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15 Computer Model to Estimate Requirements As discussed throughout the text of this publication, nu- (www.nap.edu). By using the software at that site, estimates trient requirements of horses are often best described by a of nutrient requirements can be tailored to specific horses series of equations based on an understanding of the biology more precisely than can be achieved by looking up values in of the horse. Incorporation of these equations into a com- the tables. The computer code used in the program is listed puter model provides a convenient way to calculate require- in this chapter. ments for horses in specific situations (e.g., for a specific Warning: Knowledge of nutritional constraints and lim- weight of horse and for a specific stage of the lifecycle). The itations is essential for the proper use of nutrient require- values in the tables for horses of specific weights (200, 400, ments in tables and especially those generated by computer 500, 600, and 900 kg) given in this publication were gener- programs. Because of the many variables involved and judg- ated by a computer program that uses equations and other ments that must be made in choosing inputs and interpreting information described in previous chapters. Users can ac- outputs, the NRC makes no claim for the accuracy of this cess the program at the National Academies Press website software and the user is solely responsible for risk of use. COMPUTER CODE Required Inputs AnimalType - valid values: MAINTENANCE, STALLION, GROWING, PREGNANT, LACTATING, EXERCISE MAINTENANCE STALLION GROWING PREGNANT LACTATING EXERCISE MatureWeight - kg IntakeLevel - percent of actual bodyweight Age - months MonthOfGest - Months (integer) MonthOfLact - Months (integer) MaintLevel - valid values: 1, 2, 3 1 - Low Maintenance 2 - Average Maintenance 3 - High Maintenance StallionMaintLevel - valid values: 0, 1 0 - Not Breeding 1 - Breeding 285

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286 NUTRIENT REQUIREMENTS OF HORSES WorkLoadGrow - valid values: 0, 1, 2, 3, 4 0 - None 1 - Low 2 - Moderate 3 - Heavy 4 - Very Heavy WorkLoad - valid values: 1, 2, 3, 4 1 - Low 2 - Moderate 3 - Heavy 4 - Very Heavy Outputs DM_req - kg/d DE_req - Mcal/d CP_req - g/d LYS_req - g/d Ca_req - g/d P_req - g/d Mg_req - g/d K_req - g/d VitA_req - IUx1000/d Na_req - g/d Cl_req - g/d S_req - g/d Co_req - mg/d Cu_req - mg/d I_req - mg/d Fe_req - mg/d Mn_req - mg/d Zn_req - mg/d Se_req - mg/d VitD_req - IU/d VitE_req - IU/d Thi_req - mg/d Ribo_req - mg/d SweatLoss - kg/d ——————————————————————————————————————*/ switch (AnimalType) { case “MAINTENANCE”: // Adult Horse at maintenance BodyWeight = MatureWeight; DM_req = (IntakeLevel/100) * BodyWeight; if (MaintLevel == 1) { // Minimum requirement DE_req = 0.0303 * BodyWeight; CP_req = 1.08 * BodyWeight; } if (MaintLevel == 2) { // Average requirement DE_req = 0.0333 * BodyWeight; CP_req = 1.26 * BodyWeight; } if (MaintLevel == 3) { // Elevated requirement DE_req = 0.0363 * BodyWeight; CP_req = 1.44 * BodyWeight; } LYS_req = 0.043 * CP_req; Ca_req = 0.04 * BodyWeight; P_req = 0.028 * BodyWeight;

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COMPUTER MODEL TO ESTIMATE REQUIREMENTS 287 Mg_req = 0.015 * BodyWeight; K_req = 0.05 * BodyWeight; Na_req = 0.02 * BodyWeight; Cl_req = 0.08 * BodyWeight; S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; Cu_req = 0.2 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 40; Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitA_req = 30 * BodyWeight; VitD_req = 6.6 * BodyWeight; VitE_req = 1.0 * BodyWeight; Thi_req = 0.06 * BodyWeight; Ribo_req = 0.04 * BodyWeight; break; case “EXERCISE”: BodyWeight = MatureWeight; DM_req = (IntakeLevel/100) * BodyWeight; if (WorkLoad == 1) { // Light SweatLoss = 0.0025 * BodyWeight; DE_req = (0.0333 * BodyWeight )*1.2; CP_req = (1.26 * BodyWeight) + (0.089 * BodyWeight)+ (SweatLoss * 7.8 * 2.0 / 0.79); Ca_req = (0.06 * BodyWeight); P_req = (0.036 * BodyWeight); Mg_req = (0.019 * BodyWeight); VitE_req = 1.6 * BodyWeight; Thi_req = 0.06 * BodyWeight; Ribo_req = 0.04 * BodyWeight; } if (WorkLoad == 2) { // Moderate SweatLoss = 0.005 * BodyWeight; DE_req = (0.0333 * BodyWeight )*1.4; CP_req = (1.26 * BodyWeight) + (0.177 * BodyWeight) + (SweatLoss * 7.8 * 2.0 / 0.79); Ca_req = (0.07 * BodyWeight); P_req = (0.042 * BodyWeight); Mg_req = (0.023 * BodyWeight); VitE_req = 1.8 * BodyWeight; Thi_req = 0.113 * BodyWeight; Ribo_req = 0.04 * BodyWeight; } if (WorkLoad == 3) { // Heavy SweatLoss = 0.01 * BodyWeight; DE_req = (0.0333* BodyWeight )*1.6; CP_req = (1.26 * BodyWeight) + (0.266 * BodyWeight) + (SweatLoss * 7.8 * 2.0 / 0.79); Ca_req = (0.08 * BodyWeight); P_req = (0.058 * BodyWeight); Mg_req = (0.03 * BodyWeight); VitE_req = 2.0 * BodyWeight; Thi_req = 0.125 * BodyWeight; Ribo_req = 0.05 * BodyWeight; } if (WorkLoad == 4) { // Very Heavy SweatLoss = 0.02 * BodyWeight; DE_req = (0.0363* BodyWeight )*1.9; CP_req = (1.26 * BodyWeight) + (0.354 * BodyWeight) + (SweatLoss * 7.8 * 2.0 / 0.79); Ca_req = (0.08 * BodyWeight); P_req = (0.058 * BodyWeight); Mg_req = (0.03 * BodyWeight);

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288 NUTRIENT REQUIREMENTS OF HORSES VitE_req = 2.0 * BodyWeight; Thi_req = 0.125 * BodyWeight; Ribo_req = 0.05 * BodyWeight; } LYS_req = 0.043 * CP_req; K_req = (0.05 * BodyWeight) + ((1.4/0.5) * SweatLoss); Na_req = 0.02 * BodyWeight + 3.1 * SweatLoss; Cl_req = 0.08 * BodyWeight + 5.3 * SweatLoss; S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; Cu_req = DM_req * 10.0; I_req = DM_req * 0.35; Fe_req = DM_req * 40; Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitA_req = 45 * BodyWeight; VitD_req = 6.6 * BodyWeight; break; case “STALLION”: // Stallion BodyWeight = MatureWeight; DM_req = (IntakeLevel/100) * BodyWeight; if (StallionMaintLevel == 0) // Not Breeding { DE_req = 0.0363 * BodyWeight; CP_req = 1.44 * BodyWeight; Ca_req = 0.04 * BodyWeight; P_req = 0.028 * BodyWeight; Mg_req = 0.015 * BodyWeight; K_req = 0.05 * BodyWeight; Na_req = 0.02 * BodyWeight; Cl_req = 0.08 * BodyWeight; Cu_req = 0.2 * BodyWeight; VitA_req = 30 * BodyWeight; VitE_req = 1.0 * BodyWeight; } if (StallionMaintLevel == 1) // Breeding { SweatLoss = 0.0025 * BodyWeight; // - (Assumes light workload) DE_req = 0.0363 * BodyWeight * 1.2; CP_req = 1.44 * BodyWeight + (SweatLoss * 7.8 * 2 / 0.79) + 0.089 * BodyWeight; Ca_req = 0.06 * BodyWeight; P_req = 0.036 * BodyWeight; Mg_req = 0.019 * BodyWeight; K_req = 0.05 * BodyWeight +(1.4 / 0.5) * SweatLoss; Na_req = 0.02 * BodyWeight + 3.1 * SweatLoss; Cl_req = 0.08 * BodyWeight + 5.3 * SweatLoss; Cu_req = DM_req * 10.0; VitA_req = 45 * BodyWeight; VitE_req = 1.6 * BodyWeight; } LYS_req = 0.043 * CP_req; S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; I_req = DM_req * 0.35; Fe_req = DM_req * 40; Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitD_req = 6.6 * BodyWeight; break;

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COMPUTER MODEL TO ESTIMATE REQUIREMENTS 289 case “PREGNANT”: // Pregnancy DM_req = (IntakeLevel/100) * MatureWeight; BodyWeight = MatureWeight; if (MonthOfGest < 5) { DE_req = 0.0333 * BodyWeight; CP_req = 1.26 * BodyWeight; Ca_req = 0.04 * BodyWeight; P_req = 0.028 * BodyWeight; Mg_req = 0.015 * BodyWeight; K_req = 0.05 * BodyWeight; Na_req = 0.02 * BodyWeight; Cl_req = 0.08 * BodyWeight; Cu_req = 0.2 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 40; } else { GestDay = MonthOfGest * 30.4; BirthWeight = 0.097 * MatureWeight; FetalMass = (0.0000001 * Math.pow(GestDay, 3.5512)) * 0.01 * BirthWeight; PUMass = (-0.0135 + (0.00009 * GestDay)) * BodyWeight; FetalGain = (0.00000035512 * Math.pow(GestDay, 2.5512)) * 0.01 * BirthWeight + 0.00009 * BodyWeight; DE_req = (0.0333 * BodyWeight ) + (0.0333 * 2 * (FetalMass+PUMass)) + ((0.03 * FetalGain * 9.4)+(0.2*FetalGain*5.6))/0.6; CP_req = (1.26 * BodyWeight) + (FetalGain * 1000* 2.0 * 0.2 /0.79); if (MonthOfGest < 7) { Ca_req = 0.04 * BodyWeight; P_req = 0.028 * BodyWeight; Mg_req = 0.015 * BodyWeight; K_req = 0.05 * BodyWeight; Na_req = 0.02 * BodyWeight; Cl_req = 0.08 * BodyWeight; Cu_req = 0.2 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 40; } else if (MonthOfGest < 9) { Ca_req = 0.056 * BodyWeight; P_req = 0.04 * BodyWeight; Mg_req = 0.0152 * BodyWeight; K_req = 0.05 * BodyWeight; Na_req = 0.02 * BodyWeight; Cl_req = 0.08 * BodyWeight; Cu_req = 0.2 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 40; } else { Ca_req = (0.072 * BodyWeight); P_req = (0.0525 * BodyWeight); Mg_req = (0.0153 * BodyWeight); K_req = (0.0517 * BodyWeight); Na_req = 0.022 * BodyWeight; Cl_req = 0.082 * BodyWeight; Cu_req = 0.25 * BodyWeight; I_req = DM_req * 0.4; Fe_req = DM_req * 50; } BodyWeight = BodyWeight + (FetalMass + PUMass)*1.25;

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290 NUTRIENT REQUIREMENTS OF HORSES } LYS_req = 0.043 * CP_req; S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitA_req = 60 * BodyWeight; VitD_req = 6.6 * BodyWeight; VitE_req = 1.0 * BodyWeight; Thi_req = 0.06 * BodyWeight; Ribo_req = 0.04 * BodyWeight; DailyGain = FetalGain*1.25; break; case “LACTATING”: // Lactating BodyWeight = MatureWeight; DM_req = (IntakeLevel/100) * BodyWeight; var MilkVals; var MilkProd; MilkVals = new Array(6); MilkVals[0] = 0.0326; MilkVals[1] = 0.0324; MilkVals[2] = 0.0299; MilkVals[3] = 0.0271; MilkVals[4] = 0.0244; MilkVals[5] = 0.0218; MilkProd = MilkVals[MonthOfLact-1] * BodyWeight; if (BodyWeight > 700) { DE_req = (0.0333 * BodyWeight ) + ((MilkProd * 10 * 50)/ (1000 * .6)); } else { DE_req = (0.0363 * BodyWeight ) + ((MilkProd * 10 * 50)/ (1000 * .6)); } CP_req = (1.44 * BodyWeight ) + (MilkProd * 50); LYS_req = (0.043 * 1.44 * BodyWeight) + (MilkProd * 3.3); if (MonthOfLact < 4) // Lactation - ‘early lact’ { Na_req = 0.02 * BodyWeight + (MilkProd * 0.17); Ca_req = (0.04 * BodyWeight) + ((MilkProd * 1.2)/0.5); P_req = (0.01/0.45 * BodyWeight) + ((MilkProd * 0.75)/0.45); Mg_req = (0.015 * BodyWeight) + ((MilkProd * 0.09)/0.4); K_req = (0.05 * BodyWeight) + ((MilkProd * 0.7)/0.5); } else if (MonthOfLact < 6) { Na_req = 0.02 * BodyWeight + (MilkProd * 0.14); Ca_req = (0.04 * BodyWeight) + ((MilkProd * 0.8)/0.5); P_req = (0.01/0.45 * BodyWeight) + ((MilkProd * 0.5)/0.45); Mg_req = (0.015 * BodyWeight) + ((MilkProd * 0.09)/0.4); K_req = (0.05 * BodyWeight) + ((MilkProd * 0.4)/0.5); } else { Na_req = 0.02 * BodyWeight + (MilkProd * 0.14); Ca_req = (0.04 * BodyWeight) + ((MilkProd * 0.8)/0.5); P_req = (0.01/0.45 * BodyWeight) + ((MilkProd * 0.5)/0.45); Mg_req = (0.015 * BodyWeight) + ((MilkProd * 0.045)/0.4); K_req = (0.05 * BodyWeight) + ((MilkProd * 0.4)/0.5); } Cl_req = 0.091 * BodyWeight; S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; Cu_req = 0.25 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 50;

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COMPUTER MODEL TO ESTIMATE REQUIREMENTS 291 Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitA_req = 60 * BodyWeight; VitD_req = 6.6 * BodyWeight; VitE_req = 2.0 * BodyWeight; Thi_req = 0.075 * BodyWeight; Ribo_req = 0.05 * BodyWeight; break; case “GROWING”: // Growing Animal BodyWeight = MatureWeight * (9.7 + (90.3 * (1.0 - (Math.exp(-0.0772 * Age)))))/100.0; DailyGain = MatureWeight * ( 6.97121 * Math.exp(-0.0772 * Age))/(30.4 * 100); DM_req = (IntakeLevel/100) * BodyWeight; if (WorkLoadGrow == 0) { DE_req=((56.5*Math.pow(Age,-0.145))/1000)*BodyWeight+(1.99+1.21*Age-0.021*Age*Age)*DailyGain; if (Age < 6.5) { CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.5)/0.79; Cl_req = 0.093 * BodyWeight; VitD_req = 22.2 * BodyWeight; } else if (Age < 8.5) { CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.45)/0.79; Cl_req = 0.085 * BodyWeight; VitD_req = 17.4 * BodyWeight; } else if (Age < 10.5) { CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.40)/0.79; Cl_req = 0.085 * BodyWeight; VitD_req = 17.4 * BodyWeight; } else if (Age < 11.5) { CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.35)/0.79; Cl_req = 0.085 * BodyWeight; VitD_req = 17.4 * BodyWeight; } else { CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.3)/0.79; Cl_req = 0.0825 * BodyWeight; } Mg_req = (0.015 * BodyWeight) + (1.25 * DailyGain); K_req = (0.05 * BodyWeight) + (3.0 * DailyGain); Na_req = 0.02 * BodyWeight + (1.0 * DailyGain); } if (WorkLoadGrow == 1) { // Only applied to animals > 12 mo of age SweatLoss = 0.0025 * BodyWeight; DE_req = ((56.5*Math.pow(Age,-0.145))/1000)*1.2*BodyWeight+(1.99+1.21*Age-0.021*Age*Age) *DailyGain; CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.3)/0.79 + (SweatLoss* 7.8 * 2 / 0.79)+0.089*Body Weight; Mg_req = (0.03 * BodyWeight); K_req = (0.05 * BodyWeight) + (3.0 * DailyGain) +(1.4/0.5)*SweatLoss; Na_req = 0.02 * BodyWeight + (1.0 * DailyGain) + 3.1 * SweatLoss; Cl_req = 0.0825 * BodyWeight + 5.3 * SweatLoss; } if (WorkLoadGrow == 2) { // Only applied to animals > 12 mo of age SweatLoss = 0.005 * BodyWeight; DE_req = ((56.5*Math.pow(Age,-0.145))/1000)*1.4*BodyWeight+(1.99 + 1.21*Age - 0.021*Age*Age)* DailyGain; CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.3)/0.79 + (SweatLoss* 7.8 * 2 / 0.79)+0.177* BodyWeight; Mg_req = (0.03 * BodyWeight); K_req = (0.05 * BodyWeight) + (3.0 * DailyGain) +(1.4/0.5)*SweatLoss; Na_req = 0.02 * BodyWeight + (1.0 * DailyGain) + 3.1 * SweatLoss; Cl_req = 0.0825 * BodyWeight + 5.3 * SweatLoss;

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292 NUTRIENT REQUIREMENTS OF HORSES } if (WorkLoadGrow == 3) { // Only applied to animals > 12 mo of age SweatLoss = 0.01 * BodyWeight; DE_req = ((56.5*Math.pow(Age,-0.145))/1000)*1.6*BodyWeight+(1.99 + 1.21*Age - 0.021*Age*Age )* DailyGain; CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.3)/0.79 + (SweatLoss* 7.8 * 2 / 0.79)+0.266* BodyWeight; Mg_req = (0.03 * BodyWeight); K_req = (0.05 * BodyWeight) + (3.0 * DailyGain) +(1.4/0.5)*SweatLoss; Na_req = 0.02 * BodyWeight + (1.0 * DailyGain) + 3.1 * SweatLoss; Cl_req = 0.0825 * BodyWeight + 5.3 * SweatLoss; } if (WorkLoadGrow == 4) { // Only applied to animals > 12 mo of age SweatLoss = 0.02 * BodyWeight; DE_req = ((56.5*Math.pow(Age,-0.145))/1000)*1.9*BodyWeight+(1.99 + 1.21*Age - 0.021*Age*Age )* DailyGain; CP_req = 1.44*BodyWeight+((DailyGain*1000*0.2)/0.3)/0.79 + (SweatLoss* 7.8 * 2 / 0.79)+0.354* BodyWeight; Mg_req = (0.03 * BodyWeight); K_req = (0.05 * BodyWeight) + (3.0 * DailyGain) +(1.4/0.5)*SweatLoss; Na_req = 0.02 * BodyWeight + (1.0 * DailyGain) + 3.1 * SweatLoss; Cl_req = 0.0825 * BodyWeight + 5.3 * SweatLoss; } LYS_req = 0.043 * CP_req; Ca_req = (0.072 * BodyWeight) + (32 * DailyGain); P_req = (0.04 * BodyWeight) + (17.8 * DailyGain); S_req = DM_req * 1000 * 0.0015; Co_req = DM_req * 0.05; Cu_req = 0.25 * BodyWeight; I_req = DM_req * 0.35; Fe_req = DM_req * 50; Mn_req = DM_req * 40; Zn_req = DM_req * 40; Se_req = DM_req * 0.1; VitA_req = 45 * BodyWeight; VitD_req = 20 * BodyWeight; VitE_req = 2.0 * BodyWeight; Thi_req = 0.075 * BodyWeight; Ribo_req = 0.05 * BodyWeight; break; default: alert(“Undefined Animal Type”); }