using DE intake and DE concentration
Percentage apparent digestible lysine is converted to percentage true digestible lysine True digestible lysine, % = 1.050013 × apparent digestible lysine, % + 0.022052
Percentage true digestible lysine is converted to g/day using DE intake and DE concentration
Lysine for maintenance = 0.036 × BW0.75
Lysine from tissue = Change in protein × 0.065
Total true ileal digestible lysine requirement = Sum of steps d, e, and f
True digestible amino acid requirements (g/day). The true ileal digestible lysine required for maintenance (step 3e) is multiplied by the ratio of each amino acid to lysine for maintenance (see Chapter 2, Table 2-1). The true ileal digestible lysine required for milk production (step 3d) is multiplied by the ratio of each amino acid to lysine in milk protein (Chapter 2, Table 2-1). The lysine from tissue is multiplied by the ratio of each amino acid to lysine in tissue (Chapter 2, Table 2-1). The total requirement is the sum of the requirements for maintenance, milk production, and tissue change.
True ileal digestible requirements (g/day) are converted to a percentage using the DE intake/day and the DE concentration of the diet. The true ileal digestible requirements as a percentage are converted to apparent or total using the equations in Chapter 3, Table 3-1.
Estimation of energy partitioning
ME for milk production = ((Daily pig weight gain × No. of pigs nursed × 4.92) - (90 × No. of pigs nursed))/0.72
Maintenance ME requirement = 106 × BW0.75
ME in body weight change = Daily ME change × 0.88
Temperature adjustment: 20°C is considered the optimal temperature. Above the optimal temperature, ME intake is reduced 310 kcal/°C. Below the optimal temperature, ME intake is increased 310 kcal/°C
Total ME required = Sum of steps a, b, c, and d
DE intake = ME required/0.96
Estimating potential performance
Maternal lean tissue change (Daily protein weight change (from step 1g or 2b)/0.23 × Lactation length
Maternal fat tissue change (Daily weight change × Lactation length) - Maternal lean tissue change
Estimated milk production (kg/day) (ME for milk production [step 6a] × 0.72)/1208
Crude protein (corn-soybean meal diet) Crude protein (%) = 5.22 + (15.51 × True digestible lysine, %)
Representative terms from entire chapter:
true ileal
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