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id. Mode! Evaluation and tJ Prediction Equations The evaluation of specific components of the model can be found in the relevant chapters. This chapter concerns the evaluation of the overall model relative to energy, pro- tein, and intake. The model equations are also presented in this chapter for reference. METHODOLOGY Data from experiments published in the Journal of Dairy Science from 1992 through February 2000 were used to evaluate the model. Only data from continuous lactation experiments that lasted at least 6 weeks were used (data from cross-over type experiments were not used). Twenty- f~ve papers representing 100 different diets were selected. The papers were selected so that a wide variety of ingredi- ents and production levels of cows could be evaluated. The selection was made prior to diet evaluation; all selected diets are shown in the plots. Diets varied in: 1. Forage source (corn silage and alfalfa were used in most experiments) 2. Forage:concentrate ratio 3. Fat supplementation (without and with a wide variety of fat sources) 4. Nonforage fiber sources (without and with a wide variety of nonforage fiber sources) 5. Source of starch (mostly corn "rain but sorghum and were used). barley was also fed in some experiments) 6. Corn grain processing (dry and high moisture, grind size, steam-treatment) Cows varied with respect to days in milk, milk yield, and milk composition. Twenty-three papers used Holstein cows, two papers used Jersey cows. Diet composition (ingredients) was entered into the model. Published nutrient composition of the individual ingredients was used when available. When nutrient com- position data were missing, values from the feed com- position table (Table 15-1) were used. When nutrient composition of ingredients was not published but nutrient composition of the total diet was included, nutrient compo- sition of individual ingredients (usually only the forages) were changed by no more than one standard deviation so that composition (NDF and CP) of the diet was the same as the published composition. Most studies did not include measured lignin, ash, and neutral and acid detergent insol- uble crude protein. The protein fraction and digestion rate data in the composition tables (Tables 15-2a and b) were used in all evaluations. Few papers published data on min- eral composition of the ingredients or diets, and because mean composition data on minerals (Table 15-3) has a large variance, provision of minerals was not evaluated. However, the concentration of mineral supplements was included in the diets. Mean production data (days in milk, lactation number, body weighs, and milk yield and composition) were entered into the model. Day of gestation usually was not published so a reasonable estimate was entered based on days in milk. Most papers did not include data on the age of the cows. Therefore, growth requirements were set to zero for all cows except those that were exclusively primiparous (for those cows, model generated growth requirements 1\ EVALUATION After diet and cow data were entered into the model, predicted dry matter intake, net energy allowable milk, and metabolizable protein allowable milk were compared with actual intake and milk production. Predicted net 315

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316 Nutrient Requirements of Dairy Cattle energy balance was compared with actual net energy bal- ance by including net energy provided by or needed for the measured body weight change. Sources of data used in the evaluation are shown in Table 16-1. Dry Matter Intake Mean observed dry matter intake was 22.3 kg/d and mean predicted intake was 22.1 kg/d. No evidence of a linear bias was found (Figure 16-11. Root mean square error (predicted minus observed) was 2.0 kg/d. Predicted intake was within + 5 percent of observed intake in 41 percent of the observations and 73 percent of the predicted intakes were within + 10 percent of observed intake. Energy To evaluate the energy portion of the model, intake of NED (based on actual DMI and model predicted NED concentration) was compared with NED utilization (model predicted NED for maintenance, based on actual body weight, model predicted NED for actual milk produced, and NED used for measured body weight change). The data set was as described above except two studies (4 treatment means) could not be used because body weight change was not reported. If the model is accurate, NED intake and NED use should be equal with no apparent bias. Overall, the accuracy of the model was acceptable (Figure 16-21. Intake of NED and NED use were highly correlated (r2 = 0.61; P<0.011. Energy use was within + 5 percent of NED intake for 46 percent of the observations and within 10 percent for 76 percent of the observations. Mean NED intake was 35.4 Mcal/d compared with mean NED use of 34.5, therefore, a small mean bias (0.9 Mcal of NED intake or 2.5 percent) was present. A linear bias is apparent KNEE intake = 7.8 + 0.8 x NED Use); however, within the range of NED used for most lactating cows in the United States the bias will be small (at 20 Mcal of NED use, esti- mated mean NED intake is 23.8 Mcal/day; at 30 Mcal/d NED use, estimated mean NED intake is 31.8 Mcal/day; and at 45 Mcal of NED use, estimated mean NED intake is 43.8 Mcal/day). TABLE 16-1 Sources of Data Used in the Model Evaluation (see also Figures 16-1 to 16-5) Aydin et al. (1999) Bertrand et al. (1998) Coomer et al. (1993) Dann et al. (2000) Dhiman and Satter (1993) Kalscheur et al. (1999) Khorasani et al. (1993) Khorasani et al. (1996) Kim et al. (1993) Knowlton et al. (1998) Kuehn et al. (1999) Messman et al. (1992) Mowrey et al. (1999) Overton et al. (1998) Pereira et al. (1999) Santos et al. (1998) Santos et al. (1999) Soder and Holden (1999) Stegeman et al. (1992) Tackett et al. (1996) Wattiaux et al. (1994) Weiss (1995) Weiss and Shockey (1991) Weiss and Wyatt (2000) Wilkerson et al. (1997) Protein 30 25 ,` 20 15 a) Q 0 10 a) Q 5 o 1 a) o -5 -10 O Observed ~ Deviation 0/ 10 15 20 25 Predicted DMI ka/d 30 35 FIGURE 16-1 Model predicted vs. actual dry matter intake. Values from 100 published treatments means from 25 studies. Evaluation of the protein portion of the model by com- paring MP allowable milk with actual milk is equivocal. When MP allowable milk is greater than actual milk, milk production could be limited by the physiologic state or genetic potential of the cow or by a nutrient other than MP. Higher MP allowable milk than actual milk could also mean that the model underpredicted MP requirements of the cow. When MP allowable milk was compared with actual milk, MP allowable milk was less than actual milk in only 18 (18 percent) observations (Figure 16-31. Of those 18 observations, MP allowable milk for 5, 8, and 5 observations were within 10 to 17 percent, 5 to 10 percent, or less than 5 percent of actual milk. Eighty-two percent of all treatment groups in this data set produced less milk than the model predicted could be produced from the amount of MP available. In 67 percent of the observations, MP allowable milk was more than 10 percent greater than actual milk. Other than energy, the most likely nutrients

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Mode} Evaluation and Prediction Equations 50i 40 30 20 10 10 7 1 , '0"~ ,-" , / / / 1 1 1 1 1 1 1 20 30 40 50 NEL use, Mcal/d FIGURE 16-2 NEL intake (estimated from observed dry mat- ter intake and model estimated NEL concentration) versus NEL use (estimated from model predicted maintenance and lactation requirement plus NEL needed to meet observed body weight change). Values from a data base of 96 published treatment means from 23 studies. The solid line represents y= x, the dashed line represents y = 7.8 + 0.8X. 60 . 50 40 30 20 10 o / / / / / / 1 0 10 o/ 0 ~ 50 60 1 1 1 20 30 40 MP Allowable Milk, kg/d FIGURE 16-3 Actual milk production versus model predicted MP allowable milk production. Values from 100 published treat- ment means from 25 studies. limiting milk production and causing MP allowable milk to be greater than actual milk are specific amino acids. The difference between MP allowable milk and actual milk increased as the concentration of lysine decreased from 6.5 percent of MP (Figure 16-4) and as the concentration of methionine decreased from 1.9 percent of MP (Figure 16-51. This suggests that although supply of total MP was adequate in many of these experiments, the balance of absorbable amino acids may have been incorrect and lim- ited milk production. Experiments specifically designed to test the MP requirements predicted by the model are needed. 317 51 , , , , , , , 1 -10 -5 0 5 10 15 20 25 30 MP Allowable Milk, kg/d FIGURE 16-4 Difference between MP allowable milk and actual milk versus model predicted lysine concentration of MP. Values from 100 published treatment means from 25 studies. Regression line: y = 6.54 - 0.026x. 2.4 r 2.2 2 o 1.8 1.6 1.4 1.2L -10 -5 ~ ~ it 7~, ~~!v - , l 0 5 10 15 20 25 30 MP Allowable Milk, kg/d FIGURE 16-5 Difference between MP allowable milk and actual milk versus model predicted methionine concentration of MP. Values from 100 published treatment means from 25 studies. Regression line: y = 1.90 - 0.0067x. MODEL PREDICTION EQUATIONS Model Structure The model is divided into two major components: pre- diction of requirements and supply of nutrients. Within this structure, there are submodels for young calves, main- tenance, pregnancy, growth, lactation, dry matter intake, minerals, reserves, energy and protein supply, amino acids, and diet evaluation. A glossary of the terms used in the equations is included at the end ofthe chapter. Background information explaining the committee's rationale in choos- ing the approach and coefficients used in the model is presented in the appropriate chapters. A complete listing of all of the equations in the model is included in a file on the compact disk that contains the model itself. Note, MEng is used to denote metabolizable energy (ME) in the computer program and in the equations below because ME can not be used as a variable in the programming language that we used. Animal Requirements The requirements section is divided into four main sec- tions based on physiological function: maintenance,

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318 Nutrient Requirements of Dairy Cattle growth, lactation, and pregnancy. Adjustments made for grazing activity are included in the maintenance section. There are four classes of animals in this model, lactating cow, dry cow, replacement heifer, and young calf. If differ- ent equations are used for heifers, lactating cows, or dry cows, they will be presented under the appropriate physio- logic function. The equations used to predict the require- ments and nutrient supply of the young calves are in a separate section. Maintenance MAINTENANCE ENERGY REQUIREMENTS Maintenance requirements are computed by adjusting the NEm requirement for fasting metabolism for the effects of physiologic state, activity, and, in the case of heifers, heat and cold stress. Lactating and Dry Cows The maintenance requirement for lactating cows is calculated using metabolic body size (BW0 75), and calculated with the following equation which includes an adjustment for activity: NEmaint (Meal/d) = ((BOO CW)075 X al) + NEmact Where al = 0.08 for mature cows based on the require- ment for NEm (80 kcal/kg BW075) (NRC, 1989), CW is conceptus weight and NEmact is the variable to calcu- late the requirement for activity. NEmact = distance/1000 x Trips) x (0.00045 x BOO)) + (0.0012 x (BW)) Where Distance is the distance from the pasture to the milking parlor (km), Trips is the number of times that animals go to and from the milking parlor daily, and Pasture is an adjustment for percent of the predicted dry matter intake supplied by grazing. NEmact is adjusted for differences in topography for grazing animals. Topography may be either flat or hilly. No adjustment is made if the topography is flat. If Topography = 'Hilly' Then NEmact = NEmact + (0.006 x BW) The following equations are used to calculate the net energy concentration of the diet and the amount of feed that is required to meet the maintenance requirement. NEFP = (TotalDMFed FeedMaint) x (NEl Total / TotalDMFed) x 0.65 Where NEFP = Net energy for production, TotalD- MFed = Total dry matter consumed, NEl Total = total NE (in Meals) and 0.65 is the assumed efficiency of conversion of metabolizable protein to net protein Heifers The maintenance requirements for heifers with- out stress (NEmaintNS) are calculated with the follow- . . 1ng equation: NEmaintNS (Meal/d) = (~(SBW CW)075) X ((al x COMP) + aid) + NEmact Where: SEW = shrunk body weight = 0.96 x BW, CW = conceptus weight (kg), al = 0.086 (thermoneutral maintenance require- ment (Meal/day)), a2 = 0.0007 x (20PrevTemp) (Adjustment for previous temperature effect), COMP = 0.8 + ((CS9 - 1) x 0.05) (Adjustment for previous plane of nutrition) NEmact = energy required for activity In the model, a 1-9 system for body condition scoring is used so the following equation is used to convert from the 1-5 system more commonly used in the dairy industry to the 1-9 system. The conversion to the 9-point condition score from the 5-point system is: CS9 = ((CS - 1) x 2) + 1 The following equation is used to calculate the activity requirement for grazing heifers: NEmact = (~0.0009 BW) + (0.0016 BOO)) if the heifer is grazing, otherwise it is 0. If Topography = 'Hilly' then NEmact = NEmact + (0.006 x BW) For heifers, these requirements then are adjusted for the effects of temperature that are based on surface area, heat production, tissue and coat insulation, coat condition, and temperature. First surface area (SA) and heat produc- tion (HP) (Mcal/m2/day) are calculated: SA = 0 09 x (SBW067) HP = (MEI NEFP)/SA Where NEFP = Net energy for production which equals NEGrowthDietNS (Net energy for growth avail- able in the diet with no stress, Mcal/day), HP = Heat production (Mcal/m2/day), MEI = Metabolizable energyintake(Mcal),andNEGrowthDietNS= (Total- DMFedFeedMaint) x (NEg Total/TotalDMFed) The next step is to calculate tissue insulation (TI, Meal/ m2/ C/day). For younger animals, these factors are based on age alone but, for older animals, body condition score is also considered. These factors are: Age (daysJ ' 30 31 to 183 184 to 362 - 363 Tl Factor 2.5 6.5 5.1875 x (0.3125 x CS9) 5.25 x (0.75 x CS9)

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The insulation is further affected by coat condition (Coat): Coat condition Clean/dry Some mud Wet/matted Coated with snow/mud Factor 1.0 0.8 0.5 0.2 The external insulation value, EI (C/Mcal/m2/day) is: EI = ((7.36 - (0.296 X WindSpeed) + (2.55 X HairDepth)) X Coat) X 0.8 Where WindSpeed (kph) is the average wind speed and typical HairDepth values for animals in summer are 0.63 cm (0.25 inches) and for winter 1.27 cm (0.5 inches) and Coat is the coat condition factor. The total insulation (INS, Mcal/m2/C/day) is INS = TI + EI The effects of heat and cold stress are based on lower and upper critical temperatures. The animal's lower critical temperature (LCT, C) is: LCT = 39 - (INS X HP X 0.85) If the LCT ~ ambient temperature (Temp), then MEcs = SA X (LCTTemp)/INS Where MEcs is Metabolizable energy required for cold stress (Meal/day). Otherwise, there is no cold stress. ColdStr= (~(NEDietConc/MEng Total/ TotalDMFed)) X MEcs) Where NEDietConc is the concentration of net energy in the diet (kg D M/day), MEng Total is Total ME intake (Meal/day), and TotalDMFed is total dry matter fed (kg). To calculate the effects of heat, the HeatStress variable is used. An index based on visible changes in breathing in response to heat based on breathing is used: If HeatStress = 'None' or Temp ~ 30 then HeatStr = 1 If HeatStress = 'Rapid/Shallow' then HeatStr = 1.07 If HeatStress = 'Open Mouth' then HeatStr = 1.18 The final equation to calculate the maintenance require- ment for replacement heifers is: NEMaint= ((NEMaintNS + ColdStr) X HeatStr) + NEmact Maintenance Protein Requirement LACTATING AND DRY COWS AND REPLACEMENT HEIFERS The protein requirements for maintenance for all classes of cattle except for the young calves are calculated with the following equation: Mode} Evaluation and Prediction Equations 319 MPMaint = (0.3 X (BW CW)06) + (4.1 X (BW CW)~) + (TotalDMFed X 1000 X 0.03 0.5 X ((MPBact/0.8)MPBact) + MPEndoReq Where MPMaint = Metabolizable protein required for maintenance (g/day) CW = conceptus weight Scurf Requirement = (0.3 X (BW CW) 06); Urinary Requirement = (4.1 X (BW CW) ~); Metabolic Fecal Protein Requirement = (TotalDMFed X 1000 X 0.03 - 0.5 X ((MPBact / 0.8) MPBact)); MP required for Endogenous Protein (MPEndoReq) = MPEndo/0.67; MPBact = Metabolizable protein supplied by microbial protein (g/day); MPEndo = Endogenous metabolizable protein (g/day) = 0.4 X EndCP and EndCP = Endogenous crude protein (g/day) = 11.8 X TotalDMFed. Growth ENERGY REQUIREMENTS FOR GROVVTH Replacement Heifers, Lactating and Dry Cows (1St and 2n~ Lactation only) In this section of the model, requirements for growth are calculated from shrunk body weight, SBW (0.96 X BW) and empty body weight (EBW) (see Chapter 11 for rationale). The user may choose to enter a desired rate of gain or may use the model-generated target gains. For both options, a size-scaling approach is used which requires information on mature body weight (MBW) and mature shrunk body weight (MSBW). The user may use data on mature weights from his/her herd or may rely on default values generated in the program. Accurate estimates of mature weight are needed for accurate predictions of requirements. Representative weights of mature culls cows with average body condition scores may be used to estimate mature weights (MW). MSBW= Mature shrunk body weight= 0.96 X MW SBW = Shrunk body weighs = 0.96 X BW EBW = Empty body weight = 0.891 X SBW EBG = Empty body weight gain = 0.956 X SWG The following calculation is used to calculate the ratio of the standard reference weight to mature shrunk body weight (SRW to MSBW). SRW to MSBW = 478/ MSBW EQSBW= (SBW CW) X SRW to MSBW Where EQSBW = Equivalent shrunk body weight (kg) and CW = Conceptus weight (kg).

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320 Nutrient Requirements of Dairy Cattle The equation is used to compute shrunk weight gain (SWG): SWG = 13.91 X (NEGrowthDiet 0 9~6) X (EQSBw-o 6837) Where SWG = shrunk weight gain (kg), NEGrowth- Diet = NEg in the diet (Meal) If the animal is a replacement heifer, then WG (weight gain) = SWG (shrunk weight gain), Otherwise, WG = ADG (Average daily gain) The following equations are conversions to equivalent (size-scaled) weights: EQEBW = Size-scaled empty body weight = 0.891 X EQSBW EQEBG = Size-scaled empty body weight gain 0.956 X WG Retained energy (RE) is calculated with the following equation: RE = 0.0635 X (EQEBW075) X (EQEBG1097) Protein Requirements for Growth REPLACEMENT HEIFERS, LACTATING AND DRY COWS (lST AND 2ND LACTATION ONLY) Net protein for growth (NPg) is calculated as follows: NPg = WG X (268 - (29.4 X (RE /WG)~) Where WG = weight gain (kg) (always positive) and RE = retained energy (Mcal). The efficiency with which net protein is used for gain (EffMP NPg) is then computed: If EQSBW ' 478 then EffMP NPg = (83.4 - (0.114 X EQSBW)) / 100 Otherwise EffMP NPg = 0.28908 The next step is to calculate the metabolizable protein required for growth (MPGrowth) by dividing NPg by the efficiency with which MP is converted to NP: MPGrowth = NPg / EffMP NPg If the animal is a replacement heifer, D MIAvailGrowth = DMIPreg Otherwise TotalDMFed DMIMaint DMIAvailGrowth = TotalDMFedDMIMaint- DMIPreg DMILact Where DMIAvailGrowth is the dry matter intake for growth. If Age ~ FirstCalf, then ADGwPreg = SWG + (ADGPreg / 1000) Otherwise, ADGwPreg = (EQEBG / 0.956) + (ADGPreg/ 1000) For replacement heifers only, If NEfOverMEng ~ O. then ME Growth = NEGrowth / NEgOverMEng Calculation of Target Weights and Average Daily Gain for Replacement Heifers and Animals in 1St and 2 Lactations The following set of calculations is used to compute the gain required to achieve specified target weights at first breeding, calving, and maturity which is assumed to occur at the beginning of the third lactation. It is important to ensure that appropriate mature weights, age at first calving, and calving interval data are entered or the predictions for target gain will be unrealistic. The following equations are used to calculate age at different carvings: Agelst= FirstCalf AgeSnd = Agelst + Calflnt Age3rd = AgeSnd + Calflnt AgelstBred = Agelst (280 / 30.4) It is assumed that heifers will achieve 0.55 of their mature shrunk body weight at first breeding, 0.82 at first calving, and 0.92 at 2n~ calving. At the onset of their third lactation, they are assumed to have reached their mature weight. WtlstBred = MSBW X 0.55 Wtlst = MSBW X 0.82 Wt2nd = MSBW X 0.92 Wt3rd= MSBW ADGlstBred = (WtlstWtlstBred) / ((AgeistAgelstBred) X 30.4) ADGlst = (Wt2ndWtlst) / (CI X 30.4) ADG2nd = (Wt3rdWt2nd) / (CI X 30.4) If AnimalType = "Replacement Heifer" and Age ~ AgelstBred Then ADGNonBred = (Wtlst- Bred SBW) / ((AgelstBredAge) X 30.4) Otherwise, ADGNonBred = 0 If AnimalType ~ "Replacement Heifer", then ADGNonBred= 0 If AnimalType = "Replacement Heifer" and is preg- nant then ADG = ADGlstBred Otherwise, ADG = ADGNonBred

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Mode} Evaluation and Prediction Equations 321 Pregnancy PREGNANT REPLACEMENT HEIFERS AND MATURE COWS Constants used in pregnancy calculations are: Km = conversion of ME to NE = 0.64 EffMEPreg = The efficiency with which ME is used for pregnancy = 0.14 EffMPPreg = The efficiency with which MP is used for pregnancy = 0.33 Until day 190 of pregnancy, no requirements for preg- nancy are computed in the model. The maximum number of days that a cow can be pregnant is assumed to be 279. CBW (calf birth weight) = MW X 0.06275 CW (conceptus weight) = (18 + ((DaysPreg 190) X 0.665~) X (CBW / 45) ADGPreg (AD G of the conceptus) = 665 X (CBW/ 45) MEPreg(ME required forpregnancy) = (~2 X 0.00159 X DaysPreg0.0352) X (CBW/45~/EffMEPreg MPPreg (MP required for pregnancy) = (~0.69 X DaysPreg 69.2) X (CBW/ 45~) / EffMPPreg NEPreg = Net energy required for pregnancy = MEPreg X Km Lactation If lactose content of milk is not available, MilkEn (energy content of milk) = (0.0929 X MilkFat) + (0.0547 X MilkTrueProtein / 0.93) + 0.192 If lactose content is known, MilkEn = (0.0929 X MilkFat) + (0.0547 X Milk- TrueProtein / 0.93) + (0.0395 X Lactose) The amounts of energy, protein, and fat in milk then are computed: YEn = NElact (energy in milk daily, Mcal/day) MilkEn X MilkProd YProtn (daily protein yield in milk, kg/day) = MilkProd X (MilkTrueProtein /100) Yfatn (daily fat yield in milk, kg/day) = MilkProd X (MilkFat / 100) MPLact (Metabolizable protein required for lactation) = (Yprotn / 0.67) X 1000 The following equation is used to convert to fat-cor- rected milk (FCM): FCM = 0.4 X MilkProd + 15 X (MilkFat / 100) X MilkProd Reserves The factors used to adjust weight at the current CS to expected weight at CS3. CS F~ = 0.726 CS F2 = 0.794 CS F3 = 0.863 CS F4= 0.931 CS Fs = 1.000 CS F6= 1.069 CS F7 = 1.137 CS F8 = 1.206 CS Fg = 1.274 CS5EBW = (SBW X 0.851) / ~ CS Fx) Where CS5EBW = Empty body weight at CS5 using the 1 to 9 scale and CS F = factor to calculate reserves at CS1 to 9. EBWX (Empty body weight at CSx) = CS Fx X CS5EBW AFX (Proportion of fat at CSx) = 0.037683 X X TFX (Weight of fat at CSx) = AFX X EBWX APX (Proportion of protein at CSx) = 0.200886 (0.0066762 X X) TPX (Weight of protein at CSx) = APX X EBWX ERX (Energy reserves at CSx) = (9.4 X TFX) + (5.55 X TPx) Where X varies from 1 to 9. If CS9 ~ 3, then LoselCS = ERcs9 ERCS9-2, Otherwise, LoselCS = 1000000 If CS9 ~ 3, then NElSub = 0.82 X LoselCS Otherwise, NElSub = 0.82 X (ERCs9 ER~) If CS9 ~ 7, then GainlCS = ERcss+2 ERcss Otherwise, GainlCS = 1000000 If CS9 ~ 7, then NElReq = (0.644 / 0.75) X GainlCS Otherwise, NElReq = (0.644 / 0.75) X (ERg ERcss) If EnergyBal ~ O. then deltaER = NElReq Otherwise, deltaER = NElSub Days to change condition score is calculated only for cows: If AnimalType = "Replacement Heifer", then DaysToChange = 0. Otherwise, DaysToChange = deltaER / EnergyBal Energy balance is calculated in the following equations. For Dry Cows and Lactating Cows: NEBalance = NEl Total (NEMaint + NEPreg + NELact + NEGrowth) (These groups of animals use an NE-based system.) For Replacement Heifers: MEBalance = (MEng Total (MEMaint + MEPreg + MEGrowth)) (Heifers use an ME-based system).

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322 Nutrient Requirements of Dairy CattIe Weight change in cows due to energy balance is com- puted in the following equations: For Lactating Cows: If NEBalance ~ O. Then kg weight change CALCIUM (~d) NEBalance /4.92 If NEBalance ~ O. Then kg weight change NEBalance /5.12 For Dry Cows: If NEBalance ~ O. Then kg weight change NEBalance /4.92 If NEBalance ~ O. Then kg weight change NEBalance /6.40 If the animal is gaining weight, the protein requirement for this gain must be computed. If NEBalance ~ 0 Then MPReqReserves = (Reserves WG X ProteinInGain) / 0.492 MPProvReserves = 0 RUPReqReserves = MPReqReserves / DietRUPDigest If NEBalance ~ 0 Then MPReqReserves = 0 If the animal is losing weight, the protein provided by catabolism is computed. MPProvReserves = ~1 X Reserves WG) X ProteinInGain X 0.67 RUPReqReserves = MPProvReserves /DietRUPDigest Where MPReqReserves = metabolizable protein required for reserves, MPProvReserves = metabolizable protein provided by mobilization of reserves, RUPReqRes- erves = RUP required for repletion of reserves and RUP- ProvReserves = RUP provided by mobilization of reserves. Mineral Requirements In most cases, the requirements for minerals are deter- mined for each physiologic function, maintenance, growth, lactation, and pregnancy, but for some minerals this approach has not been followed. The maintenance compo- nent of the mineral requirement includes fecal, urinary, sweat, and miscellaneous losses. Because the bioavailability of minerals from various sources differs, the amount of the total mineral in the diet that is absorbable is determined. Growth requirements for minerals are calculated for heif- ers during their first lactation, but not during their first dry period or during the second lactation. All calculations for milk mineral requirements are done on a 4 percent fat corrected milk basis (FCM). The equa- tion to convert to FCM is: FCM = (0.4 X MilkProd) + (15 X ~ MilkFat / 100) X MilkProd) Fecal If DaysInMilk ~ O. then Fecal = 3.1 X (BOO/ 100) If DaysInMilk = O. then Fecal = 1.54 X (BOO/ 100) Urinary Urine = 0.08 X (BOO/ 100) Sweat Sweat = 0 Pregnancy If DaysPreg ~ l9O, then Fetal = 0.02456 X Exp(~0.05581 - (0.00007 X DaysPreg)) X DaysPreg) 0.02456 X Exp(~0.05581 - (0.00007 X (DaysPreg 1~) X (DaysPreg 1~) If DaysPreg c l9O, then Fetal = 0 Lactation If DaysInMilk ~ O. then If breed = Holstein or Milking Shorthorn, then Milk = 1.22 X Milk Prod If breed = Jersey, then Milk = 1.45 X Milk Prod Otherwise, Milk = 1.37 X Milk Prod Growth If BW ~ 0 and WG ~ O. Then Growth = (9 83 X (MW022) X (BW-022~) X (WG/0.96) PHOSPHORUS (id) Fecal IfAnimalType = Cow,then Fecal = 1 X TotalDMFed Otherwise, Fecal = 0.8 X TotalDMFed Urine Urine = 0.002 x BW Miscellaneous Misc= 0 Sweat Sweat = 0 Pregnancy If DaysPreg190 Then Fetal = 0.02743 x Exp(~0.05527 (0.000075 x DaysPreg)) X DaysPreg)) 0.02743 x

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Mode} Evaluation and Prediction Equations 323 Exp(~0.05527 (0.000075 X (DaysPreg 1~) X POTASSIUM (g/day) (DaysPreg 1~) Otherwise, Fetal = 0 Lactation If DaysInMilk ~ O. then Milk phosphorus = 0.9 X MilkProd Growth If BW ~ 0 and WG ~ O. then Growth = (1.2 + (4.635 X (MW022) X (BW-022~) X (WG / 0.96) MAGNESIUM (g/day) Fecal Fecal = 0.003 X BW Urine Urine = 0 Miscellaneous Misc = 0 Sweat Sweat = 0 Pregnancy If DaysPreg ~ 190 Then Fetal = 0.33 g/day Otherwise, Fetal = 0 Lactation If DaysInMilk ~ O. Then Milk = 0.15 X MilkProd SODIUM (g/day) Growth Growth = 0.45 X (WG / 0.96) CHLORINE (g/day) Fecal Fecal = 2.25 X (BOO/ 100) Urine Urine = 0 Miscellaneous Misc = 0 Sweat Sweat = 0 Pregnancy If DaysPreg ~ 190 Then Fetal = 1 Otherwise, Fetal = 0 Lactation Milk= 1.15 X MilkProd Growth Growth = 1 X (WG / 0.96) Fecal If AnimalType = Lactating cow Fecal = 6.1 X TotalDMFed Otherwise Fecal = 2.6 X TotalDMFed Urine Urine = 0.038 X BW Sweat If Temp ~ 25, then Sweat = 0 If Temp 25 to SO, then Sweat = 0.04 X (BW / 100) If Temp ~ SO, then Sweat = 0.4 X (BW / 100) Miscellaneous Misc = 0 Pregnancy If DaysPreg ~ 190 Then Fetal = 1.027 Otherwise, Fetal = 0 Lactation Milk= 1.5 X MilkProd Growth Growth = 1.6 X (WG / 0.96) Fecal For lactating cows, Fecal = 0.038 X BW Otherwise, Fecal = 0.015 X BW Urine Urine = 0 Miscellaneous Misc = 0 Sweat If Temp ~ 25, then Sweat = 0 If Temp 25 to SO, then Sweat = 0.1 X (BW / 100) If Temp ~ SO, then Sweat = 0.5 X (BW / 100) Pregnancy If DaysPreg ~ l9O, then Fetal = 1.39 If DaysPreg ' l9O, then Fetal = 0 Lactation Milk= 0.63 X MilkProd Growth Growth = 1.4 X (WG /0.96)

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324 Nutrient Requirements of Dairy Cattle SULFUR (g/day) A non-factorial approach is used to determine the sulfur requirement. Total = 2 X TotalDMFed COBALT (mg/day) A non-factorial anoroach is used to determine the cobalt requirement. 1 1 Total = 0.11 X TotalDMFed COPPER (mayday) Fecal Fecal = (0.0071 X BW) Urine Urine = 0 Sweat Sweat= 0 Miscellaneous Misc = 0 Pregnancy If DaysPreg ~ 10O, then Fetal = 0.5 mg/day If 100 c DaysPreg c 225, then Fetal = 1.5 mg/day If DaysPreg ~ 225, then Fetal = 2 mg/day Lactation Milk= 0.15 X MilkProd Growth Growth = 1.15 X (WG / 0.96) IODINE (mg/day) = 0 = 0 = 0 Miscellaneous Misc = 0 Fetal Fetal = 0 Lactation If DaysInMilk ~ O. then Milk = If DaysInMilk = O. then Misc Growth Growth= 0 . .5 X (BW / 100) 0.6X (BW/100) IRON (mg/day) = 0 = 0 = 0 Miscellaneous Misc= 0 Pregnancy If DaysPreg ~ l9O, then Fetal = 18 Otherwise, Fetal = 0 Lactation Milk= 1 X MilkProd Growth Growth = 34 X (WG / 0.96) MANGANESE (mg/day) Fecal Fecal = 0.002 X BW = 0 Sweat Sweat = 0 Miscellaneous Misc= 0 Pregnancy If DaysPreg ~ l9O, then Fetal = 0.3 Otherwise, Fetal = 0 Lactation If DaysInMilk ~ O. then Milk = 0.03 X MilkProd Growth Growth = 0.7X (WG/0.96) SELENIUM (mid) A non-factorial approach is used to determine the selenium requirement. Total = 0.3 X TotalDMFed ZINC (mg/day) Fecal Fecal = 0.033 X BW Urine Urine = 0.012 X BW

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Sweat Sweat = 0 Miscellaneous Misc = 0 Pregnancy If DaysPreg ~ l9O, then Fetal = 12 Otherwise, Fetal = 0 Lactation Milk= 4 X MilkProd Growth Growth = 24 X (WG / 0.96) VITAMIN A (1000 IU/kg) A non-factorial approach is used to determine the Vitamin A requirement. If AnimalType = Lactating Cow, Dry Cow, or Replace- ment Heifer with DaysPreg ~ 259, then Total = O.llXBW If AnimalType = Replacement Heifer with DaysPreg c 259, then Total = 0.08 X BW VITAMIN D (1000 IU/kg) A non-factorial approach is used to determine the Vitamin D requirement. The requirement is 0.03 XBW. VITAMIN E (IU/kg) A non-factorial approach is used to determine the Vitamin E requirement. If the animal is grazing and the AnimalType = Dry Cow, then Vit E required = 0.5 X BW If the animal is grazing and the AnimalType = Lactating Cow or Replacement Heifer, Then Vit E required = 0.26 X BW If the animal is not grazing and the AnimalType Dry Cow, then Total = 1.6 X BW If the animal is not grazing and the AnimalType Lactating Cow or Replacement Heifer, then Vit E required = 0.8 X BW Dry Matter Intake Predictions LACTATING AND DRY COWS , = The equation to predict intake for lactating cows (DMI- Lact) is: DMILact = (((BW075)X 0.0968) + (0.372 X FCM) 0.293) X Lag Mode} Evaluation and Prediction Equations 325 Low intake in early lactation is adjusted using the Lag variable for lactating cows: Lag= 1 e`-ixo.is2xtwo~+367~y The equation for predicting the dry matter intake of dry cows (DMIDry) in the last 21 days of pregnancy is: DMIDry = ((1.97 - (0.75 X e`0~6X`DaYsPreg-28011)) lOO)XBW REPLACEMENT HEIFERS Heifer intakes are adjusted for environmental tempera- ture and conditions using the coat condition (CoatCond) variable to calculate CCFact, the adjustment factor. In the following section, we describe how the environmental adjustments are made and then provide the equation for heifer intake (DMI RH). If CoatCond = Clean/Dry, then CCFact = 1 If CoatCond = Some Mud, then CCFact = 1 If CoatCond = Wet/Matted, then CCFact = 0.85 If CoatCond = Covered with Snow/Mud, then CCFact = 0.7 Heifer intake also is adjusted for temperature effects (TempFact). At temperatures ~ 35, night cooling also affects intake: If Temp ~ -15, then TempFact = 1.16 If-15 ' Temp c 5, then TempFact = 1.07 If-5 c Temp c 5, then TempFact = 1.05 If 5 c Temp c 15, then TempFact = 1.03 If 15 c Temp c 25, then TempFact = 1.00 If 25 c Temp c 35, then TempFact = 0.9 If Temp ~ 35 without night cooling, then TempFact = 0.65 If Temp ~ 35 with night cooling, then TempFact = 0.9 Predicted intake also is adjusted for the effects of age with the SubFact variable: If Age c 12, Then SubFact = 0.1128 If Age ~ 12, Then SubFact = 0.0869 The energy concentration of the diet affects intake using the DivFact variable. For lactating and dry cows, net energy diet concentration is calculated as follows: NEDietConc = NEl Total / Total DMFed For replacement heifers, the equation is: NEDietConc = NEm Total /Total DMFed If NEDietConc ~ 1, then DivFact = 0.95 Otherwise DivFact = NEDietConc Because intake decreases immediately prior to calving, an adjustment to intake is made in this period as well.

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326 Nutrient Requirements of Dairy Cattle If DaysPreg ~ 210 and if DivFact ~ O. then DMI RH = ((BW075) X (((0.2435 X NEDietConc) (0.0466 X (NEDietConc2)) SubFact) / DivFact)) X TempFact X CCFact If DaysPreg ~ 210 and ~ 259, then an intake adjustment factor (DMIRH Factor) is used to adjust the intake of heifers. This DMIRH Factor is multipled by DMI RH to obtain the predicted DMI for heifers. The DMIRH- Factor is calculated as follows: DMIRH Factor = (1 + ((210DaysPreg) X 0.0025)) if DaysPreg ~ 210 and ~ 259 Otherwise DMIRH Factor = 1 If DaysPreg ~ 259, then DMI RH = ((1.71 (o 69e`0.35XDa~Preg2801))) / 100 X BW SUPPLY CALCULATIONS Energy The percent concentrate in the ration is calculated based on the amounts of feeds designated as "Concentrate" that are fed. PercentConc = (ConcSum / TotalDMFed) X 100 For feeds that are not classified as Vitamin/Mineral sup- plements, TDN at 1X maintenance (TANS) and at the actual increment above maintenance is calculated. TDNX = (Feedx.TDN / 100) X (DMFed X 1000) TDN ACtx = (Feedx.TDN ACtx / 100) X (DMFed X 1000) The following calculations are used to determine the energy value of all feeds that are not classified as Calf Feeds or as Vitamins/Minerals. A different set of calculations is used to calculate the energy value of the milk-based calf feeds, and vitamin and mineral supplements are assumed not to contain energy. Non-fiber Carbohudrate (NFC) amounts and It is assumed that nonmember carbohydrate digestibility, NFCDigest= 0.98 The total digestible NFC = tdNFC = NFCDigest X (100NDFCPFatAsh + NDFIP) X PAF Where NFCDigestibility = non-fiber carbohydrate digestibility, NDF = neutral detergent fiber, CP = crude protein, Fat = Fat, NDFIP = neutral detergent insoluble protein, and PAF = processing adjustment factor. The tdNFC is calculated for each feed and the amounts from the individual ration components are added together. Crude Protein Contribution to Energy The contribution of protein to the energy supply is com- puted in the next set of calculations. Different routines are used to calculate protein digestibility depending on how the feed is classified using the energy equation class (Ener- gyEqClass) that divides feeds into forages, concentrates, or feeds of animal origin also is used. Protein digestibility of forages is calculated with the following equation: tdCP = Exp((-1.2 X (ADFIP / CP))) X CP Where tdCP = total digestible Crude Protein, ADFIP = Acid detergent insoluble protein, and CP = crude protein. Below is the equation to calculate protein digestibility of feeds (tdCP) containing proteins from animal sources: tdCP = (CPDigest X CP) For all other classes of feeds, tdCP = (1 - (0.4 X (ADFIP / CP))) X CP Contribution of Fat to the Energy Supply If Fat ~ 1, then tdFat = 0 Otherwise, tdFat = (Fat 1) X 2.25 If Category = Fat and EnergyEqClass = Fatty Acid, TDN = Fat X FatDigest X 2.25 DE = 0.094 X FatDigest X Fat If Category = Fat and EnergyEqClass = Fat, TDN = 10 + ((Fat 10) X FatDigest X 2.25) DE = (FatDigest X (Fat 10) X 0.094) + 0.43 TDN Calculations Adjustments are made based on feed type in the calcula- tions of TDN. TDN and DE are computed with the follow- ing equations if the feed is an Animal Protein: TDN = (CPDigest X CP) + ((Fat 1) X 2.25) + ((NFCDigest X (100 CPAsh Fat)) - 7) DE = (tdNFC X 0.042) + (tdCP X 0.056) + (0.094 X (tdFat/2.25)) - 0.3 For feeds that are not Animal Proteins or Fats and that do contain some NDF (forages, many by-products, concentrates), the following equations are used: TDN = tdNFC + tdCP + tdFat + dNDF 7 DE = (tdNFC X 0.042) + (dNDF X 0.042) + (tdCP X 0.056) + (0.094 X (tdFat /2.25)) - 0.3 The equation below is used for feeds that do not contain NDF, that are not primarily fat and that are not derived from animals (molasses, for example):

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Mode} Evaluation and Prediction Equations 327 TDN = ((0.98 X PAF) X (100CPFatAsh)) + (CP X (1 - (0.4 X (ADFIP / CP)))) + ((2.25 X (Fat 1) - 7)) DE = (0.98 X PAF) X (0.042 X (100 CP Fat Ash)) + (CP X (0.056 X (1 - (0.4 X (ADFIP / CP))))) + (0.094 X (Fat 1)) - 0.3 The equations for feeds with fat and ash are: TDN = ((0.98 X PAF) X (100 FatAsh)) + ((2.25 X (Fat 1) - 7)) DE = (0.98 X PAF) X (0.042 X (100 FatAsh)) + (0.094 X (Fat 1)) - 0.3 No energy values are calculated for Vitamins or Minerals. Energy Caloulations and Conversions For animals other than young calves, the ratio of total dry matter intake to intake used to meet the maintenance requirement (DMI to DMIMaint) is calculated with the following equations. For replacement heifers DMI to DMIMaint = TotalTDN / (0.035 X (SBW075)) Where DMI to DMIMaint is the amount of intake needed to meet the maintenance requirement, TotalTDN = Total dietary TDN, and SEW = shrunk body weight. For lactating and mature cows DMI to DMIMaint = TotalTDN / (0.035 X (BW075)) For young calves DMI to DMIMaint = TotalTDN / (0.035 X (CalfBW075)) Fat Adjustment After the total amount of fat in the diet has been deter- mined (code not shown), it is necessary to make an adjust- ment to the TDN value if the diet contains more than 3 percent fat. Fat digestibility is calculated differently for feeds classified as fatty acids than for other fats. The equa- tions below show how fat digestibility is calculated for The equation for heifers is 1) fat supplements classified as fats, 2) fat supplements MEng = 0.82 X DE classified as fatty acids, and 3) for other feeds: 1). DigestibleFat= 10 + ((Fat 10) X FatDigest) 2). DigestibleFat = Fat X FatDigest 3). DigestibleFat= Fat 1 If (Fat Total / TotalRegDMFed) ~ 0.03 Then Adj TDN = TDNConc (((TotalFat) - 3) X (TotalDigestibleFat / TotalFat) X 2.25) TDNConc = Adj TDN / ((100 - (TotalFat - 3)) / 100) Discount Variable This variable is used to discount TDN to account for depressed digestibility of feeds above maintenance levels. It used to calculate energy availability for all classes of animals except young calves. If a feed is not a milk-based calf feed and contains energy, then DiscountVariable = ((0.18 X TDNConc) - 10.3) X (DMI to DMIMaint 1) Where DiscountVariable = Factor used to discount TDN, TDNConc = TDN concentration in the ration, and DMI to DMIMaint is the amount of the speci- fied ration needed to meet the maintenance requirement. The discount variable cannot be ~ 0 and, if the TDN of a feed is ~ GO, then the DiscountVariable = 1. Otherwise Discount= (TDNConcDiscountVariable)/TDNConc For feeds other than milk-based calf feeds and if TDN- Conc ~ O. then TDN ActX= TDN X Discount Different discounts are applied depending on the fat content of the ration. These discounts apply to all classes of animals except young calves. If Fat ' 3 and if the animal is a dry cow or a lactating cow, then MEng = (1.01 X DiscDE) - 0.45 + (0.0046 X (Fat 3)) If Fat ~ 3 and the animal is a heifer, then MEng= 0.82 X DE Net energy for lactation for feeds having more than 3% fat is computed. NEl = (0.703 X MEng) - 0.19 + ((((0.097 X MEng) + 0.19) / 97) X (Fat 3)) If the feeds have ~ 3% fat, the equation to compute ME for lactating and dry cows is MEng= (1.01 X DiscDE) - 0.45 The equation to compute the NEl of low fat feeds is: NEl = (0.703 X MEng) - 0.19 For feeds that are not classified as fats MEforNEg= 0.82 X DE NEg = 1.42 X MEforNEg 0.174 X MEforNEg2 + 0.0122 X MEforNEg 3 - 1.65 NEm = 1.37 X MEforNEg 0.138 X MEforNEg2 + 0.0105 X MEforNEg 3 - 1.12

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328 Nutrient Requirements of Dairy Cattle Otherwise, MEng= DiscDE NEl = 0.8 X DiscDE NEm = 0.8 X MEng NEg= 0.55 X MEng Computation of the total energy values for the diet. MEng Total = TotalMEConc X TotalRegDMFed NEUTotal = TotalNElConc X TotalRegDMFed NEg Total = TotalNEgConc X TotalRegDMFed NEm Total = TotalNEmConc X TotalRegDMFed If AnimalType is not "Replacement Heifer", then NEDietConc = NE Total / TotalRegDMFed If AnimalType is "Replacement Heifer", then NEDietConc = NEm Total / TotalRegDMFed Protein Supply and Requirements Microbial yield (MCP Total) is calculated as a percent- age of discounted TDN (TDN Act Total): MCP Total = 0.13 X TDN Act Total The following equation is used to calculate the amount of crude protein from each feed. CPX = (FeedxCP /100) X (DMFed X 1000) To calculate the site of digestion of protein, both passage (kp) and digestion (kc) rates are needed. Separate passage equations are used for concentrates, dry forages, and wet forages. Concentrate Kp = 2.904 + (1.375 X BW DMI) (0.02 X PercentConc) Dry Forage Kp = 3.362 + (0.479 X BW DMI) (0.017 X FeedxNDF) (0.007 X PercentConc) Wet Forage Kp = 3.054 + (0.614 X BW DMI) The amount of RDP in a specific feed is calculated using the following equation. It is assumed that all of Protein A is ruminally available and that none of Protein C is degraded in the rumen. Thus, only Protein B is affected by digestion and passage rates. If (Feedx.Kd + Kp) ~ 0 Then RDPX = ((Feedx.Kd / (Feedx.Kd + Kp)) X (~(Feedx.PrtB / 100) X (FeedxCP /100~) X FeedxDMFed)~) + (~(FeedxPrtA / 100) X (FeedxCP / 100~) X FeedxDMFed) Otherwise, RDPX = 0 The amount of ruminally-undegraded protein is obtained by subtraction: RUPX = (CPX (RDPX X 1000~) / 1000 If RUP Total ~ O. then DietRUPDigest = TotalDigestedRUP / RUP Total Otherwise, DietRUPDigest = 0. The requirement for RDP is calculated in the follow- . . sing equation. RDPReq = 0.15294 X TDN Act Total RDPSup = TotalDMFed X 1000 X DietCP X CP RDP RDPBal = RDPSup RDPReq RUPSup = CP Total RDPSup RUPReq = TotalCPReq (MPBact + MPEndo)) / DietRUPDigest The efficiency of microbial crude protein synthesis can- not exceed 0.85. If MCP Total ~ (0.85 X (RDP Total X 1000~), then MCP Total = (0.85 X (RDP Total X 1000~) CP required = RUPreq + RDPReq MPBalance = (~(MPFeed X 1000) + MPBact + MPEndo) (MPMaint + MPPreg + MPLact + MPGrowth)) Amino Acids The amino acid supply is calculated using the following equation with arginine (Arg) as an example. The structure of this equation is similar for all of the amino acids that are considered in the model. TArg = TArg + (~(DMFed / TotalDMFed) X (CP / 100) x ((RUPx X 1000) / CPX) X (Arg/ 100) X TotalDMFed) X 1000) Where TArg = Total arginine, DMFed = quantity of feed X fed, TotalDMFed = Total dry matter fed, CP = % Crude Protein, RUPX = RUP in feed X, CPX = crude protein in feed X. The next step is to calculate the total digestible supply of each amino acid. Below is the equation for Dig TArg. The equations for the other amino acids have the same format. Dig TArg = Dig TArg + (~(DMFed/ TotalDMFed) X (CP / 100) X ((RUPX X 1000) / CPx) X (FeedxRUPDigest /100) X (Arg/ 100) X TotalDMFed) X 1000)

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Where Dig TArg = Total digestible arginine, RUPDigest = RUP digestibility of feed X The total essential amino acid supply before the contri- bution of the microbial protein has been added (EAATotal- BeforeMP) is calculated. EAATotalBeforeMP = (TArg + THis + TIle + TLeu + TLys + TMet + TPhe + TThr + TTrp + TVal) The variables xl and x2 are used in the following sets of calculations of the total amount of each amino acid supplied. The equations to calculate the total amounts of each amino acid follow. In all equations, it is assumed that: If EAATotalBeforeMP ~ 0 then xl = ((TArg (or other amino acid) / EAATotalBefore- MPP X 100) Otherwise xl = 0 If ((RUP Total X 1000) + EndCP + MCP Total) 0 then x2 = ((RUP Total X 1000) / ((RUP Total X 1000) + EndCP + MCP Total)) X 100 Otherwise, x2 = 0 TotalArg = 7.31 + (0.251 X xl) TotalHis = 2.07 + (0.393 X xl) + (0.0122 X x2) TotalIle = 7.59 + (0.391 X xl) (0.0123 X x2) TotalLeu = 8.53 + (0.41 X xl) + (0.0746 X x2) TotalLys = 13.66 + (0.3276 X xl) (0.07497 X x2) TotalMet = 2.9 + (0.391 X xl) (0.00742 X x2) TotalPhe = 7.32 + (0.244 X xl) + (0.029 X x2) TotalThr= 7.55 + (0.45 X xl) (0.0212 X x2) TotalVal = 8.68 + (0.314 X xl) The total essential amino acid supply is calculated below: TotalEAA = 30.9 + (0.863 X EAATotalBeforeMP) + (0.433 X MCP Total) Total flows of RUP of specific amino acids are calcu- lated below: TotalRUPArgFlow= 0.863 X TArg TotalRUPHisFlow= 0.863 X THis TotalRUPIleFlow= 0.863 X TIle TotalRUPLeuFlow= 0.863 X TLeu TotalRUPLysFlow= 0.863 X TLys TotalRUPMetFlow= 0.863 X TMet TotalRUPPheFlow= 0.863 X TPhe TotalRUPThrFlow= 0.863 X TThr TotalRUPTrpFlow= 0.863 X TTrp TotalRUPValFlow= 0.863 X TVal Duodenal flow (g/day) is calculated using an equation of the form below for each amino acid. Arginine is given as an example. Arg Flow = (TotalArg / 100) X TotalEAA Mode} Evaluation and Prediction Equations 329 The contribution of microbial crude protein and endoge- nous protein to the amino acid supply is calculated as follows. The form of this equation is similar for all ~ am~no ac~us. TotalMCPEndArgFlow= Arg Flow- TotalRUPArgFlow The next step is to calculate the supply of each amino acid in RUP that is digestible. The form of the equation for each amino acid is similar to that given for arginine below: If TArg ~ O. then dTotalRUPArg = TotalRUPArgFlow X (Dig TArg / TArg) Otherwise, dTotalRUPArg = 0 The amount of a specif~c amino acid that is digestible and is of microbial or endogenous origin then is calculated. Arginine is used as the example but similar calculations are made for all amino acids. dTotalMCPEndArg = 0.8 X TotalMCPEndArgFlow The flow of digestible arginine, or other amino acids) then is calculated. Dig Arg Flow = dTotalRUPArg + dTotalMCPEndArg The protein in the duodenum must be converted from crude protein to a metabolizable protein basis. Microbial crude protein is converted to metabolizable protein with an eff~ciency of 0.64: MPBact= 0.64 X MCP Total MPFeed= TotalDigestedRUP MPEndo = 0.4 X EndCP The next computation is to determine the percent of a specific amino acid of metabolizable protein. The arginine equation is similar to those of the other amino acids. If (MPBact + (MPFeed X 1000) + MPEndo) ~ O. then ArgPctMP = 100 X (Dig Arg Flow/ (MPBact + (MPFeed X 1000) + MPEndo)) Otherwise, ArgPctMP = 0 Minerals Two sets of equations for the calculation of the supply of minerals are presented here for all classes of animals except for young calves. Both the amount of mineral sup- plied and the amount of the mineral that is absorbable are calculated. The f~rst equations are for the macrominerals using calcium as an example. In the mineral equations, d is used for mineral supplements instead of x to denote the feed.

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330 Nutrient Requirements of Dairy Cattle Supplied = Supplied + ((Feed,Ca / 100) X Feed DMFed) Absorbable = Absorbable + (~(Feed`Ca/100) X Feed, DMFed) X (Feed, CaBio)) The second set of equations represents those used for trace minerals using zinc as an example. Supplied = Supplied + (Feed,Zn X Feed,DMFed) Absorbable = Absorbable + ((Feed`Zn X Feed, DMFed) X (Feed, ZnBio)) Ration density (RD) = Supplied / TotalDMFed YOUNG CALF SUB-MODEL Both the requirements and supply portions of the young calf sub-model are in this section. Requirements ENERGY REQUIREMENTS For young calves, the efficiencies with which feeds are used for maintenance and gain, Km and Kg, for milk-based and other feeds are fixed. Milk-fed CalfKm = 0.8 for milk-based feeds CalfKg = 0.69 for milk-based feeds Fed Milk and Starter CalfKm = 0.75 if the feed is not milk-based CalfKg = 0.57 if the feed is not milk-based The equation to calculate the basal maintenance require- ment of a calf without stress is: NEmCalf= 0.086 X (CalfBW075) The next step is to calculate the CalfKm and CalfKg for the proposed ration using the fixed efficiencies of conver- sion of ME to NEm and NEg. CalfKg = CalfKg + (0.57 X (FeedxDMFed X FeedxMEng)) NonMineralFeeds = NonMineralFeeds + (FeedxDMFed X FeedxMEng) If NonMineralFeeds ~ 0 Then CalfKm = CalfKm / NonMineralFeeds CalfKg = CalfKg / NonMineralFeeds LOWER TEMPERATURE ADJUSTMENTS TO CALF MAINTENANCE REQUIREMENT The maintenance requirement for young calves is adjusted to account for cold stress as follows: Temperature Calves > Temperature Calves < ( C) 2 months ( C) 2 months >5 0 ~ 15 0 0 to 5 0.13 10 to 15 0.13 -5 to 0 0.27 5 to 10 0.27 - 10 to - 5 0.40 0 to 5 0.40 - 15 to - 10 0.54 - 5 to 0 0.54 -20to-15 0.68 -lOto-5 0.68 -25to-20 0.81 -15to-10 0.86 - 30 to - 25 0.94 - 20 to - 15 0.94 <-30 1.07 -25 to -20 1.08 -25 to -30 1.21 ~ - 30 1.34 The resulting equation for the maintenance requirement of young calves with the temperature adjustment is: NEmCalf = (NEmCalf X (l+TempFactor)) The next step is to recalculate ME required for mainte- nance with the NEm that has been adjusted for tempera- ture effects. If CalfKm ~ 0 Then MEMaint = NEmCalf / CalfKm Otherwise MEMaint = 0 The following equation is used to calculate the amount of intake devoted to meeting the maintenance requirement: If the feed is classified as a calf feed (milk-based) and if cMEng ~ O. Then If DietNEmCalf ~ 0 Then CalfKm = CalfKm + (0.86 X (FeedxDMFed X FeedxcMEng)) CalfKg = CalfKg + (0.69 X (FeedxDMFed X FeedxcMEng)) An adjustment is made to ensure that no energy values are computed from mineral supplements: NonMineralFeeds = NonMineralFeeds + (FeedxDMFed X FeedxcMEng) For all other classes of feeds if MEng ~ 0 CalfKm = CalfKm + (0.75 X (FeedxDMFed X FeedxMEng)) DMIForNEmCalf= NEmCalf/DietNEmCalf Else DMIForNEmCalf = 0 A similar calculation is used to calculate the dry matter intake available for growth and the net energy available for growth: DMIForGrowth= (TotalDMFed DMIForNEmCalf) NEFGCalf= DMIForGrowth X DietNEmCalf If CalfKg ~ 0 Then MEFGCalf = NEFGCalf/ CalfKg Else MEFGCalf = 0

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If NEFGCalf ~ O Then EnergyADGCalf= Exp(~0.8333 X (Log(~1.19 X NEFGCalf) / (0.69 X (CalfBW0355)))))) CALF PROTEIN REQUIREMENTS Caltprotein requirements are computed with the follow- ing equation: ProteinReqCalf = CalfADG X 0.188 (30 g N/kg gain = 187.5 g Net Protein / kg gain) Total apparently digested protein (TotalADP) is calcu- lated as follows where 0.93 and 0.75 are the assumed digest- ibilities of milk-based feeds and starter feeds respectively: TotalADP + ((TotalMilkCP X 0.93) + (TotalStart- erCP X 0.75)) X 1000 The ratio of ADP to CP is calculated as follows: ADP to CP = TotalADP / ((TotalMilkCP + TotalStarterCP) X 1000) Calf Protein Maintenance Requirements EUN = Endogenous urinary N losses = 0.2 X (CalfBW075) MFN = Metabolic fecal N = (MilkDMI X 1.9) + (StarterDMI X 3.3)) BV = Biological value = (0.8 X (TotalMilkCP / TotalCP)) + (0.7 X (TotalStarterCP / TotalCP)) ADPmaint = 6.25 X (((1 / BV) X (EUN + MFN)) MFN) CPmCalf = ADPMaint / ADP to CP if ADP to CP>O ADPgrowth = (ProteinReqCalf X 1000) / BV Mode} Evaluation and Prediction Equations 331 TABLE 16-2 Ration Densities of Required Minerals for Three Categories of Feeds for Calves Mineral Milk-Replacer Starter Grower 1.0 0.7 0.07 0.4 0.65 0.25 0.29 100 40 40 10 0.5 0.11 0.3 9 0.6 50 0.7 0.45 0.1 0.15 0.65 0.2 0.2 40 10 0.25 0.1 0.3 4 0.6 25 0.6 0.4 0.1 0.14 0.65 0.2 0.2 50 40 40 10 0.25 0.1 0.3 4 0.6 25 If TotalDMFed>O Then RDReq = ((MilkFeeds X m) + (CalfStarter X n) + (RegFeeds X o)) / TotalDMFed Where m = concentration of mineral X in MilkFeeds, n = concentration of mineral X in calf starter, and o = concentration of mineral X in regular feeds. Calf Supply and Diet Evaluation In the calf submodel, milk-based feeds are in a separate category in the feed library because the energy values for these feeds are calculated differently from feeds that may be used as starter feeds. Any feed in the library except for the milk-based calf feeds may be used as a starter feed. The information for the starter feeds is taken from the appropriate category of the main feed library. ADPAllowGain = ((TotalADP ADPmaint) X Calf Energy and Protein BV) / 0.188 CALF MINERAL REQUIREMENTS A factorial approach is not used to estimate mineral requirements for young calves. The requirements for calves are based on the amounts of milk-based feed, starter, and grower that are offered. It is assumed that the values pre- sented in Table 10 = 6 for milk replacers, calf starter, and grower meet the mineral requirements of the young calf. Table 16-2 indicates the desired ration densities for each of the three categories of feeds (milk-based calf feeds, calf starter, and calf grower). The densities for calf grower are used as the standard for all feeds in the Feed Library except milk-based feeds and calf starter. To calculate the desired concentrations of each mineral, the following equation is used: The energy calculations to obtain TDN, DE, and ME are included in the main energy computation section. To get the appropriate energy and protein values, the totals from the calf feeds are calculated and then the totals from the other feeds are obtained. Finally, the contributions from the two groups of feeds are added together. In the following sets of calculations, it is assumed that the initial value of the variable is 0. TotalNEm = TotalNEm + (DMFed X cNEm) TotalNEg = TotalNEg + (DMFed X cNEg) TotalME = TotalME + (DMFed X cMEng) TotalCP = TotalCP + (DMFed X (cCP / 100~) TotalDCP = TotalDCP + (DMFed X (cDCP/ 100~) If Category = "Calf Feed Milk" Then MilkDMI = MilkDMI + DMFed MilkME = MilkME + (DMFed X cMEng)

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332 Nutrient Requirements of Dairy Cattle TotalMilkADP = TotalMilkADP + (DMFed X (cDCP / 100~) TotalMilkCP = TotalMilkCP + (DMFed (cCP / 100)) Otherwise StarterDMI = StarterDMI + DMFed StarterME = StarterME + (DMFed X cMEng) TotalStarterADP = TotalStarterADP + (DMFed X (cDCP / 100)) TotalStarterCP = TotalStarterCP + (DMFed X (cCP / 100)) To convert starter/regular feeds from CP to cDCP: cDCP = 0.75 X CP Here are the equations to obtain the total values: TotalNEm = TotalNEm + NEm Total TotalNEg = TotalNEg + NEg Total TotalME = TotalME + MEng Total DietNEmCalf = TotalNEm / TotalDMFed DietNEgCalf = TotalNEg / TotalDMFed DietMECalf = TotalME / TotalDMFed Mature Weights Mature weight is used both to estimate the target growth rates of replacement heifers and to predict calf birth weights. The user has the option of entering the mature weight based on herd observations or of using default values. The default weights for various breeds are: A~yshire Brown Swiss Guernsey Holstein Jersey Milldng Shorthorn 545 kg 682 kg 500 kg 682 kg 454 kg 568 kg Calf birth weight is calculated from mature weight using the following equation: CBW From MW= 0.06275 X MW R E F E R E N C E S Aydin, G., R. J. Grant, and O. R. J. 1999. Brown midrib sorghum in diets for lactating dairy cows. J. Dairy Sci. 82:2127-2135. Bertrand, J. A., F. E. Pardue, and T. C. Jenkins. 1998. Effect of ruminally protected amino acids on milk yield and composition of Jersey cows fed whole cottonseed. J. Dairy Sci. 81:2215-2220. Coomer, J. C., H. E. Amos, C. C. Williams, and J. G. Wheeler. 1993. Response of early lactation cows to fat supplementation in diets with different nonstructural carbohydrate concentrations. J. Dairy Sci. 76:3747-3754. Dann, H. M., J. K. Drackley, G. C. McCoy, M. F. Hutjens, and J. E. Garrett. 2000. Effects of yeast culture (Saccharomyces cerevisiae) on prepartum intake and postpartum intake and milk production of Jersey cows. J. Dairy Sci. 83:123-127. Dhiman, T. R., and L. D. Satter.1993. Protein as the first-limiting nutrient for lactating dairy cows fed high proportions of good quality alfalfa silage. J. Dairy Sci. 76:1960-1971. Kalscheur, K. F., J. H. Vandersall, R. A. Erdman, R. A. Kohn, and E. Russek Cohen. 1999. Effects of dietary crude protein concentration and degradability on milk production responses of early, mid, and late lactation dairy cows. J. Dairy Sci. 82:545-554. Khorasani, G. R., G. D. Boer, and J. J. Kennelly. 1996. Response of early lactation cows to ruminally undegradable protein in the diet. J. Dairy Sci. 79:446-453. Khorasani, G. R., E. K. Okine, J. J. Kennelly, and J. H. Helm. 1993. Effect of whole crop cereal grain silage substituted for alfalfa silage on performance of lactating dairy cows. J. Dairy Sci. 76: 3536-3546. Kim, Y. K., D. J. Schingoethe, D. P. Casper, and F. C. Ludens. 1993. Supplemental dietary fat from extruded soybeans and calcium soaps of fatty acids for lactating dairy cows. J. Dairy Sci. 76:197-204. Knowlton, K. F., B. P. Glenn, and R. A. Erdman. 1998. Performance, ruminal fermentation, and site of starch digestion in early lactation Holstein cows fed corn grain harvested and processed differently. J. Dairy Sci. 81:1972-1985. Kuehn, C. S., J. G. Linn, D. G. Johnson, H. G. Jung, and M. I. Endres. 1999. Effect of feeding silages from corn hybrids selected for leafiness or grain to lactating dairy cattle. J. Dairy Sci. 82:2746-2755. Messman, M. A., W. P. Weiss, P. R. Henderlong, and W. L. Shockey. 1992. Evaluation of pearl millet and field peas plus triticale silages for midlactation dairy cows. J. Dairy Sci. 75:2769-2775. Mowrey, A., M. R. Ellersieck, and J. N. Spain. 1999. Effect of fibrous by-products on production and ruminal fermentation in lactating dairy cows. J. Dairy Sci. 82:2709-2715. National Research Council.1989. Nutrient Requirements of Dairy Cattle, 6th rev. ea., Washington, DC: National Academy Press. Overton, T. R., L. S. Emmert, and J. H. Clark. 1998. Effects of source of carbohydrate and protein and rumen-protected methionine on per- formance of cows. J. Dairy Sci. 81 :221-228. Pereira, M. N., E. F. Garrett, G. R. Oetzel, and L. E. Armentano. 1999. Partial replacement of forage with nonforage fiber sources in lactating cow diets. I. Performance and health. J. Dairy Sci. 82:2716-2730. Santos, F. A. P., J. T. Huber, C. B. Theurer, R. S. Swingle, J. M. Simas, K. H. Chen, and P. Yu. 1998. Milk yield and composition of lactating cows fed steam-flaked sorghum and graded concentrations of ruminally degradable protein. J. Dairy Sci. 81:215-220. Santos, J. E. P., J. T. Huber, C. B. Theurer, L. G. Nussio, M. Tarazon, and F. A. P. Santos. 1999. Response of lactating dairy cows to steam- flaked sorghum, steam-flaked corn, or steam-rolled corn and protein sources of differing degradability. J. Dairy Sci. 82:728-737. Soder, K. J., and L. A. Holden. 1999. Dry matter intake and milk yield and composition of cows fed yeast prepartum and postpartum. J. Dairy Sci. 82:605-610. Stegeman, G. A., D. P. Casper, D. J. Schingoethe, and R. J. Baer. 1992. Lactational responses of dairy cows fed unsaturated dietary fat and receiving bovine somatotropin. J. Dairy Sci. 75:1936-1945. Tackett, V. L., J. A. Bertrand, T. C. Jenkins, F. E. Pardue, and L. W. Grimes. 1996. Interaction of dietary fat and acid detergent fiber diets of lactating dairy cows. J. Dairy Sci. 79:270-275.

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Mode} Evaluation and Prediction Equations 333 Wattiaux, M. A., D. K. Combs, and R. D. Shaver. 1994. Lactational responses to ruminally undegradable protein by dairy cows fed diets based on alfalfa silage. J. Dairy Sci. 77:1604-1617. Weiss, W. P. 1995. Full lactation response of cows fed diets with different sources and amounts of fiber and ruminal degradable protein. J. Dairy Sci. 78:1802-1814. Weiss, W. P., and W. L. Shockey. 1991. Value of orchardgrass and alfalfa silages fed with varying amounts of concentrates to dairy cows. J. Dairy Sci. 74:1933-1943. Weiss, W. P., and D. J. Wyatt. 2000. Effect of oil content and kernel processing of corn silage on digestibility and milk production by dairy cows. J. Dairy Sci. 83:351-358. Wilkerson, V. A., B. P. Glenn, and K. R. McLeod. 1997. Energy and nitrogen balance in lactating cows fed diets containing dry or high moisture corn in either rolled or ground form. J. Dairy Sci. 80:2487-2496.