UPDATING MATHEMATICAL MODELS USED I N THE DIET FORMULATION PROCESS By Rodrigo Araujo de Souza A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Animal Science Doctor of Philosophy 2018 ABSTRACT UPDATING MATHEMATICAL MODELS USED IN THE DIET FORMULATION PROCESS By Rodrigo Araujo de Souz a The hypothes i s of this dissertation wa s that deriving statistical models using advanced statistical techniques and a database collected in recent years w ould yield predictions that better fit the current dairy production system than the models of the NRC (2001) . In chapter three , we determined the effects of dry matter intake ( DMI ), b ody weight ( BW ), and diet characteristics on total tract digestibilities of dry matter, neutral detergent fiber, and starch ( DMD , NDFD , and StarchD , respectively) in high - producing dairy cows using a database compo sed of 1,942 observations from 662 cows in 54 studies from Michigan, Ohio, and Georgia. Our results suggest that DMD decreases as intake increase s but at a lower rate than the model of NRC (2001). Both NDFD and StarchD were best estimated with diet chara cteristics as well as intake; starch content has a much greater impact on NDFD than does intake. In chapter four , we modeled DMI in Holstein dairy cows based on milk energy ( MilkE ), BW, change in body weight ( ), body condition score ( BCS ), height ( Ht ), days in milk ( DIM ), and parity (primiparous and multiparous) using a database conta in ing 47,253 weekly observations on 3,607 cows enrolled in 57 studies from 8 states across the US. The proposed model was validated against the NRC (2001) prediction equatio n for DMI using an independent dataset . The proposed model outperformed the NRC (2001) model to predict DMI. Whereas both models were similar at predict ing DMI during early - lactation (1 75 DIM), the proposed model outperformed the NRC (2001) during mid - and late - lactation (76 368 DIM). In chapter five , we performed a meta - regression using data from 5 experiments conducted at Michigan State University to determine the effect of dietary fatty acid ( FA ) composition on digestibilities of DM, NDF, FA, 16 - ca rbon FA, 18 - carbon FA , and digestible energy ( DMD, NDFD, FAD , 16 - CD , 18 - CD , and EnergyD , respectively) and on DE intake ( DEI ). The final database was composed of 423 individual observations collected on 183 lactations from 124 Holstein mid - lactation cows r eceiving diets that varied on FA composition. P almitic and stearic were the FAs with greate st impact s on digestibilities and DEI ; palmitic increased DEI when included in the diet up to 1.2% of DM, and stearic linearly decreased DEI. In chapter six , we conducted a meta - regression analysis on 129 treatment means from 26 peer - reviewed publications to predict body composition ( EBFat , EBProtein , EBAsh , and EBWater ) as a percentage of empty body weight ( EBW ) in Holsteins. The statistical models contained t he random effect of study and fixed effects of method (direct, carcass, and dilution), stage (heifer and cow), and one of the three possible ways to express EBW (4 th order polynomial of EBW - polEBW , natural logarithm of EBW - lnEBW , or EBW to the power of 0.75 EBW^0.75 ), average daily gain ( ADG ) for heifers, and BCS for cows. Additionally, the models were weighted by the inverse of the standard deviations of the studies. Compared to NRC 2001, the proposed model suggest s that fat c ontent of the gain, and thus the energy content of gain, is greater for young heifers and less for older heifers than the values predicted by NRC 2001. iv ACKNOWLEDGMENTS Completing this dissertation is one of the most challenging trials I have ev er faced. It pushed my creative thinking and my learning to the limit, and I certainly would not have gotten here without the support of the many caring people in my life. My first words of appreciation and gratitude are to my Adviser , Dr. Mi chael J. VandeHaar, who accompanied me through this journey, con tinual ly monitoring my work and stimulating the scholar in me. I time and i nput to make my Ph.D. experience productive and inspiring. The joy and enthusiasm he has for this research were contagious and motivational for me, even during difficult times in the Ph.D. In addition, I would like to thank Dr. Adam L. Lock, Dr. Robert J. Tempelman, Dr. Michael S. Allen, and Dr. Cristopher A. Wolf for accepting their positions on my committee and for their helpful discussions and comments. Most importantly, I would like to thank them for challenging my work and guiding me through every step of the process. I also gratefully acknowledge the funding sources that made my Ph.D . work possible. I was funded by the Brazilian Government ( CNPq ) during my Ph.D . , and I was honored to be a W ithout B ; without th ese support s , nothing would have been possible. My time at Michigan State University ( MSU ) was made much more enjoyable in large part due to my friends and the professors and various other MSU staff members that became a part of my life. Lastly, I would like to thank my family for all of their love, patience, and encouragement. For my parents who raised me with a love of knowledge and supported me in all my dreams , I am grateful . Most of all , I am thankful for my supportive and encouraging wife , Alejandra , who helped me during the final s tages of this Ph.D. v TABLE OF CONTENT S LIST OF TABLES ................................ ................................ ................................ ..................... viii LIST OF FIGURES ................................ ................................ ................................ ..................... xi KEY TO ABBREVIATIONS ................................ ................................ ................................ ... xvi CHAPTER 1 INTRODUCTION ................................ ................................ ................................ . 1 CHAPTER 2 LITERATURE REVIEW ................................ ................................ ..................... 4 DAIRY FARM PROFITABILITY ................................ ................................ ......................... 4 DIETARY FORMULATION ................................ ................................ ................................ .. 7 DRY MATTER INTAKE ................................ ................................ ................................ ....... 12 NUTRIENT DIGESTIBILITY ................................ ................................ .............................. 16 FAT SUPPLEMENTATION AND ENERGY INTAKE ................................ .................... 20 BODY COMPOSITION IN HOLSTEIN CATTLE ................................ ............................ 24 APPENDICES ................................ ................................ ................................ ......................... 28 APPENDIX A Tables ................................ ................................ ................................ .......... 29 APPENDIX B Figures ................................ ................................ ................................ ......... 31 REFERENCES ................................ ................................ ................................ ........................ 33 CHAPTER 3 PREDICTING NUTRIENT DIGESTIBILITY IN HIGH - PRODUCING DAIRY COWS ................................ ................................ ................................ ............................ 45 ABSTRACT ................................ ................................ ................................ ............................. 45 CHAPTER 4 UPDATING PREDICTIONS OF DRY MATTER INTAKE OF LACTATING DAIRY COWS ................................ ................................ ................................ ... 47 ABSTRACT ................................ ................................ ................................ ............................. 47 INTRODUCTION ................................ ................................ ................................ ................... 48 MATERIALS AND METHODS ................................ ................................ ........................... 50 Data ................................ ................................ ................................ ................................ ....... 50 Statistical Analyses ................................ ................................ ................................ ............... 52 Modeling Process ................................ ................................ ................................ .................. 53 Cross - validation ................................ ................................ ................................ .................... 56 Independent validation process ................................ ................................ ............................. 57 RESULTS ................................ ................................ ................................ ................................ 58 DISCUSSION ................................ ................................ ................................ .......................... 61 CONCLUSION ................................ ................................ ................................ ....................... 64 APPENDICES ................................ ................................ ................................ ......................... 65 APPENDIX A Tables ................................ ................................ ................................ .......... 66 APPENDIX B Figures ................................ ................................ ................................ ......... 73 APPENDIX C Supplemental Table ................................ ................................ ..................... 79 APPENDIX D SAS Macro: Model Validation ................................ ................................ .... 81 REFERENCES ................................ ................................ ................................ ........................ 92 vi CHAPTER 5 DIETARY FATTY ACID COMPOSITION AND DIGESTIBLE ENERGY IN LACTATING DAIRY COWS ................................ ................................ .............................. 95 ABSTRACT ................................ ................................ ................................ ............................. 95 INTRODUCTION ................................ ................................ ................................ ................... 96 MATERIALS AND METHODS ................................ ................................ ........................... 98 Database ................................ ................................ ................................ ................................ 98 Statistical Analysis ................................ ................................ ................................ .............. 100 RESULTS ................................ ................................ ................................ .............................. 101 Dry matter digestibility (DMD) ................................ ................................ .......................... 102 NDF digestibility (NDFD) ................................ ................................ ................................ .. 103 Total FA digestibility (FAD) ................................ ................................ .............................. 103 16 - carbon FA digestibility (16 - CD) ................................ ................................ .................... 104 18 - carbon FA digestibility (18 - CD) ................................ ................................ .................... 104 Energy digestibility (EnergyD) ................................ ................................ ........................... 105 Digestible energy intake expressed in Mcal/d and Mcal/k g of DM (DEIday and DEIkg, respectively) ................................ ................................ ................................ ........................ 106 DISCUSSION ................................ ................................ ................................ ........................ 107 Dry matter digestibility (DMD) ................................ ................................ .......................... 109 NDF digestibility (NDFD) ................................ ................................ ................................ .. 110 Total, 16 - carbon, and 18 - carbon FAs digestibility (FAD, 16 - CD, and 18 - CD, respectively) ................................ ................................ ................................ ................................ ............. 111 Energy digestibility (EnergyD) ................................ ................................ ........................... 112 Digestible energy intake (DEI) ................................ ................................ ........................... 113 CONCLUS IONS ................................ ................................ ................................ ................... 114 APPENDICES ................................ ................................ ................................ ....................... 115 APPENDIX A Tables ................................ ................................ ................................ ........ 116 APPENDIX B Figures ................................ ................................ ................................ ....... 126 APPENDIX C Supplemental Tables ................................ ................................ ................. 139 APPENDIX D Supplemental Figures ................................ ................................ ................ 148 REFERENCES ................................ ................................ ................................ ...................... 157 CHAPTER 6 BODY COMPOSITION OF HOLSTEIN CATTLE ................................ ... 161 ABSTRACT ................................ ................................ ................................ ........................... 161 INTRODUCTION ................................ ................................ ................................ ................. 162 MATERIALS AND METHODS ................................ ................................ ......................... 164 Literature search and selection of peer - reviewed manuscripts ................................ ........... 164 Database ................................ ................................ ................................ .............................. 164 Model derivation ................................ ................................ ................................ ................. 166 Model evaluation ................................ ................................ ................................ ................ 169 Energy and protein requirements for growth in heifers and net energy provided by the change in body condition score in cows ................................ ................................ ............. 170 RESULTS ................................ ................................ ................................ .............................. 170 Model derivation ................................ ................................ ................................ ................. 170 Model evaluation ................................ ................................ ................................ ................ 172 Proposed models for body composition. ................................ ................................ ............. 174 DISCUSSION ................................ ................................ ................................ ........................ 177 vii Body composition in heifers and net energy and net protein requirements for growth ...... 177 Body composition in cows and net energy per kilogram of empty body weight change ... 180 CONCLUSIONS ................................ ................................ ................................ ................... 182 APPENDICES ................................ ................................ ................................ ....................... 183 APPENDIX A Tables ................................ ................................ ................................ ........ 184 APPENDIX B Figures ................................ ................................ ................................ ....... 195 APPENDIX C Supplemental Tables ................................ ................................ ................. 209 APPENDIX D Supplemental Figures ................................ ................................ ................ 212 REFERENCES ................................ ................................ ................................ ...................... 218 CHAPTER 7 CONCLUSION ................................ ................................ ................................ 22 2 viii Table 2.1. Cost structure of dairy farm per hundredweight (cwt) of milk sold in 2017. .............. 30 Table 4.1. Frequency of number of studies, diets, cows, and lactations by state. ........................ 67 Table 4.2. Nu mber of observations (n), mean, and standard deviation (SD) of the covariates used to model (Training dataset) and validate (Validation dataset) the proposed equations for dry matter intake. ................................ ................................ ................................ ......................... 68 Table 4.3. Fit Statistics for the cross - validation across studies of the candidate models (LIN: linear, NLIN: non - linear) using the modeling dataset . ................................ ......................... 69 Table 4.4. Fit Statistics for the across study stage of lactation (early, mid, and late) specific cross - validation performance of the proposed and NRC (2001) models using the independent vali dation dataset. ................................ ................................ ................................ ................. 70 Table 4.5. Fit Statistics for the cross - validation across studies of the proposed model and simplified model using the validation dataset. ................................ ................................ ...... 71 Table 4.6. Nonlinear adjustment of days in milk on the predicted dry matter intake estimated by the proposed (primiparous and multiparous) and NRC (2001) models. ............................... 72 Supplemental Table 4.1. Prediction of DMI using the two - step model on crossbreeds and pure Jersey dairy cows in total mixed ration and grazing system. ................................ ................ 80 Table 5.1. Descriptive summary of the variables included in the database. ............................... 117 Table 5.2. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on dry matter digestibility . ................................ ................................ ................................ ........................ 118 Table 5.3. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on NDF digestibility . ................................ ................................ ................................ ........................ 119 Table 5.4. Effect of dry matter intak e (DMI, kg/d) and diet composition (% of DM) on total fatty acids digestibility . ................................ ................................ ................................ ............... 120 Table 5.5. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on 16 - carbon fatty acids digestibility . ................................ ................................ ................................ ....... 121 Table 5.6. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on 18 - carbon fatty acids digest ibility . ................................ ................................ ................................ ....... 122 ix Table 5.7. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on energy digestibility . ................................ ................................ ................................ ........................ 123 Table 5.8. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on digestible energy intake (Mcal/d) . ................................ ................................ ................................ ....... 124 Table 5.9. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on digestible energy concentration (Mcal/kg of DM) . ................................ ................................ ............. 125 Supplemental Table 5.1. Effect of dry matter intake (SD) and diet composition (SD) on dry matter digestibility . ................................ ................................ ................................ ............. 140 Supplemental Table 5.2. Effect of dry matte r intake (SD) and diet composition (SD) on NDF digestibility . ................................ ................................ ................................ ........................ 141 Supplemental Table 5.3. Effect of dry matter intake (SD) and diet composition (SD) on total fatty acids digestibility . ................................ ................................ ................................ ....... 142 Supplemental Table 5.4. Effect of dry matter intake (SD) and diet composition (SD) on 16 - carbon fatty acids digestibility . ................................ ................................ ........................... 143 Supplemental Table 5.5. Effect of dry matter intake (SD) and diet composition (SD) on 18 - carbon fatty acids digestibility . ................................ ................................ ........................... 144 Supplemental Table 5.6. Effect of dry matter intake (SD) and diet composition (SD) on energy digestibility . ................................ ................................ ................................ ........................ 145 Sup plemental Table 5.7. Effect of dry matter intake (SD) and diet composition (SD) on digestible energy intake (Mcal/d) . ................................ ................................ ...................... 146 Supplemental Table 5.8. Effect of dry mat ter intake (SD) and diet composition (SD) on digestible energy concentration (Mcal/kg of DM) . ................................ ............................. 147 Table 6.1. Descriptive summary of the quantitative variables included in the database. ........... 185 Table 6.2. Model evaluation through 100 - fold cross - validation for water composition by stage (heifers and cows) and model (polEBW, ln EBW, and EBW^0.75) . ................................ .. 186 Table 6.3. Model evaluation through 100 - fold cross - validation for fat composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . ................................ .. 187 x Table 6.4. Model evaluation through 100 - fold cross - validation for protein composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW ^0.75) . ................................ .. 188 Table 6.5. Model evaluation through 100 - fold cross - validation for ash composition by stage (heifers and cows) . ................................ ................................ ................................ .............. 189 Table 6.6. Model evaluation through 100 - fold cross - validation for fat - free mass composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . ......................... 190 Table 6.7. Estimated coefficient for the models derived on the first step of the modeling process (named as baseline) using the natural logarithm for empty body weight (lnEBW). .......... 191 Table 6.8. Relationship between empty body weight and average daily gain (ADG, kg/d) on the energy required for growth calculated based on the proposed model and the NRC (20 01) . ................................ ................................ ................................ ................................ ............. 192 Table 6.9. Relationship between empty body weight and average daily gain (ADG, kg/d) on the protein required for growth calculated based on the proposed model and the NRC (2001) . ................................ ................................ ................................ ................................ ............. 193 Table 6.10. Relationship between body condition score (BCS) and empty body weight composition (% of EBW) on net energy content per ki logram of EBW 1 change estimated using the proposed models 1 and the NRC (2001) . ................................ .............................. 194 Supplemental Table 6.1. Relationship between empty body weight on the energy re quired for growth calculated based on the baseline model and the NRC (2001). ............................... 210 Supplemental Table 6.2. Relationship between empty body weight on the protein required for growth calculated based on the baseline model and the NRC (2001). ............................... 211 xi Figure 2.1. Milk ( ) and feed ( ) prices from 1997 to 2017 per hundredweight. The prices are adjusted to 2017 values ( adjusted used the inflation for each year; LBS, 2018). ................. 32 Figure 4.1. Distribution of the number of observations in the training ( ) and in the validation ( ) datasets. ................................ ................................ ................................ ........................... 74 Figure 4.2. Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2001 ( ) and the proposed ( ) models for the early - lactation period (1 to 75 days in milk). Each data point (NRC 2001 - , Proposed model - ) represents the raw (a) and the adjusted for random effects (b) individual weekly DMI. ................................ ...................... 75 Figure 4.3. Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2001 ( ) and the proposed ( ) models for the mid - lactation period (76 to 175 days in milk). Each data point (NRC 2001 - , Proposed model - ) represents the r aw (a) and the adjusted for random effects (b) individual weekly DMI. ................................ ................ 76 Figure 4.4. Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2 001 ( ) and the proposed ( ) models for the late - lactation period (greater than 176 days in milk). Each data point (NRC 2001 - , Proposed model - ) represents the raw (a) and the adjusted for random effects (b) individual weekly DMI. ................................ ................ 77 Figure 4.5. Curve of lactation on the average Holstein dairy cow. Where the solid lines represent the observed milk energy (MilkE, ), observed dry matter intake (DMI, ), and observed body weight (BW, ), and the dashed lines represent the predicted dry matter intake by the NRC 2001 ( ) and proposed ( ) models. ................................ ......... 78 Figure 5.1. Eff ect of the inclusion of dietary palmitic (a) and stearic (b) on dry matter digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ) . .. 127 Figure 5.2. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linoleic (d) on NDF digestibility. Data points represent the adjus ted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ ......................... 128 Figure 5.3. Effect of the inclusion of dietary palmitic (a) and stearic (b) on total fatty acid digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and s tudy 5: ) . .. 130 xii Figure 5.4. Effect of the inclusion of dietary palmitic (a) and stearic (b) on 16 - carbon fatty acids digestibility. Data points represent the adju sted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ) . .. 131 Figure 5.5. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linoleic (d) on 18 - carbon fatty acids digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ 132 Figure 5.6. Effect of the inclusion of dietary palmitic (a), stearic (b), and linolenic on energy digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). .. 134 Figure 5.7. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linolenic (d) on digestible energy intake (DEI, Mcal/d). Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ........................... 135 Figure 5.8. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linolenic (d) on digestible energy intake (DEI, Mcal/d). Data points represent the adjusted for study effect individual observations and are coded by the st udy (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ........................... 137 Supplemental Figure 5.1. Effect of the inclusion of dietary oleic (a), linoleic (b), and linolenic (c) on dry matter digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ ......................... 149 Supplemental Figure 5.2. Effect of the inclusion of dietary linolenic on NDF digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ............................. 150 Supplementa l Figure 5.3. Effect of the inclusion of dietary oleic (a), linoleic (b), and linolenic (c) on FA digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; stu dy 4: , and study 5: ). ................................ ................................ ................................ ......................... 151 Supplemental Figure 5.4. Effect of the inclusion of dietary oleic (a), linoleic (b), and linolenic (c) on 16 - carbon FA digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ ......................... 152 xiii Supplemental Figure 5.5. Effect of the inclusion of dietary linolenic on 18 - carbon FA digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). .. 153 Supplemental Figure 5.6. Effect of the inclusion of dietary oleic (a) and linol eic (b) on energy digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). .. 154 Supplemental Figure 5.7. Effect of the inclusion of dietary linoleic on digestible energy intake (DEI, Mcal/d) . Data points represent the adjusted for study effect individual observations and are coded by the stud y (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ ................................ ............. 155 Supplemental Figure 5.8. Effect of the inclusion of dietary linoleic on digestible energy intake (DEI, Mcal/kg of DM) . Data points represent the adjusted for study effect individual observati ons and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). ................................ ................................ ................................ ......................... 156 Figure 6.1. Empty body water (EBWater) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques), and the size of the points represents the average daily gain. ................................ ................................ ....... 196 Fig ure 6.2. Empty body fat (EBFat) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect. The color represents the met hod used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques), and the size of the points represents the average daily gain. ................................ ................................ ....... 197 Figure 6.3. Empty body protein (EBProtein) composition in heifers as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques), and the size of the points represents the average daily gain. ................................ ........................... 198 Figure 6.4. Empty body ash (EBAsh) composition in heifers as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect. The color represents the method us ed to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques), and the size of the points represents the average daily gain. ................................ ................................ ....... 199 xiv Figure 6.5. Fat - free mass (FFM) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for t he study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques), and the size of the points represents the average daily gain. ................................ ................................ ....................... 200 Figure 6.6. Water ( ), fat ( ), protein ( ), and ash ( ) of the tissue deposited during growth at an average daily gain of 0.600 (a), 0.800 (b), and 1.00 (c) kg/d. ................................ ........ 201 Figure 6.7. The net energy requirements for growth estimated using the proposed models (solid lines) and the NRC 2001 (dashed lines) for three rates of g rowth are represented by the thickness of each corresponding line. The average daily gain for each division is represented by three scenarios: restricted (R), normal (N), and elevated (E). ................................ ....... 202 Figure 6.8. The net protein requirements for growth estimated using the proposed models (solid lines) and the NRC 2001 (dashed lines) for three rates of growth are represented by the thickness of each corresponding line. The average daily gain for each division is represented by three scenarios: restricted (R), normal (N), and elevated (E). ................................ ....... 203 Figure 6.9. Empty body water (EBWater) co mposition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques), and the solid line represents the proposed model. ................................ ................................ ................................ ................................ .. 204 Figure 6.10. Empty body fat (EBFat) composition in cows as a function of body condition score ( BCS). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques), and the solid line represents the proposed m odel. ................................ ................................ ................................ ................................ ............. 205 Figure 6.11. Empty body protein (EBProtein) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques), and the solid line represents the proposed model. ................................ ................................ ................................ ................................ .. 206 Figure 6.12. Empty body ash (EBAsh) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect. The color represents the me thod used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques), and the solid line represents the proposed model. ................................ ................................ ................................ ................................ .. 207 xv Figure 6.13. Fat - free mass (FFM) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect. The color represents the method used to determine the body composition ( - direct measur ement of EBW composition; and - dilution techniques), and the solid line represents the proposed model. ................................ ................................ ................................ ................................ ............. 208 Supplemental Figure 6.1. Empty body water (EBWater) c omposition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. ................................ ................................ ................ 213 Supplemental Figure 6.2. Empty body fat (EBFat) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. ................................ ................................ ................ 214 Supplemental Figure 6.3. Empty body protein (EBProtein) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. ................................ ................................ ................ 215 Supplemental Figure 6.4. Empty body ash (EBAsh) composition i n heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. ................................ ................................ ................ 216 Supplemental Figure 6.5. Fat - free mass (FFM) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. ................................ ................................ ................................ .................... 217 xvi 16 - C 16 - carbon fatty acid s 16 - CD 16 - carbon fatty acid s digestibility 18 - C 18 - carbon fatty acid s 18 - CD 18 - carbon fatty acid s digestibility ADF Acid detergent fiber ADG Average daily gain ALFALFA%DM Alfalfa as a percentage of dry matter BCS Body condition score BW Body weight BWBCS3 Body weight adjusted to a body condition of 3 C16:0 Palmitic acid C18:0 Stearic acid C18:1 Oleic acid C18:2 Linoleic acid C18:3 Linolenic acid Ca - PFA Calcium salts of palm FA CCC Concordance correlation coefficient CORNSIL Corn silage CORNSIL%DM Corn silage as a percentage of dry matter CP Crude protein DE Digestible energy xvii DEI Digestible energy intake DEIday Digestible energy intake expressed as Mcal per day DEIkg Digestible energy intake expressed as Mcal per kilogram of intake DIM Days in milk DMD Digestibility of dry matter intake DMI Dry matter intake DMI%BW Dry matter intake as a percentage of body weight DMI %BW^0.75 Dry matter intake as a percentage of metabolic body weight EBAsh Empty body ash EBFat Empty body fat EBProtein Empty body protein EBW Empty body weight EBW^0.75 Empty body weig ht to the power of 0.75 EBWater Empty body water ED Energy digestibility EE Ether extract EQEBG Size - scaled empty body weight gain EQEBW Size - scaled empty body weight FA Fatty acids FAD Fatty acids digestibility FCM Fat - corrected milk FFM Fat - free mass fNDF Forage NDF xviii GE Gross energy GRASS%DM Grass as a percentage of dry matter HFERM Highly fermentable corn source HFERM%DM Highly fermentable corn source as a perce n tage of dry matter HOT Hepatic oxidation theory HPO Hydrogenated triacylglycerides from palm oil Ht Height iNDF Indigestible neutral detergent fiber LIN Linear lnEBW Natural logarithm of empty body weight ltADG Lifetime average daily gain BW^0.75 Metabolic body weight BW ^0.75 BCS3 Metabolic body weight adjusted to a body condition score of 3 MFERM Moderately fermentable corn source MFERM%DM Moderately fermentable corn source as a percentage of dry matter MI Michigan MidAge Age at the mid of the experiment MilkE Milk energy MM Multiple s of maintenance MSEP Mean square error of prediction MSU Michigan State University MY Milk yield NDF Neutral detergent fiber xix NDFD Neutral detergent fiber digestibility NE g Net energy for growth NE L Net energy for lactation NFC Nonfiber carbohydrate NFFS Nonforage fiber sources NFFS%DM Nonforage fiber sources as a percentage of dry matter nfNDF Nonforage NDF NLIN Nonlinear NP g Net protein for growth NRC National Research Coun ci l OH Ohio OM Organic matter OSU Ohio State University OthersFA Others fatty acids PC Predictive correlation coefficients pdNDF Potential digestible neutral detergent fiber PMM Peak milk month polEBW 4 th order polynomial of EBW RE Retained energy RMSE Root mean square error RMSEP Root mean square error of prediction SAS Statistical analysis system SE Standard error xx SED Standard error of the difference SEM Standard error of the mean StarchD Starch digestibility SWG Shrunk weight gain TDN Total digestible nutrients TDN 1x Total digestible nutrients at maintenance level UGA University of Georgia US United States VIF Variance inflation factors WOL Week of lactation Change in body weight 1 Dairy farms profit margins have steadily decreased over the last 20 years, and nowadays many farmers are struggling to financially thrive in a market with low milk prices and high production costs. To overcome this scenario , farms have undertaken two strategies: 1) increas ing herd size in order to dilute fixed costs and enjoy the economic benefits of large - scale production , and 2) increa sing milk production and the level of efficiency in the conversi on of feed into milk. D iet plays a critical role in the process of improving farm productivity while also controlling costs . Diet is one of the most significant cost s involved in running a dairy farm ; and consequently , farmers tend to be reluctant to incre ase spending on rations. However, diet has a direct impact on milk yield, milk composition, animal health, and reproduction, and wise investments in nutrition should . Thus , diet ha s become a major cost driver , with a direct impact on primary source of income. Given this information, a possible way to help dairy farms overcome the current challenges of low milk prices and high production costs is to formula te more precise and tailored diets to maximize nutrition and, ultimately , improve dairy farm profits. Currently, t he most commonly used and globally recognized system for formulat ing and evaluat ing dairy cattle diets is the National Research Council Nutrient Requirements of Dairy Cattle ( NRC ). Although other softwar e have been developed to formulate dairy diets (i.e., CNCPS, Spartan Dairy, DAIR4, PCDAIRY, CPM, AMTS), the NRC still serves as the primary reference book and, more often than not , the NRC equations are applied in other software. 2 The NRC publications pass through a rigorous evaluation process. S ince its first publication in 1945 , the NRC has undergone eight revisions. The current version, the NRC (2001), incorporates many improvements from the previous edition , including significant chang es and updates in the statistical requirements, diet digestibilities , and nutritional recommendations, as well as changes in the software itself . However, the models and prediction equations incorporated in the NRC (2001) were derived from dat a collected during the 19 80s and 19 90s . A lot has changed since this data was collected. Cows are much bigger, producing much more milk , and under a different management system (i.e. , grazing vs . confined) than in the past . Also, research h as helped formulate a much deeper understanding o f the physiological factors underlying animal nutrition, and more data is available to derive new models. Many researchers are f ocusing on evaluating and updating the outdated equations proposed by NRC (2001). The hypotheses of this disser t ation are th at equations derived from a la r ger and newer database would increase the accuracy and pre c ision of the prediction and better rep r esent the current dairy production systems. The obj ective s of this dissertation share a similar focus: 1) to develop new prediction equations for dry matter, NDF, and starch dige stibility at production level (chapter 3 ) ; 2) to model dry matter intake in Holstein dairy cows based on milk energy, live body weight, change in live body weight, body condition score, height, days in milk, and parity (chapter 4 ) ; 3) to evaluate the effect of palmitic, stearic, oleic, linoleic, and linolenic on dry matter, NDF, fatty acid, energy digestibility, and dig estible ener gy intake (chapter 5 ) , and 4) to develop prediction equations to estimate body composition in heifers and cows using data collected in Holsteins and appl y th ese equations to determine the net energy and net protein 3 requirements for growth, and the net ener gy per kilogram of empty body weight in mature animals (chapter 6) . 4 D AIRY FARM PROFITABILITY In 1997, the average milk price received by dairy farmers was $13.30/cwt, without adjusting for inflation (NASS - USDA, 2018); once the 1997 price was adjusted for inflation to 2017 values, the milk price was $20.33/cwt (BLS, 2018). In comparison , the averag e milk price in 2017 was $17.60/cwt (NASS - USDA, 2018), indicating a decrease of 13.4% in the inflation corrected milk price over the 20 - year period from 1997 to 2017 (Figure 2.1). Th is decrease in milk price can be explained by multiple factors, such as c hanges in global dairy markets (Hemme, 2017; Stephenson, 2017) and the increase in milk supply to the U.S. market at a higher rate than the increase in milk demand. In fact, the U . S average commercial milk stocks increased from 2 , 671 million kilograms in 1990 to 6 , 216 million kilograms in 2010 (NASS - USDA, 2018). Furthermore, although they represent a smaller niche market, there has also been an increase in milk alternative products, such as soy, almond, and coconut products . To make this scenario even more difficult, the price of dairy feed has also increased. In 1997, the price of dairy feed was $3.80/cwt; once the 1997 price was adjusted for inflation to 2017 values, the dairy feed price was $6.14/cwt (BLS, 2018). In contrast, the average price of dai ry feed in 2017 was $ 7.26/cwt . This indicates an increase of 18.7% in the price of dairy feed from 1997 to 2017 (ERS - USDA, 2018) (Figure 2.1). 5 Declining milk price s and increasing dairy feed prices have resulted in many modern dairy farmers hardly being able to recoup production costs . The average production cost in 2017 was $22.27/cwt (ERS - USDA, 2018), and the average milk price for the same year was $17.60 (NASS - USDA, 2017). Unfortunately, this phenomenon is not unique to 2017 . Dairy farmers have been struggling with low milk prices and high dairy feed prices for many consecutive years. The average production cost from 2010 to 2017 was $23.62/cwt (ERS - USDA, 2018) , and the average milk price for the same period was $18.75/cwt (NASS - USDA, 2018), indicati ng that the milk price covered on average only 79.4% of production costs, resulting in farmers losing money. The cost structure of a dairy farm divides production cost s into two categories: allocated overhead and operating costs. On the average US dairy farm, a llocated overhead costs represented 39.4% of production cost s in 2017 . The most significant allocated overhead costs included the capital recovery of machinery and equipment, the opportunity cost of unpaid labor, and hired labor, representing 17.0, 11.1, and 7.37% of the production cost, respectively (ERS - USDA, 2018). On the other hand, operating costs represented 60.6% of the production cost, and the most significant costs associated with this category were feed, followed by veterinary and medicine , and custom services, representing 47.1, 3.74, and 2.60% of the production cost, respectively (ERS - USDA, 2018). The 2017 dairy farm cost structure is presented in Table 2.1. As mentioned previously, dairy farmers have been forced to adopt specific strategi es to overcome the financial challenges of high production costs and low milk prices. In order to optimize the use of facilities, machinery, labor, and capital invested into the business , dairy farm ers have expan ded their business via either natural growth ( by investing more money and resources into the business ) or via mergers and acquisitions. Th is expansion of dairy farms is 6 responsible for the decreas ing number of dairy farms and increasing size of dairy farms in the last ten years (2007 to 2017) . Durin g this time period, the U.S. experienced a decrease in the number of dairy operations from 53,132 to 40,219 and an increase in the herd size per farm from 173 to 234 milking cows (NASS - USDA, 2018). Dairy farmers have also felt significant pressure to incre ase both production and efficiency. Despite an observed increase in milk production per cow from 9,164 to 10 ,4 06 kg /year (NASS - USDA, 2018) during the period of 2007 - 2017 , there is still room for improvement . In order to further increase production and ef ficiency, advances in herd genetics, management, health, comfort, and nutrition are crucial. Advances in herd genetics have had a fundamental impact in allowing lasting and persistent improvements (Veerkamp, 1998; VandeHaar et al., 2016; Hardie et al., 201 7; Miglior et al., 2017; Weigel et al., 2017) ; however, when compared to dietary changes, these effect s have a more long - term effect and are not immediately apparent. In contrast, enhancements in management (Bewley et al., 2017; Roche et al., 2009), health (Risco, 2017; Overton et al., 2017), welfare (Fraser and Koralesky, 2017; von Keyserlingk and Weary, 2017), reproduction (Moore and Hasler, 2017; Stevenson and Britt, 2017), and nutrition (VandeHaar and St - Pierre, 2006; Grant and Dann, 2017; Schingoethe, 2017) have a much more immediate effect on farm profits. Given that feed is the most significant cost involved in a dairy farm (Table 2.1) and has a direct impact on m ilk production and animal health (McGuffey, 2017), improvement s in animal nutrition ha ve been the primary concern of the majority of farmers, and much research has been conducted in this field. Overall , research on animal nutrition has focused on understan ding the biological mechanism s involv ed in the control of feed intake (Ingvartsen and Andersen, 2000; 7 Allen, 2000; Allen et al. 2009), the conversion of feed into animal products (VandeHaar, 1998; Hall and Mertens, 2017; VandeHaar and Tempelman, 2017; Karl sson et al., 2018), nutrient partitioning (Allen and Piantoni, 2014; Baumgard et al., 2017), feed supplements that improve milk yield (Casper, 2017; Goff, 2017; Ferreira and Weiss, 2017; Schwab and Broderick, 2017; Palmquist and Jenkins, 2017), and a speci fic diet for each stage of lactation and level of production (Contreras - Govea et al., 2015; Kalantari et al., 2016; VandeHaar and Tempelman, 2017). The innovation s and improvements developed by animal nutrition research are translated to dairy farms through new commercial products, nutritional recommendations, and, ultimately, changes in diet formulation. In this sense, diet formulation is the link between advance s in animal nutrition research a nd the diets used in dairy farms. In order for farmers to reap the benefits of advance s in animal nutrition research and to improve their financial situation, it is fundamental that these advances are translated to dairy farmers via diet formulation. Thus , th e goal of this dissertation is to help dairy farmers improve their financ es by improving the statistical models that play a critical role in the diet formulation process. D IETARY FORMULATION The initial publication about the use of computer - based softw are to formulate dairy diets dates back to at least the 1960s . Bath (1966) used linear programming to test rapidly all combinations of feed ingredients , which would meet specific nutrient requirements and select the formula which met them at the lowest cost and therefore formul ate the least - cost concentrate mix. 8 Applying the computer - based program proposed by Bath (1966), Bath et al. (1968) evaluated four concentrated mix es that varied in price from $4.49, $2.99, and $1.05 per ton less than the control diets and found that diets formulated using the least - cost method proposed by Bath (1966) could improve dair profit s by reducing diet cost while maintaining producti on. Given the success and the vast potential of computer - based software on diet formulation, many other researchers started to work on the improvement and development of new programs. Chandler and Walker (1972) developed statistical models that calculated animal requirements based on the Dairy NRC (1971) . These statistical models included dry matter intake, and the requirements of crude protein, net energy, calcium, and phosphorus. The program proposed by Chandler and Walker (1972) gave nutritionists the ab ility to determine changes in nutrient requirements immediately as a result of variable productive conditions . As an alternative to the least - cost system, Bath (1975) proposed a maximum - profit ration formulation program. The maximum - profit system maximized profit by adjusting ration composition and milk production to the feed and milk prices. Brown and Chandler (1978) incorporated equations to predict milk yield ( MY ) and dry matter intake ( DMI ) into a computer - based maximum - profit ration formulation program . By combining the maximum - profit ration formulation program with prediction equations of MY and DMI, the program proposed by Brown and Chandler (1978) had the advantage of automatically adjus t ing intake and milk production rates to correspond to changing economic situations. Since these early publications , much research has been done to evaluate and improve diet formulation software (Jones et al., 1978; Black and Hlubik, 1978; Stallings and McGilliard, 9 1984; Colenbrander et al., 1986; Galligan et al., 1986 ; Weaver et al., 1988) . N owadays, the software most often used to evaluate or formulate diets are the NRC Dairy 2001 and CNCPS, with many derivations such as the Spartan Dairy, PCDAIRY, CPM, and AMTS. The diet formulation software combine s many statistical nutritional requirements, the DMI, and the nutrient digestibility of the diet required to meet the nutrient needs of the animal. Regardless of the software used by the nutritionist to formulate and/or evaluate the diet, th e software capability is limited to the accuracy and precision of its statistical models. Hence, constant review and modernization of these models are required to keep the software updated with current knowledge i n the field of dairy nutrition and adequate ly support current production systems. Additionally, information from recent research can be used to increase the accuracy of the equations that underlie nutrient requirements. To illustrate this point, since the first edition of the NRC Dairy in 1945, th ere were eight revisions (1950, 1956, 1958, 1966, 1971, 1978, 1988, and 2001) to reflect the most recent knowledge in the field of dairy cattle nutrition. In its first edition, the NRC Dairy had 21 pages and focused on the discussion of nutrient deficiency symptoms. In contrast, in its current edition, the NRC 2001 had 401 pages and is a reference book on all aspects of nutrition and feeding. It is clear that as time progresses, the amount of information also grows. Although there have been constant efforts to keep the NRC updated, the NRC (2001) equations were developed based on a 19 90s database. Since the 19 90s, a lot has changed, of milk. In recognition of the need for a revision, the NRC 2001 is undergoing an update, and most likely will issue a newly revised edition during the following year. In fact, many recent 10 publications have been focused on the evaluation of the NRC (2001) models and suggested new techniques and updates. As an example, W hite et al. (2017a) evaluated the NRC (2001) and found substantial mean and slope bias on the NRC (2001) predictions of nutrient digestibility, and proposed new models for digestibility of fiber, fat, protein, and non - fiber ca rbohydrate. In a similar work, White et al. (2017b) evaluated the NRC (2001) rumen degradable and undegradable protein system and reported a poor statistic al fit of the model. As an alternative, White et al. (2017b) derived a new system based on the predic tion of postruminal appearance rates of A, B, and C protein fractions for different feed types. This new proposed system had a superior statistical fit than the system based on the passage and digestion rate used in the NRC (2001). Moraes et al. (2018) eva luated the metabolizable protein system proposed on the NRC (2001) and found that metabolizable protein requirements either for maintenance plus lactation or exclusively for lactation, were slightly smaller than NRC (2001) at low yields but greater than th e requirements from the current system at high yields. Other publications have focused in other areas such as microbial nitrogen flow (Roman - Garcia et al., 2016; White et al., 2016), absorbed amino acids (Estes et al., 2018), physically adjusted NDF ( White et al., 2017c; White et al., 2017d), and phosphorus balance (Feng et al., 2016). Despite the extensive efforts to update the statistical models proposed in the NRC (2001), there are still many models that need to be revised and areas to be further explored, such as the predictions of DMI [Equation 2.1], the rate of decline in digestibility with level of feeding [Equation 2.2], fat supplemen tation and its effect on energy digestibility and energy intake, retained energy, net protein requirements for growth [Equation 2.3 and Equation 2.4, 11 respectively], and tissue energy contained per kilogram of empty body weight (EBW) in mature cows. These e quations are shown below. [Equation 2.1; NRC, 2001] where is 4 percent fat - corrected milk (kg /d ), is body weight (kg), and is week of lactation. [Equation 2.2; NRC, 2001] w here the discount is a multiplying factor to the that represents the digestibility at the production level, is the total digestible energy at maintenance level as a percent of dry matter intake and it is for the entire diet, and is expressed as incremental intake above maintenance. [Equation 2.3; NRC, 2001] where is the size - scaled empty body weight, and is the size - scaled empty body weight gain. [Equation 2.4; NRC, 2001] 12 where is shurnk weight gain , and is retained energy. D RY MATTER INTAKE There is a long history of studies focusing on the biological factor s regulating DMI and the development of prediction equations for DMI. The earliest of these studies were published in the Journal of Dairy Science and Journal of Animal Science in the late 19 50s and early 19 60s (Crampton et al., 1957; McCullough, 1959; Conrad et al., 1964; Baile, C.A., 1971; Brown et al., 1977). Based on many research observations, Brown and Chandler (1978) w ere the pioneers in incorporating prediction equations for DMI i n computer - based software. Subsequent studies have show n that DMI is better modeled through nonlinear models ; however, due to computational limitations, Brown and Chandler (1978) developed a r esponse surface and divided the lactation into four smaller segments which were defined more adequately by linear models. I n this initial model, Brown and Chandler (1978) used the equation to predict DMI per unit of milk that was proposed by Brown et al. ( 1977) . This equation predicted DMI to produce at low, mid, and high production points of each segment, while crude fiber, concentrate, and crude protein were held constant at median values. Nowadays, our understanding of factors regulating the DMI in dairy cows has increased . Allen (2000) discussed the effects of diet on short - term regulation of DMI and emphasized the importance of fiber content, ease of hydrolysis of starch and fiber, particle size, particle fragility, silage fermentation products, concent ration and characteristics of fat, and the amount and ruminal degradation of the protein. In addition to the diet characteristics, Allen (2000) also discussed the effect of metabolic fuels on the regulation of DMI . Allen (2000) recognized that 13 propionate h ad a fundamental r o le i n the metabolic control of DMI ; however, the mechanism behind the effect of propionate in the regulation of DMI was not yet clear. This mechanism was further understood and published nine years later. Allen et al. (2009) discussed th e metabolic control of feed intake and proposed an integrated mechanism known as hepatic oxidation theory ( HOT ) explaining how hepatic fuel oxidation sen ds signals to the brain feeding centers and controls DMI . This theory explained the effect s of the many fuels arriving in the liver (i.e., propionate, acetate, glucose, lactate, and NEFA) and emphasized the crucial role of propionate i n regulating DMI. Fur th ermore, Allen et al. (2009) indicated that hepatic oxidation likely controls feed intake to a greater extent for ruminants in a feedlot setting consuming high - starch diets, for cows with low nutrient requirements (late lactation and dry cows), and for animals in a lipolytic state (periparturient cows) than for ruminants fed high - forage diets o r with very high - nutrient requirements (cows at peak lactation) (Allen et al., 2009). Animals fed high - forage diets or those with very high - nutrient requirements are likely to have the ir intake limited by the time required for chewing or by distension with in the gastrointestinal tract (Allen, 2000). The gastrointestinal tract contains mechanoreceptors that can sense the distention of the tract. When activated , the mechanoreceptors se nd signals to the enteric nervous system and to the central nervous system to terminate the consumption of feed. In ruminants, the reticulorumen is the segment most likely to limit the DMI due to distention (Allen, 1996). Besides the mechanoreceptors, hormonal control like the cholecystokinin can also be responsive to the flo w of ingesta through the gastrointestinal tract and stimulate the center of satiety to cease the DMI (Baile et al., 1983; Choi et al., 2000; Allen, 2000). 14 Moving from the regulation and control of DMI to the optimization and evaluation of DMI, Weiss (2015) demonstrated that DMI is a function of the cow, diet, environment, facilit ies , and management, and interaction s among th e se factors. Cow factors such as milk yield, stage of lactation, and body weight will determine potential DMI. Factors associated with diet (i.e., ingredients, nutrients, physical form, digestibility), environment (i.e., temperature, humidity), and facilities and management (i.e., access to feed and water, bunk space, grouping) set actual DMI, which is never higher than the potential DMI. In this sense, the goal is to provide a proper diet and remove facilit y and management factors that limit intake. Withi n the context of DMI prediction and its use i n diet formulation, the accurate measurement and prediction of DMI are essential for the fo rmulation of balanced, economical diets and the diagnosis of milk yield losses (Roseler et al. 1997a). Despite the effort s of many researchers to derive a prediction equation for DMI that consider s factors related to animal, diet, and environment (NRC, 198 9; Kertz et al., 1991; Fox et al., 1992; Holter and Urban, 1992; Rayburn and Fox, 1993; Holter et al., 1997); including all these factors in a unique statistical model is very challenging. In fact, these variables account for only about 40% of the variation in the prediction of DMI (Roseler et al., 1997a; Roseler et al., 1997b). Today, the most used prediction equations for DMI are based only on animal factors (body weight, milk yield, and stage of lactation); hence, the prediction of DMI represents the average intake across many diets in different environments for any given animal factors. For example, the NRC (2001) predicts DMI based on metabolic body weight ( BW^.75 ), four percent fat - corrected milk ( FCM ), and a week of lactation ( WOL ) [Equation 2 .1]. 15 The NRC (2001) prediction equation was derived by combining the equation of Rayburn and Fox (1993) with an adjustment for the week of lactation developed by Roseler et al. (1997a). In the study conducted by Rayburn and Fox (1993) , data from 1,284 Hols tein cows over 149 treatment periods were used to evaluate alternative methods of predicting DMI and derive a new DMI prediction equation. I n Roseler et al. (1997a) , data on complete lactation from 241 Holstein cows were used to improve the prediction for DMI of lactating cows fed highly digestible high energy diets. Fox et al. (2004) proposed an alternative equation to estimate DMI based on body weight ( BW ), FCM, and adjustment factors for night cooling, mud depth, and month post - calving when p eak milk yie ld ( MY ) occurred. T his model combined animal factors with environmental factors and resulted in the adoption of th e proposed equations by the CNCPS. However, the CNCPS h as updated soon after, resulting in the inclusion of the equation utilized by NRC (2001 ) for lactating dairy cows (Tylutki et al., 2008) instead . N ew DMI prediction equations have been derived using mid - infrared spectroscopy on milk samples (Shetty et al., 2017), incorporating the lipostatic theory (Kennedy, 1953) into a dynamic model based on dairy cow performance (Ellis et al., 2006), and adding the rumination time to the prediction of DMI (Clement et al., 2014). However , the NRC (2001) prediction equation is still the most used on diet formulation software (CNCPS, Spartan Dairy, CPM, AMTS) . Even though the DMI equation proposed by the NRC (2001) was derived from large datasets (as described above) and underwent extensive evaluations, this equation was based on data animal data from the late 19 80s and 19 90s, and may not be accurate for current dairy cows. 16 Given this information, , we proposed an equation to predict DMI based on milk energy, body weight, body condition score, parity, and days in milk. The pr oposed model was derived using data collected from 3,607 Holstein cows enrolled in 57 studies from 8 states across the US. N UTRIENT DIGESTIBILITY While the DMI and diet composition establishes nutrients consumed by animals, the most significant factor aff ecting nutrient availability in lactating dairy cows is the digestibility of nutrients in the ration (Casper, 2017). Thus, digestibility is a decisive factor in the process of diet formulation. Due to the fundamental importance of digestibility and its rel ationship with DMI, digestibility has been studied since the 19 50s. It is well - known that digestibility decreases wit h intake (Crampton et al., 1957; Conrad et al., 1964; Tyrell and Moe, 1975; Colucci et al., 1982; VandeHaar, 1998; Casper and Mertens, 200 8; Casper, 2017). However, the difficult part of the relationship between digestibility and DMI is accurately predict ing the reduction in digestibility as intake increases. The equation used by the NRC (2001) to estimate digestibility is composed of the di etary total digestible nutrients measured at maintenance level ( TDN 1x ), and the intake expressed as multiples of maintenance [Equation 2.2]. The primary concept behind the NRC (2001) equation is that digestibility declines with the level of feeding . H oweve r , the rate of decline in digestibility is associated with the digestibility of the diet at maintenance (Wagner and Loosli, 1967; NRC, 2001). First, to use the NRC (2001) system , the TDN 1x of feeds must be estimated. The NRC (2001) used a summative approach to derive TDN 1x , in which truly digestible nutrient fractions 17 (nonfiber carbohydrate, crude protein for forages, crude protein for concentrate, fatty acids, and NDF) are calculated based on a set of equations using diet composition, feedstuff processing, source of protein meal, and type of fat supplement (Weiss et al., 1992; NRC, 2001). Once the truly digestible nutrients are estimated, they are summed, and the metabolic fecal total diges tible nutrient is subtracted (fixed value of 7) to calculate the TDN 1x (NRC, 2001). The second component in the NRC (2001) equation is the intake expressed as multiples of maintenance, where multiple of maintenance is calculated based on the energy intake above maintenance. For example, if a lactating cow is consuming 40 Mcal /d of net energy for lactation ( NE L , Mcal) , and it is estimated that 10 Mcal /d of NE L are for maintenance (~ 636 kg of BW; NE L maintenance = BW 0.75 * 0.08; NRC, 2001), then the intake i s at 4X the maintenance (Eastridge, 2002). The NRC (2001) system was a significant improvement from the previous NRC (1989) system , which used a constant depression on digestibility of 4% per multiple of maintenance. However, the NRC (2001) digestibility s ystem still faces some problems. First, it applies a linear decrease in the diet digestibility as intake increases . VandeHaar (1998) demonstrated that a curvilinear d ecrease better represents the depression on digestibility. Second, the equation was derive d based primarily on data obtained from animals at low to moderate levels of intake and may not adequately describe digestibility of the current high - producing dairy cows, which often have intake greater than 4X the maintenance. Finally, the NRC (2001) d ec rease is applied to the entire diet, even though the literature already suggested that feeds should have specific discount factors (Van Soest, 1984). Furthermore, recent research suggested that the intake has a different effect on each dietary fraction ( Wh ite et al., 2017a). 18 An alternative approach to the NRC (2001), is the CNCPS system which uses passage and degradation rates assigned to carbohydrate and protein fractions to determine digestibility (Van Amburgh et al., 2015). On the current CNCPSv6.5, each of the eight carbohydrate fractions and five protein factions has its own degradation rate (Van Amburgh et al., 2015), and passage rates were assigned to forage, concentrate, and liquid pools as a function of intake (Higgs et al., 2015). Although the conc ept of dividing the carbohydrate and proteins in to homogeneous fractions and assign ing specific degradation rates is an appealing approach , it has many flaws. First, the two - pool structure used i n the CNCPS does not account for the fractional rate of release from the non - escapable to the escapable fractions (selective retention and two sequential pools; Allen and Mertens, 1988). Second, the degradation rates assigned to each fraction were determin ed mostly using in vitro or situ techniques and may not truly represent degradation rates in vivo . Third, the models are so detailed that there is no data to parameterize them (Allen, 2011; Allen and VandeHaar, 2016). Finally, France et al. (2000) conclude d that mechanistic models are less accurate than empirical models because of their increased complexity and numerous inputs. As discussed above, both the NRC (2001) and the CNCPSv6.5 systems to determine digestibility at production level have limitations a nd require improvements. Accordingly, recent publications have been focused o n this area. Nousaiainen et al. (2009) performed meta - analyses using 497 dietary treatment means from 92 studies to evaluate the effects of forage and concentrate factors on total diet digestibility. In this publication, the authors determined that forage quality, the proportion of concentrate, CP content, fibrous by - product, and NDF digestibility are fund amen tal in determining diet digestibility. Using the same database, Huhtanen et al. (2009) investigated the effect of feeding level and diet composition on 19 digestibility. He found that TDN for lactating cows could be calculated using organic matter ( OM ) digestibility at a maintenance level determined either in vivo in sheep or by u sing in vitro methods, DMI, crude protein ( CP ) content, and proportion of forage in the diet. In regard to nutrient digestibility, White et al. (2017a) built a database composed of 550 treatment means from 192 studies and derived prediction equations for NDF, fat, protein, and nonfiber carbohydrate ( NFC ). In their paper, the authors derived independent equations for legume, corn silage, and other forages to predict NDF digestibility; separate fatty acid ( FA ) digestion coefficients for different fat supplem ents (animal fats, oils, and other fat types) and the basal diet; unique CP digestibility equations for forages, animal protein feeds, plant protein feeds, and other feeds; and NFC digestibility coefficients for grain - specific starch digestibilities. Final ly, the authors concluded that future work should more thoroughly investigate opportunities to account for the relationships between DMI and nutrient digestibilities ( White et al., 2017). Moreover, Ferrareto et al. (2013) investigated the effect of cereal grain type and corn grain harvesting and processing methods on digestion . Boerman et al. (2015) examined the intestinal digestibility of individual long - chain fatty in lactating cows . Weld and Armentano (2017) performed a meta - analysis to determine the eff ects of supplemental fat on fiber digestibility. However, these meta - analyses included only the treatment means of the contributing factors available in the studies summarized. When treatment means are used, the ability to quantify variability among animal s within the same diet is reduced, and therefore valuable information about the effects of DMI on digestibility is lost. In digestibility in high - , we further investigated the effect s of intake and diet composition on the digestibility of dry matter, NDF, and starch, and proposed new prediction 20 equations. For this analysis, we used a database containing 1,942 individual observations from 662 cows on 195 different treatments. F AT SUPPLE MENTATION AND ENERGY INTAKE As discussed above, DMI and nutrient digestibility determine the amount of nutrients absorbed by the animals that can then be used for maintenance and production. However, among all the nutrients absorbed by the animal, the lack of energy is the most likely to limit production i n the high - producing lactating cow (Eastridge, 2002). For example, it is well - established that most animals undergo a period of negative energy balance during the beginning period of lactation (Bauman and Currie, 1980). In light of this , fat supplements are often added to dairy cattle diets with the goal of increasing energy intake in order to increase milk energy output or energy balance (Allen and Piantoni, 2014). However, the response to fat supplementat ion has been inconsistent . In many experiments , fat supplement s have increased energy intake ; however, in other experiments, fat supplements have depressed DM digestibility and DMI (Allen, 2000). In order to investigate the se varied responses to fat supple mentation, Allen (2000) constructed a database composed of treatment means from 60 studies to examine the effect of different sources of supplemental fat (oilseeds, unprocessed animal fat, hydrogenated FA & triglycerides, and calcium salts of palm FA Ca - PFA ) on DMI and found differences among sources. Ca - PFA statistically decreased DMI on 11 of the 24 comparisons and resulted in a numerical decrease in DMI in 22 of the 24 comparisons; in contrast, the other sources of fat seem ed to have little impact on D MI (Allen, 2000). To further investigate the effect s of different fat supplements, Weiss and Wyatt (2004) compared the effect s of Ca - PFA and hydrogenated triacylglycerides from palm oil ( HPO ) on 21 dietary digestible energy ( DE ). In agreement with Allen (20 00), Weiss and Wyatt (2004) also reported that DMI was reduced when cows were fed the high - concentration of Ca - PFA. However, the digestibility of energy, dry matter, and organic matter, were higher for diets with Ca - PFA than for the diets with HPO. As a re sult, cows fed Ca - PFA produced more milk than cows fed the control or HPO diets. Finally, the authors concluded that supplementing diets with Ca - PFA increased DE intake. However, due to the negative effects on DMI, the relative increase was less than that for DE concentration (Weiss and Wyatt, 2004). Another important source of variation regarding fat supplements is the degree of saturation. As discussed by Allen (2000) , unsaturated FA has higher hypophagic effects than saturated FA. To investigate the effe ct of degree of saturation, Harvatine and Allen (2006) linearly substituted 2.5% FA from saturated fat supplements (prilled, hydrogenated free fatty acids) for partially unsaturated fat supplements (calcium soaps of long - chain FA) and reported that increas ing unsaturated fat supplements decreased milk fat yield and tended to reduce intake of digestible energy. Additionally, animals receiving the diet high in unsaturated FA experienced milk fat depression with decreased milk fat yield associated with increas ed concentrations of trans - 10, cis - 12 conjugated linoleic acid , and total trans C18:1 FAs in milk. In 2011, Weiss et al. investigated the effects of fat supplements that differ ed in FA composition (chain length and degree of saturation) and chemical form (free FA, Ca - PFA, and triacylglyceride) . Weiss et al. (2011) compared a control diet (2.9% of DM as long - chain FA) to three diets with 3% added FA. The three fat supplements were mostly saturated free FA, Ca - PFA, and triacylglyceride. The authors observed a positive effect of free FA on the digestibility of FA, and concluded that free FA supplements were much more digestible than triacylglyceride supplements. 22 Current research on fa t supplementation is focusing on the specific effect s of each free FA supplement on digestibility, energy intake, nutrient partitioning, and production. Lock et al. (2013) compared a control diet without supplemental fat to a diet with palmitic ( C16:0 ) enr iched (~85% C16:0) fat supplement (2% of DM). The authors did not observe a difference i n milk yield or milk protein yield, but the diet with C16:0 - enriched supplement increased milk fat concentration and milk fat yield. Furthermore, the treatment with sup plemental fat decreased DMI and increased the conversion of feed in to milk. Lastly, the authors suggested that these results should be evaluated under different milk production levels. Following the publication of these results, Piantoni et al. (2013) ass essed the effect of C16:0 supplementation in dairy cows varying the level of production. Piantoni et al. (2013) compared a control diet without supplemental fat to a diet supplemented with C16:0 (2% of DM) using dairy cows ranging in milk production from 3 4 to 66 kg/d. The authors did not f ind a significant interaction between diets and preliminary milk yield ; and therefore, the effect of supplemental C16:0 was independent of the level of production. In regards to the production variable , the di et with supplemental C16:0 increased milk fat percentage and yields of milk, milk fat, and 3.5% fat - corrected milk compared to the control diet. With respect to the response s from the digestibility variables, the diet with supplemental C16:0 increased the total - tract digestibility of NDF and organic matter, but decreased FA digestibility compared to the control diet. Rico et al. (2014) evaluated the effects of diets containing C16:0 or stearic ( C18:0 ) fat supplements (2% of DM) on the production end efficie ncy of cows with a milk production ranging from 38 to 65 kg/d. The authors concluded that the results were consi s tent across the 23 level of production and C16:0 supplementation improved milk fat concentration and yield, as well as the efficiency of feed conv ersion into milk compared with C18:0 supplementation. Finally, in a recent meta - analysis , Weld and Armentano (2017) used 108 fat - supplemented treatment means from 38 publications to summarize the effect of fat supplementation on the total - tract digestibili ty of NDF ( ttNDFd ) in lactating dairy cattle. The authors categorized the fat supplements as medium - chain FA (C12 and C14), oil, C16, animal - vegetable, tallow, Ca - PFA, calcium salts of long - chain FA, and saturated fat. In this meta - analysis, the authors fo und that medium - chain FA and unsaturated vegetable oil decreased ttNDFd , and adding 3% of calcium salts of long - chain FA or saturated fats increased ttNDFd. In regards to DMI and digestible energy intake, adding fats, other than those with medium - chain FA, consistently increased the DE density of the diet. However, due to reduced DMI, this increased energy density may not result in increased digestible nutrient intake (Weid and Armenano, 2017). Despite the many research studies conducted to determine the effect of free FAs on dairy cattle production, feed efficiency , and nutrient digestibility, a comprehensive examination of the effect of specific free FA on digestibility of dry matter, NDF, fatty acid, and energy, as well their effect on digestible energy intake is still lacking . In , we performed a meta - regression using data from 5 experiments conducted at Michigan State University to determine the effect of dietary FA composition on dry matter, NDF, total FA, 16 - carbon FA, 18 - carbon FA, energy digestibilities, and digestible energy intake. 24 B ODY COMPOSITION IN HOLSTEIN CATTLE Wh ereas the previous se ctions focused on how to meet the nutritional requirements of dairy co ws ; the main focus in this se ction is ac cu rately determining what these nutritional requirements are. Of particular importance, is the net energy and the net protein required for growth ( NE g and NP g , respectively) in dairy heifers , and the energy supply/re quired per kilogram of change on empty body weight ( EBW ) in dairy cows. With this in mind, NE g and NP g can be estimated from the energy and protein content of the tissue deposited during growth (NRC, 2001). The NRC (2001) predicts NE g and NP g using Equatio ns 2.3 and 2.4, respectively. These equations were proposed and validated by Fox et al. (1999), wh o modified the equation proposed by the Beef NRC (1996) to compute growth requirements in dairy cattle. T he Beef NRC (1996) adopted the equations initially proposed by Garrett (1980) and Garrett (1987) and further adjusted by Fox et al. (1992) and Tylutki et al. (1994). Until today, Garrett (1980) has been one of the most extensive and comprehensive studies e valuat ing energy utilization in growing cattle. Garrett (1980) derived an equation to predict retained energy ( RE ) as a function of the rate of gain and EBW . Garret (1980) us ed data from 72 comparative slaughter experiments that together evaluated the carc asses of 1,843 and 330 British - breed steers and heifers, respectively, and 52 Charolais steers, all of which had received hormonal implants, and 861 and 405 British - breed steers and heifers, respectively, which had not received implants. In a second paper, using th is same database , Garrett (1987) derived equations to determine the fat and protein content of the gain as a function of the estimated RE. Subsequently , Fox et. (1992) used a size scale 25 approach to modify the proposed equations (Garrett, 1980 and Garrett, 1987) for all classes of beef and dairy cattle, which was later refined and validated by Tylutki et al. (1994). Fox et al. (1999) also modified the Beef NRC (1996) equations used to compute growth requirements, target weights, and energy reserves to develop a growth model for dairy cattle. I n the growth model proposed by Fox et al. (1999), the equation proposed i n the Beef NRC (1996) were size scaled for dairy breeds , and a set of prediction equations were derived to estimate NE g and NP g . This mode l was then evaluated using data from serially slaughtered nonimplanted Holstein heifer s published by Fortin et al. (1980) and Anrique et al. (1990). The authors concluded that the proposed model successfully predicted NE g and NP g of dairy cattle, accountin g for 96% of the variation in energy retained with a 4% bias. At that time, the development of a growth model based exclusively on data collected in dairy cattle was almost impossible due to the lack of data. The size scaling approach used by Fox et al. (1 999) offered a great alternative because the original equations were derived using a large dataset (Garrett, 1980) and the predictions seemed to have a good fit to dairy cattle. However, some discrepancies still needed to be addressed. For example, the siz e scale approach assumes that the chemical composition of gain is similar among animals at the same proportion of mature BW (NRC, 2001), but this may not be true in remarkab ly different production systems, as is the case. As mentioned above, in addition to being based on beef breeds raised on a feedlot diet, most of the data came from animals with hormonal implants. In contrast, replacement dairy heifers are raised receiving diets with much more forage than feedlot diets and without hormonal implants. 26 Since the NRC (2001), many studies have been published reporting data on body composition in dairy cattle raised within dairy farm conditions ; and therefore, data is now available to develop a growth model based on data collected from dairy cattle. For example, Moallem et al. (2004) evaluated the effect of bovine somatotropin and rumen - undegradable protein on body composition in 24 Holstein heifers. In this study the author evaluated body composition in animals at 5 and 10 months with an average body weight of 7 2 and 185 kg of EBW, respectively, and body composition of 66% water, 5% ash, 19% protein, and 9% fat at 5 months and 61% water, 5% ash, 19% protein, and 13% fat at 10 months. Brown et al. (2005) evaluated carcass composition in Holstein heifer calves prov ided with different amounts of energy and protein intake. In this study, the average daily gain ( ADG ) for the first period (2 - 8 weeks) varied from 0.379 to 0.668 kg /d , and in the second period (8 - 14 weeks) ADG varied from 0.400 to 1.13 kg/d. The authors di d not f ind a difference in carcass composition for the first period, but in the second period , as ADG increased , the fat content in the carcass also increased. Th ese results suggested that the effect of ADG in body composition is small in calves from 2 to 8 weeks. Investigating the effect of nutrien t density in the milk replace ment and feeding rate , Hill et al. (2008) foun d that empty body fat increased from 17% to 24 % from the control (20% CP and 21% fat, fed at 441 g of DM/d) to the high - dens ity treatment (27% CP and 28% fat, fed at 951 g of DM/d) within the same feeding rate, and had the maximum fat content of 27% fat on the high - dens ity treatment and high feeding r ate (27% CP and 28% fat, fed at 951 g of DM/d). However, treatments and feeding rate also affected ADG . T he control treatment and the high - dens ity and high - feeding rate had ADG of 0.368 and 0.736 kg/d, respectively. Although the 27 authors attributed the diff erence in body fat to the change in nutrient density, the ADG was likely an essential factor in the differences found in regards to body composition. In regards to the type of FA added to the milk replacer, Mills et al. (2010) fed 36 Holstein bulls from bi rth to 85 kg of body weight with three diets varying in triglycerides, a control diet with no added medium - chain triglyceride, a diet with 32% medium - chain triglycerides primarily as caprylate (8 carbons), and a diet with 32% medium - chain triglycerides pri marily as laurate (12 carbons). A lthough the diet with caprylate had lower ADG than the control diet and the diet with laurate (0.880, 0.990, and 0.940 kg/d, respectively), the authors did not observe a difference i n body composition. Based on this, the au thors suggested that the medium - chain triglyceride may influence body composition since the animals differed i n ADG but not body composition. Nevertheless, the differences i n ADG reported in this paper were very small ; and therefore, if diet were to impact body composition , it likely would have much less importance than ADG. As discussed above, there is a need to improve the accuracy of predicti ng NE g and NP g in dairy breeds, and since there is now enough data published on body composition collected from Ho lstein animals, it is possible to derive more specific and accurate models to predict NE g and NP g using data only from Holsteins. Thus , we performed a meta - regression using data collected from 26 studie s that reported body composition in Holstein animals in order to derive prediction equations for body composition and applied them to determine NE g and NP g in Holstein heifers. 28 APPENDICES 29 APPENDIX A Tables 30 Table 2 .1. Cost structure of dairy farm per hundredweight ( cwt ) of milk sold in 2017. Items US$/cwt % of production cost Operating costs Feed 10.50 47.1% Veterinary and medicine 0.83 3.74% Bedding and litter 0.24 1.06% Marketing 0.26 1.17% Custom services 0.58 2.60% Fuel, lube, and electricity 0.51 2.30% Repairs 0.56 2.51% Other operating costs 0.00 0.00% Interest on operating capital 0.01 0.050% Total operating costs 13.49 60.6% Allocated overhead Hired labor 1.64 7.37% Opportunity cost of unpaid labor 2.46 11.1% Capital recovery of machinery and equipment 3.80 17.0% Opportunity cost of land (rental rate) 0.02 0.1% Taxes and insurance 0.22 1.0% General farm overhead 0.64 2.9% Total allocated overhead 8.79 39.4% Source: ERS - USDA (https://www.ers.usda.gov/) 31 APPENDIX B Figures 32 Figure 2.1. Milk ( ) and feed ( ) prices from 1997 to 2017 per hundredweight. The prices are adjusted to 2017 value s (adjusted used the inflation for each year; LBS, 2018). 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Dairy Sci. 87:1446 1454. 44 Weiss, W.P., H.R. Conrad, and N.R. St - Pierre. 1992. A theoretically based model for predicting total digestible nutrient values of forages and concentrate s. Anim. Feed Sci. Technol. 39:95 110. Weld, K.A, and L.E. Armentano. 2017. The effects of adding fat to diets of lactating dairy cows on total - tract neutral detergent fiber digestibility: A meta - analysis. J. Dairy Sci. 100:1766 1779. https://doi.or g/10.3168/jds.2016 - 11500. 45 ABSTRACT Our objective was to determine the effects of dry matter intake ( DMI ), body weight ( BW ), and diet characteristics on total tract digest ibilities of dry matter, neutral detergent fiber, and starch ( DMD , NDFD , and StarchD , respectively) in high - producing dairy cows. Our database was composed of 1,942 observations from 662 cows in 54 studies from Michigan, Ohio, and Georgia. On average, cows ate 23 ± 4.5 kg DM/d, weighed 669 ± 79 kg, and produced 38 ± 10 kg of milk/d. Diets were 31 ± 5% NDF, 27 ± 6% starch, 2.6 ± 1.2% fatty acids, and 17 ± 1.4% crude protein. Digestibility means were 66 ± 6, 42 ± 11 and 93 ± 5% for DMD, NDFD, and StarchD, respectively. Forage sources included corn silage, alfalfa, and grasses. Corn source wa s classified by its ruminal fermentability. Data were analyzed using a mixed effects model including diet chemical composition, forage source, and corn source, all expressed as a percentage of DM; DMI as a percentage of BW ( DMI%BW ); location; and 2 - way int eractions as fixed effects. Cow, block, period, treatment, and study were included as random effects. Best fitting candidate models were generated using backward and stepwise regression methods. Additionally, the simplest model was generated using only DMI and location as fixed effects and all random effects. Candidate models were cross - validated across studies, and the resulting predictive correlation coefficients across studies ( PC ) and root mean square error of prediction ( RMSEP ) were compared by t - test. For each nutrient, the digestibility model that resulted in the highest PC and lowest RMSEP was determined to be the best fitting model. We observed heterogeneous coefficients among the different locations, suggesting that specific location 46 factors influe nce digestibilities. The overall location - averaged best fitting prediction equations were: DMD = 69 0.83 x DMI%BW (PC = 0.22, RMSEP = 5.39); NDFD = 53 + 0.26 x Grass%DM - 0.59 x Starch%DM + 3.06 x DMI%BW 0.46 x DMI%BW2 (PC=0.53, RMSEP=9.70); and Starch D = 96 + 0.19 x HFERM%DM 0.12 x Starch%DM 1.13 x DMI%BW (PC=0.34, RMSEP=4.77); where HFERM%DM is highly - fermentable corn source as percentage of DM. Our results confirm that digestibility is reduced as DMI increases albeit at a lower rate than that rep orted in NRC (2001). Furthermore, dietary starch depresses NDFD. While DMD can be predicted based on DMI only, the best predictions for NDFD and StarchD require diet characteristics in addition to DMI. Chapter available at the Journal of Dairy Science. Fo r more information, access the original publication as follow: de Souza, R.A., R.J. Tempelman, M.S. Allen, W.P. Weiss, J.K. Bernard, and M.J. VandeHaar. 2017. Predicting nutrient digestibility in high - producing dairy cows. J. Dairy Sci. 101: 1123 1135 47 ABSTRACT Our objective was to model dry matter intake ( DMI ) in Holstein dairy cows based on milk energy ( MilkE ), body weight ( BW ), change in body weight ( ), body condition score ( BCS ), height ( Ht ), days in milk ( DIM ), and parity (primiparous and multiparous). Our database included 47,253 weekly observations on 3,607 cows enrolled in 57 studies from 8 states across the US. The means ± standard deviations of t hese variables were 24 ± 5 kg DMI, 30 ± 6 Mcal/d DIM. Data analysis was performed using a random regression model containing location, experiment within location, diet within experiment and location and cow within experiment as random effects whereas the fixed effects included the linear effects of the covariates described previously and all possible 2 - way interactions between parity and the other covariates. A nonlinea r ( NLIN ) mixed model analysis was developed using a two - step approach. In the first step, we used a linear model component of the NLIN model to predict DMI using only data from mid - lactation dairy cows (76 to 175 DIM) without including information on DIM. In the second step, a nonlinear adjustment for DIM using all data from 0 to 368 DIM was estimated. Additionally, the NLIN model was compared to a linear ( LIN ) model containing a fourth - order polynomial for DIM using data throughout all of the lactation (0 to 368 DIM) in order to assess the utility of a n NLIN model for the prediction of DMI. In summary, a total of 8 candidate models were evaluated; i.e., four ways to express energy required for maintenance (BW, BW 0.75 , BW adjusted for BCS of 3, and BW 0.75 a djusted to a BCS of 3) x 2 modeling strategies (LIN 48 versus NLIN). The candidate models were compared using a 100 - fold across study cross - validation study, with the best fitting model chosen as the proposed model. The metrics used in the validation were th e mean bias, slope bias, concordance correlation coefficient ( CCC ), and root mean square error of prediction ( RMSEP ). The proposed prediction equation was: DMI (kg/d) = ((3.7 + Parity*5.7) + 0.305 * MilkE (Mcal/d) + 0.022 * BW (kg) + ( 0.689 + Parity*( 1.87)) * BCS) *(1 (0.212 + Parity*0.136 * ) (Mean bias = 0.021 kg, Slope bias = 0.059, CCC = 0.72, and RMSEP = 2.89 kg), where Parity is equal to 1 if animal is multiparous and 0 otherwise. Finally, the proposed model was validated against the NRC (2001) prediction equation for DMI using an independent dataset used exclusively for the validation purpose (13,953 weekly observations on 2,005 Holstein cows) in a similar approach described above. The proposed model had smaller mean bias and RMSEP, and higher CCC than the equation suggested by NRC to predict DMI and has potential to benefit nutritionists with diet formulation. INTRODUCTION Actual or accurately estimated dry matter intake ( DMI ) is essential for the formulation of diets to prevent underfeeding or overfeeding of nutrients and to promote efficient nutrient use (NRC, 2001). Equations used to predict DMI of lactating dairy cows are based on existing databases that contain observed intake and predictor variables such as milk ene rgy ( MilkE ), body weight, and days in milk ( DIM ). Consequently, the accuracy and precision of these predictions are dependent on the quality of the database and the use of appropriate statistical analysis to derive the prediction equations. Traditionally, the prediction of DMI in lactating dairy cows is based on milk production and the energy required for maintenance, which together represents the major energy 49 expenditures of the lactating dairy cow (VandeHaar et al., 2016). Furthermore, due to the peculiar ities of each stage of lactation (i.e., transition and early lactation dairy cows; Allen et al., 2009), it is crucial to consider the effect of DIM. The most recent edition of the Nutrient Requirements of Dairy Cattle (NRC, 2001) includes an empirical equa tion to estimate DMI of lactating Holstein cows based on animal factors that could be easily measured or known, as follows: where FCM = 4 percent fat - corrected milk (kg/d), BW = bo dy weight (kg), and WOL = week of lactation; NRC, 2001. This prediction equation was based on data collected on 1,284 Holstein cows using the equation proposed by Rayburn and Fox (1993) and further modified by Fox (1999). Also, the nonlinear effect of the week of lactation was based on Roseler et al. (1997). A more recent and much larger database of weekly DMI data from many research stations was used by Lu et al. (2017) to estimate the genetic and nongenetic components of regression of DMI on milk energy a nd maintenance as a function of various management and environmental factors. Similarly, Tempelman et al. (2015) developed station - specific prediction equations for DMI but without distinguishing genetic from non - genetic components as in Lu et al. (2017). Nevertheless, both studies used only data between 50 and 200 DIM (Tempelman et al., 2015; Lu et al., 2017), and therefore might not be valid for predicting DMI outside that range of DIM. The objective of this study was to derive a prediction equation for DMI based on animal factors using a more recent database better reflective of current dairy production systems. Our 50 data was comprised of the updated version of the database used in Tempelman et al. (2015) that included data from animals between 1 and 368 DIM and to validate the developed prediction equation against the NRC 2001 prediction for DMI using an independent dataset. We hypothesized that an equation derived from this larger and newer database would increase the accuracy and precision of DMI predi ctions compared to the equation provided in NRC (2001). MATERIALS AND METHODS D ata The database was composed of individual weekly observations of DMI, MilkE, body weight ( BW ), metabolic BW ( BW 0.75 ), body condition score ( BCS ), change on BW ( ), height ( H t ), DIM, and parity (primiparous and multiparous) from ten research stations across the US. Additionally, we calculated BW adjusted to a BCS of 3 ( BWBCS3 , kg) and BW 0.75 adjusted to a BCS of 3 ( BW^0.75BCS3 , kg) as a function of BW and BCS [ and ]. To calculate the BWBCS3, was assumed that one - unit shift in BCS causes a 8.4% change in BW, as determined by Souza and VandeHaar (2018) using a database composed of 2,181 Holstein cows. The milk energy was calculated according to NRC (2001). Recording frequencies of the variables included in the database varied from daily, thrice weekly, twice weekly, weekly, and biweekly depending on the variable and the research station. In order to standardize variables as weekly means across all studies, each variable (i.e., MILKE, BW, BCS, BW, and Ht) on each animal on the same treatment for each experiment was analyzed using a 5 th order polynomial linear regression model on days since the start of that 51 parti cular treatment . Subsequently, the predicted values from these animal - specific analyses were used to calculate weekly means for each animal on a particular treatment. The final database was composed of 61,206 weekly observations on 4,785 Holstein dairy cows from 105 studies (Table 4.1). About 36% (22,045 weekly observations) of this data was previously described by Tempelman et al. (2015), but using only their data from US research stations (University of Florida, Gainesville; Iowa State Universit y, Ames; Michigan State University, East Lansing; University of Wisconsin, Madison; United States Dairy Forage Research Center, Madison; and USDA Animal Genomics and Improvement Laboratory, Beltsville) to be consistent with other data added to this databa se. The remaining 64% (39,161 weekly observations) of the data came either from locations already used in Tempelman et al. (2015) but collected in more recent experiments or collected at DIM less than 50 or greater than 200 (50% of all data) at these same stations or from new locations (14% of the data) including the Purina Animal Nutrition Center (Gray Summit, MO), Cargill Research & Development Center (Minneapolis, MN), Miner Institute (Chazy, NY),The Ohio State University (Columbus, OH), and Virginia Te ch University (Blacksburg, VA). Our final database was thereby composed of records from cows between 1 and 368 DIM and collected in research stations across the US (Florida, Iowa, Maryland, Michigan, Missouri, New York, Ohio, Virginia, and Wisconsin) from 2007 to 2016. All the data were collected from lactating Holstein dairy cows offered a total mixed ration once per day and milked two or three times per day. Finally, the final database was subdivided into two independent datasets. The first dataset, compr ised of 47,253 weekly observations from 3,743 lactations (1,769 primiparous and 1,974 multiparous) on 3,607 cows, was used in the model assessment process (referred to as the ations from 52 2,202 lactations (1,120 primiparous and 1,082 multiparous) on 2,005 cows, was used in the independent validation process. The distribution of the number of observations in each dataset throughout the lactation is presented in Figure 1. The crit eria used to determine the separation of the database into two datasets (model assessment and independent validation datasets) was based on the number of weekly observations per cow. Studies that provided 7 or more weekly observations per cow constituted the model assessment dataset, whereas the remaining smaller studies constituted the independent validation dataset. Basic summary statistics of the raw weekly data for each of the two datasets are provided in Table 4.2. Statistical Analyses All data anal ysis was performed using SAS v. 9.4 (SAS Institute Inc., Cary, NC). For numerical stability, all covariates were standardized to have a mean of zero and a standard deviation of 1 using PROC STANDARD and the functions MEAN=0 and STD=1. All covariates were j ointly checked for multicollinearity using variance inflation factors ( VIF , multicollinearity analysis). In this paper, we will refer to the models that initiated the modeling processes as the ng processes and were used in cross - - These models are more carefully explain ed in the subsequent sections. 53 Modeling Process The nonlinear ( NLIN ) modeling process was composed of two major phases. The first phase was the development of a linear model to predict DMI in mid - lactation cows (76 175 DIM) without the inclusion of DIM as a covariate. The second phase was the inclusion of the nonlinear effect of DIM on DMI across the entire modeling dataset including early (1 - 75 DIM), mid (76 - 175 DIM), and late - lactation (176 - 368 DIM). For the first phase of the modeling process, we spe cified a starting model that contained the fixed effects of partial linear regressions on MilkE, the corresponding BW measure (BW, all possible two - way interactions betwe en parity and the other covariates. Location, experiment within location, diet within experiment and location, and cow within experiment and location were treated as random effects. Furthermore, the model also included diet specific partial regressions of DMI on MilkE and on BW, recognizing that the partial regressions of DMI on MilkE and on BW could depend upon diet compositions. The generic starting model is presented in Equation [4.1]. [4.1] where ( p = parity, c = cow, d = diet, e = experiment, l = location) is the observed DMI; ( is the intercept specific to diet d , is the partial regression 54 coefficient of DMI on MilkE specific to diet d , is the partial regression coefficient of DMI on BW (BW, BW^0.75, BWBCS3, or BW^0.75BCS3), specific to diet d , is the partial regression coefficient of DMI on ; is the partial regression coefficient of DMI on BCS; is the partial regression coefficient of DMI on ( p = primiparous or multiparous); are the effects for the two - way interactions between the corresponding covariates and parity. All other terms were random effects including ~ NIID ( ) for cow c = 1 to 2,805, for diet d = 1 to 153, ~ NIID ( ) for experiment e = 1 to 57, ~ NIID ( ) for location l = Florida, Iowa, Maryland, Michigan, Minnesota, New York, Virginia, and Wisconsin with being the error term. We assumed a multivariate normal distribution for diet effects and diet - specific partial regressions on Milk E and BW as follows. [4.2] Note that the specification in Equation [4.2] also allowed for non - zero covariances, , , and (i.e., off - diagonals of G) between diet - specific intercepts and slopes for MilkE, between diet - specific intercepts and slopes for BW, and between diet - specific slopes for MilkE and body weight, respectively. The starting models described above Equation [4.1] were subjected to model selection, which was composed of two phases. During the first phase, each of the full models was subjected to a backward model selection method using the SAS procedure PROC GLMSELECT with the 55 option HIERARCHY = SINGLE, such that the model was forced to in clude the corresponding main effects if the interaction between any two effects were deemed to be significant. Since the PROC GLMSELECT procedure does not allow for the specification of random effects, the model was limited to the specification of fixed e ffects only in this first stage of model selection. During the second phase of model selection, the model chosen by the PROC GLMSELECT procedure was analyzed using the PROC HPMIXED procedure, in which the above - mentioned random effects were included. The f ixed effects with the highest P values were successively removed until only significant fixed effects ( P < 0.05) and all specified random effects remained in the model, yielding a linear mixed model as a candidate model to predict DMI for mid - lactation dai ry cows. With this model selection process, we created four different candidate models (i.e., four different ways to express the covariate BW; namely, BW, BW^0.75, BWBCS3, and BW^0.75BCS3). The NLIN model involved the estimation of the nonlinear effect of DIM on DMI using the SAS procedure NLMIXED. The nonlinear adjustment was based on the adjustment factor proposed by Roseler et al. (1997; i.e., , where is peak milk month and is week of lactation) with fu rther modifications as follows 1) key coefficients included the effect of parity to allow for parity specific effects, 2) removal of the PMM term because information was not available in our dataset, and 3) inclusion of a term which determines the maximum possible discount ( in Equation [4.3] below). The generic model used during the second phase is presented in Equation [4.3]. . [4.3] 56 Here DMI is the observed DMI , is the predicted DMI from candidate linear submodel c ( c =1 to 4) based on the four different ways to express the covariate BW, is the coefficient that determines the maximum possible discount for DIM for primiparous cows, specifies the dif ference for this discount between multiparous and primiparous cows, is the nonlinear regression coefficient on DIM for primiparous cows with specifying the difference for this coefficient between multiparous and primiparous cows Furthermore , Pari ty is the dummy variable ( Parity = 0 for primiparous and Parity = 1 for multiparous) for parity in Equation [4.3] whereas is the error term assumed to be normally identically and independently distributed.. To verify the importance of using a nonlinear adjustment for DIM in the prediction of DMI, we refitted the 4 linear candidate models (based on model selection) to the entire training dataset by adding a fourth - order polynomial for DIM and all possible 2 - way interactions with parity as fixed effects as part of a linear ( LIN ) modeling strategy. Hence our model comparison involved a total of 8 candidate models (4 different ways to express BW x NLIN vs. LIN). Cross - validation The eight candidate models were formally compared using a 5 - fold acro ss study cross - validation repeated 20 times using the training dataset of 47,253 weekly observations as described earlier . That is, for each of the 20 cross - validations replicates, the data was partitioned across rather than within studies into five nearl y equal - sized subsets each involving all data from 20% of the studies, such that for one - fold , 4 of these subsets were used for training with the remaining subset used for validation. Hence, across five folds, each subset took a turn being the validation dataset. The candidate models were compared for fit criteria such as mean bias, slope bias, concordance correlation coefficient ( CCC ), mean square error of prediction ( MSEP ), root 57 mean square error of prediction ( RMSEP ), and the decomposition of MSEP in me an bias, slope bias, and random error (as % of MSEP) (Tedeschi, 2006). To determine our proposed model, the fit criteria were analyzed using the PROC GLIMMIX procedure of SAS v.9. 4 (SAS Institute Inc., Cary, NC) according to the following model (Equation [4.4]): [4.4] where is one of the fit statistics of interest; is the overall mean; is the random effect of fold ( i = 1 to 100); is the fixed effect of corresponding BW measure ( j = BW, BW^0.75, BWBCS3, or BW^0.75BCS3), is the fixed effect of strategy ( l = LIN and NLIN), is the interaction between corresponding BW and strategy, and is the residual error. The candidate model that consistently had superior fit statistics was considered the best fitting model and, therefore, our proposed model. A generic SAS code for model validation (using only linear models) and a short explanation is available in t he Supplementary Material 4.1. Independent validation process As an independent validation process beyond the cross - validation strategy described previously, the proposed model was compared to the DMI prediction equation proposed on the NRC (2001) using th e independent validation dataset of 13,953 weekly observations involving smaller studies with 6 or less weekly observations per cow. That is, for each of 20 validation replicates, the data was partitioned across studies into five nearly equal - sized subsets , each subset involving all data from 20% of the studies. For each fold, the fit statistics (CCC, MSEP, 58 RMSEP, and decomposition of MSEP) were computed as described previously. The major difference between the previously described cross - validation study and this independent validation study was that the same entire training dataset of 47,253 weekly observations involving all of the larger studies (>7 records per cow) was used for each validation subset such that predictions for each validation subset were based on the same fixed effects and variance components as based on the proposed model. Furthermore, to facilitate stage - specific comparisons, the validation dataset was partitioned further according to the stage of lactation (early: 1 to 75 DIM; mid: 76 to 175 DIM ; and late: 176 to 368 DIM). The various fit statistics were compared using the PROC GLIMMIX procedure of SAS v.9. 4 (SAS Institute Inc., Cary, NC) according to the following model (Equation [4.5]): [4.5] where is the fit statistic of interest; is the overall mean; is the random effect of fold ( i = 1 to 100); is the fixed effect of model ( j = Proposed or NRC), is the fixed effect of stage of lactation ( k = early, mid, or late), is the fixed effect of the interaction between model and stage, and is the residual error. RESULTS Regarding the four different measures to express BW (BW, BW^0.75, BWBCS3, or BW^0.75BCS3), we did not observe any difference in their ability to predict DMI based on the cross - validation ( P > 0.9, results not shown). The fact that we did not observe differences between the four ways to express BW might be b ecause all measures were highly correlated with each other (r = 0.96 to 0.99) and all cows in our dataset were Holsteins. Thus, for the remainder 59 of the paper, we only show and discuss data for the models developed using BW, due to its simplicity and appli cability. During the model assessment process, the main effect of and the interactions of Parity with MilkE, BW, and were removed from the starting model ( P > 0.05). With respect to the nonlinear effect of DIM in the NLIN model, parity was an impor tant ( P < 0.01) source of variation for the maximum discount on DMI due to DIM ( ; but the effect of parity on the estimated nonlinear coefficient for DIM ( was not significant ( P = 0.68) and there fore removed. The NLIN model was superior to the LIN model for all fit statistics, and therefore we selected a nonlinear relationship for the effect of DIM on DMI (Table 4.3). We propose the NLIN model with body weight expressed in BW as in Equation [4.6]. DMI (kg/d) = [(3.7 + Parity * 5.7) + 0.305 * MilkE (Mcal/d) + 0.022 * BW (kg) + ( 0.689 + Parity * ( 1.87)) * BCS] * [1 (0.212 + Parity* 0.136 * ] [4.6] where Parity is equal to 1 if animal is multiparous and 0 if primiparous. T he diagonal values of the estimated G matrix, which represent the estimated variance components for the diet specific intercept, MilkE, and BW, respectively, were 0.56, 0.056, and 0.000247. The estimated DMI for multiparous animals adjusted to the mean values of MilkE, BW, BCS, and DIM as reported in Table 4.2 and using Equation [4.6] is 24.46 kg. Based on the multivariate normality assumption as invoked in Equation [4.3], th is implies 60 that roughly 95% of the diets lead to a mean intake within 24.46 ± 2 * or [22.99kg,25.98kg] for multiparous animals adjusted to mean values of MilkE, BW, BCS, and DIM. Similarly, 95% of the diets would have a partial regression of DMI on MilkE of 0.305 (from Equation [4.6]) ± 2 * or [ - 0.17kg/Mcal, 0.78kg/Mcal] whereas 95% of the diets would have a partial regression of DMI on BW of 0.022 (from Equation [4.6]) ± 2 * or [ - 0.01kg/kg, 0.053kg/kg]. This variability across diets naturally reflects , for example, differences in the energy density across different diets whereas negative lower bounds likely reflect that these diet effects are either not precisely normal ly distributed or based on the relatively small number of observations. For the comparison of the proposed model (Equation [4.6]) and the NRC (2001) DMI prediction equation, the effects of model, stage, and interaction between model and stage were highly s ignificant ( P the proposed NLIN model was superior to the NRC (2001) model for all fit statistics (Table 4.4). the prediction equations per formed better for cows during mid - lactation (CCC, slope bias, MSEP, RMSEP), followed by early - lactation and lastly by late - lactation. The interaction between model and stage of lactation was significant, where the proposed model was slightly better than th e NRC (2001) model for early lactation but much superior t o NRC (2001) for mid - and late - lactation (Table 4.4). The predicted vs. observed plot for each stage of lactation is presented in Figures 4.2, 4.3, and 4.4. On dairy farms, diets are fed to a group of animals that contains a mix of primiparous and multiparous cows. In this case, Equation [4.6] can be modified to represent the proportion 61 between primiparous and multiparous in the group. As an example, in our training dataset the ratio between primipar ous and multiparous were 44:66, and therefore, to use the equation for the entire training dataset the estimated coefficient for parity will be multiplied by 0.66 (proportion of multiparous cows in the dataset). As a result, the prediction equation for DMI for the average cow in the training dataset is presented in Equation [4.7]. The Equation [4.7] was named as a simplified proposed model. [4.7] The difference in the prediction of DMI by the proposed model (Equation [4.6]) and the simplified proposed model (Equation [4.7]) is presented in Table 5. We recommend the use of the Equation [4.6] rather than the Equation [4.7]. However, when parity inf ormation is not known the Equation [4.7] could be used as an alternative. DISCUSSION This study shows that the NRC 2001 model does a reasonably good job of predicting intake in Holstein cows, but the proposed model was clearly superior to the NRC 2001 mode l in the independent validation analysis, especially during the mid - and late - lactation. We suspect this is because we had data from more cows and included parity and BCS in our prediction. The DIM adjustment for the prediction of DMI is necessary due to the peculiarities of different postpartum stages over and beyond the effects of MilkE or BW (Dann et al., 1999; Drackley, 1999; Chan et al., 2006; Janovick et al., 2011; Allen, 2014). For the proposed model, as in Roseler (1997), the greatest discounts in DMI are early in lactation and not important after 62 70 DIM (Table 4.6). Multiparous animals had proportionately greater deviance in the effect of DIM on DMI than primiparous in early lactation (Table 4.6). As an example, at the onset of the lactation (1 DIM ), multiparous cows have a discount of 21% on the predicted DMI based on its MilkE, LBW, and BCS, whereas primiparous cows have a discount of 13%. The NRC (2001) applies a more aggressive discount due to DIM on the DMI than the proposed model as shown in T able 4.6. The difference in the effect of DIM on DMI observed between the two equations may be from differences in the covariates used to derive the equation. That is, whereas the proposed model included the effect of parity and DIM expressed as days, the NRC (2001) does not account for differences in parity and use the week of lactation. Furthermore, the NRC (2001) prediction equation for DMI was derived mostly with data th lower milk production and lower body size than the animals in our database (mostly data collected post - 2007). Additionally, since 2000, many researchers have focused on better understanding the mechanisms that control feed intake and the development of strategies to maximize intake during early - lactation (Drackley, 1999; Allen, 2000; Grummer et al., 2004; Allen et al., 2005; Allen and Bradford, 2006; Allen et al., 2009). With the advancement in these areas, we believe that differences in management, envi ronments, and diet formulation could explain the difference observed between the proposed and NRC (2001) models with respect to the effect of DIM. The estimated partial regression coefficients of DMI on milk production and energy required for maintenance based on the proposed model, 0.305 kg/Mcal and 0.022 kg/kg of LBW, respectively, differed from that of the NRC (2001) model using FCM and BW^0.75, 0.372 kg/kg of FCM and 0.0968 kg/kg 0.75 of BW, respectively (which convert to 0.330 kg/Mcal and 0.018 kg/kg of LBW). In other words, the proposed model assumes a lower DMI per unit of MilkE 63 than the NRC (2001) model but a higher DMI required for maintenance. However, as described above, our analysis also suggested important variability across diets on these est imated partial coefficients . T herefore, the differences observed between the estimated coefficients and the NRC (2001) model likely depends on diet differences as well. The fact that the proposed model implies a lower DMI per unit of milk can be attributed to two broad categories of factors: animal and/or diet characteristics. The database used in this analysis is composed of animals that likely have greater milk production as compared to the database utilized by the NRC (2001). With respect to diet charact eristics, the diets fed to the cows in our database might have been higher in concentrates than the diets fed to the cows used in the NRC (2001) equation because they were higher producers. Additionally, Tempelman et al. (2015), using data only from mid - la ctation cows, estimated coefficients for MilkE ranging from 0.30 to 0.38 and for BW^0.75 ranging from 0.10 to 0.13, for the US stations, which are more close to the estimated coefficients in this paper than the coefficients reported by the NRC (2001). Figu re 4.5 illustrates the behavior of the proposed and NRC (2001) models over a lactation curve of a dairy cow using the observed DMI, MilkE, and BW of the average cow in the validation dataset. A substantial difference between the proposed model and the NRC (2001) DMI prediction equation is that our model includes the effect of BCS. The effect of BCS was highly significant ( P < 0.01). The estimated coefficient for BCS suggested that for each 1 - unit increase on BCS the animal reduces her intake by 0.69 and 2.6 kg/d for primiparous and multiparous, respectively. This result implies that thinner animals are hungrier and consume more feed than fatter animals, which agrees with long - term mechanisms associated with the maintenance of BW (i.e., leptin; Block et al., 2003; Allen, 2014). The interaction between parity and BCS suggested 64 that BCS has a greater impact on DMI for multiparous cows than for primiparous cows. This fact was expected since primiparous animals are still growing while multiparous animals are gener ally close to mature size. We derived the Equation [4.7] to illustrate how the proposed model (Equation [4.6]) would be applied to a group of cows where the proportion of primiparous and multiparous animals are known. CONCLUSION The proposed model to predict DMI contains the effect of MilkE, LBW, BCS, parity, and DIM. This model differs from the NRC (2001) DMI prediction equation in regards that the NRC model contain s only FCM, MBW, and WOL. Comparing both models, proposed model and NRC (2001), usin g an independent validation dataset, both models were similar to predict DMI during early - lactation (1 75 DIM), the proposed model outperformed the NRC (2001) during mid - and late - lactation (76 368 DIM). Finally, in regard to the estimated coefficients for milk and body weight, the proposed model suggests a lower DMI for both milk production and the energy required for maintenance. 65 APPENDICES 66 AP PENDIX A Tables 67 Table 4.1. Frequency of number of studies, diets, cows, and lactations by state . Station 1 No. of studies No. of diets No. of cows No. of lactations No. of weekly records Average number of weekly records per lactation AGIL 3 6 675 998 10,847 10.9 UF 17 54 523 643 6,222 9.7 ISU 3 5 955 1,021 10,457 10.2 MSU 21 76 339 540 5,922 11.0 CRDC 1 23 237 361 1,454 4.0 PANC 2 2 177 206 2,984 14.5 Miner 2 7 125 125 1,301 10.4 OSU 2 11 124 124 1,851 14.9 VT 6 18 111 112 943 8.4 UW 43 132 1,431 1,695 17,472 10.5 FRC 5 10 88 120 1,804 12.4 TOTAL 105 344 4,785 5,945 61,206 10.3 1 AGIL = USDA Animal Genomics Improvement Laboratory, UF = University of Florida, ISU = Iowa State University, MSU = Michigan State University, CRDC = Cargill Research & Development Center, PANC = Purina Animal Nutrition Center, Miner = Miner Institute, OSU = The Ohio State University, VT = Virginia Tech, UW = University of Wisconsin - Madison, FRC = USDA Forage Research Center 68 Table 4.2. Number of observations (n), mean, and standard deviation (SD) of the covariates used to model (Training dataset) and validate (Validation dataset) the proposed equations for dry matter intake . Variables 1 Training dataset Validation dataset n Mean SD n Mean SD DMI, kg/d 47,253 24.4 4.62 13,953 24.1 4.53 MilkE. Mcal/d 47,253 29.4 6.30 13,953 29.1 6.47 BW, kg 47,253 625 81.7 13,953 631 86.9 BW ^0.75 , kg 0.75 47,253 125 12.2 13,953 126 13.0 42,867 0.039 0.217 11,265 0.005 0.309 BCS (scale 1 to 5) 31,631 3.04 0.457 9,050 2.99 0.429 Ht (cm) 9,759 149 5.92 6,401 149 7.31 DIM (days) 47,253 105 50.0 13,953 114 61.7 1 DMI = dry matter intake, MilkE = milk energy, BW = body weight, BW ^0.75 = metabolic body days in milk. 69 Table 4.3. Fit Statistics for the cross - validation across studies of the candidate models (LIN: linear, NLIN: non - linear) using the modeling dataset . Fit Statistics 1 LIN 2 NLIN 2 SEM 3 P - value 4 CCC 0.751 0.800 0.006 <0.01 Mean Bias - 0.53 0.008 0.059 <0.01 Slope Bias 0.050 0.033 0.009 0.03 MSEP 10.9 6.83 0.143 <0.01 RMSEP 3.20 2.61 0.073 <0.01 Decomposition of MSEP, % Mean Bias 13.6 6.90 0.616 <0.01 Slope Bias 1.96 2.28 0.184 0.09 Random Error 84.4 90.8 0.647 <0.01 1 CCC: concordance correlation coefficient, MSEP: mean square error of prediction, RMSEP: root mean square error of prediction; 2 The two modeling strategies, where the LIN model is a linear model including a fourth - order polynomial of DIM , and the NLIN model contain the nonlinear effect of DIM; 3 Standard error of the mean common to both LIN and NLIN; 4 For the mean comparison of LIN and NLIN 70 Table 4.4. Fit Statistics for the across study stage of lactation (early, mid, and late) specific cross - valid ation performance of the proposed and NRC (2001) models using the independent validation dataset . Fit Statistics 1 Proposed Model NRC (2001) Model SEM 3 P - values Early 2 Mid 2 Late 2 Early 2 Mid 2 Late 2 Model Stage Model*Stage CCC 0.717 Aa 0.735 Aa 0.688 Ab 0.702 Ba 0.681 Ba 0.645 Bb 0.010 <0.01 <0.01 0.01 Mean Bias - 0.281 Aa 0.058 Ab 0.293 Aa - 0.801 Ba - 1.54 Bb - 1.45 Ba 0.012 <0.01 <0.01 <0.01 Slope Bias - 0.031 Aa 0.028 Ab 0.068 Ac - 0.137 Ba - 0.117 Bb - 0.016 Bc 0.014 <0.01 <0.01 <0.01 MSEP 10.2Ac 7.13 Aa 8.42 Ab 11.8 Bc 10.5 Ba 11.3 Bb 0.339 <0.01 <0.01 <0.01 RMSEP 3.19 Ac 2.67 Aa 2.90 Ab 3.42 Bc 3.23 Ba 3.32 Bb 0.048 <0.01 <0.01 <0.01 Decomposition of MSEP, % Mean Bias 7.15 Aa 3.45 Ab 8.02 Ab 12.0 Ba 25.9 Bb 24.2 Bb 1.57 <0.01 <0.01 <0.01 Slope Bias 2.73 c 0.74 a 3.91 b 5.24 c 2.28 a 1.32 b 0.564 0.13 <0.01 <0.01 Random Error 90.2 Aa 95.8 Ab 88.1 Ac 82.7 Ba 71.8 Bb 74.5 Bc 1.60 <0.01 <0.01 <0.01 1 CCC: concordance correlation coefficient, MSEP: mean square error of prediction, RMSEP: root mean square error of prediction; 2 Stage of lactation: early - 1 to 75 days in milk; mid - 76 to 175 days in milk; and late - 176 to 368 days in milk; 2 Mean bias; 3 Standard error of the mean common to all models; different capital letter within the fit statistic represent statistical differences for model; and different lower letter within the fit statistic represent statistical differences for stage 71 Table 4.5. Fit S tatistics for the cross - validation across studies of the proposed model and simplified model using the validation dataset. Fit Statistics 1 Proposed 2 Simplified 2 SEM 3 P - value 4 CCC 0.721 0.714 0.006 0.52 Mean Bias 0.021 0.025 0.004 0.47 Slope Bias 0.059 0.062 0.009 0.01 MSEP 8.36 9.05 0.241 0.01 RMSEP 2.89 3.01 0.038 0.01 Decomposition of MSEP, % Mean Bias 5.70 6.32 0.667 0.02 Slope Bias 2.11 2.15 0.218 0.85 Random Error 92.2 91.5 0.646 0.02 1 CCC: concordance correlation coefficient, MSEP: mean square error of prediction, RMSEP: root mean square error of prediction; 2 The proposed model with parity effect and the simplified model using the proportion of the primiparous: multiparous (44:56) cows in the training dataset; 3 Standard error of the mean common to both LIN and NLIN; 4 For the mean comparison of LIN and NLIN 72 Table 4.6. Nonlinear adjustment of days in milk on the predicted dry matter intake estimated by the proposed (primiparous and multiparous) and NRC (2001) models. Days in Milk Proposed Model Primiparous Proposed Model Multiparous NRC 2001 10 0.875 0.795 0.624 20 0.927 0.880 0.714 30 0.957 0.929 0.783 40 0.975 0.958 0.835 50 0.985 0.976 0.875 60 0.991 0.986 0.905 70 0.995 0.992 0.928 80 0.997 0.995 0.945 90 0.998 0.997 0.958 100 0.999 0.998 0.968 110 0.999 0.999 0.976 120 1.000 0.999 0.982 130 1.000 1.000 0.986 140 1.000 1.000 0.989 150 1.000 1.000 0.992 73 APPENDIX B Figures 74 a) Figure 4. 1. Distribution of the number of observations in the training ( ) and in the validation ( ) datasets. 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 Number of observations Days in milk 75 a) b) Figure 4.2. Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2001 ( ) and the proposed ( ) models for the early - lactation period (1 to 75 days in milk). Each data point (NRC 2001 - , Proposed model - ) represents the raw (a) and the adjusted for random effects (b) individual weekly DMI. 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Observed, kg/d Predicted, kg/d 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Observed, kg/d Predicted, kg/d 76 a ) b) Figure 4. 3 . Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2001 ( ) and the proposed ( ) models for the mid - lactation period (76 to 175 days in milk). Each data point ( NRC 2001 - , Proposed model - ) represents the raw (a) and the adjusted for random effects (b) individual weekly DMI. 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Observed, kg/d Predicted, kg/d 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Observed, kg/d Predicted, kg/d 77 a ) b) Figure 4. 4 . Plot of the predicted versus observed dry matter intake (DMI) using the NRC 2001 ( ) and the proposed ( ) models for the late - lactation period (greater than 176 days in milk). Each d ata point ( NRC 2001 - , Proposed model - ) represents the raw (a) and the adjusted for random effects (b) individual weekly DMI. 10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45 Observed, kg/d Predicted, kg/d 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Observed, kg/d Predicted, kg/d 78 Figure 4. 5 . Curve of lactation on the average Holstein dairy cow. Where the solid lines represent the observed milk energy (MilkE, ), observed dry matter intake (DMI, ), and observed body weight (BW, ), and the dashed lines represent the predicted dry matter intake by th e NRC 2001 ( ) and proposed ( ) models . 600 620 640 660 680 700 720 15 20 25 30 35 40 45 0 50 100 150 200 250 300 LBW (kg) Intake (kg/d) and MilkE (Mcal/d) Days in milk 79 APPENDIX C Supplement al Table 80 Supplemental Table 4.1. Prediction of DMI using the two - step model on crossbreeds and pure Jersey dairy cows in total mixed ration and grazing system. Study Ref Breed Country System DMI (kg/d) BW (kg) DIM (d) MilkE (Mcal/d) BCS Leiva et al., 2018 J. Dairy Sci. 10: 1 - 14 Gir x Holstein Brazil Total mixed ration 22 ± 1.6 573 105 16.5 3.41 23 ± 1.6 587 105 17.0 3.48 Coffey et al., 2017 J. Dairy Sci. 100: 7556 - 7568 Jersey x Holstein Ireland Grazing system 17 ± 0.2 467 129 21.4 2.97 16 ± 0.2 466 129 17.5 2.96 15 ± 0.2 443 129 17.5 2.96 Al - Marashdeh et al., 2016 J. Dairy Sci. 99: 7123 - 7132 Jersey x Friesian New Zeland Grazing system 12 ± 0.2 465 207 10.8 3.27 10 ± 0.2 466 207 11.6 3.35 11 ± 0.2 466 207 12.1 3.31 Hynes et al., 2016 J. Dairy Sci. 99: 8111 - 8120 Swedish Red x Holstein Ireland Grazing system 20 ± 0.5 573 157 19.0 2.39 Kristensen et al., 2015 J. Dairy Sci. 98: 263 - 274 Jersey Denmark Total mixed or partial mixed ration 19 ± 1.2 414 191 21.4 3.00 Vance et al., 2012 J. Dairy Sci. 95: 1527 - 1544 Jersey x Holstein Ireland Total mixed ration 20 ± 0.7 578 150 23.0 3.00 Grazing system 18 ± 0.7 528 150 18.4 3.00 Xue et al., 2011 J. Dairy Sci. 94: 1455 - 1464 Jersey x Holstein United Kingdom Total mixed ration 15 ± 0.4 466 175 15.0 2.70 18 ± 0.4 473 175 17.3 2.75 Prendiville et al., 2009 J. Dairy Sci. 92: 6176 - 6185 Jersey Ireland Grazing system 15 ± 0.2 369 175 12.4 2.93 Jersey x Holstein 16 ± 0.2 448 175 13.9 3.00 Heins et al., 2008 J. Dairy Sci. 91: 3716 - 3722 Jersey x Holstein United States Total mixed ration 22 ± 0.4 467 75 21.0 2.90 81 APPENDIX D SAS Macro: Model Validation 82 DATA example; INPUT A$ B$ C$ Y X1 X2 X3 X4 X5 X6; DATALINES ; A1 B1 C1 23 7 11 20 25 32 39 A1 B1 C2 16 9 14 15 26 31 39 A1 B2 C1 18 9 14 20 29 34 39 A1 B2 C2 23 7 15 17 26 31 39 A1 B3 C1 18 8 14 20 28 35 38 A1 B3 C1 . 8 . 20 28 35 38 A1 B3 C2 22 8 10 15 25 34 36 A1 B4 C1 16 10 13 19 29 33 40 A1 B4 . 16 . 13 19 . 33 40 A1 B4 C2 18 10 12 16 28 32 39 A2 B1 C1 16 8 11 19 30 35 40 A2 B1 C2 16 8 14 15 28 33 37 A2 B2 C1 17 7 14 19 30 33 35 A2 B2 C2 20 9 12 16 29 32 39 A2 B3 C1 28 9 11 20 25 33 38 A2 B3 C2 11 9 10 15 27 33 39 A2 . C1 21 5 13 15 25 . 36 A2 B4 C1 21 5 13 15 25 35 36 A2 B4 C2 12 5 14 17 30 31 36 A3 B1 C1 17 5 14 20 25 35 35 A3 B1 C2 27 10 15 17 28 32 37 . B1 . 17 5 14 . 25 35 35 A3 B2 C1 19 9 11 15 27 30 35 A3 B2 C2 29 6 13 15 28 35 35 A3 B3 C1 26 9 11 19 30 31 37 A3 B3 C2 19 10 14 19 27 32 39 A3 B4 C1 19 8 10 17 28 30 35 A3 B4 C2 10 9 11 20 28 34 36 A4 B1 C1 20 6 11 18 30 35 37 A4 B1 C2 25 7 14 20 28 33 35 A4 B2 C1 21 5 13 16 26 35 38 A4 B2 C2 17 9 10 20 27 31 35 A4 B3 C1 12 9 15 20 27 31 38 A4 B3 . 12 . 15 20 27 31 . A4 B3 C2 10 10 14 15 30 33 35 A4 B4 C1 23 8 12 17 26 3 2 35 A4 B4 C2 13 9 13 16 30 33 35 A5 B1 C1 29 6 13 17 26 32 39 A5 B1 C2 26 10 14 20 30 33 37 A5 B2 C1 28 5 14 18 30 33 36 A5 B2 C2 28 5 12 19 26 35 40 A5 . C1 17 7 . 20 27 33 40 A5 B3 C1 17 7 11 20 27 33 40 83 A5 B3 C2 12 10 12 18 28 32 35 A5 B4 C1 10 5 12 17 27 32 38 A5 B4 C2 20 7 11 19 26 32 35 ; ODS HTML CLOSE ; ODS HTML ; TITLE 'HPMixed model analysis' ; TITLE2 'Observations that need to be thrown out because of missing covariates' ; PROC HPMIXED DATA = example; CLASS A B C; /*enter your classificatory variables*/ MODEL Y = X1 X2 X3 X4 X5 X6 /*fit the fullest model*/ / SOLUTION CL ; RANDOM int / SUBJECT =A; /*enter first set of random effects here (if necessary)*/ RANDOM int / SUBJECT =B; /*enter second set of random effects here (if necessary)*/ RANDOM int / SUBJECT =C TYPE = un; /*enter third set of random effects here (if necessary)*/ OUTPUT OUT =output1 PRED =predm RESID =residm; RUN ; TITLE ; TITLE2 ; TITLE3 ; DATA exampleclean ( DROP =predm residm); SET output1; IF predm eq . THEN DELETE ; IF Y eq . THEN DELETE ; /* Y is the response variable*/ run ; DATA exampleclean; SET exampleclean; record = _n_; RUN ; DATA _null; SET exampleclean; CALL symput( 'total' ,_n_) /* Number of records in cleaned - up data*/ ; RUN ; ***** Create the cross - validation folds for each several random partitions of the data *****; %MACRO cvfold(npartition,nfold,n_size); %DO partition = 1 %TO &npartition %BY 1 ; DATA temp; DO record = 1 TO &total; random_num = ranuni( - 1 ); OUTPUT; END; RUN; 84 PROC SORT DATA=temp; BY random_num; RUN; DATA partition&partition (DROP=counter random_num); SET temp; counter = _n_; fold&partition = floor(&nfold*(counter - 1 )/&n_size)+ 1 ; RUN; PROC SORT DATA=partition&partition; BY reco rd; RUN; %END ; %MACRO append2 ; %DO i = 1 %TO &npartition ; partition&i %END ; %MEND append2; DATA finalpartition; MERGE % append2 ; BY record; RUN ; TITLE "Double check on balance of folds within each partition" ; PROC FREQ DATA =finalpartition ; TABLE fold1 - fold&npartition; RUN ; %MEND cvfold; ***** Macro to conduct the cross - validation *****; %MACRO cvrandom(npartition,nfold,datasource,model); PROC DATASETS LIBRARY=work NOLIST; DELETE CVsummary&model; RUN; %DO partition = 1 %TO &npartition %BY 1 ; %DO fold = 1 %TO &nfold %BY 1 ; DATA partition&partition.fold&fold; MERGE &datasource finalpartition(keep=fold&partition record); BY record; IF fold&partition =&fold THEN DO; partition = 'validation' ; Y = . ; /* Y is t he response variable*/ END; ELSE partition = 'training' ; RUN; ODS EXCLUDE ALL; 85 PROC HPMIXED DATA= partition&partition.fold&fold; ID record partition; CLASS A B C; /*enter your classificatory variables*/ MODEL Y = % fixedeffects ; /* Y is the response variable*/ % randomeffects ; OUTPUT OUT=p&partition&fold PRED=pred; RUN; ODS EXCLUDE NONE; DATA pcheck&partition&fold; UPDATE p&partition&fold &datasource; BY record; RUN; ODS EXCLUDE ALL; PROC CORR DATA =pcheck&partition&fold COV OUTP=COV&partition&fold ; WHERE partition = 'validation' ; VAR Y Pred; /* Y is the response variable*/ RUN; ODS EXCLUDE NONE; ** Save key statistics; DATA null; SET cov&partition&fold; **variance for obs; IF _TYPE_= "COV" and _NAME_ = "Y" THEN CALL symput( 'var1' ,Y); /* Y is the response variable*/ **variance for pred; IF _TYPE_= "COV" and _NAME_ = "pred" THEN CALL symput( 'var2' ,pred); **covariance between obs and pred; IF _TYPE_= "COV" and _NAME_ = "Y" THEN CALL symput( 'cov12' ,pred); **mean for obs; IF _TYPE_= "MEAN" THEN CALL symput( 'mean1' ,Y); /* Y is the response variable*/ **mean for pred; IF _TYPE_= "MEAN" THEN CALL symput( 'mean2' ,pred); **correlation between obs and pred; IF _TYPE_= "CORR" and _NAME_ = "Y" THEN CALL symput( 'cor12' ,pred); RUN; DATA ccc&partition&fold; **compute CCC and correlation; ccc = 2 *&cov12/(&var1+&var2+(&mean1 - &mean2)** 2 ); corr = &cor12; fold = &fold; partition = &partition; RUN; DATA SSEP&partition&fold; **compute MSEP and RMSEP and its components; SET pcheck&partition&fold ; WHERE partition = 'validation' ; 86 msep = (Y - pred)** 2 ; odev = (Y - &mean1); pdev = (pred - &mean2); RUN; PROC MEANS DATA=SSEP&partition&fold SUM N NOPRINT; VAR msep odev pdev; OUTPUT OUT=msep&partition&fold (drop=_type_ _freq_) SUM= N= /AUTONAME; RUN; DATA msep&partition&fold (KEEP=msep rmsep ECT ECR ED fold partition); SET msep&partition&fold; msep = msep_Sum/msep_N; rmse p = sqrt(msep); s2p = (pdev_N - 1 )*&var2/pdev_N; s2o = (odev_N - 1 )*&var1/odev_N; **compute mean bias as % of MSEP; ECT = (((&mean2 - &mean1)** 2 )* 100 )/MSEP; **compute slope bias % of MSEP; ECR = (((sqrt(s2p) - &cor12*sqrt(s2o))** 2 )* 100 )/MSEP; **compute random error % of MSEP; ED = ((( 1 - &cor12** 2 )*s2o)* 100 )/MSEP; fold = &fold; partition = &partition; RUN; DATA slopebias&partition&fold; SET pcheck&partition&fold; WHERE partition = 'validation' ; residual = Y - pred; **compute slope bias for residuals on centered predictions; pred_dev = pred - &mean2; RUN; ODS EXCLUDE ALL; PROC REG DATA=slopebias&partition&fold ; MODEL residual=pred_dev; ODS OUTPUT ParameterEstimates = ParameterEstimates&Partition&Fold; RUN; ODS EXCLUDE NONE; PROC TRANSPOSE DATA=ParameterEstimates&Partition&Fold OUT=slopebiasestimates&partition&fold ; RUN; DATA slopebiasestimates&partition&fold (KEEP = fold partition intercept_res slope_res); SET slopebiasestimates&partition&fold; IF _NAME_ = "Estimate" ; fold = &fold; partition = &partition; intercept_res = COL1; slope_res = COL2; 87 RUN; DATA catchall&partition&fold; MERGE ccc&partition&fold msep&partition&fold slopebiasestimates&partition&fold; BY partition fold; RUN; PROC APPEND BASE=CVsummary&model DATA=catchall&partition&fold FORCE; RUN; PROC DATASETS LIBRARY=work NOLIST; DELETE pearson&partition&fold msep&partition&fold cov&partition&fold partition&partition.fold&fold slopebiase stimates&partition&fold; RUN; %END ; %END ; DATA CVsummary&model; SET CVsummary&model; model = &model; fixed = "%fixedeffects" ; random = "%randomeffects" ; RUN; ODS results ON; TITLE "Final summary statistics for Model &model" ; PR OC PRINT DATA=CVsummary&model; RUN; %MEND cvrandom; ***** Validation structure *****; %LET npartition=2; /* specify number of partitions */ %LET nfold = 5; /* specify number of folds per partition */ % cvfold (&npartition,&nfold,&total); ** Model Description; * Model 1; %LET model = 1; %MACRO fixedeffects ; X1 X2 /* define the fixed effects for Model 1*/ %MEND fixedeffects; %MACRO randomeffects ; RANDOM int /SUBJECT=A; /* define the random effects for Model 1*/ RANDOM int /SUB JECT=B; /* define the random effects for Model 1*/ RANDOM int /SUBJECT=C TYPE=un; /* define the random effects for Model 1*/ %MEND randomeffects; % cvrandom (&npartition,&nfold,exampleclean,&model); 88 * Model 2; %LET model = 2; %MACRO fixedeffects ; X3 X4 /* define the fixed effects for Model 2*/ %MEND fixedeffects; %MACRO randomeffects ; RANDOM int /SUBJECT=A; /* define the random effects for Model 2*/ RANDOM int /SUBJECT=B; /* define the random effects for Model 2*/ RANDOM int /SUBJECT=C TYPE=un; /* define the random effects for Model 2*/ %MEND randomeffects; % cvrandom (&npartition,&nfold,exampleclean,&model); * Model 3; %LET model = 3; %MACRO fixedeffects ; X5 X6 /* define the fixed effects for Model 3*/ %MEND fixedeffects; %MACRO randomeffects ; RANDOM int /SUBJECT=A; /* define the random effects for model 3*/ RANDOM int /SUBJECT=B; /* define the random effects for model 3*/ RANDOM int /SUBJECT=C TYPE=un; /* define the random effects for model 3*/ %MEND randomeffects; % cvrandom (&npartition,&nfold, exampleclean,&model); ** Models comparisons; DATA CVsummary; SET CVsummary1 CVsummary2 CVsummary3; block = compress(partition||fold); RUN ; %MACRO comparemodels(response); OD S EXCLUDE ALL; TITLE "Summary for comparing models for &response" ; PROC MIXED DATA=CVsummary; CLASS block model; MODEL &response = model; LSMEANS model /diff; RANDOM block; ODS OUTPUT lsmeans=lsmeans&response; ODS OUTPUT diffs=diffs&response; RUN; ODS EXCLUDE NONE; PROC PRINT DATA=lsmeans&response; RUN; PROC PRINT DATA=diffs&response; RUN; 89 PROC DATASETS LIBRARY=work NOLIST; DELETE lsmeans&response diffs&response; RUN; %MEND comparemodels; % comparemodels (corr) % comparemodels (ccc) % comparemodels (intercept_res) % comparemodels (slope_res); % comparemodels (msep); % comparemodels (ECT); % comparemodels (ECR); % comparemodels (ED); % comparemodels (rmsep); QUIT ; Instructions on how to use the SAS macro The provided code is a generic SAS macro for model validation. We intend to provide a starting code for researchers that want to perform model validation in SAS; adaptations in the code are needed to fit the specificity of each database and the researcher goals. Given that, each researcher is in cha rge to develop his codes, and he can use as a start point the proposed generic SAS code. To use the generic SAS code for model evaluation , the user will need to enter the following information: observed, fixed, and random variables. In the generic SAS code , the and C All random variables are classificatory variables. By default, the code allow s comparison of 3 models using two partitions and five folds. In th e code, we included several comments to facilitate the adaptation of the generic SAS code to the case of each researcher. Please, follow the comments and pay attention if your variables have a different name from the variables used in the example. 90 Finally, the output is composed of 4 parts: (1) HPMixed model analysis, (2) Double check on the balance of folds within each partitioning, (3) Final summary statistics, and (4) Summary for comparing models. (1) HPMixed model analysis: check if the code is reading the database properly. (2) Double check on the balance of folds within each partitioning: here you can check how the database is partitioned. (3) Final summary statistics: here is an overview of the fit statistics parameters and the fixed and random effect s included in the model. By default, the code allows three models, so in this part of the output will be generated three tables, each one for one model. The fit statistic parameters are coded as: ccc: concordance coefficient correlation; corr: correlation between observed and predicted; msep: mean square error of prediction; rmsep: root mean square error of prediction; ECT: mean bias (as % of MSEP, decomposition of the MSEP); ECR: slope bias (as % of MSEP, decomposition of the MSEP); ED: random error (as % of MSEP, decomposition of the MSEP); intercept_res = mean bias; 91 slope_bias= slope bias; (4) Summary for comparing models: in this part of the report each fit statistic parameter has two tables. The first table is testing if the estimated coefficie nt is different from zero, and i n the second table is the comparison between the three models. 92 REFERENCES 93 REFERENCES Allen, M.S. 2000. Effects of diet on short - term regulation of feed intake by lactating dairy cattle. J. Dairy Sci. 83: 83:1598 - 1624. Allen, M.S., B.J. Bradford, and K.J. Harvatine. 2005. The cow as a model to study food intake regulation. Ann. Rev. 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Chan, P.S.; J.W. West; and J.K. Bernard. 2006. Effect of Prepartum Dietary Calcium on Intake and Serum and Urinary Mineral Concentrations of Cows. J. Dairy Sci. 89:704 713. Dann, H.M.; G.A. Varga; and D.E. Putnam. 1999. Improving Energy Supply to Late Gestation and Early Postpartum Dairy Cows. J Dairy Sci 82:1765 1778. Drackley, J.K. 1999. Biology of Dairy Cows During the Transition Period: the Final Frontier?. J Dairy Sci 82:2259 2273. Fox, D.G.; L.O. Tedeschi; T.P. Tylutki; J.B. Russell; M.E. Van Amburgh; L.E. Chase; A.N. Pell; and T.R. Overton. 2004. The Cornell Net Carbohydrate and Protein System model for evaluating herd nutrition and nutrient excretion. Animal Feed Science an d Technology. 112:29 78. Grummer, R.R.; D.G. Mashek; and A. Hayirli. 2004. Dry matter intake and energy balance in the transition period. Vet Clin North Am Food Anim Pract. 20:447 - 70. doi 0.1016/j.cvfa.2004.06.013 Janovick, N.A.; Y.R. Boisclair; and L.K. D rackley. 2011. Prepartum dietary energy intake affects metabolism and health during the periparturient period in primiparous and multiparous Holstein cows. J. Dairy Sci. 94:1385 1400. 94 Lu, Y.; M.J. Vandehaar; D.M. Spurlock; K.A. Weigel; L.E. Armentano; C.R. Staples; E.E. Connor; Z. Wang; M. Coffey; R.F. Veerkamp; Y. de Haas; and R.J. Tempelman. 2017. Modeling genetic and nongenetic variation of feed efficiency and its partial relationships between component traits as a function of management and environmenta l factors. J. Dairy Sci. 100:412 427. NRC. 2001. Nutrient Requirements of Dairy Cattle. 7th rev. ed. Natl. Acad. Press, Washington, DC. Polsky, L.; and M.A.G. von Keyserlingk. 2017. Invited Review: Effects of heat stress on dairy cattle welfare. J. Dairy S ci. 100: 1 - 13. http://dx.doi.org/10.3168/jds.2017 - 12651 Roseler, D.K.; D.G. Fox; L.E. Chase; A.N. Pell; and W.C. Stone. 1997. Development and Evaluation of Equations for Prediction of Feed Intake for Lactating Holstein Dairy Cows. J Dairy Sci 80:878 893. Spurlock, D. M., J. C. Dekkers, R. Fernando, D. A. Koltes, and A. Wolc. 2012. Genetic parameters for energy balance, feed efficiency, and related traits in Holstein cattle. J. Dairy Sci. 95:5393 5402. Tedeschi, L.O. 2006. Assessment of the adequacy of math ematical models. Agri. Syst. 89:225 - 247. Tempelman R.J; D.M. Spurlock; M. Coffey; R.F. Veerkamp; L.E. Armentano; K.A. Weigel; Y. de Haas; C.R. Stamples; E.E. Connor; Y. Lu; and M.J. VandeHaar. 2015. Heterogeneity in genetic and nongenetic variation and ene rgy sink relationships for residual feed intake across research stations and countries. J. Dairy Sci. 98:2013 2026. Tylutki, T.P.; D.G. Fox; V.M. Durbal; L.O. Tedeschi; J.B. Russell; M.E. Van Amburgh; T.R. Overton; L.E. Chase; and A.N. Pell. 2008. Cornell Net Carbohydrate and Protein System: A model for precision feeding of dairy cattle. Animal Feed Science and Technology. 143:174 202. VandeHaar, M.J, L.E. Armentano, K. Weigel, D.M. Spurlock, R.J. Tempelman, and R. Veerkamp 2016. Harnessing the genetics of the modern dairy cow to continue improvements in feed efficiency. J. Dairy Sci. 99:4941 4954 Yao, C., D. M. Spurlock, L. E. Armentano, C. D. Page, M. J. VandeHaar, D. M. Bickhart, and K. A. Weigel. 2013. Random Forests approach for identifying addi tive and epistatic single nucleotide polymorphisms associated with residual feed intake in dairy cattle. J. Dairy Sci. 96:6716 6729. 95 ABSTRACT The objective of this study was to determine the effect of dietary FA composition on dry matter ( DM ), neutral detergent fiber ( NDF ), FA, 16 - carbon FA, 18 - carbon FA digestibilities, and digestible energy intake per kilogram of DMI ( DMD , NDFD , FAD , 16 - CD , 18 - CD , EnergyD , and DEIkg respectively). The database for this study was composed of 423 individual observations collected on 183 lactations from 124 Holstein mid - lactation cows receiving diets that varied in FA composition in 5 experiments conducted at Michigan State University . The range s of C16:0, C18:0, C18:1, C18:2, and C18:3 were 0.33 to 1.9, 0.04 to 0.88, 0.42 to 1.0, 1.05 to 2.0, and 0.17 to 0.30 % of DM, respectively. Starch and forage NDF ( fNDF ) content varied from 26 to 29 and 19 to 21 % of DM, respectively, and DMI varied from 14 to 40 kg/d. The meta - regression was performed using the following fixed effects: all the FA variables described above, the FA variables ' respective quadratic terms, 2 - way interactions between each FA categor y and starch, fNDF, and DM I. The following were random effects and allowed for study - specific intercepts and slopes on DMI; c ow nested within block and experiment, period nested within the experiment, and block nested within the experiment . The following effects were observed: C16: 0 had a quadratic effect and C18:0 had a negative linear effect for DMD. Positive linear effects of C16:0, C18:1, and C18:2 were observed f or NDFD , a quadratic effect of C18:0 was also observed for NDFD . C16:0 and C 18:0 decreased linearly FAD. Quadratic e ffects of C16:0 and a negative linear effect of C18:0 were observed on the 16 - CD. A positive linear effect of C16:0 and a negative linear effect of C18:0, C18:1, and C18:2 were observed on 96 1 8 - CD . Quadratic effects of C16:0 and C18:0, and a positive linear effect of C18:3 were observed on EnergyD. Furthermore, quadratic effects of C16:0, C18:1, C18:2, and C18:3, as well as a negative linear effect of C18:0 were observed on DEIkg. To summarize, C16:0 and C18:0 were the FAs with the greatest impact on digestibi l it y and DEI kg . It is worth mentioning that C18:2 also caused an impact; however, the impact occurred at lower magnitudes than C16:0 and C18:0. Lastly, C16:0 increased DEI kg when included in the diet up to 1.21% of DM, and C18:0 linearly decreased DEI kg . Similarly, to C16:0 , when C18:2 was included in the diet up to 1.60% of DM, and DEIkg increased. INTRODUCTION Traditionally, fat supplements are added to dairy cow diets to increase dietary energy density and therefore increase energy intake. Ho wever, the effect of supplemental fat on energy intake is dependent on its potential impacts on dry matter intake ( DMI ) (Palmquist and Jenkins, 2017; Allen, 2000) and digestibility of fatty acids and other nutrients (Boerman et al., 2015; Weld and Armentan o, 2017). In this regard, the effect of fat supplements on DMI is variable and usually depends on the type of fat being fed (Rabiee et al., 2012). For instance, in a meta - regression of 29 treatment means compiled from the literature, Allen (2000) observed that saturated fatty acid ( FA ) supplements did not affect DMI. In contrast, the hypophagic effect of feeding fat seems to be more pronounced for unsaturated than saturated FA supplements (Harvatine and Allen, 2006); with DMI decreasing linearly as the degr ee of unsaturation increases (Pantoja et al., 1994) and the chain length of FA infused into the abomasum increases that palmitic acid ( C16:0 ) and stearic acid ( C18: 0) decreased DMI (Lock et al., 2013; Rico et al., 2014a), while most of the studies reported that DMI was not affected when the animals were fed 97 at 1.5 - 2.3% of diet DM compared with a nonfat control diet (Piantoni et al., 2013; Piantoni et al., 2015; Boerm an et al., 2017). Regarding FA digestibility ( FAD ), previous studies have indicated differences in intestinal digestibility among different FA, including C16:0, C18:0, and oleic acid ( C18:1 ) (Boerman et al., 2015; Glasser et al., 2008). Recently, Boerman e t al. (2017) fed increasing levels of a C18:0 - enriched supplement (~93% C18:0) to dairy cows and observed no positive effect on production responses. This was likely associated with the pronounced decrease in total FAD as FA intake increased. In contrast, Rico et al. (2017) fed increasing levels of a C16:0 - enriched supplement (~89% C16:0) to dairy cows and observed a slight decrease in total FAD as FA intake increased, as well as a positive effect on production response when C16:0 - enriched supplement was in cluded up to 1.5% diet DM in the diet. Although there are differences among specific free FAs digestibilities, the amount of FA included in the diet is relatively small for lactating dairy cattle when compared with other nutrients; and therefore, changes i n FAD may have minimal effects on animal performance. However, different responses to specific free FAs supplements may be due to their impa ct on overall DM digestibility ( DMD ) and digestible energy intake ( DEI ). While this consideration was necessary, we were not aware of any research that has determined the impact of dietary FA profile and digestibility on energy digestibility ( EnergyD ) and DEI. Furthermore, potentially of greater importance was the fact that fat supplements may affect the digestibility o f other nutrients, such as fiber (Palmquist, 1991). A recent meta - analysis highlighted that the FA profile of supplemental fat might affect NDF digestibility ( NDFD ; Weld and Armentano, 2017). Weld and Armentano (2017) observed 98 that Ca - salts of palm FA did not affect NDFD while feeding saturated FA supplements (C16:0 + C18:0) increased NDFD. Additionally, recent studies feeding highly enriched C16:0 supplements have shown increases in NDFD (Piantoni et al., 2013; de Souza et al., 2016; Rico et al., 2017). Th erefore, changes in the intake and digestibility of other nutrients due to fat supplementation may , in turn, affect the digestible energy available for milk production, body reserves, or both. Studies that investigated effects of dietary FA composition on and nutrient digestibility have consistently shown that FA profile has a crucial impact on intake, nutrient digestibility, and energy partitioning (de Souza et al., 2017; Boerman et al., 2017). However, no study has yet been report ed with a comprehensive analysis of the effect of dietary FA profile and other dietary factors on the DEI. With that in mind, our goal was to evaluate how dietary FA composition, in conjunction with other dietary factors, affects DEI. We hypothesized that fat supplements with a higher concentration of C16:0 would increase the di gestible dietary energy because of the positive effect of FA on NDFD. MATERIALS AND METHODS Database Our database was composed of the individual data points from 5 experiments perfor med between 2015 and 2017 at Michigan State University ( MSU ) that were designed to investigate the effect of dietary FA profile on animal performance, energy balance, and metabolism of lactating (25 to 180 DIM) Holstein dairy cows. In summary, the experime nts used either a block, a Latin - square, or a split - plot design. Cows were housed in individual tie stalls and fed 115% of expected daily intake. 99 Additionally, cows were milked twice a day. The data regarding the milk yield, the feed offered, and the feed refused by the cows were recorded daily. The final database contained 423 observations from 183 lactations of 124 Holstein dairy cows with 20 treatments from 5 experiments. Two of these experiments were published in a peer - reviewed journal (de Souza et al. , 2018; de Souza and Lock, 2018a), and three studies are still in the writing stage. Samples of all diet ingredients (0.5 kg) and orts from each cow (~12.5%) were collected daily for five consecutive days to determine the apparent total - tract digestibility of nutrients. During the same week, fecal samples (500g) were collected every 15 hours during five days, representing every 3 hours of a 24 - hour period to account for diurnal variation s . Diet ingredients, orts, and fecal samples were dried at 55 o C in a forced - air oven for 72 hours for dry matter ( DM ) determination. Dried samples were ground with a Wiley mill (1 - mm screen; Arthur H. Thomas, Philadelphia, PA). Feed ingredients, orts, and feces were analyzed for neutral detergent fiber ( NDF ), crude protein ( CP ), and starch concentration as described by Boerman et al. (2015). Fatty acid concentrations in feed ingredients, orts, and feces were determined as described by Lock et al. (2013). Gross energy was assayed by bomb calorimeter (Parr Instrument Inc., Mol ine, IL). Indigestible NDF was used as an internal marker to estimate fecal output to determine apparent total tract digestibility of nutrients (Cochran et al., 1986). Indigestible NDF was e valu ated as NDF after a 240 - h in vitro fermentation (Van Soest et al., 1991). The variables included in the database were dietary starch (% of DM), NDF (% of DM), forage NDF ( fNDF , % of DM), non - forage NDF ( nfNDF , % of DM), total FA (% of DM), C16:0 (% of DM), C18:0 (% of DM), C18:1 (% of DM), linoleic acid ( C18:2 , % of DM), linolenic acid ( C18:3 , % of DM), others FA ( OthersFA , % of DM; OthersFA = total FA C16:0 C18:0 cis - 9 C18:1 C18:2 C18:3), gross energy ( GE, Mcal/kg), nutrient 100 digestibility (NDF, total FA, 16 - carbon FA, 18 - carbon FA, and energy, all expresse d in percentage), DEI expressed as Mcal/d and Mcal/kg of DM ( DEIday and DEIkg , respectively ), DMI (kg/d), and variables related to experimental design (period, block, and square). The description of the variables mentioned above is presented in Table 5.1. Statistical Analysis All the statistical analyses were performed using SAS v. 9.4 (SAS Institute Inc., Cary, NC). The first step to complete the statistical analyses was to standardize the covariates to have a mean of zero and a standard deviation of 1 us ing SAS PROC STANDARD. This step was necessary to provide numerical stability for the following analyses. Based on the standardized database, a random regression model using SAS PROC HPMIXED was fitted to each of the six nutrient digestibilities (DMD, NDFD , FAD, 16 - CD, 18 - CD, and EnergyD) and DEI (DEIday and DEIkg) according to the following model [Equation 5.1]: [5.1] where is one of the six nutrient digestibilities (DMD, NDFD, FAD, 16 - CD, 18 - CD, and EnergyD) and DEI (DEIday and DEIkg) of the i th cow within the j th period, b th block, and k th 101 the study; is the overall mean; are the partial regression coefficients of on DMI with study - specific slope, starch, fNDF, nfNDF, C16:0, C18:0, C18:1, C18:2, and C18:3, respectively; are the partial regression coefficients of on the 2 - way interactions between the covariates; are the partial regression coefficients of on the quadratic effect of the covariates; is the random effect of the i th cow nested within the j th period, b th block, and k th study; is the random effect of the j th period nested within the k th study; is the random effect of the b th block nested within the k th study; is the random effect of the k th study; and is residual. The distribution of the residuals was checked with normal probability and studentized residuals. Data points with a studentized residual greater than 3.5 ± SD were considered outliers. Main effects were declared signific ant at P P multicollinearity using the variance inflation factor ( VIF ) test. As part of defining our working model for each of the six nutrient digestibilities and the 2 DEI expressions, the variables with the highest P - values were successively removed until only significant variables (main effect: P < 0.05; interactions P < 0.15) remained in the model. RESULTS The mo del containing all the main effects showed multicollinearity problems (VIF > 10, for main effects). T o remove the multico l linearity problem s , the variables of OtherFA and nfNDF, with their respective quadratic and interaction terms were removed from the Eq uation 102 [5.1]. The OtherFA variable was removed from the model due to it s calculation methodology which was highly correlated with other variables (it was calculated based on the difference between the total FA in the diet and the sum of C16:0, C18:0, C18:1 , C18:2, and C18:3 ). In the case of nfNDF, all diets were formulated to have a target of NDF of 30% of DM, and so the sum of fNDF and nfNDF was close to 30% in all diets; with that fNDF and nfNDF were highly correlated. We removed the nfNDF because it represented a much smaller fraction of the diet than the fNDF. The final models and the estimated coefficients from DMD, NDFD, FAD, 16 - CD, 18 - CD, EnergyD, DEIday, and DEIkg, are presented in Tables 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, and 5.9, respectively. Figures containing the FAs that had a non - significant effect ( P > 0.05) are presented in the Supplementary Material (Figures Supplemental Figure 5.1, Supplemental Figure 5.2, Supplemental Figure 5.3, Supplemental Figure 5.4, Supplemental Figure 5.5, and Su pplemental Figure 5.6). D ry matter digestibility (DMD) Dietary C16:0 affected DMD linearly and quadratically (estimated coefficients linear: 3.02 ± 0.30, quadratic: - 5.66 ± 1.08; P < 0.01, Figure 5.1) and interacted with starch content (estimated coeffi cient: - 1.26 ± 0.46; P = 0.01). Dietary C18:0 decreased DMD linearly (estimated coefficient: - 6.48 ± 1.19; P < 0.01, Figure 5.1), and its interaction with starch content was also significant (estimated coefficient: 9.37 ± 2.67; P < 0.01). None of the other FA had a significant impact on DMD (C18:1: P = 0.79, C18:2: P = 0.15, and C18:3: P = 0.61). With respect to DMI, fNDF, and starch content, only DMI was significant and it had a linear and quadratic effect on DMD (estimated coefficients linear: - 0.01 ± 0 .06, quadratic: - 103 0.02 ± 0.01; P = 0.01, Table 5.2) and interacted with fNDF content (estimated coefficient: 0.20 ± 0.08; P = 0.01). The main effects of fNDF and starch content on DMD were not significant (estimated coefficients fNDF: - 0.76 ± 1.16; P = 0. 51; starch: 1.58 ± 1.03; P = 0.13), but both remained in the model due to their interactions with other covariates, as described above. NDF digestibility (NDFD) Increasing dietary C16:0 and C18:1 increased NDFD linearly (estimated coefficient - palmitic: 1 .71 ± 0.67; P = 0.01, oleic: 5.12 ± 2.11; P = 0.02, Figure 5.2). Also, C16:0 interacted with fNDF (estimated coefficient: 1.38 ± 0.65). Dietary C18:0 had a linear and quadratic effect on NDFD (estimated coefficients linear: 16.4 ± 5.40; quadratic: - 34.3 ± 10.6; P = 0.01, Figure 5.2). The C18:2 dietary concentration decreased NDFD linearly (estimated coefficient: - 4.87 ± 1.24; P < 0.01; Figure 5.2), and C18:3 was not significant ( P = 0.72). Although the main effects of DMI and fNDF on NDFD were not signifi cant ( P = 0.58 and P = 0.34, respectively), they remained in the model because of the significant interaction between DMI and fNDF (estimated coefficient: 0.27 ± 0.13; P = 0.03) and the fNDF interaction with C16:0 (as shown above). Starch content was not s ignificant ( P = 0.42). Total FA digestibility (FAD) Both C16:0 and C18:0 linearly reduced FAD (estimated coefficient for C16:0: - 1.71 ± 0.51; P = 0.01; for C18:0: - 11.0 ± 1.10; P = 0.01; Figure 5.3). The dietary concentration of C18:1, C18:2, and C18:3 did not affect FAD (C18:1: P = 0.06, C18:2: P = 0.11, C18:3: P = 0.71). 104 Dry matter intake had a linear and quadratic effect on FAD (estimated coefficients linear: - 0.34 ± 0.12; qua dratic: - 0.03 ± 0.01; P = 0.03) and fNDF content had a negative linear effect on FAD (estimated coefficient: - 1.93 ± 0.53; P = 0.01) on FAD. Starch content was not significant ( P = 0.86). 16 - carbon FA digestibility (16 - CD) Palmitic had a linear and quadrat ic effect on 16 - CD (estimated coefficients linear: - 9.41 ± 0.60; quadratic: - 8.04 ± 2.27; P = 0.01, Figure 5.4). Interestingly, increasing dietary C18:0 linearly decreased 16 - CD (estimated coefficient: - 8.18 ± 1.66; P < 0.01, Figure 5.4), but it interact ed with DMI (estimated coefficient: 0.69 ± 0.42; P = 0.11) and fNDF content (estimated coefficient: 11.7 ± 6.22; P = 0.06). The dietary concentrations of C18:1, C18:2, and C18:3 did not affect 16 - CD (C18:1: P = 0.07, C18:2: P = 0.11, C18:3: P = 0.33). Alth ough the main effects of DMI and fNDF on 16 - CD were not significant ( P = 0.51 and P = 0.65, respectively), they remained in the model because of the significant interaction between DMI and fNDF (estimated coefficient: 0.39 ± 0.18; P = 0.03), and their inte ractions with C18:0 (as described above). Starch content did not affect 16 - CD ( P = 0.41). 18 - carbon FA digestibility (18 - CD) Increasing dietary C16:0 linearly increased 18 - CD (estimated coefficient: 1.57 ± 0.52, P = 0.01; Figure 5.5), whereas increasing di etary C18:0, C18:1, and C18:2 linearly decreased 18 - CD (estimated coefficient C18:0: - 14.0 ± 1.03, P < 0.01; C18:1: - 3.80 ± 1.89, P = 0.04; and C18:2: - 7.44 ± 2.30, P = 0.01; Figure 5.5). Additionally , C18:0 interacted with fNDF content 105 (estimated coeffi cient: 17.4 ± 5.37, P = 0.01). The dietary concentration of C18:3 did not impact 18 - CD ( P = 0.34). Dry matter intake had a linear and quadratic effect (estimated coefficients linear: - 0.37 ± 0.12 ; quadratic: - 0.04 ± 0.01; P = 0.01), starch content had a negative linear effect on 18 - CD (estimated coefficient: - 3.87 ± 0.80, P < 0.01), and both interacted with each other (estimated coefficient: - 0.32 ± 0.14, P = 0.02). Finally, increasing dietary fNDF content linearly increased 18 - CD (estimated coefficient: 1.92 ± 0.85, P = 0.02). Energy digestibility (EnergyD) The dietary concentrations of C16:0 and C18:0 had a linear and quadratic effect on EnergyD (estimated coefficients for C16:0 linear: 1.15 ± 0.49; quadratic: - 6.65 ± 1.4 9; P < 0.01; estimated coefficients for C18:0 linear: 7.30 ± 3.77; quadratic: - 24.8 ± 7.19; P = 0.01; Figure 5.6). The dietary concentration of C18:3 did not impact EnergyD ( P = 0.16), but it interacted with starch content (estimated coefficient: - 51.3 ± 28.2, P = 0.07). The concentration of C18:1 and C18:2 did not impact energy digestibility (C18:1: P = 0.80, C18:2: P = 0.46). Dry matter intake and fNDF content had a linear and a quadratic effect on EnergyD (estimated coefficients for DMI linear: - 0.09 ± 0.10, quadratic: - 0.02 ± 0.01, P = 0.01; estimated coefficients for fNDF linear: - 1.59 ± 1.14, quadratic: - 4.92 ± 1.69, P = 0.01). Starch content was not significant ( P = 0.30) but remained in the model because of its interaction with C18:3 (as described above). 106 Digestible energy intake expressed in Mcal /d and Mcal/kg of DM (DEIday and DEIkg, respectively) The FA had the same main effect regardless of whether DEI was expressed a s Mcal/d or Mcal/kg of DM, except for C18:2. The concentration of C16:0, C18:1, and C18:3 linearly and quadratically affected DEIday (estimated coefficients for DEIday for C16:0 - linear: 0.39 ± 0.85, quadratic: - 31.6 ± 3.72, P < 0.01; for C18:1 - linear: 15.2 ± 5.45, quadratic: - 33.9 ± 14.1, P = 0.01; for C18:3 - linear: 325 ± 45.6, quadratic: - 4,527 ± 608; P < 0.01, Figure 5.7; estimated coefficients for DEIkg for C16:0 - linear: 0.03 ± 0.03, quadratic: - 0.51 ± 0.09, P < 0.01; for C18:1 - linear: 0.04 ± 0.14, quadratic: - 0.90 ± 0.47, P = 0.05; for C18:3 - linear: 5.88 ± 0.91, quadratic: - 60.0 ± 14.6, P < 0.01; Figure 5.8), and increasing dietary C18:0 linearly decreased DEIday and DEIkg (estimated coefficients for DEIday: - 16.7 ± 2.01, P < 0.01; Figu re 5.7; estimated coefficients for DEIkg: - 0.39 ± 0.06, P < 0.01; Figure 5.8). Increasing dietary C18:2 linearly increased DEIday (estimated coefficient: 21.4 ± 2.86, P < 0.01; Figure 5.7), while it linearly and quadratically affected DEIkg (estimated coef ficients linear: 0.16 ± 0.11, quadratic: - 1.85 ± 0.45, P < 0.01; Figure 5.8). For DEIday two interactions occurred - C16:0 and C18:0 interacted with starch content (estimated coefficient for the interaction with C16:0: - 3.60 ± 0.80, P < 0.01; and interac tion with C18:0: - 18.1 ± 5.95, P = 0.01). For DEIkg, only C18:1 interacted with starch content (estimated coefficient: - 0.74 ± 0.21, P = 0.01). Dry matter intake and starch content had a positive linear effect on DEIday (estimated coefficients for DMI: 2.8 3 ± 0.07, P < 0.01; Starch: 3.86 ± 0.94, P < 0.01). The main effect of 107 fNDF content on DEIday was not significant ( P = 0.72), but it remained in the model because of it s interact ion with DMI (estimated coefficient: 0.25 ± 0.08, P = 0.01). For DEIkg, DMI ha d a quadratic effect (estimated coefficients linear: - 0.003 ± 0.005, quadratic: - 0.001 ± 0.0003, P = 0.01) and interacted with fNDF content (estimated coefficient: 0.01 ± 0.001, P = 0.09). The main effect of starch content on DEIkg was a positive linear effect (estimated coefficient: 0.14 ± 0.04, P = 0.01). DISCUSSION As documented by Palmquist and Jenkins (2017), the initial studies with fat supplementation on dairy cows were based on feeding high levels of tallow and oilseeds. As research in the field of fat supplementation advanced, there was a shift from tallow and oilseeds to rumen - protected sources, and a focus on the degree of saturation of fat supplements was developed to overcome the problems of fat supplementation. These problems were associated with fiber digestibility, rumen fermentation, and milk composition (Jenkins and Palmiquist, 1984; Palmiquist and Jenkins, 2017). Importantly, research has evolved from feeding the traditional animal - and plant - based fats to a new interest in the effects o f feeding individual FA s , extending beyond their energy contribution to include potentially structural, metabolic, and physiological effects (Palmquist and Jenkins, 2017). Nowadays, we recognize that the FA profile of supplemental fat has a significant imp act on nutrient digestibility, energy intake, and milk composi t ion (Allen, 2000; Mosley et al., 2007; Lock et al., 2013; Piantoni et al., 2013; De Souza et al., 2017; Boerman et al., 2017; Weld and Armentano, 2017). 108 In accordance with the most recent rese arch related to FA profile, our results showed that the FA included in our analysis (C16:0, C18:0, C18:1, C18:2, and C18:3) had a specific effect on the DMD, NDFD, FAD, EnergyD, and DEI. In addition to their main effects, in some cases (as shown in the res ults) FA interacted with dietary starch and fNDF. An essential point to consider in our analysis was that all of the five studies were designed to investigate the effect of dietary FA on the nutrient digestibility and production responses of dairy cows. Co nsequently, the diets were formulated to have similar starch and fNDF content across treatments. That being said, the variation s in starch and fNDF content in the diets used in this analysis were minimal (starch lower quartile: 27.4%, upper quartile: 28. 5%; fNDF lower quartile: 19%, upper quartile: 21%; Table 5.1), allowing us to investigate mainly the effect of FA profile. However, this also limited our ability to examine the impact of starch and fNDF content and potentially the interaction between the se factors with dietary FA. The fact that we had small variations on starch, fNDF, and DMI resulted in a more modest effect of these covariates on the dependent variables than the covariates associated with FA profile, as shown by the estimated coefficien ts when expressed in standard deviations units ( Supplemental Tables 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, and 5.7). Accordingly, our discussion focused on the effect of the FA profile. Another essential characteristic of our database was that the majority of the t reatments had levels of C18:0 ranging from 0.04 to 0.23% of the DM (only three treatments with higher levels of C18:0 - 0.67, 0.72, and 0.88% of DM) and levels of C18:3 ranging from 0.17 to 0.22% of the DM (only two treatments with higher levels of C18:3 0.25 and 0.30% of DM). In this situation, when there was a gap in the distribution of the covariates, we were prone to the risk of 109 misinterpretation of the data because there was no continuous information along the range of the covariates (C18:0 and C18:3 ). In the following discussion, for practical purposes, we discussed the effect of the FA profile on the dependent variables using the estimated coefficients on the original scale (% of DM, Tables 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, and 5.9). However, when com paring the relative importance of each estimated coefficient for each FA, we used the standardized coefficients (1 STD, Supplemental Tables 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, and 5.8). Dry matter digestibility (DMD) The dietary concentration of C16:0 had a quadratic effect on DMD, due to DMD increasing from 60 to 67% when C16:0 increased from 0.33 to 1.45% of DM (Figure 5.1a). Once 1.45% of DM was reached, the DMD had a slight decrease (Figure 5.1a). These results corroborate with Piantoni et al. (2013), wh ich observed an increase in DMD when comparing a control diet (0.44% of DM of C16:0) to a high diet (2.41% of DM of C16:0). Additionally, there was a significant interaction between C16:0 and starch content. This interaction suggested that C16:0 had a more positive effect on DMD in diets with lower levels of starch as opposed to diets with a high level of starch. In normal conditions, starch was one of the most digestible fractions of the diet (93% digestible, de Souza et al., 2018). Hence, C16:0 would have a lower impact on DMD in diets with high s tarch content. Furthermore, although this interaction was significant, it had a minimal biological effect. Whereas C16:0 had a positive effect on DMD, C18:0 linearly decreased DMD by 6.5% per 1% increase of C18:0 in the diet. Similarly, Boerman et al. (2017) reported a tendency for a linear decrease in DM digestibility when dietary levels of C18:0 increased from 0.07 to 2.19% of 110 diet DM. Chamberlain and DePeters (2017) also reported a tendency for decreasing the o rganic matter digestibility when increasing the C18:0 content from 0.01 to 0.11% of DM. Additionally, C18:0 interacted with starch content, whereas the negative effect of C18:0 on DMD was associated with diets containing high levels of starch. NDF digestib ility (NDFD) Palmitic and C18:1 increased the NDFD by 1.71 and 5.12% per 1% increase in the diet, respectively (Figure 5.2). Piantoni et al. (2013) reported a similar positive effect of C16:0 on NDFD, where increasing C16:0 from 0.46 to 2.41% of DM increas ed NDFD from 35.7 to 39.0% of NDFD. Rico et al. (2014) observed interaction between C16:0 and the level of production, where on high producing cows (~ 42 kg/d) the NDFD increased from 31.2 to 33.4% when C16:0 increased from 0.58 to 2.12% of DM. de Souza an d Lock (2018b) reported an increase in NDF digestibility when feeding a Ca - salts of palm FA (45% C16:0 and 38% C8:1) compared with a nonfat control diet, which was attributed to a reduction in DMI caused by the supplemental fat. In a recent meta - analysis, Weld and Armentano (2017) observed that calcium salts of palm FA did not affect NDF digestibility, while saturated prilled fat containing a mixture of C16:0 and C18:0 increased NDF digestibility. Stearic had a quadratic effect, increasing the NDFD from 39 to 44% when C18:0 increased from 0.04 to 0.44% of DM (Figure 5.2b). Piantoni et al. (2015) reported a tendency for an increase in NDFD when feeding a C18:0 enriched supplement (diet C18:0 increased from 0.09% to 1.96% of DM). Contrary to our results, Cham berlain and DePeters (2017) did not observe a decrease in NDFD when adding C18:0. However, Chamberlain and DePeters (2017) included C18:0 up to 0.11% of DM. At this level of inclusion , we also observed a small effect of 111 C18:0 on NDFD. In this sense, our re sults were corroborated because C18:0 had an adverse impact on NDFD only at high levels of inclusion. Total, 16 - carbon, and 18 - carbon FAs digestibility (FAD, 16 - CD, and 18 - CD, respectively) Both C16:0 and C18:0 were the only FA that affected FAD (Figures 5.3a and 5.3b). Research shows that FA digestibility usually decreases as FA intake increases (Palmquist, 1991). When comparing the standardized coefficients, the effect of C18:0 on FAD was 2.6 times greater than the effect of C16:0. Feeding C18:0 - enriched FA supplements have been shown to decrease FA digestibility in dairy cows (Piantoni et al., 2015; Boerman et al., 2017) and sheep (Toral et al., 2016). Additionally, Chamberlain and DePeters (2017) observed that increasing the proportion of C18:0 to C16:0 in supplemental fat (2% diet DM) reduced total FA digestibility in dairy cows. By our results, Boerman et al. (2015) also reported a decrease in FAD with the increase of the total FA intake and duodenal flow. Potential reasons for the reduction in FA dige stibility includes a limitation in lysolecithin secretion reducing the flux of FA into micelles (Boerman et al., 2015a), and possible saturation of absorptive sites in the intestine (Glasser et al., 2008). Similarly, to FAD, only C16:0 and C18:0 affected 1 6 - CD. At low levels of C16:0 (0.3 to 0.9% of DM), there was a minimal effect of C16:0 on 16 - CD, which was reasonably stable at around 76%. However, at high levels of C16:0, from 1.1 to 1.91% of DM, the 16 - CD was dropped to 63% (Figure 5.4a). In a meta - regr ession performed by Boerman et al. (2015), the authors also reported a decrease in 16 - CD with the increase of the duodenal flow of C16:0; however, on their meta - regression the effect of C16:0 was much smaller than the one reported in our study. Piantoni et al. (2013) also observed a decrease in 16 - CD when increasing C16:0 from 112 0.46 to 2.21% of DM. Interestingly, we foun d that increasing C18:0 also decreased 16 - CD (Figure 5.4b). These results suggested that the profile of FA reaching the intestine is most li kely the primary factor that impacts digestibility, rather than the total amount of FA reaching the intestine. On the 18 - CD, all the FA included in the analysis had a significant effect, except C18:3. Increasing C16:0 increased 18 - CD linearly (Figure 5.5a) . Stearic, C18:1, and C18:2 linearly decreased 18 - CD (Figures 5.5b, 5.5c, and 5.5d). Based on the standardized coefficients, C18:0 was the most critical FA, followed by C18:2 and C18:1. Boerman et al. (2015) reported the same effect of C18:0 on 18 - CD, wher e 18 - CD was dramatically decreased with the increase of C18:0. Energy digestibility (EnergyD) As expected, EnergyD had a very similar pattern to DMD and NDFD. Palmitic had a linear and quadratic effect on EnergyD. When C16:0 was included from 0.33 to 1.27% of DM, it increased EnergyD from 63.3 to 69.3%. After 1.27% of C16:0 was reached, EnergyD decreased to 66.6% until the maximum level of C16:0 inclusion in our database was achiev ed (1.91% of DM) (Figure 5.6a). Conversely, C18:0 had a small effect on Energ yD at low levels of inclusion and an adverse impact when included at high levels. Energy digestibility increased from 67.3 to 69.7% as C18:0 increased from 0.04 to 0.35% of DM. However, after 0.35% of C18:0 was reached, EnergyD drastically dropped to 62.8% when C18:0 level reached 0.88% of DM (Figure 5.6b). Weiss and Wyatt (2004) also reported an increase in EnergyD when increasing the ratio C16:0:C18:0. In their study, treatment s with a high level of C18:0 had an EnergyD of 66.4% and the treatments high on C16:0 had an EnergyD of 69.5%. In contrast, Weiss et al. (2011) did not 113 detect differences in EnergyD when evaluating different types of supplemental fat. However, it is important to point out w hat kind s of supplemental fat vary not only according to the FA profile but also to the method of protection and degree of esterification. Linolenic increased EnergyD by 22.6% when increased by 1 - unit in the diet. However, C18:3 interacted with starch content, and the positive effect of C18:3 was associated with die ts with a low level of starch (Figure 5.6c). When comparing the standardized coefficients, C18:0 had the most impact on EnergyD followed by C16:0 and C18:3. The C18:0 effect was associated with the decrease in EnergyD when included in levels higher than 0. 35% of DM, which is likely associated with the reduction in FA digestibility reported for this FA. In contrast, C16:0 increased EnergyD, probab ly due to its effect on fiber digestibility. Digestible energy intake (DEI) Palmitic increased DEIday from 72.5 t o 96.1 Mcal/d when it was increased from 0.33 to 1.19% of DM. Once levels higher than 1.19% of DM were achieved , C16:0 dropped DEIday down to 79.8 Mcal/d at 1.91% of DM. Additionally, the interaction between C16:0 and starch content was statistically signi ficant and suggested that C16:0 had a more positive effect on DEIday in diets with low starch content. Although the interaction was statistically significant, it had a minimal biological impact. Similarly, to the DEIday, C16:0 increased DEIkg from 2.7 to 3 .08 Mcal/kg of DM when it was increased from 0.33 to 1.21% of DM (Figure 5.8a). Similar to our results, Weiss et al. (2011), also reported an increase in DEIkg when they increased C16:0 from 0.44 to 2.09% of DM. In contrast to C16:0, which increased DEIda y and DEIkg in low to mid - levels , C18:0 linearly decreased DEIday by 16.7 Mcal/d (Figure 5.7b) and DEIkg by 0.39 Mcal/kg of DM 114 (Figure 5.8b) per 1 - unit increase. For DEIday, there was an essential interaction between C18:0 and starch content, indicating th at the adverse effect of C18:0 on DEIday was associated with increased levels of starch in the diet (Figure 5.8b). These results are in agreement with the negative effects of this FA on DM digestibility and mainly FA digestibility. When oleic was increased from 0.42 to 0.92% of DM, it increased DEIday from 89.2 to 97.7 Mcal/d. After 0.92% was reached, DEIday had a slight drop to 97.5 Mcal/d at the maximum level of C18:1 inclusion (1.00% of DM) (Figure 5.7c). Although the main effect of C18:1 was significant for DEIday, its main effect on DEIkg was minimal, and its biological importance was dependent on the starch content. At low levels of starch, C18:1 increased DEIkg; and at high levels of starch, C18:1 decreased DEIkg (Figure 5.8c). CONCLUSIONS In conclusion, C16:0 and C18:0 were the FAs with the most significant impact on digestibility and EnergyD. The primary effect of C16:0 on EnergyD was associated with the increase on EnergyD when C16:0 was increased in the diet from 0.33 to 1.27% of DM. In con trast, the primary effect of C18:0 on EnergyD was associated with the decrease on EnergyD when C18:0 was increased from 0.35 to 0.88% of DM. C16:0 increased DEI when included in the diet up to 1.20% of DM, and C18:0 linearly decreased DEI . 115 APPENDICES 116 APPENDIX A Tables 117 Table 5. 1. Descriptive summary of the variables included in the database . Variable 1 Mean SD Lower Quartile Median Upper Quartile DMI, kg/d 29.9 3.45 27.7 29.8 32.1 Dietary Composition, % of DM Starch 27.9 0.736 27.4 28.0 28.5 NDF 29.8 0.776 29.0 29.7 30.8 fNDF 20.2 0.776 19.0 20.3 21.0 nfNDF 9.67 0.880 8.70 9.80 10.8 Fatty Acids Palmitic 1.19 0.528 0.610 1.26 1.68 Stearic 0.203 0.220 0.070 0.130 0.230 Oleic 0.696 0.145 0.630 0.660 0.790 Linoleic 1.56 0.278 1.29 1.67 1.81 Linolenic 0.202 0.023 0.180 0.200 0.210 OthersFA 0.227 0.059 0.220 0.230 0.250 Digestibilities, % Dry matter 64.4 4.13 61.5 64.7 67.4 NDF 41.5 5.30 38.1 41.6 44.9 Fatty Acids 76.1 6.38 71.8 76.7 80.7 16 - Carbon 72.7 8.02 66.9 73.6 79.0 18 - Carbon 79.8 7.02 75.6 81.6 85.2 Energy 65.8 5.18 62.1 65.9 69.3 Digestible Energy Intake Mcal /d 88.8 11.0 82.5 89.2 95.8 Mca l /kg of DM 2.97 0.211 2.83 2.99 3.11 1 DMI = dry matter intake, fNDF = forage NDF, nfNDF = non - forage NDF, OthersFA = total fatty acids - (palmitic + stearic + oleic + linoleic + linolenic) 118 Table 5. 2. Effect of dry matter intake (DMI, kg /d ) and diet composition (% of DM) on dry matter digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 66.4 0.980 <0.01 DMI (linear) - 0.014 0.064 0.83 DMI (quadratic) - 0.018 0.007 0.01 Starch 1.58 1.03 0.13 fNDF - 0.756 1.16 0.52 Palmitic (linear) 3.02 0.303 <0.01 Palmitic (quadratic) - 5.66 1.08 <0.01 Stearic - 6.48 1.19 <0.01 DMI*fNDF 0.203 0.078 0.01 Starch*Palmitic - 1.26 0.459 0.01 Starch*Stearic 9.37 2.67 <0.01 1 fNDF = forage NDF, 2 S tandard error 119 Table 5. 3. Effect of dry matter intake (DMI, kg /d ) and diet composition (% of DM) on NDF digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 42.5 0.857 <0.01 DMI 0.057 0.103 0.58 fNDF 0.960 1.00 0.34 Palmitic 1.71 0.667 0.01 Stearic (linear) 16.4 5.40 <0.01 Stearic (quadratic) - 34.3 10.6 <0.01 Oleic 5.12 2.11 0.02 Linoleic - 4.87 1.24 <0.01 DMI*fNDF 0.270 0.126 0.03 fNDF*Palmitic 1.38 0.653 0.03 1 fNDF = forage NDF, 2 Standard error 120 Table 5. 4. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on total fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 76.5 0.601 <0.01 DMI (linear) - 0.374 0.133 0.01 DMI (quadratic) - 0.029 0.013 0.02 fNDF - 1.49 0.694 0.03 Palmitic - 1.71 0.508 <0.01 Stearic - 11.0 1.10 <0.01 1 fNDF = forage NDF, 2 Standard error 121 Table 5 .5 . Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on 16 - carbon fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 74.5 1.24 <0.01 DMI - 0.096 0.145 0.51 fNDF - 0.605 1.34 0.65 Palmitic (linear) - 9.41 0.596 <0.01 Palmitic (quadratic) - 8.04 2.27 <0.01 Stearic - 8.18 1.66 <0.01 DMI*fNDF 0.394 0.178 0.03 DMI*Stearic 0.688 0.425 0.11 fNDF*Stearic 11.76 6.22 0.06 1 fNDF = forage NDF, 2 Standard error 122 Table 5. 6. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on 18 - carbon fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 79.9 0.570 <0.01 DMI (linear) - 0.375 0.117 <0.01 DMI (quadratic) - 0.038 0.012 <0.01 Starch - 3.87 0.797 <0.01 fNDF 1.92 0.846 0.02 Palmitic 1.57 0.520 <0.01 Stearic - 14.0 1.03 <0.01 Oleic - 3.80 1.89 0.04 Linoleic - 7.44 2.30 <0.01 DMI*Starch - 0.317 0.139 0.02 fNDF*Stearic 17.4 5.37 <0.01 1 fNDF = forage NDF, 2 Standard error 123 Table 5.7. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on energy digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 69.2 1.59 <0.01 DMI (linear) - 0.092 0.098 0.35 DMI (quadratic) - 0.022 0.008 <0.01 Starch 1.09 1.05 0.30 fNDF (linear) - 1.59 1.14 0.16 fNDF (quadratic) - 4.92 1.69 <0.01 Palmitic (linear) 1.15 0.491 0.02 Palmitic (quadratic) - 6.65 1.49 <0.01 Stearic (linear) 7.30 3.77 0.05 Stearic (quadratic) - 24.7 7.19 <0.01 Linolenic 22.6 16.0 0.16 Starch*Linolenic - 51.3 28.2 0.07 1 fNDF = forage NDF, 2 Standard error 124 Table 5.8. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on digestible energy intake (Mcal /d ) . Effect 1 Estimated Coefficient SE 2 P - value Intercept 96.0 1.47 <0.01 DMI 2.83 0.067 <0.01 Starch 3.86 0.936 <0.01 fNDF 0.358 1.02 0.72 Palmitic (linear) 0.388 0.851 0.65 Palmitic (quadratic) - 31.6 3.72 <0.01 Stearic - 16.7 2.01 <0.01 Oleic (linear) 15.2 5.45 <0.01 Oleic (quadratic) - 33.9 14.1 <0.01 Linoleic 21.4 2.86 <0.01 Linolenic (linear) 325 45.6 <0.01 Linolenic (quadratic) - 4527 608 <0.01 DMI*fNDF 0.245 0.079 <0.01 Starch*Palmitic - 3.60 0.801 <0.01 Starch*Stearic - 18.1 5.95 <0.01 1 fNDF = forage NDF, 2 Standard error 125 Table 5.9. Effect of dry matter intake (DMI, kg/d) and diet composition (% of DM) on digestible energy concentration (Mcal/kg of DM) . Effect 1 Estimated Coefficient SE 2 P - value Intercept 3.08 0.056 <0.01 DMI (linear) - 0.003 0.005 0.46 DMI (quadratic) - 0.001 0.000 <0.01 Starch 0.144 0.038 <0.01 fNDF 0.003 0.058 0.95 Palmitic (linear) 0.027 0.029 0.35 Palmitic (quadratic) - 0.508 0.091 <0.01 Stearic - 0.386 0.064 <0.01 Oleic (linear) 0.045 0.143 0.75 Oleic (quadratic) - 0.899 0.465 0.05 Linoleic (linear) 0.159 0.108 0.14 Linoleic (quadratic) - 1.85 0.447 <0.01 Linolenic (linear) 5.88 0.912 <0.01 Linolenic (quadratic) - 60.1 14.6 <0.01 DMI*fNDF 0.009 0.001 0.09 Starch*Oleic - 0.738 0.207 <0.01 1 fNDF = forage NDF, 2 Standard error 126 APPENDIX B Figures 127 a) b) Figure 5.1. Effect of the inclusion of dietary palmitic (a) and stearic (b) on dry matter digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5 : ) . 50 60 70 80 0 200 400 600 800 Adj. DM digestibility, % Palmitic, g/day 50 60 70 80 0 50 100 150 200 250 300 350 Adj. DM digestibility, % Stearic, g/day 128 a) b) Figure 5.2. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linoleic (d) on NDF digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; stud y 4: , and study 5: ). 20 30 40 50 60 0 200 400 600 800 Adj. NDF digestibility, % Palmitic, g/day 20 30 40 50 60 0 50 100 150 200 250 300 350 Adj. NDF digestibility, % Stearic, g/day 129 c) d) 20 30 40 50 60 50 125 200 275 350 Adj. NDF digestibility, % Oleic, g/day 20 30 40 50 60 200 300 400 500 600 700 800 900 Adj. NDF digestibility, % Linoleic, g/day 130 a) b) Figure 5. 3. Effect of the inclusion of dietary palmitic (a) and stearic (b) on total fatty acid digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and s tudy 5: ) . 50 60 70 80 90 0 200 400 600 800 Adj. total FA digestibility, % Palmitic, g/day 50 60 70 80 90 0 50 100 150 200 250 300 350 Adj. total FA digestibility, % Stearic, g/day 131 a) b) Figure 5.4. Effect of the inclusion of dietary palmitic (a) and stearic (b) on 16 - carbon fatty acids digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ) . 50 60 70 80 90 0 200 400 600 800 Adj. 16 - C digestibility, % Palmitic, g/day 50 60 70 80 90 0 50 100 150 200 250 300 350 Adj. 16 - C digestibility, % Stearic, g/day 132 a) b) Figure 5.5. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linoleic (d) on 18 - carbon fatty acids digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 60 70 80 90 0 200 400 600 800 Adj. 18 - C digestibility, % Palmitic, g/day 50 60 70 80 90 0 50 100 150 200 250 300 350 Adj. 18 - C digestibility, % Stearic, g/day 133 c) d) 50 60 70 80 90 50 100 150 200 250 300 350 Adj. 18 - C digestibility, % Oleic, g/day 50 60 70 80 90 200 300 400 500 600 700 800 Adj. 18 - C digestibility, % Linoleic, g/day 134 a) b) c) Figure 5.6. Effect of the inclusion of dietary palmitic (a), stearic (b), and linolenic on energy digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 60 70 80 90 0 200 400 600 800 Adj. energy digestibility, % Palmitic, g/day 50 60 70 80 90 0 50 100 150 200 250 300 350 Adj. energy digestibility, % Stearic, g/day 50 60 70 80 90 50 60 70 80 90 Adj. energy digestibility, % Linolenic, g/day 135 a) b) Figure 5.7. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linolenic (d) on digestible energy intake (DEI, Mcal/d). Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 20 40 60 80 100 120 0 200 400 600 800 Adj. digestible energy intake, Mcal/Day Palmitic, g/day 20 40 60 80 100 120 0 50 100 150 200 250 300 350 Adj. digestible energy intake, Mcal/Day Stearic, g/day 136 c) d) 20 40 60 80 100 120 50 100 150 200 250 300 350 Adj. digestible energy intake, Mcal/Day Oleic, g/day 20 40 60 80 100 120 50 60 70 80 90 Adj. digestible energy intake, Mcal/Day Linolenic, g/day 137 a) b) Figure 5.8. Effect of the inclusion of dietary palmitic (a), stearic (b), oleic (c), and linolenic (d) on digestible energy intake (DEI, Mcal/d). Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 2.0 2.5 3.0 3.5 4.0 0 200 400 600 800 Adj. digestible energy intake, Mcal/kg of DM Palmitic, g/day 2.0 2.5 3.0 3.5 4.0 0 50 100 150 200 250 300 350 Adj. digestible energy intake, Mcal/kg of DM Stearic, g/day 138 c) d) 2.0 2.5 3.0 3.5 4.0 50 100 150 200 250 300 350 Adj. digestible energy intake, Mcal/kg of DM Oleic, g/day 2.0 2.5 3.0 3.5 4.0 50 60 70 80 90 Adj. digestible energy intake, Mcal/kg of DM Linolenic, g/day 139 APPENDIX C Supplemental Tables 140 Suppl emental Table 5. 1. Effect of dry matter intake (SD) and diet composition (SD) on dry matter digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 66.4 0.980 <0.01 DMI (linear) - 0.047 0.222 0.83 DMI (quadratic) - 0.216 0.081 0.01 Starch 1.16 0.755 0.13 fNDF - 0.587 0.897 0.52 Palmitic (linear) 1.59 0.160 <0.01 Palmitic (quadratic) - 1.58 0.301 <0.01 Stearic - 1.43 0.263 <0.01 DMI*fNDF 0.543 0.209 0.01 Starch*Palmitic - 0.489 0.179 0.01 Starch*Stearic 1.52 0.433 <0.01 1 fNDF = forage NDF, 2 Standard error 141 Supplemental Table 5. 2. Effect of dry matter intake (SD) and diet composition (SD) on NDF digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 42.5 0.857 <0.01 DMI 0.198 0.356 0.58 fNDF 0.745 0.773 0.34 Palmitic 0.902 0.352 0.01 Stearic (linear) 3.61 1.19 <0.01 Stearic (quadratic) - 1.67 0.515 <0.01 Oleic 0.743 0.307 0.02 Linoleic - 1.35 0.344 <0.01 DMI*fNDF 0.722 0.337 0.03 fNDF*Palmitic 0.566 0.268 0.03 1 fNDF = forage NDF, 2 Standard error 142 Supplemental Table 5. 3. Effect of dry matter intake (SD) and diet composition (SD) on total fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 76.5 0.601 <0.01 DMI (linear) - 1.29 0.457 0.01 DMI (quadratic) - 0.350 0.152 0.02 fNDF - 1.16 0.539 0.03 Palmitic - 0.904 0.268 <0.01 Stearic - 2.43 0.243 <0.01 1 fNDF = forage NDF, 2 Standard error 143 Supplemental Table 5.4. Effect of dry matter intake (SD) and diet composition (SD) on 16 - carbon fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 74.5 1.24 <0.01 DMI - 0.333 0.499 0.51 fNDF - 0.470 1.04 0.65 Palmitic (linear) - 4.97 0.315 <0.01 Palmitic (quadratic) - 2.24 0.635 <0.01 Stearic - 1.80 0.366 <0.01 DMI*fNDF 1.05 0.475 0.03 DMI*Stearic 0.522 0.323 0.11 fNDF*Stearic 2.01 1.06 0.06 1 fNDF = forage NDF, 2 Standard error 144 Supplemental Table 5.5. Effect of dry matter intake (SD) and diet composition (SD) on 18 - carbon fatty acids digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 79.9 0.570 <0.01 DMI (linear) - 1.29 0.404 <0.01 DMI (quadratic) - 0.448 0.144 <0.01 Starch - 2.85 0.586 <0.01 fNDF 1.49 0.656 0.02 Palmitic 0.829 0.275 <0.01 Stearic - 3.09 0.226 <0.01 Oleic - 0.551 0.274 0.04 Linoleic - 2.07 0.639 <0.01 DMI*Starch - 0.804 0.353 0.02 fNDF*Stearic 2.98 0.919 <0.01 1 fNDF = forage NDF, 2 Standard error 145 Supplemental Table 5.6. Effect of dry matter intake (SD) and diet composition (SD) on energy digestibility . Effect 1 Estimated Coefficient SE 2 P - value Intercept 69.2 1.59 <0.01 DMI (linear) - 0.317 0.339 0.35 DMI (quadratic) - 0.267 0.091 <0.01 Starch 0.798 0.775 0.30 fNDF (linear) - 1.23 0.883 0.16 fNDF (quadratic) - 2.96 1.02 <0.01 Palmitic (linear) 0.609 0.259 0.02 Palmitic (quadratic) - 1.86 0.416 <0.01 Stearic (linear) 1.61 0.831 0.05 Stearic (quadratic) - 1.20 0.349 <0.01 Linolenic 0.517 0.365 0.16 Starch*Linolenic - 0.86 0.475 0.07 1 fNDF = forage NDF, 2 Standard error 146 Supplemental Table 5.7. Effect of dry matter intake (SD) and diet composition (SD) on digestible energy intake (Mcal /d ) . Effect 1 Estimated Coefficient SE 2 P - value Intercept 96.0 1.47 <0.01 DMI 9.77 0.232 <0.01 Starch 2.84 0.688 <0.01 fNDF 0.278 0.788 0.72 Palmitic (linear) 0.205 0.449 0.65 Palmitic (quadratic) - 8.81 1.04 <0.01 Stearic - 3.68 0.444 <0.01 Oleic (linear) 5.11 0.791 <0.01 Oleic (quadratic) - 0.923 0.297 <0.01 Linoleic 5.93 0.793 <0.01 Linolenic (linear) 7.45 1.04 <0.01 Linolenic (quadratic) - 2.37 0.319 <0.01 DMI*fNDF 0.656 0.212 <0.01 Starch*Palmitic - 1.40 0.311 <0.01 Starch*Stearic - 2.93 0.965 <0.01 1 fNDF = forage NDF, 2 Standard error 147 Supplemental Table 5. 8 . Effect of dry matter intake (SD) and diet composition (SD) on digestible energy concentration (Mcal/kg of DM) . Effect 1 Estimated Coefficient SE 2 P - value Intercept 3.08 0.056 <0.01 DMI (linear) - 0.012 0.016 0.46 DMI (quadratic) - 0.014 0.004 <0.01 Starch 0.106 0.028 <0.01 fNDF 0.002 0.045 0.95 Palmitic (linear) 0.014 0.015 0.35 Palmitic (quadratic) - 0.142 0.025 <0.01 Stearic - 0.085 0.014 <0.01 Oleic (linear) 0.006 0.021 0.75 Oleic (quadratic) - 0.019 0.010 0.05 Linoleic (linear) 0.044 0.030 0.14 Linoleic (quadratic) - 0.142 0.034 <0.01 Linolenic (linear) 0.135 0.021 <0.01 Linolenic (quadratic) - 0.031 0.008 <0.01 DMI*fNDF 0.025 0.001 0.09 Starch*Oleic - 0.079 0.022 <0.01 1 fNDF = forage NDF, 2 Standard error 148 APPENDIX D Supplemental Figures 149 a) b) c) Supplemental Figure 5.1. Effect of the inclusion of dietary oleic (a), linoleic (b), and linolenic (c) on dry matter digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 55 60 65 70 75 80 50 100 150 200 250 300 350 Adj. DM digestibility, % Oleic, g/day 50 55 60 65 70 75 80 200 300 400 500 600 700 800 900 Adj. DM digestibility, % Linoleic, g/day 50 55 60 65 70 75 80 50 55 60 65 70 75 80 85 90 Adj. DM digestibility, % Linolenic, g/day 150 Supplemental Figure 5.2. Effect of the inclusion of dietary linolenic on NDF digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; stu dy 2: ; study 3: ; study 4: , and study 5: ). 20 30 40 50 60 50 55 60 65 70 75 80 85 90 Adj. NDF digestibility, % Linolenic, g/day 151 a) b) c) Supplemental Figure 5.3. Effect of the inclusion of dietary oleic (a), linoleic (b), and linoleni c (c) on FA digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 60 70 80 90 50 100 150 200 250 300 350 Adj. FA digestibility, % Oleic, g/day 50 60 70 80 90 200 300 400 500 600 700 800 900 Adj. FA digestibility, % Linoleic, g/day 50 60 70 80 90 50 55 60 65 70 75 80 85 90 Adj. FA digestibility, % Linolenic, g/day 152 a) b) c) Supplemental Figure 5.4. Effect of the inclusion of dietary oleic (a), linoleic (b), and linolenic (c) on 16 - carbon FA digestibility. Data points represent the adjusted for study effect individual observations and a re coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 60 70 80 90 50 100 150 200 250 300 350 Adj. 16 - C digestibility, % Oleic, g/day 50 60 70 80 90 200 300 400 500 600 700 800 Adj. 16 - C digestibility, % Linoleic, g/day 50 60 70 80 90 50 55 60 65 70 75 80 85 90 Adj. 16 - C digestibility, % Linolenic, g/day 153 Supplemental Figure 5.5. Effect of the inclusion of dietary linolenic on 18 - carbon FA digestibility. Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ) . 50 60 70 80 90 50 55 60 65 70 75 80 85 90 Adj. 18 - C digestibility, % Linolenic, g/day 154 a) b) Supplemental Figure 5.6. Effect of the inclusion of dietary oleic (a) and linoleic (b) on energy digestibility. Data points represent the adjusted for study e ffect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 50 60 70 80 90 50 100 150 200 250 300 350 Adj. Energy digestibility, % Oleic, g/day 50 60 70 80 90 200 300 400 500 600 700 800 900 Adj. Energy Digestibility, % Linoleic, g/day 155 Supplemental Figure 5.7. Effect of the inclusion of dietary linoleic on digestible energy intake (DEI, Mcal/d) . Data points represent the adjusted for study effect individual observations and are coded by the study (study 1: ; study 2: ; study 3: ; study 4: , and study 5: ). 20 40 60 80 100 120 200 300 400 500 600 700 800 900 Adj. Digestible energy intake, Mcal/Day Linoleic, g/day 156 Supplemental Figure 5.8. Effect of the inclusion of dietary linole ic on digestible energy intake (DEI, Mcal/kg of DM) . 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Dairy Sci. 101: 3110 - 3117. 161 ABSTRACT Our objective was to predict body fat, protein, ash, and water composition ( EBFat , EBProtein , EBAsh , and EBWater ) as a percentage of empty body weight ( EBW ) in heifers and cows using only data from Holsteins cattle . In order to accomplish our objective , we conducted a meta - regression analysis o f 129 treatment means from 26 peer - reviewed publications. Methods to determine composition included direct analysis of EBW, analysis of carcass or rib, and dilution of deuterium oxide or urea. Means and standard devia tions for the variables included in the analysis were 11 ± 5 % EBFat, 19 ± 2 % EBProtein, 4 ± 1 % EBAsh, 66 ± 4 % EBWater, 158 ± 122 kg EBW, and 0.77 ± 0.24 kg average daily gain ( ADG ) for heifers , and 22 ± 6 % EBFat, 16 ± 1 % EBProtein, 4 ± 1 % EBAsh, 60 ± 5 % EBWater, 479 ± 54 kg EBW, and 2.9 ± 0.4 body condition score ( BCS ) for cows. The first step was a mixed model with a random effect of study , fixed effects of method (direct, carcass, and dilution), stage (heifer and cow), and one of three possible ways to express EBW (4 th order polynomial of EBW - polEBW , natural logarithm of EBW - lnEBW , or EBW to the power of 0.75 EBW^0.75 ). Additionally, the models were weighted by the inverse of the standard deviation of each respective stud y . The models deri ved during the first step were named baseline. The second step involved adding the effects of ADG for heifers and BCS for cows to the baseline models. To evaluate the se models, we perform ed cross - validation s within the dataset to select the best fitting mo dels based on the concordance correlation coefficient ( CCC ), mean square error of prediction ( MSEP) , its decomposition, and root MSEP ( RMSEP ). Based on the cross - validation, the best fitting models were the ones developed using lnEBW. The proposed heifer m odels for EBFat and EBProtein were: EBFat = - 162 6.0 + 1.37*lnEBW 15.3*ADG + 5.23*lnEBW*ADG (CCC=0.88, RMSEP=0.99); EBProtein = 23 1.12*lnEBW (CCC=0.59, RMSEP=1.43). The proposed cow models for EBFat and EBProtein were: EBFat = 1.6 + 6.9*BCS (CCC=0.92, RMS EP=2.1); EBProtein = 21 1.9*BCS (CCC=0.88, RMSEP=0.54). T he proposed models were further used to determine energy and protein requirements for growth and for EBW change in mature animals. The proposed models suggest that the energy requirement for growth is less for older heifers and more for younger he ifers than what the NRC 2001 predicted . INTRODUCTION The literature contains many papers showing the importance of having a well - designed growth program for replacement heifers due to its impact on future milk production and the economics associated with milk production (Van Amburgh, 2017; Bach, Khan, and Miller - Cushon, 2017; Hoffman, 2017; Overton and Dhuyvetter, 2017). McCandlish (1922) was one of the first to publish a review showing the effects of age of cow, gestation period, the season of freshening, birth weight of calves, and rate of growth on grow th and nutrition of dairy calves. In th at paper, the author emphasized the relationship between nutrition and average daily gain ( ADG ). S ince then , many s tudies have focused on better understanding the relationship between nutrition and ADG, as well as their effect on mammary gland development and future milk production ( Radcliff et al , 2000; Lammers, Heinrichs, and Kensinger, 1999; Radcliff et al., 2000 ; N RC, 2001; Moallen et al ., 2004; Shamay et al. , 2005 ; Davis Rincker et al , 2008 ). T wo requirements must be considered in diet formulation for growing animals : requirements for maintenance and requirements for growth (NRC, 2001). Requirements for maintenance can be determined experimentally using metabolic chambers , while requirements 163 for growth can be determined based on body composition during growth. Accordingly, different rates of growth can be achieved by supplying the energy and protein requi red for each specific rate of growth. As animals achieve maturity, change s in body composition primarily reflect depletion or repletion of tissues when diets provide insufficient or excess energy (NRC, 2001) . By appropriately predicting the changes in body composition with changes in body condition score , we can better account for the amount of energy associated with changes in the body weight o f mature animals. Thus , the prediction of body composition is a crucial step in determining the energy and protein requirements for growing animals and deposition of energy in mature animals. Howeve r, there are no prediction models for body composition in dairy breeds derived primarily with data collected in dairy breeds . The NRC (2001) model for energy and protein re quirements for growth of replacement calves and heifers, and body composition at different body condition scores ( BCS ) for mature animals was developed based on Fox et al. (1999), which adjusted the Beef NRC (1996) body composition model to dairy breeds by using a size scal e approach. The size scale approach assumes that the chemical composition of gain is similar among animals at the same proportion of mature BW (NRC, 2001), but this may not be true in dairy and beef cattle . In the past 20 years new data collected in Holstein animals have become available. We hypothesize d that new prediction models for body composition derived from more recent data collected using Holstein cattle w ould better fit the current dairy production system and provide better predi ctions of energy and protein retention during growth. Our objective was to derive prediction models for body composition by performing a meta - regression of data from Holstein cattl e so that we can use these models to determine net energy and net protein 164 re quirements for growth o f replacement heifers and the energy retained or lost with change s in empty body weight ( EBW ) in mature animals. MATERIALS AND METHODS Literature search and selection of peer - reviewed manuscripts We used Google Scholar (https://schol ar.google.com/), PubMed (https://www.ncbi.nlm.nih.gov/pubmed/), and Science Direct (http://www.sciencedirect.com/) search engines to search for peer - reviewed manuscripts that contain ed data f or body composition in dairy c attle . The search terms included oxide - 40 liquid , The search for manuscripts was performed during August 2017 to March 2018 and included manuscripts published until February 2 018. Additionally, we used publications cited in NRC (2001). The study inclusion criteria were (1) peer - reviewed manuscript published in English, (2) body composition measured in dairy cattle breeds, (3) reported body weight ( BW ) or EBW, (4) reported ADG a nd BCS for growing and mature animals, respectively, and (5) at least one of the following: body water composition, body fat composition, body protein composition, and body ash composition (with respective measurement of the error around the mean). Only ma nuscripts that satisfied the inclusion criteria were used. We also included data from a PhD dissertation (Meyer , 2007 ) because it contains relevant data. Data base In total, we found 31 studies that published data on dairy breeds including Holstein or European Friesian (26 studies), Jersey (2 studies), and Holstein cross - breed s (1 study) animals 165 published between 1986 and 2017 . Due to the lack of data available in regards to breeds other than Holstein, we decided to l imit this study to Holstein cattle a nd removed the three studies performed with Jersey and cross - breed cattle . After further narrowing the database only to in cl ude studies that reported the variables needed to perform the meta - regression, 26 studies remained that together reported 129 treatm ent means. The body composition was determined using carcass composition ( n = 3 studies ) , deuterium oxide ( n = 7 studies), EBW composition ( n = 18 studies), potassium - 40 liquid scintillation detection ( n = 1 study), rib composition ( n = 1 study), and urea dilution ( n = 5 studies). These techniques are explained at Radcliff et al . ( 1997), Martin and Ehle ( 1986), Donnelly and Hutton (1976) , Belyea et al . ( 1978), Davis Rincker et al . ( 2008), Swartz et al . ( 1991) , respectively . The se metho d s were categorized as : direct (EBW composition), carcass (carcass composition and rib composition), and dilution (deuterium oxide, potassium - 40 liquid, and urea). The variables included in the database were: study, treatment, method used to determine bod y composition, statistical method used in each corresponding study (fixed effect or mixed model), stage (growth or mature), year of publication (from 1986 to 2017) , length of the study (days), sex, BW, EBW , BCS, ADG, age (days), EBWater, EBFat, EBProtein, EBAsh, and whether standard error of the mean ( SEM ), standard error of the difference ( SED ), or root mean square error ( RMSE ) were reported. In addition to the se variables, we calculated the fat - free mass ( FFM ) as a percentage of EBW and lifetime ADG ( ltAD G ) as kilograms per day . Fat - free mass as % of EBW was calculated according to the following formula: FFM = 100 EBFat; the SEM for the computed FFM was assumed to be equal to the SEM of EBFat adjusting to the same coefficient of variance for both variabl es. Lifetime ADG was calculated according to the 166 following formula: ltADG = (EBW - 40)/age at the end of the experiment , assuming an average birth EBW of 40 kg (Hickson et al. , 2015) . A summary of the variables included in the database is provided in Table 6.1. T o have a standard measurement of the error around the mean across all 26 studies, when necessary, we adjusted the reported error to be comparable to the SEM as suggested on Roman - Garcia et al. (2016). Then, for the statistical analysis, the SEM was t runcated at half of the mean SEM (Firkins et al ., 2001). Finally, since fixed effect models tend to have higher SEM (Littell et al. , 1998), within each statistical method (fixed effect and mixed model), the SE M was standardized to the mean o f their respect ive distributions (Roman - Garcia et al. , 2016). Model derivation To derive the prediction equations for body composition in Holstein animals , a 2 - step meta - regression using SAS PROC MIXED (SAS Institute inc., Cary, NC) was performed. D uring the first step, we developed three possible baseline models that used three different ways to express the covariate EBW (4 th order polynomial of EBW - polEBW , natural logarithm of EBW lnEBW , or metabolic EBW EBW^0.75 ) is presented on [Equation 6.1] . Also, the models were weighted by the inverse of the standardized SEM as explained above. [6.1, baseline] 167 where ( i = method, j = stage, and k = study) is the observed EBWater, EBFat, EBProtein, EBAsh, or FFM; , , and are the partial coefficients corresponding to the intercept, method ( i = direct, carcass, or dilution), stage ( j = growing or mature), EBW (polEBW, lnEBW, or EBW^0.75), respectively; , , and are the partial coefficents correspon d ing to the 2 - way interactions between the covariates ; are the fourth - order polynomial terms for the effect of Year; is the random effect of study ( k = 1 to 26); and is the error term. During the second step, the baseline was a djusted to the fixed effect of ADG and age at the mid point of each experiment ( MidAge ) for heifers and adjusted to the fixed effect of BCS for cows. The ADG, MidAge, and BCS were included using a 4 th order polynomial and possible 2 - way interactions. As des cribed in step one, models contained the random effect of study and were weighted by the inverse of the standardized SEM. The models used on the second step for heifers and cows are presented in [Equation 6.2] and [Equation 6.3], respectively. [6.2, heifers] where ( k = study) is the observed EBWater, EBFa t, EBProtein, EBAsh, or FFM; , , and are the partial coefficients corresponding to the intercept, predicted body composition using the baseline ( Equation 6.1, b = polEBW, lnEBW, and EBW^0.75), 4 th order polynomial on ADG, and the 4 th 168 order polynomial on MidAge, respectively; , , and are the partial coefficents corresponting to the 2 - way interactions between the covaviates; is the random effect of study ( k = 1 to 19); and is the error term. [ 6. 3, cows] where ( k = study) is the observed EBWater, EBFat, EBProtein, EBAsh, or FFM; , , and are the partial coefficients corresponding to the intercept, predicted body composition using the baseline ( Equation 6. 1, b = polEBW, lnEBW, and EBW^0.75), and the 4 th order polynomial on BCS, respec tively; the partial coefficents corresponting to the interaction between the covaviates; is the random effect of study ( k = 1 to 7); and is the error term. Finally, models were subjected to backward elimination to remove nonsignificant variables. During this process, the covariate with the highest nonsignificant P - value was removed during successive runs until only significant effects remained in the model ( P < 0.05). Nonsignificant terms that had significant interaction or higher polynomial order were not removed from the model. Once the final models were defined, we checked for multicollinearity among variables using the variation inflation factor ( VIF ) test ; the cutoff used to determine collinearity for main effects was a VIF greater than 10 and for interactions was VIF greater than 100. For all the models, residuals were analyzed using the SAS PROC UNIVARIATE (SAS 169 Institute inc., Cary, NC) ; normal quantiles plot s , distribution and probability plot s , and studentized residual s were considered for detecting outliers . Data points were only removed if they were considered outliers in at least two of these methods analyses described above, where the cutoff for stu dentized residuals was ± 3.5 SD. Model e valuation Finally, the precision and accuracy of the final models were assessed by 5 - fold cross - validation with 20 random repetitions as described in De Souza et al . ( 2018 ) . The fit statistic parameters calculated we re: mean bias, slope bias, concordance correlation coefficient ( CCC ), the mean square error of prediction ( MSEP ), root mean square error of prediction ( RMSEP ), and decomposition of MSEP (mean bias, slope bias, and random error). T he fit statistics parameters were analyzed to determine the best way to express EBW (polEBW, lnEBW, expEBW), using the PROC GL I MMIX procedure of SAS v.9. 4 (SAS Institute Inc., Cary, NC) according to the following model [Equation 6.4]: [6.4] where is one of the fit statistic s of interest; is the overall mean; is the random effect of fold ( i = 1 to 100); is the fixed effect of stage ( s = growing or mature); is the fixed effect of corresponding EBW ( j = polEBW, lnEBW, or expEBW), and is the residual error. Similarly, to the test of [Equation 6.4] , we compared the models using ADG and ltADG. However, in this model, there was no effect of stage be cause only the models developed for heifers had the effect of ADG or ltADG. 170 Energy and protein requirements for growth in heifers and net energy provided by the change in body condition score in cows Once chosen , the proposed models EBFat and EBProtein wer e used to determine net energy and net protein requirement s for growth ( NE g and NP g , respectively) in heifers and net energy associated with the change i n BCS of cows. For energy calculation s we assumed that fat and protein contain 9.29 and 5.55 Mcal of energy per kilogram, respectively , as their chemical energy composition (NRC, 2001). The NP g was calculated as the protein content of the gain. RESULTS Model derivation Step 1 Baseline The effects of body composition measurement method (direct, carcass, and dilution) were not significant ( P > 0.15) for EBFat, EBProtein, EBAsh, and FFM regardless of BW expression. For EBWater, significance of measurement method was P < 0.01, P < 0.01, and P = 0.03 for the 3 ways of expressing EBW (polEBW, lnEBW, and EBW ^ 0.75). The effect of stage was not statistically significa n t as a covariate for body composition except for two cases. Stage was significant in models that used polEBW . S tage also was signi ficant fo r EBProtein ( P < 0.01) regardless of EBW expression, and, with stage in the model, EBW was not significant ( P > 0.3) . However, w ithout stage in the model, EBW was significant ( P < 0.02 for all expressions of EBW ). W hen the residual plots from both models for EBProtein 171 (with stage or with EBW) were compared , the model using stage consistently overpredict ed EBProtein in older heifers, whereas the model using EBW had an unbiased residual. Thus , we decided to use the model with EBW and not with the sta ge. For EBWater, EBFat and FFM, there was no effect of the stage ( P > 0.05). Without stage in the model, EBW was a significant covariate for body composition regardless of expression method (polEBW, lnEBW, and EBW^0.75) except for EBash ( P > 0.08 for all m odels). M odels that contained polEBW used the quadratic term for EBW to determine EBWater, EBFat, and FFM ( P < 0.02 for all linear and quadratic terms ) , whereas only the linear term was used for EBProtei n ( P = 0.01). Both lnEBW and EBW^0.75 were significan t covariates for EBW on EBWater, EBFat, EBProtein, and FFM ( P < 0.02 for all terms) . The effect of year on body composition was not significant in any of the models. However, animals increased i n b ody size throughout the years . Step 2 Using th e term for Mi dAge along with ADG or ltADG and the predicted value from the baseline caused multico l linearity problem s (VIF greater than 10 for all models). MidAge was th e variable with greate st VIF, a fter removing MidAge, the multico l linearity problem was re solved, and the VIF for the rema in ing variables was less than 10 . For both ADG and ltADG, none of the models used higher order polynomials. W hen the effect of ADG or ltADG w as significant, it interact ed linearly with the predicted value from the baseline. The eff ects of ADG and ltADG were similar for most models and differed only for EBWater when using polEBW. For EBWater, u sing ADG yield ed a significant effect of the 172 interaction between predicted values from the baseline and ADG ( P < 0.01). Using ltADG resulted in an interaction that was not significant ( P = 0.18). The interaction between ADG or ltADG and the baseline predictions was significant for EBFat and FFM regardless of EBW expression. This interaction was also significant for EBProtein and EBWater except for the model using polEBW and ltADG. For the EBAsh models, none of the fixed effects (predicted values fro m the baseline, ADG or ltADG, an d interaction) were significant ( P > 0.05). The effect of BCS was linearly significant for EBWater, EBFat, EBProtein, and FFM (all with P < 0.01) but not EBAsh, and none of the models had higher order polynomials. In addition , the interactions between the baseline predicted value from the baseline and BCS were significant. For the models develop ed using lnEBW , neither the main effect of lnEBW or the interactions with the baseline predictions were significant. However , for models developed with polEBW and EBW^0.75 interactions of BCS and the baseline predictions were significant. Model evaluation The strategy used to eva luate the proposed models was to compa re the main effect of the three possi ble ways to express EBW ( polEBW, lnEBW, and EBW^0.75) to the stage - specific (heifers and cows) performance using the interaction between stage and EBW. Although the main effect of t he stage was signific ant ( P < 0.05) for most of the fit statistics for all body compositions . The comparison is unfair because of the substantial difference between the 173 number of observations between both stages (Table 6.1) ; and therefore, we will not disc uss the main effect of the stage. First, analyzing the fit statistics of the baseline models, the models using lnEBW outperformed the models using polEBW and EBW^0.75 for all body composition terms (EBWater, EBFat, EBProtein, EBAsh, and FFM) on the majorit y of the fit statistics analyzed (mean bias, slope bias, CCC, MSEP, decomposition of MSEP, and RMSEP data not shown). Although the final decision on which expression of EBW yielded best predictions of body composition was based on the models created on s tep 2, this indicates that EBW should be expressed using lnEBW. On the evaluation of the models generated on step 2, EBWater, EBFat, EBProtei n, EBAsh, and FFM (Tables 6.2 , 6. 3 , 6. 4 , 6. 5 , and 6. 6 , respectively) , there were smaller effect of the expression s of EBW than th ose observed in the baseline analyse s. However, comparing the models generated on step 2 for heifers, the model using lnEBW outperform ed the EBW^0.75 on EBWater, EBFat, EBProtein, and FFM. As an alternative, the polEBW was bet ween the other two models. Since there were no effect s of EBW on EBAsh (lnEBW, polEBW, and EBW^0.75, P > 0.05 for all) , the covariates representing EBW were removed from the EBAsh models . For the cow data, the effect of expression of EBW were not significant for all body composition terms regardless of the expression used (lnEBW, polEBW, and EBW^0.75, P > 0.05 for all) , and, therefore, the ef fect s of EBW were removed from all models. Furthermore, our ultimate goal was to calculate the NE g and NP g which use only the models developed for EBFat and EBProtein. For EBFat, models derived using lnEBW and polEBW had similar performance on the model evaluation analysis. However, lnEBW 174 outperformed EBW^0.75 for CCC (0.88 vs 0.86, P = 0.04; respectively), MSEP (0.99 vs 1.66, P < 0.01, respectively), and RMSEP (0.99 vs 1.29, P < 0.01; respectively); whereas polEBW and EBW^0.75 did not differ ( P > 0.05, for all fit statistics). For EBProtein, lnEBW was the only model to have a slope bias not different from zero (0.089, P = 0.17), whereas polEBW and EBW^0.75 had significant slope bias ( - 0.73 and - 0.97, P < 0.02; respectively). Additionally, polEBW had lower MSEP than polEBW and EBW^0.75 (2.11, 3.14, and 4.23, P < 0.05 for all comparisons; respectively) and lower RMSEP than polEBW and EBW^0.75 (1.43, 1.75, and 2.03, P < 0.05 for all comparisons; respectively). Because lnEBW was overall as good or better than the alternatives in model fit, and because lnEBW result s in equations for body composition that can be easily converted to equations for determining the composition of gain , we selected the models developed using lnEBW for our proposed models. Finally, we found no difference in the 100 - fold cross - validation mo del fit when we compared ADG with ltADG in the body composition model for heifers (data not shown). Because ADG and ltADG had similar value as covariates, and because we did not know the actual birth weight of the animals used in the analysis, we selected the models using reported ADG for our proposed models. Proposed models for body composition . As described previously, we use d lnEBW and reported ADG in our final proposed models of body composition and retained energy associated with growth or body condition change . Retained energy and protein are equivalent to the Net Energy and Net Protein requirements for growth or body condition change. 175 The EBWater model was the only model for which method to determine body composition was significant . T he es timated partial regression coefficients for direct, carcass and dilution were 0.00 ± 0.00, 0.442 ± 0.408, and - 3.79 ± 1.93, respectively , and these coefficients were added to the intercept using a weighted average based on the number of observations genera ted by each method (direct = 61, carcass = 24, and dilution = 43). Following are the proposed models for body composition in heifers (EBWater, EBFat, EBProtein, EBAsh, and FFM; Equations 6.5, 6.6, 6.7, 6.8, and 6.9, respectively) and the proposed models for body composition in cows (EBWater, EBFat, EBProtein, EBAsh, and FFM; Equations 6.10, 6.11, 6.12, 6.13, and 6.14, respectively). The baseline models developed on the first step of the modeling process are presented in Table 6. 7 and figures are presented in Supplementary Material 6.1, 6.2, 6.3, 6.4, and 6.5. [6.5, heifers] [6.6, heifers] [6.7, heifers] 176 [6.8, heifers] [6.9, heifers] [6.10, cows] [6.11, cows] [6.12, cows] [6.13, cows] [6.14, cows] where is the natural logarithm of empty body weight (kg), is the average daily gain (kg/d), and is body condition score (scale 1 5). 177 Based on the proposed models, we calculated the NE g and NP g (Table 6. 8 and 6. 9 , respectively) and net energy provided per kilogram of EBW change as a function of BC S (Table 6.10 ). Additiona l ly, the NE g and NP g calcul a ted using the base model are presented on Supplementary Material ( Supplemental Table 6.1 and Supplemental Table 6.2, respectively). DISCUSSI ON Most systems to determine body composition in dairy cattle assume that cattle from different breeds have similar body composition at a given level of matur ity ; and therefore, they use a size - scal ing approach to adjust body composition across breeds (NRC, 2001; CSIRO, 2007; INRA, 2007; CNCPS Fox and Van A mburgh, 2003). Because data on body composition of dairy cattle was limited, the size - scaling approach was a reasonable method to predict their bod y composition . However, data used to develop the size - scaling approach came mostly from steers of beef breeds being fed typical high grain feedlot diets (Beef NRC, 1996) ; based on our results, we suggest that even after size - scaling, these systems do not accurately represent body composition in dairy heifers . Cattle fed high grain diets in feedlots deposit more fat per unit BW than the typical dairy heifer fed a higher forage diet or a diet at restricted intake for slower growth . Our proposed models for growing animals are considerably different from the system suggested in the NRC (2001). Body composition in heifers and net energy and net protein requirements for growth The EBW and ADG for heifers ranged from 25 kg and 0.150 kg /d to 350 kg and 1.27 kg / day , respectively. Within this range, our proposed models suggested that EBWater (Equation 6.5, Figure 6.1) decreases as lnEBW (estimated coefficient: 0.391 ± 0.023, P < 0.01) and ADG 178 (estimated coefficient: 14.5 ± 2.24, P < 0.01) increase , with a negative interaction (estimated coefficient: - 5.41 ± 0.280, P < 0.01) between the covariates. In contrast, EBFat (Equation 6.6, Figure 6.2) increases as lnEBW (estimated coefficient: 1.37 ± 0.026, P < 0.01) and ADG (estimated coefficient: - 15.3 ± 0.438, P < 0.01) increase , with a positive interaction (estimated coefficient: 5.23 ± 0.034, P < 0.01) between the covariates. Whereas, EBProtein (Equation 6.7, Figure 6. 3) decreases as lnEBW (estimated coefficient: - 1.12 ± 0.275, P < 0.01) increase. The EBAsh (Equation 6.8, Figure 6.4) were fixed at 3.81% ± 0.303 ( P < 0.01), respectively. Finally, the FFM had a very similar pattern to EBWater. The FFM (Equation 6.9, Figure 6.5) decreases as lnEBW (estimated coefficient: - 3.04 ± 0.027, P < 0.01) and ADG (estimated coeffic ient: 8.67 ± 3.25, P < 0.01) increase , with a negative interaction (estimated coefficient: - 3.52 ± 0.030, P < 0.01) between the covariates. Analyzing the fit statistics parameters, the EBWater, EBFat, and FFM models with the effect of both lnEBW and ADG had CCC values of 0.85, 0.88, and 0.87, respectively; RMSEP values of 2.02 (3.05% of the observed mean), 0.99 (9.12% of the observed mean), and 2.27 (2.55% of the observed mean), respectively; and most of the MSEP associated with the random error (87, 9 2, and 92%, respectively). The EBProtein with only the effect of lnEBW had CCC of 0.59, RMSEP of 1.43 (7.73% of the observed mean), and 89% of the MSEP associated with the random error. The EBAsh was a fixed value and had CCC of 0.41, respectively; RMSEP o f 0.93 (24.3% of the observed mean), respectively; and 82% of the MSEP associated with the random error. 179 Although, to the best of our knowledge, there are no formal recommendations for the model evaluation parameters in the literature, our goal was to have CCC > 0.85, RMSEP < 10% of the observed mean and MSEP associated with the random error > 90% (personal communication Dr. Eremias Kebreab) . Within these goals, the EBWater, EBFat, and FFM surpassed our thresholds and are considered proper prediction mode ls. The EBProtein had CCC lower than our threshold. However, this was expected because of the small effect of lnEBW on EBProtein , and the proposed model seems appropriate considering the low RMSEP. The EBAsh was the model with the worst fit statistics para meters. In this regard, the EBAsh did not achieve the thresholds established for the fit statistic parameters. However, since the EBAsh is not used in the calculations to determine the NE g and NP g , this did not impact the application of the proposed model in the calculation of NE g and NP g . With respect to the requirements, we used the proposed models to determine the composition of the tissue deposited during the growth (Figure 6.6 ) and based on its composition we calculated the NE g and NP g . The NE g and NP g are dependable on the EBW and ADG (Table 6. 8 and 6. 9 ) . H owever , the effect of EBW is much greater for NE g than NP g . In order to compare the requirements calculated using the proposed model and the requirements suggested in the NRC 2001, we created three g rowth programs for replacement heifers based on the ADG and EBW observed in our database (Figure 6.7 and 6.8). The three scenarios were restricted, normal, and elevated. These scenarios allow for different ADG according to the EBW, wherein all scenarios t he EBW varied from 40 to 400kg and the ADG ranged from 0.164 to 0.817 kg, 0.215 180 to 0.990 kg, and 0.250 to 1.188 kg for the scenarios restricted, normal, and elevated, respectively. The assigned ADG for each scenario w as based on the ADG in our database. Af ter comparing the proposed models to the NRC (2001), the proposed model starts with higher NE g and lower NP g than the NRC (2001). In contrast, as the animals grow the proposed model suggests lower NE g and higher NP g than the NRC (2001). Whereas, for NE g , differences between models were even higher in the scenarios restricted and normal (Figure 6.7). Regarding the NP g , the NRC (2001) requirements become flat after 200 kg EBW, and after 400 kg EBW achieves a plateau. On the proposed model, since lnEBW had a small impact on EBProtein the calculated NP g using the proposed model increases as we increased the ADG and the EBW (Figure 6.8). The fact that NRC (2001) suggested a much faster increase i n the NE g than the proposed model did implies that , on the NRC (20 01) system , heifers were depositing more fat and less protein than on the proposed model at any given ADG and EBW levels. This difference may be due to the NRC (2001) roots i n the Beef NRC (1996), in which it is expected that steers from beef breeds fed feedlot diets will gain more fat than dairy heifers fed typical dairy - replacement diets. This is supported by the fact that, as we increased the ADG , both systems become more similar in this case, dairy heifers fed to have high ADG become more similar to steers in a feedlot. Body composition in cows and net energy per kilogram of empty body weight change Analyz ing the models derived for cows that started with the baseline using lnEBW indicates that the effect of predicted value from the baseline was not significa nt for any of the body composition variables (EBWater, EBFat, EBProtein, EBAsh, and FFM) . The natural 181 logarithm function used in the baseline suggest s a minimal effect of EBW on body composition for animals with EBW greater than 450 kg . S ince the majority of our cow data is above 450 kg EBW we expected that the baseline derived using lnEBW would not be significant for cows as shown by the proposed models. Our data supported the NRC (2001) finding that body composition in cows is related only wit h BCS, and not with EBW. According to our data, for a 1 - unit increase in BCS the EBWater, EBProtein, and FFM decrease 4.98 (± 0.312), 1.89 (± 0.266), and 7.02 (± 1.09), respectively; whereas EBFat increases 6.91 (± 0.117) and EBAsh is fixed at 4.49 (± 0.16 7) (Figures 6.9, 6.10, 6.11, 6.12, and 6.13). These changes are very similar to the ones proposed in the NRC (2001); except for EBAsh, where the proposed model does not change the EBAsh content, and the NRC (2001) decreases EBAsh by 0.44% per 1 - unit increa se on BCS. Although the changes in body composition associated with the change in BCS on both the NRC (2001) and the proposed model are similar, the initial values (BCS equals to 1) for body composition are different on both models, especially for EBFat an d EBProtein. The proposed model starts with 8.48 EBFat and 19.1% EBProtein , and the NRC (2001) starts with 3.77 EBFat and 19.4% EBProtein (Table 6.10 ). Accordingly, the models differ on the energy content per kilogram of EBW change . T he proposed model sugg ested that the energy content ranged from 6.67 to 8.16 Mcal/kg of EBW change, assuming that a cow with BCS of 3 has a BW of 700 kg and the BW change 9.7% per 1 - unit change in BCS (calculated based on the data used to derive the equations) (Table 6.1 0 ) . T he NRC (2001) ranged from 5.14 to 9.59 Mcal/kg of EBW change. 182 Finally, it is essential to consider the limitation of our database on cows. First, from the six studies used in our analysis, four studies used dilution techniques to determine body composition ; and therefore, our analysis is prone to errors associated with dilution techniques. Second, although the BCS ranged from 2.1 to 3.9 which is likely the range of BCS observed in dairy farms the majority of the data came from cows with BCS between 2.5 an d 3.0 (lower and upper quartiles) ; and therefore, the variation on BCS was very small. Given this information , the proposed models must be used with caution, and additional data is required to derive prediction equations for body composition in cows correc tly. CONCLUSIONS Our analysis supports that the fat content of gain, and thus the energy content of gain, is higher for youn g heifers and less for older heifers than that suggested by NRC 2001. The differences between the proposed and NRC (2001) models for heifers may be because NRC (2001) used the size - scaling method to adjust a model derived for beef cattle to dairy cattle. In contrast, the proposed model was derived exclusively from data collected i n Holsteins. Concerning the composition of cows, we founded similar changes in body composition per 1 - unit change in BCS to the NRC (2001). However, the starting body composition (BCS 1) differ between both models. By starting with higher EBFat, the proposed models suggest higher energy content per kilo gram of EBW change at low BCS than the NRC (2001). However, as BCS increase, the NRC (2001) implies greater energy content per kilogram of EBW change than the proposed model. 183 APPENDICES 184 APPENDIX A Tables 185 Table 6. 1. Descriptive summary of the quantitative variables included in the database . Heifers Cows count mean SD 1 count mean SD 1 Body Composition, % of EBW 2 Water 79 66.2 4.09 21 60.2 4.85 Fat 88 10.9 5.00 36 21.8 6.01 Protein 91 18.5 1.58 37 15.9 1.28 Ash 81 3.81 1.13 21 4.49 1.07 Fat - free mass 88 89.0 5.00 36 78.2 6.02 EBW 2 , kg 91 158 122 37 479 54 ADG 3 , kg 91 0.775 0.235 - - - ltADG 4 , kg 91 0.593 0.286 - - - MidAge 5 , d 91 258 243 - - - BCS 6, 1 to 5 - - - 37 2.87 0.44 1 Standard deviation, 2 Empty body weight, 3 Average daily gain reported in the experiment, 4 Lifetime average daily gain, 5 Age at the middle of the experiment, 6 Body condition score 186 Table 6. 2 . Model evaluation through 100 - fold cross - validation for water composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . Fit Statistic Heifers Cows SEM 4 P - value polEBW 1 lnEBW 2 EBW^0.75 3 polEBW 1 lnEBW 2 EBW^0.75 3 Model Stage Model*Stage Mean observed, % 66.2 60.2 - - - - Mean predicted, % 66.4 66.4 66.4 60.3 60.2 59.9 0.165 0.35 <0.01 0.55 Mean bias - 0.283 bB - 0.236 aB - 0.296 bA - 0.101 aB - 0.041 aB 0.286 bA 0.059 <0.01 <0.01 0.01 Slope bias - 0.048 aB - 0.014 aA - 0.079 aC 0.120 cB - 0.098 bA - 0.234 aC 0.035 <0.01 0.40 <0.01 CCC 5 0.86 aA 0.85 aA 0.82 aB 0.77 bA 0.85 aA 0.71 cB 0.020 <0.01 <0.01 0.02 MSEP 6 4.26 aA 4.21 aA 5.36 bB 2.26 bA 1.54 aA 3.77 cB 0.166 <0.01 <0.01 <0.01 Decomposition of MSEP, % of MSEP Mean bias 6.75 6.58 5.72 20.9 20 23.2 1.85 0.82 <0.01 0.50 Slope bias 8.34 AB 6.44 A 10.4 B 27.9 AB 23.1 A 32.6 B 1.99 <0.01 <0.01 0.38 Ra n dom error 84.9 aAB 87.0 aA 83.9 aB 51.2 aAB 56.8 aA 44.2 bAB 2.24 <0.01 <0.01 0.09 RMSEP 7 2.04 aB 2.02 aA 2.27 bC 1.44 bB 1.20 aA 1.79 cC 0.045 <0.01 <0.01 <0.01 1 Empty body weight expressed as a polynomial, 2 Empty body weight expressed as natural logarithm, 3 Empty body weight expressed to the power of 0.75, 4 Standard error of the mean across all models, 5 Concordance correlation coefficient, 6 Mean square error of prediction, 7 Square root o f the mean square error of prediction, 8 Different uppercase letters in the same row represent differences among models across stages (main effect of model), 9 Different lowercase letters in the same row represent difference within stage (interaction between m odel and stage) 187 Table 6. 3 . Model evaluation through 100 - fold cross - validation for fat composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . Fit Statistic Heifers Cows SEM 4 P - value polEBW 1 lnEBW 2 EBW^0.75 3 polEBW 1 lnEBW 2 EBW^0.75 3 Model Stage Model*S tage Mean observed, % 10.9 21.8 - - - - Mean predicted, % 11.1 a 11.1 a 11.2 a 20.1 a 20.1 a 19.5 b 0.167 0.14 <0.01 0.11 Mean bias 0.158 aA 0.136 aA 0.158 aB - 0.020 aA - 0.021 aA 0.573 bB 0.061 <0.01 0.60 <0.01 Slope bias - 0.010 aA 0.006 abAB 0.039 bB 0.026 aA 0.021 aAB - 0.049 bB 0.014 <0.01 0.28 <0.01 CCC 5 0.87 abA 0.88 aA 0.86 bB 0.92 aA 0.92 aA 0.87 bB 0.007 <0.01 <0.01 <0.01 MSEP 6 1.28 abA 0.99 aA 1.66 bB 4.68 aA 4.47 aA 8.12 bB 0.208 <0.01 <0.01 <0.01 Decomposition of MSEP, % of MSEP Mean bias 3.92 a 3.34 a 3.59 a 10.5 a 10.41 a 13.7 b 1.02 0.27 <0.01 0.11 Slope bias 4.74 4.61 5.32 13.2 12.6 12.5 1.27 0.94 <0.01 0.87 Ra n dom error 91.3 92.0 91.3 76.3 77.1 73.8 1.46 0.44 <0.01 0.58 RMSEP 7 1.13 abA 0.99 aA 1.29 bB 2.11 aA 2.06 aA 2.79 bB 0.044 <0.01 0.31 <0.01 1 Empty body weight expressed as a polynomial, 2 Empty body weight expressed as natural logarithm, 3 Empty body weight expressed to the power of 0.75, 4 Standard error of the mean across all models, 5 Concordance correlation coefficient, 6 Mean square error of prediction, 7 Square root of the mean square error of prediction, 8 Different uppercase letters in the same row represent differences among models across s tages (main effect of model), 9 Different lowercase letters in the same row represent difference within stage (interaction between model and stage) 188 Table 6. 4 . Model evaluation through 100 - fold cross - validation for protein composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . Fit Statistic heifers cows SEM 4 P - value polEBW 1 lnEBW 2 EBW^0.75 3 polEBW 1 lnEBW 2 EBW^0.75 3 Model Stage Model*Stage Mean observed, % 18.5 15.9 - - - - Mean predicted, % 18.5 18.5 18.7 16.0 16.0 15.9 0.0.45 0.06 <0.01 0.74 Mean bias 0.060 A 0.088 A 0.135 B - 0.097 A - 0.006 A 0.038 B 0.036 0.02 <0.01 0.63 Slope bias - 0.727 bB 0.089 aA - 0.969 cC - 0.460 bB 0.011 aA - 0.456 bC 0.043 <0.01 0.33 <0.01 CCC 5 0.56 aB 0.59 aA 0.66 bB 0.59 cB 0.88 aA 0.68 bB 0.021 <0.01 <0.01 <0.01 MSEP 6 3.14 bB 2.11 aA 4.23 cC 1.48 bB 0.32 aA 1.60 bC 0.081 <0.01 <0.01 <0.01 Decomposition of MSEP, % of MSEP Mean bias 5.68 5.11 4.72 10.8 11.4 9.91 1.06 0.59 <0.01 0.83 Slope bias 17.7 B 5.81 A 21.4 C 22.5 B 11.7 A 25.8 C 1.67 0.03 <0.01 0.17 Ra n dom error 76.6 B 89.1 A 73.9 C 66.7 B 76.9 A 64.3 C 1.71 <0.01 <0.01 0.27 RMSEP 7 1.75 bB 1.43 aA 2.03 cC 1.19 bB 0.54 aA 1.23 bC 0.025 <0.01 <0.01 <0.01 1 Empty body weight expressed as a polynomial, 2 Empty body weight expressed as natural logarithm, 3 Standard error of the mean across all models, 4 Empty body weight expressed to the power of 0.75, 5 Concordance correlation coeffic i ent, 6 Mean square error of prediction, 7 Square root of the mean square error of prediction, 8 Differ ent uppercase letters in the same row represent differences among models across stages (main effect of model), 9 Different lowercase letters in the same row represent difference within stage (interaction between model and stage) 189 Table 6. 5 . Model evaluation through 100 - fold cross - validation for ash composition by stage (heifers and cows) . Fit Statistic Heifers Cows SEM 1 Mean observed, % 3.81 4.49 - Mean predicted, % 3.81 4.49 0.031 Mean bias - 0.013 - 0.048 0.0030 Slope bias 0.365 - 0.426 0.126 CCC 2 0.41 0.42 0.037 MSEP 3 0.881 0.2578 0.063 Decomposition of MSEP, % of MSEP Mean bias 5.14 23.6 1.66 Slope bias 12.8 23.7 2.44 Ra n dom error 82.1 52.7 2.27 RMSEP 4 0.928 0.494 0.033 1 Standard error of the mean across both stages, 2 Concordance correlation coefficient, 3 Mean square error of prediction, 4 Square root of the mean square error of prediction 190 Table 6.6 . Model evaluation through 100 - fold cross - validation for fat - free mass composition by stage (heifers and cows) and model (polEBW, lnEBW, and EBW^0.75) . Fit Statistic Heifers Cows SEM 4 P - value polEBW 1 lnEBW 2 EBW^0.75 3 polEBW 1 lnEBW 2 EBW^0.75 3 Model Stage Model*Stage Mean observed, % 89.0 78.2 - - - - Mean predicted, % 88.6 88.9 88.9 79.6 79.9 80.2 0.173 0.07 <0.01 0.76 Mean bias 0.106 B - 0.159 A - 0.181 A 0.267 B 0.023 A - 0.232 A 0.072 <0.01 0.10 0.20 Slope bias - 0.181 bB 0.039 aA - 0.170 bC - 0.020 bB 0.021 aA - 0.112 cC 0.013 <0.01 <0.01 <0.01 CCC 5 0.81 cB 0.87 aA 0.84 bC 0.93 aB 0.92 aA 0.83 bC 0.009 <0.01 <0.01 <0.01 MSEP 6 8.71 cB 5.27 aA 7.81 bC 4.70 aB 4.72 aA 10.2 bC 0.274 <0.01 <0.01 <0.01 Decomposition of MSEP, % of MSEP Mean bias 5.00 a 3.59 a 4.23 a 9.48 a 10.3 ab 12.8 b 0.997 0.25 <0.01 0.12 Slope bias 11.9 bB 4.61 aA 12.5 bB 9.46 aB 12.6 aA 12.4 aB 1.23 <0.01 0.07 <0.01 Radom error 83.1 bB 91.8 aA 83.3 bC 81.1 aB 77.0 bA 74.8 bC 1.51 <0.01 <0.01 <0.01 RMSEP 7 2.91 cB 2.27 aA 2.76 bC 2.07 aB 2.12 aA 3.16 bC 0.051 <0.01 <0.01 <0.01 1 Empty body weight expressed as a polynomial, 2 Empty body weight expressed as natural logarithm, 3 Empty body weight expressed to the power of 0.75, 4 Standard error of the mean across all models, 5 Concordance correlation coefficient, 6 Mean square error of prediction, 7 Square root of the mean square error of prediction, 8 Different uppercase letters in the same row represent differences among models across stages (main effect of model), 9 Different lowercase letters in the same row represent difference within stage (interaction between model and stage) 191 Table 6. 7 . Estimated coefficient for the models derived on the first step of the modeling process (named as baseline) using the natural logarithm for empty body weight (lnEBW). Empty body water, % of EBW Empty body fat, % of EBW Effect Coeff. 1 SE 2 P - value Effect Coeff. 1 SE 2 P - value Intercept 3 86.6 4.72 <0.01 Intercept - 18.5 4.50 <0.01 lnEBW - 4.14 0.910 <0.01 lnEBW 6.09 0.848 <0.01 Empty body protein, % of EBW Empty body ash, % of EBW Effect Coeff. 1 SE 2 P - value Effect Coeff. 1 SE 2 P - value Intercept 27.1 1.46 <0.01 Intercept 4.20 0.431 <0.01 lnEBW - 1.87 0.275 <0.01 lnEBW - - - Fat - free mass, % of EBW Effect Coeff. 1 SE 2 P - value Intercept 118 4.50 <0.01 lnEBW - 6.09 0.847 <0.01 1 Estimated coefficient, 2 tandard error, 3 Intercept contains the effect of the method used to determine body composition (direct composition of EBW, estimated based on carcass and rib composition, or dilution techniques). The estimated coefficient for each me thod were 0.0, 0.44, and - 3.79 for direct, carcass, and dilution, respectively. 192 Table 6.8 . Relationship between empty body weight and average daily gain (ADG, kg/d) on the energy required for growth calculated based on the proposed model a nd the NRC (2001) . Empty body weight during growth (kg) ADG Proposed 1 NRC 2001 (Mature weight 700kg) 60 120 240 360 480 60 120 240 360 480 Net Energy, Mcal /d 0.40 0.57 0.65 0.72 0.76 0.79 0.33 0.55 0.93 1.26 1.56 0.60 0.99 1.13 1.28 1.37 1.43 0.51 0.86 1.45 1.96 2.44 0.80 1.49 1.74 1.99 2.14 2.24 0.70 1.18 1.99 2.69 3.34 1.00 2.07 2.45 2.83 3.06 3.21 0.90 1.51 2.54 3.44 4.27 1.20 2.74 3.27 3.81 4.13 4.35 1.10 1.84 3.10 4.20 5.22 Net Energy, Mcal/kg 0.40 1.43 1.61 1.79 1.90 1.97 0.82 1.38 2.32 3.15 3.91 0.60 1.64 1.89 2.14 2.28 2.39 0.85 1.44 2.42 3.27 4.06 0.80 1.86 2.17 2.49 2.67 2.80 0.88 1.48 2.48 3.37 4.18 1.00 2.07 2.45 2.83 3.06 3.21 0.90 1.51 2.54 3.44 4.27 1.20 2.28 2.73 3.18 3.44 3.63 0.91 1.54 2.58 3.50 4.35 1 Empty body fat (%) = 6.05 + 1.37*lnEBW 15.3*ADG + 5.23*lnEBW*ADG and Empty body protein (%) = 22.6 1.12*lnEBW, where lnEBW = natural logarithm of empty body weight and ADG = average daily gain assuming using empty body gain (EBG) as ADG = EBG/0.85 ; values in italic are outside the range of the database used to derive the proposed model 193 Table 6.9 . Relationship between empty body weight and average daily gain (ADG, kg/d) on the protein required for growth calculated based on the proposed model and the NRC (2001) . Empty body weight during growth (kg) ADG Proposed 1 NRC 2001 (Mature weight 700kg) 60 120 240 360 480 60 120 240 360 480 Net Protein, g /d 0.40 67 64 61 59 58 98 91 80 70 61 0.60 101 96 92 89 87 146 135 118 103 89 0.80 135 129 122 119 116 194 180 156 135 116 1.00 169 161 153 148 145 242 224 193 167 142 1.20 202 193 184 178 174 289 267 230 198 168 Net Protein, g/kg 0.40 169 161 153 149 145 244 227 200 175 153 0.60 169 161 153 149 145 243 226 197 172 149 0.80 169 161 153 148 145 242 225 195 169 145 1.00 169 161 153 148 145 242 224 193 167 142 1.20 168 161 153 148 145 241 223 192 165 140 1 Empty body fat (%) = 6.05 + 1.37*lnEBW 15.3*ADG + 5.23*lnEBW*ADG and Empty body protein (%) = 22.6 1.12*lnEBW, where lnEBW = natural logarithm of empty body weight and ADG = average daily gain assuming using empty body gain (EBG) as ADG = EBG/0.85 ; values in italic are outside the range of the database used to derive the proposed model 194 Table 6.1 0 . Relationship between body condition score (BCS) and empty body weight composition (% of EBW) on net energy content per kilogram of EBW 1 change estimated using the proposed models 1 and the NRC (2001) . BCS Proposed NRC (2001) Body composition Energy, Mcal/kg of EBW change 2 Body composition Energy, Mcal/kg of EBW change 2 Water Fat Protein Ash Water Fat Protein Ash 1.0 67.9 8.48 19.1 4.48 6.62 69.4 3.77 19.4 7.46 5.14 1.5 65.4 11.9 18.1 4.48 6.84 (6.62) 66.7 7.5 18.8 7.02 5.72 (5.14) 2.0 62.9 15.4 17.2 4.48 7.06 (6.84) 64.0 11.3 18.1 6.58 6.41 (5.72) 2.5 60.4 18.8 16.2 4.48 7.28 (7.06) 61.4 15.1 17.4 6.15 6.98 (6.41) 3.0 57.9 22.3 15.3 4.48 7.50 (7.28) 58.7 18.8 16.8 5.71 7.61 (6.98) 3.5 55.4 25.8 14.3 4.48 7.72 (7.50) 56.0 22.6 16.1 5.27 8.32 (7.61) 4.0 52.9 29.2 13.4 4.48 7.94 (7.72) 53.4 26.4 15.4 4.83 8.88 (8.32) 4.5 50.4 32.7 12.4 4.48 8.16 (7.94) 50.7 30.2 14.8 4.43 9.59 (8.88) 5.0 48.0 36.1 11.5 4.48 (8.16) 48.1 33.9 14.1 3.96 (9.59) 1 Assuming that an average cow with BCS 3 has 700 kg of BW, and 1 - unit change in BCS is associated with 9.7% change in BW (average of the database used to derive the equations; 2 Tissue energy contained in 1 kg of EBW gain (loss) going to the next higher (low er) 0.5 BCS 195 APPENDIX B Figures 196 Figure 6.1. Empty body water (EBWater) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) , and the size of the points represents t he average daily gain. 50 55 60 65 70 75 80 0 100 200 300 400 EBWater, % of EBW EBW, kg < 0.30 kg/d 0.3 1 - 0.50 kg/d 0.51 - 0.70 kg/d 0.71 - 0.90 kg/d > 0.391kg/d 197 Figure 6.2. Empty body fat (EBFat) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) , and the size of the points represents the average daily gain. 0 5 10 15 20 25 0 100 200 300 400 EBFat, % of EBW EBW, kg < 0.30 kg/d 0.3 1 - 0.50 kg/d 0.51 - 0.70 kg/d 0.71 - 0.90 kg/d > 0.391kg/d 198 Figure 6.3. E mpty body protein (EBProtein) composition in heifers as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of E BW composition; - carcass and rib composition; and - dilution techniques) , and the s ize of the points represents the average daily gain. 0 5 10 15 20 25 30 0 100 200 300 400 EBProtein, % of EBW EBW, kg < 0.30 kg/d 0.3 1 - 0.50 kg/d 0.51 - 0.70 kg/d 0.71 - 0.90 kg/d > 0.391kg/d 199 Figure 6.4. Empty body ash (EBAsh) composition in heifers as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) , and the s ize of the points re presents the average daily gain. 0 5 10 15 20 25 30 0 100 200 300 400 EBAsh, % of EBW EBW, kg < 0.30 kg/d 0.3 1 - 0.50 kg/d 0.51 - 0.70 kg/d 0.71 - 0.90 kg/d > 0.391kg/d 200 Figure 6.5. Fat - free mass (FFM) composition in heifers for the rates of growth of 0.600 ( ), 0.800 ( ), and 1.000 ( ) kg/d as a function of empty body weight (EBW). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) , and the s ize of the points represents the average daily gain. 70 75 80 85 90 95 100 0 100 200 300 400 Fat - free mass, % of EBW EBW, kg < 0.30 kg/d 0.3 1 - 0.50 kg/d 0.51 - 0.70 kg/d 0.71 - 0.90 kg/d > 0.391kg/d 201 a) b) c) Figure 6.6. Water ( ), fat ( ), protein ( ), and ash ( ) of the tissue deposited during growth at an average daily gain of 0.600 (a), 0.800 (b), and 1.00 (c) kg /d . 0 20 40 60 80 100 55 85 115 145 175 205 235 265 295 325 355 Composition of the gain, % Empty body weight, kg 0 20 40 60 80 100 55 85 115 145 175 205 235 265 295 325 355 Composition of the gain, % Empty body weight, kg 0 20 40 60 80 100 55 85 115 145 175 205 235 265 295 325 355 Composition of the gain, % Empty body weight, kg 202 Figure 6.7. The net energy requirement s for growth estimated using the proposed models (solid lines) and the NRC 2001 (dashed lines) for three rates of growth are represented by the thickness of each corresponding line. The average daily gain for each division is represented by three scenarios: restricted (R), normal (N), and elevated (E). 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0 100 200 300 400 500 NEg, Mcal/d Empty body weight (kg) E: 0.30 kg/d N: 0.26 kg/d R: 0.20 kg/d E: 0.56 kg/d N: 0.47 kg/d R: 0.38 kg/d E: 0.88 kg/d N: 0.73 kg/d R: 0.60 kg/d E: 1.14 kg/d N: 0.95 kg/d R: 0.78 kg/d E: 1.45kg/d N: 1.25 kg/d R: 1.00 kg/d 203 Figure 6.8. The net protein requirement s for growth estimated using the proposed models (solid lines) and the NRC 2001 (dashed lines) for three rates of growth are represented by the thickness of each corresponding line. The average daily gain for each division is represented by three scenarios: restricted (R), normal (N), and elevated (E). 0 50 100 150 200 250 300 0 100 200 300 400 500 NPg, g/d Empty body weight (kg) E: 0.30 kg/d N: 0.26 kg/d R: 0.20 kg/d E: 0.56 kg/d N: 0.47 kg/d R: 0.38 kg/d E: 0.88 kg/d N: 0.73 kg/d R: 0.60 kg/d E: 1.14 kg/d N: 0.95 kg/d R: 0.78 kg/d E: 1.45kg/d N: 1.25 kg/d R: 1.00 kg/d 204 Figure 6.9. Empty body water (EBWater) composition in cows as a function of body condition score (BCS). Each p oint represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques) , and the solid line represent s the proposed model. 40 50 60 70 80 0 1 2 3 4 5 EBWater, % of EBW BCS 205 Fi gure 6.10. Empty body fat (EBFat) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques) , and the solid line represent s the proposed model. 0 10 20 30 40 0 1 2 3 4 5 EBFat, % of EBW BCS 206 Figure 6.11. Empty body protein (EBProtein) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques) , and the solid line represent s the proposed model. 0 10 20 30 0 1 2 3 4 5 EBProtein, % of EBW BCS 207 Figure 6.12. Empty body ash (EBAsh) comp osition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect . T he color represents the method used to determine the body composition ( - direct measurement of EBW composition; and - dilution te chniques) , and the solid line represent s the proposed model. 0 5 10 15 20 25 30 0 1 2 3 4 5 EBAsh, % of EBW BCS 208 Figure 6.13. Fat - free mass (FFM) composition in cows as a function of body condition score (BCS). Each point represents the adjusted value for the study effect . T he color represents the metho d used to determine the body composition ( - direct measurement of EBW composition; and - dilution techniques) , and the solid line represent s the proposed model. 60 70 80 90 0 1 2 3 4 5 FFM, % of EBW BCS 209 APPENDIX C Supplemental Tables 210 Supplemental Table 6.1. Relationship between em pty body weight on the energy required for growth calculated based on the baseline model and the NRC (2001). Empty body weight during growth (kg) ADG 1 Proposed 2 NRC 2001 (Mature weight 700kg) 60 120 240 360 480 60 120 240 360 480 Retained Energy, Mcal/day 0.40 0.85 0.98 1.11 1.18 1.24 0.33 0.55 0.93 1.26 1.56 0.60 1.28 1.47 1.66 1.77 1.85 0.51 0.86 1.45 1.96 2.44 0.80 1.70 1.96 2.21 2.36 2.47 0.70 1.18 1.99 2.69 3.34 1.00 2.13 2.45 2.77 2.96 3.09 0.90 1.51 2.54 3.44 4.27 1.20 2.56 2.94 3.32 3.55 3.71 1.10 1.84 3.10 4.20 5.22 Retained Energy, Mcal/kg of gain - 2.13 2.45 2.77 2.96 3.09 0.90 1.51 2.54 3.44 4.27 1 Average daily gain on body weight gain; 2 Values in italic are outside the range of the database used to derive the proposed model 211 Supplemental Table 6.2. Relationship between empty body weight on the protein required for growth calculated based on the baseline model and the NRC (2001). Empty body weight during growth (kg) ADG 1 Proposed 2 NRC 2001 60 120 240 360 480 60 120 240 360 480 Retained Protein, g /day 0.40 70 65 60 57 55 98 91 80 70 61 0.60 105 98 90 85 82 146 135 118 103 89 0.80 140 130 120 114 109 194 180 156 135 116 1.00 176 163 150 142 137 242 224 193 167 142 1.20 211 195 180 171 164 289 267 230 198 168 Retained Protein, g /kg of gain - 176 163 150 142 137 242 224 193 167 142 1 Average daily gain on body weight gain; 2 Values in italic are outside the range of the database used to derive the proposed model 212 APPENDIX D Supplemental Figures 213 Supplemental Figure 6.1. Empty body water (EBWater) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. 50 55 60 65 70 75 80 0 100 200 300 400 500 600 700 EBWater, % of EBW EBW, kg 214 Supplemental Figure 6. 2 . Empty body fat (EBFat) composition in heifers ( - direct measurement of EBW composition; - carcass and rib compo sition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline . 0 5 10 15 20 25 30 0 100 200 300 400 500 600 700 EBFat, % of EBW EBW, kg 215 Supplemental Figure 6.3. Empty body protein (EBProtein) composition in heifers ( - direct me asurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. 0 5 10 15 20 25 30 0 100 200 300 400 500 600 700 EBProtein, % of EBW EBW, kg 216 Supplemental Figure 6.4. Empty body ash (EBAsh) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by t he baseline. 0 5 10 15 20 25 30 0 100 200 300 400 500 600 700 EBAsh, % of EBW EBW, kg 217 Supplemental Figure 6.5. Fat - free mass (FFM) composition in heifers ( - direct measurement of EBW composition; - carcass and rib composition; and - dilution techniques) and cows ( - direct measurement of EBW composition; and - dilution techniques) predicted by the baseline. 70 75 80 85 90 95 100 105 0 100 200 300 400 500 600 700 FFM, % of EBW EBW, kg 218 REFERENCE S 219 REFERENCES Bach, A., M.A. Khan, and E.K. Miller - Cushon. 2017.Calf transition: Managing and feeding the calf through weaning. Large Dairy Herd Management, 3 rd ed. American Dairy Science Association, Champaign, IL. http// doi:10.3168/ldhm.0630. Belyea, R.L., G.R. Frost, F.A. Martz, J.L. 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American Dairy Science Association, Champaign, IL. http// doi:10.3168/ldhm.0630. 222 As discussed in the previous chapters, feed plays an essential role o n the modern dairy farm. F eed represents the major cost within dairy operations, and it is the main input allowing the increase of milk production. Hence, by optimizing feed utilization, farms can greatly improve profitability. Much research on dairy nutrition has focused on understanding the mechanisms associated with the conversion of feed into milk and the development of strategies to improve the efficiency of this process. Ultimately, dairy farmers benefit from advances in the field of dairy nutrition research by using new research recommendations and technologies to improve diets. These transfers of technology from the research centers to commercial farms are made through diet formulation. Diet formulation is performed by dairy nutritionists using diet formulation software, which uses a set of prediction equations to match animal requirements with the nutrients available through a diet. Finally, the prediction equations used in diet formulation software must constantly be evalua ted and updated to incorporate the discoveries generated by research and to represent the current and advanced production systems. In this dissertation we proposed updates to the prediction equations for digestibility at production level ( chapter 3) and fo r dry matter intake ( chapter 4), investigated the effect of free FA on digestible energy ( chapter 5), and developed a model to predict net energy and net protein requirements for growth ( chapter 6). The proposed models represent a significant improvement o n the accuracy of predictions when compared to the models proposed by the NRC (2001) and 223 have the potential to be incorporated in diet formulation software. By incorporating the proposed models in the diet formulation software, dairy nutritionist s will hav e a more precise and accurate model for formulat ing diets. An important area that should be further investigated and incorporated into the diet formulation software is the impact of free FA on digestible energy ( chapter 5). The current diet formulation sof tware does not account for the effect of specific free FAs and, as demonstrated in this dissertation, there is a great potential to explore the benefits of specific free FAs in regard to nutrient digestibility and digestible energy intake. Finally, althoug h improvements in the accuracy and precision of statistical models used in the diet formulation process are essential for dairy farmers to enjoy the benefits of advance s in the dairy nutrition field, grouping strategies is a major management factor that li mits the usefulness of more precise diet formulation software. Farm managers need to adopt grouping strategies based on the nutritional needs of each dairy category. It is impossible to have a tailored diet if the diet is offered to a heterogeneous group o f animals. Therefore, it is necessary to generate recommendations and extension material focusing on nutritional grouping strateg ies . Dairy farmers will benefit the most from work performed in this dissertation by combining precision in diet formulation wi th nutritional grouping strategies.