# Evaluation and Development of a Nutrition Model to Predict Intake and Growth of Suckling Calves

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Base Model

^{®}(Version 2312 Build 16.0.17126.20132) using published equations. The diet was a daily-adjusted intake of milk and forage. Similar to Lancaster et al. [25], daily milk intake was predicted using 1 of 2 equations. The first set of equations was that from the National Academies of Science, Engineering, and Medicine [10] (NASEM):

_{F}

^{2}) × ((BW

^{(−0.3895 − 0.0197 × PKM2)}) × e

^{(BW × (−0.00244 − 0.00337 × PKM) − 1.3594 × PKM)}× ((BW

^{(0.4477 × PKM)}) × (−32.5704 + (27.9016 − 7.66732 × DE

_{F}) × DE

_{F}) × e

^{((0.0588 + 0.00018 × BW) × PKM2)}+ (BW

^{(1.3895 + 0.0197 × PKM2)}) × e

^{(BW × (0.00244 + 0.00337 × PKM) + 1.3594 × PKM)}× (0.4738 + DE

_{F}× (−0.4059 + DE

_{F}× (0.11154 − 0.003273 × PKM) + 0.01191 × PKM) − 0.0139046 × PKM) + (BW

^{(0.3895 + 0.0197 × PKM2)}) × e

^{(BW × (0.00244 + 0.00337 × PKM) + 1.3594 × PKM)}× (−10.3049 + DE

_{F}× (8.82778 + DE

_{F}× (−2.42586 + 0.362681 × PKM) − 1.31981 × PKM) + 1.54065 × PKM)))

_{F}is the digestible energy concentration of forage (Mcal/kg DM); BW is current calf body weight (kg); and PKM is peak milk yield (kg/d).

_{F}is the digestible energy concentration of forage (Mcal/kg DM); and RFDMI is the relative DMI of forage adjustment for forage DE (kg/d).

_{F}is forage digestible energy intake (Mcal/kg BW); DEI

_{M}is milk digestible energy intake (Mcal/d); DE

_{F}is the digestible energy concentration of forage (Mcal/kg DM); and BW is current calf body weight (kg).

^{−0.6837}× RE

^{0.9116}

^{0.75}× 0.077) ÷ NEm

#### 2.2. Model Evaluation Data

#### 2.2.1. Dairy Calf Intake and Body Weight Dataset

#### 2.2.2. Beef Calf Intake and Body Weight Dataset

#### 2.3. Model Adjustment Data

#### 2.3.1. Calf Growth

^{b}

^{0.75})

^{b}

^{b}× EBW

^{c}

#### 2.3.2. Forage Digestibility

#### 2.3.3. Milk Composition

#### 2.4. Model Evaluation

#### 2.4.1. Evaluation Metrics

#### 2.4.2. Milk Intake

#### 2.4.3. Forage Intake

#### 2.4.4. Body Weight

## 3. Results

#### 3.1. Dairy Calf Intake and Body Weight Dataset

#### 3.1.1. Milk Intake

#### 3.1.2. Original Nutrition Model

#### 3.1.3. Adjusted Nutrition Model

^{0.78512}× EBW

^{−0.14361}

^{2}0.825), an intercept not different from zero, and a slope not different from one (Table S5).

#### 3.2. Beef Calf Intake and Body Weight Dataset

#### 3.2.1. Milk Intake

#### 3.2.2. Original Nutrition Model

#### 3.2.3. Adjusted Nutrition Model

^{0.75})

^{0.70834}

^{0.70834}× EBW

^{−0.53126}

^{2}) of 0.777, an intercept not different from zero, and a slope not different from one (Table S18).

#### 3.2.4. Exploration of Model Deviation

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

^{b}× EBW

^{c}) to predict empty body weight gain in the dairy cattle serial slaughter dataset; Table S6: Descriptive statistics of the forage in vitro/in vivo digestibility dataset used to develop and evaluate forage digestibility equation; Table S7: Evaluation of in vitro versus in vivo digestibility in the forage digestibility dataset; Table S8: Evaluation of dry versus organic matter digestibility in the forage digestibility dataset; Table S9: Published equations evaluated to predict in vivo dry matter digestibility from in vitro dry matter digestibility in the forage digestibility dataset; Table S10: Evaluation of published equations to predict in vivo DMD from in vitro DMD in the forage digestibility dataset; Table S11: Cross-validation of the final equation (OMD = a + b × IVDMD) to predict in vivo organic matter digestibility in the forage digestibility dataset; Table S12: Descriptive statistics of the milk composition dataset used to develop milk energy equation; Table S13: Regression coefficients (±SE), least square means, and fit statistics for mixed model equations developed to predict milk composition in beef cows; Table S14: Cross-validation of the final mixed effect models to predict milk composition in beef cows; Table S15: Descriptive statistics of the beef cattle serial slaughter dataset used to evaluate the empty body weight gain Equation (8a) and develop a new equation; Table S16: Evaluation of the empty body weight gain Equation (8a) in the beef cattle serial slaughter dataset; Table S17: Fit statistics for equations developed to predict empty body weight gain (kg/d) in beef cattle serial slaughter dataset; Table S18: Cross-validation of the final mixed effect equation (EBG = a × (RE/EBW

^{0.75})

^{b}) to predict empty body weight gain in the beef cattle serial slaughter dataset.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Observed milk intake and predicted milk yield using milk yield equations over the suckling period in the dairy calf dataset. NASEM = milk yield Equation (1a–c); WOOD = milk yield Equation (2a–e); and BOTH = combination of NASEM used when estimated peak milk yield was > 10 kg/d and WOOD used when estimated peak milk yield was ≤ 10 kg/d.

**Figure 2.**Observed and predicted forage intake (

**a**) and body weight (

**b**) for the 5 forage intake equations over the suckling period in the dairy calf intake and body weight dataset using the original model. Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

**Figure 3.**Observed and predicted forage intake (

**a**) and body weight (

**b**) for the 5 forage intake equations over the suckling period in the dairy calf intake and body weight dataset using the adjusted model. Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

**Figure 4.**Observed and predicted milk intake using milk yield equations over the suckling period in the beef calf intake and body weight dataset. Calves were born in March and April. NASEM = milk yield Equation (1a–c) and WOOD = milk yield Equation (2a–e).

**Figure 5.**Observed and predicted forage intake (

**a**) and body weight (

**b**) for 5 forage intake equations over the suckling period in the beef calf intake and body weight dataset using the original model. Calves were born in March and April. Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

**Figure 6.**Observed and predicted forage intake (

**a**) and body weight (

**b**) for 5 forage intake equations over the suckling period in the beef calf intake and body weight dataset using the adjusted model. Calves were born in March and April. Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

**Table 1.**Descriptive statistics of the dairy calf intake and body weight dataset used to evaluate forage intake and growth models.

Item | Mean | SD | Minimum | Maximum |
---|---|---|---|---|

Birth date, Julian d | 208.70 | 24.35 | 170 | 257 |

Birth weight, kg | 44.9 | 9.0 | 36.0 | 57.0 |

30-d BW, kg | 61.6 | 12.3 | 35.0 | 92.0 |

30-d milk intake, kg/d | 6.65 | 2.75 | 2.50 | 12.08 |

30-d forage intake, kg DM/d | 0.08 | 0.09 | 0.00 | 0.41 |

60-d BW, kg | 85.0 | 17.0 | 49.0 | 117.0 |

60-d milk intake, kg/d | 7.25 | 3.15 | 2.50 | 12.69 |

60-d forage intake, kg DM/d | 0.29 | 0.30 | 0.00 | 1.33 |

90-d BW, kg | 115.8 | 23.1 | 71.0 | 165.0 |

90-d milk intake, kg/d | 7.27 | 3.51 | 2.37 | 12.83 |

90-d forage intake, kg DM/d | 0.88 | 0.57 | 0.16 | 2.14 |

115-d BW, kg | 142.6 | 26.7 | 84.0 | 184.0 |

115-d milk intake, kg/d | 6.65 | 3.04 | 2.14 | 11.83 |

115-d forage intake, kg DM/d | 1.55 | 0.64 | 0.39 | 2.58 |

145-d BW, kg | 168.1 | 29.8 | 104.0 | 220.0 |

145-d milk intake, kg/d | 5.90 | 2.99 | 1.84 | 10.46 |

145-d forage intake, kg DM/d | 2.26 | 0.66 | 1.08 | 3.33 |

165-d BW, kg | 187.2 | 33.9 | 117.0 | 239.0 |

165-d milk intake, kg/d | 5.27 | 2.67 | 1.60 | 9.34 |

165-d forage intake, kg DM/d | 2.98 | 0.71 | 1.22 | 4.79 |

195-d BW, kg | 212.2 | 38.0 | 127.0 | 269.0 |

195-d milk intake, kg/d | 4.44 | 2.27 | 1.34 | 8.45 |

195-d forage intake, kg DM/d | 3.83 | 0.52 | 2.55 | 4.84 |

**Table 2.**Descriptive statistics of the beef calf intake and body weight dataset used to evaluate forage intake and growth models.

Item | Mean | SD | Minimum | Maximum |
---|---|---|---|---|

Birth date, Julian | 86.75 | 12.84 | 60 | 122 |

Birth weight, kg | 34.8 | 3.4 | 23.1 | 41.8 |

April BW, kg | 61.0 | 9.7 | 40.0 | 80.6 |

April milk yield, kg/d | 6.43 | 1.49 | 3.40 | 9.99 |

May BW, kg | 78.3 | 11.3 | 55.4 | 99.0 |

May milk yield, kg/d | 5.90 | 1.49 | 3.13 | 10.44 |

May forage intake, kg DM/d | 0.47 | 0.21 | 0.20 | 10.16 |

June BW, kg | 96.8 | 13.4 | 68.5 | 119.8 |

June milk yield, kg/d | 4.95 | 1.44 | 1.32 | 8.40 |

June forage intake, kg DM/d | 1.45 | 0.69 | 0.47 | 3.14 |

July BW, kg | 120.1 | 16.6 | 83.5 | 148.4 |

July milk yield, kg/d | 4.82 | 1.45 | 2.27 | 8.40 |

July forage intake, kg DM/d | 1.85 | 0.72 | 0.92 | 5.05 |

Aug. BW, kg | 145.9 | 18.9 | 103.5 | 177.9 |

Aug. milk yield, kg/d | 3.38 | 0.95 | 1.35 | 6.81 |

Aug. forage intake, kg DM/d | 2.62 | 0.64 | 1.45 | 4.36 |

Sept. BW, kg | 165.3 | 21.1 | 116.1 | 202.5 |

Sept. milk yield, kg/d | 3.61 | 1.12 | 1.13 | 5.90 |

Sept. forage intake, kg DM/d | 3.57 | 0.84 | 2.36 | 6.14 |

**Table 3.**Comparison of milk yield equations to predict milk intake in the dairy calf intake and body weight dataset.

Item ^{1} | NASEM | WOOD | Both |
---|---|---|---|

CCC | 0.951 | 0.954 | 0.969 |

Cb | 0.991 | 0.996 | 1.000 |

MB (SD), kg/d | 0.393 (0.919) | −0.253 (0.927) | −0.045 (0.771) |

MB, % | 6.44 | −4.14 | −0.74 |

Intercept ± SE | 0.9094 ± 0.0753 | 0.2690 ± 0.0842 | 0.1622 ± 0.0728 |

Slope ± SE | 0.9096 ± 0.0115 | 0.9179 ± 0.0118 | 0.9662 ± 0.0106 |

Pr > F | <0.0001 | <0.0001 | 0.0025 |

^{1}NASEM = milk yield Equation (1a–c); WOOD = milk yield Equation (2a–e); CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 4.**Comparison of original models using 5 forage intake equations to predict forage intake and body weight simultaneously in the dairy calf intake and body weight dataset.

Item | Eq91 ^{1} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

Forage Intake | |||||

CCC ^{2} | 0.878 | 0.920 | 0.729 | 0.874 | 0.234 |

Cb | 0.957 | 0.999 | 0.797 | 0.921 | 0.257 |

MB (SD), kg/d | −0.259 (0.722) | −0.023 (0.546) | −0.954 (0.984) | −0.527 (0.580) | −5.055 (3.698) |

MB, % | −17.49 | −1.58 | −64.4 | −35.6 | −341.16 |

Intercept ± SE | 0.2266 ± 0.0326 | 0.1322 ± 0.0332 | 0.0135 ± 0.0360 | −0.0563 ± 0.0283 | −0.1712 ± 0.0397 |

Slope ± SE | 0.7188 ± 0.0134 | 0.8956 ± 0.0163 | 0.6005 ± 0.0113 | 0.7639 ± 0.0109 | 0.2513 ± 0.0049 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Body Weight | |||||

CCC | 0.876 | 0.929 | 0.819 | 0.864 | 0.402 |

Cb | 0.908 | 0.951 | 0.833 | 0.878 | 0.423 |

MB (SD), kg | −26.439 (16.932) | −18.005 (15.271) | −36.952 (23.855) | −30.847 (17.077) | −122.473 (84.252) |

MB, % | −21.54 | −14.67 | −30.1 | −25.13 | −99.78 |

Intercept ± SE | −7.9868 ± 1.6539 | 1.8476 ± 1.2441 | 7.0021 ± 1.0362 | −0.5910 ± 1.0313 | 25.1856 ± 1.5894 |

Slope ± SE | 0.8763 ± 0.0102 | 0.8589 ± 0.0080 | 0.7248 ± 0.0058 | 0.8030 ± 0.0061 | 0.3978 ± 0.0057 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

^{1}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{2}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 5.**Comparison of original models using 5 forage intake equations to predict forage intake separately in the dairy calf intake and body weight dataset when observed body weight was used in the model

^{1}.

Item ^{3} | Eq91 ^{2} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

CCC | 0.935 | 0.936 | 0.958 | 0.964 | 0.640 |

Cb | 0.998 | 0.997 | 0.99 | 0.995 | 0.690 |

MB (SD), kg/d | −0.008 (0.503) | 0.097 (0.471) | −0.176 (0.366) | −0.131 (0.342) | −1.366 (1.171) |

MB, % | −0.55 | 6.57 | −11.9 | −8.83 | −92.26 |

Intercept ± SE | 0.1745 ± 0.0288 | 0.1655 ± 0.0287 | −0.0298 ± 0.0224 | −0.0328 ± 0.0216 | −0.0674 ± 0.0340 |

Slope ± SE | 0.8763 ± 0.0140 | 0.9503 ± 0.0150 | 0.9109 ± 0.0103 | 0.9387 ± 0.0102 | 0.5416 ± 0.0093 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

^{1}Linear regression of observed body weight on day of age was used to predict body weight for the dairy calf intake and body weight dataset (CCC = 0.980; Cb = 0.987; MB, kg = −8.662; MB, % = −6.23).

^{2}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{3}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 6.**Comparison of original and adjusted models to predict body weight separately in the dairy calf intake and body weight dataset when observed forage intake was used in the model

^{1}.

Item ^{2} | Original EBG Equation | New EBG Equation |
---|---|---|

CCC | 0.926 | 0.992 |

Cb | 0.938 | 0.999 |

MB (SD), kg/d | −20.966 (11.365) | −0.135 (7.368) |

MB, % | −17.08 | −0.11 |

Intercept ± SE | −6.4356 ± 1.0076 | −1.7250 ± 0.7569 |

Slope ± SE | 0.8989 ± 0.0064 | 1.0129 ± 0.0056 |

Pr > F | <0.0001 | 0.0643 |

^{1}Polynomial linear regression of observed forage intake on day of age was used to predict forage intake for the dairy calf dataset (CCC = 0.988; Cb = 0.999; MB, kg/d = −0.01; MB, % = −0.41).

^{2}EBG = empty body weight gain; CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 7.**Comparison of adjusted models using 5 forage intake equations to predict forage intake and body weight simultaneously using the new empty body weight gain Equation (13) in the dairy calf intake and body weight dataset.

Item | Eq91 ^{1} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

Forage Intake | |||||

CCC ^{2} | 0.914 | 0.766 | 0.881 | 0.901 | 0.412 |

Cb | 0.984 | 0.825 | 0.967 | 0.973 | 0.451 |

MB (SD), kg/d | 0.229 (0.500) | 0.600 (0.594) | 0.268 (0.561) | 0.252 (0.513) | −2.561 (2.527) |

MB, % | 15.47 | 40.53 | 18.11 | 17.02 | −172.88 |

Intercept ± SE | 0.2588 ± 0.0298 | 0.3072 ± 0.0294 | 0.2037 ± 0.0343 | 0.1928 ± 0.0312 | 0.1269 ± 0.0347 |

Slope ± SE | 0.9761 ± 0.0167 | 1.3382 ± 0.0231 | 1.0539 ± 0.0206 | 1.0489 ± 0.0184 | 0.3328 ± 0.0064 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Body Weight | |||||

CCC | 0.978 | 0.940 | 0.968 | 0.969 | 0.701 |

Cb | 0.991 | 0.973 | 0.995 | 0.995 | 0.739 |

MB (SD), kg/d | 3.472 (10.701) | 10.934 (15.392) | 4.749 (13.263) | 4.807 (13.190) | −47.540 (48.220) |

MB, % | 2.83 | 8.91 | 3.87 | 3.92 | −38.73 |

Intercept ± SE | −9.6804 ± 0.9940 | 0.7530 ± 1.5226 | 2.4086 ± 1.3481 | 2.7352 ± 1.3383 | 29.2959 ± 1.5428 |

Slope ± SE | 1.1103 ± 0.0077 | 1.0911 ± 0.0124 | 1.0198 ± 0.0104 | 1.0176 ± 0.0103 | 0.5488 ± 0.0078 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

^{1}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{2}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 8.**Comparison of milk yield equations to predict milk intake in the beef calf intake and body weight dataset.

Item ^{1} | NASEM | WOOD |
---|---|---|

CCC | 0.796 | 0.820 |

Cb | 0.993 | 0.991 |

MB (SD), kg/d | 0.206 (1.078) | 0.063 (0.969) |

MB, % | 4.29 | 1.31 |

Intercept ± SE | 1.0875 ± 0.1719 | 0.3321 ± 0.1850 |

Slope ± SE | 0.8087 ± 0.0350 | 0.9433 ± 0.0371 |

Pr > F | <0.0001 | 0.1673 |

^{1}NASEM = milk yield Equation (1a–c); WOOD = milk yield Equation (2a–e); CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 9.**Comparison of original models using 5 forage intake equations to predict forage intake and body weight simultaneously in the beef calf intake and body weight dataset.

Item | Eq91 ^{1} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

Forage Intake | |||||

CCC ^{2} | 0.613 | 0.476 | 0.167 | 0.491 | 0.348 |

Cb | 0.745 | 0.752 | 0.278 | 0.706 | 0.608 |

MB (SD), kg/d | 0.389 (0.802) | 0.433 (0.963) | 1.160 (1.064) | 0.565 (0.910) | 0.409 (1.037) |

MB, % | 19.36 | 21.51 | 57.67 | 28.07 | 20.33 |

Intercept ± SE | −0.6318 ± 0.1251 | 0.1182 ± 0.1605 | 0.1346 ± 0.1714 | 0.0939 ± 0.1391 | −0.3867 ± 0.2296 |

Slope ± SE | 1.6294 ± 0.0720 | 1.1992 ± 0.0940 | 2.2045 ± 0.1873 | 1.3254 ± 0.0878 | 1.4965 ± 0.1374 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Body Weight | |||||

CCC | 0.762 | 0.76 | 0.574 | 0.766 | 0.766 |

Cb | 0.899 | 0.898 | 0.757 | 0.874 | 0.909 |

MB (SD), kg/d | 10.224 (21.910) | 10.946 (21.887) | 17.594 (26.833) | 11.911 (23.166) | 7.114 (22.379) |

MB, % | 9.18 | 9.83 | 15.79 | 10.69 | 6.39 |

Intercept ± SE | −11.3177 ± 4.5786 | −8.3620 ± 4.5074 | −11.4078 ± 6.2286 | −10.2020 ± 4.9313 | −18.4033 ± 4.9166 |

Slope ± SE | 1.2129 ± 0.0436 | 1.1922 ± 0.0432 | 1.3092 ± 0.0645 | 1.2223 ± 0.0479 | 1.2447 ± 0.0457 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

^{1}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{2}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 10.**Comparison of original models using 5 forage intake equations to predict forage intake separately in the beef calf intake and body weight dataset when observed body weight was used in the model

^{1}.

Item | Eq91 ^{2} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

CCC ^{3} | 0.834 | 0.725 | 0.630 | 0.738 | 0.528 |

Cb | 0.983 | 0.953 | 0.830 | 0.959 | 0.727 |

MB (SD), kg/d | 0.016 (0.653) | 0.112 (0.800) | 0.555 (0.806) | 0.196 (0.787) | 0.418 (0.894) |

MB, % | 0.81 | 5.58 | 27.56 | 9.73 | 20.76 |

Intercept ± SE | −0.0222 ± 0.0915 | 0.0721 ± 0.1176 | 0.4491 ± 0.1001 | 0.2499 ± 0.1061 | −0.3290 ± 0.1520 |

Slope ± SE | 1.0193 ± 0.0408 | 1.0211 ± 0.0557 | 1.0723 ± 0.0590 | 0.9701 ± 0.0515 | 1.4684 ± 0.0891 |

Pr > F | 0.8283 | 0.0854 | <0.0001 | 0.0005 | <0.0001 |

^{1}Linear regression of observed body weight on day of age was used to predict body weight for the beef calf intake and body weight dataset (CCC = 0.992; Cb = 0.999; MB, kg = 0.722; MB, % = 0.72).

^{2}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{3}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 11.**Comparison of original models to predict body weight in the beef calf intake and body weight dataset when observed forage intake was used in the model

^{1}.

Item | Original ^{2} | New Forage Digestibility | New Milk Energy | New EBG Equation | New Combination |
---|---|---|---|---|---|

CCC ^{3} | 0.821 | 0.883 | 0.863 | 0.901 | 0.931 |

Cb | 0.913 | 0.957 | 0.946 | 0.981 | 0.985 |

MB (SD), kg/d | 10.796 (18.441) | 7.260 (16.097) | 6.998 (17.324) | 1.757 (16.143) | −5.965 (13.045) |

MB, % | 9.69 | 6.52 | 6.28 | 1.58 | −5.35 |

Intercept ± SE | −11.0374 ± 3.5433 | −7.8853 ± 3.0152 | −13.3124 ± 3.3515 | −10.5959 ± 3.1486 | −8.3616 ± 2.5005 |

Slope ± SE | 1.2170 ± 0.0338 | 1.1454 ± 0.0277 | 1.1945 ± 0.0308 | 1.1127 ± 0.0275 | 1.0204 ± 0.0203 |

Pr > F | <0.0001 | < 0.0001 | <0.0001 | < 0.0001 | <0.0001 |

^{1}Polynomial linear regression of observed forage intake on day of age was used to predict forage intake for the beef calf intake and body weight dataset (CCC = 0.972; Cb = 1.000; MB, kg/d = −0.011; MB, % = −0.53).

^{2}Original = model using observed in vitro forage dry matter digestibility, standard milk energy concentration (0.72 Mcal/kg), empty body weight gain Equation (8a); New Forage Digestibility = adjusted model substituting estimated in vivo forage organic matter digestibility for observed in vitro forage dry matter digestibility; New Milk Energy = adjusted model substituting estimated daily milk energy concentration for the standard milk energy concentration; New EBG Equation = adjusted model substituting the developed empty body weight gain equation for the original empty body weight gain Equation (8a); New Combination = adjusted model combining the changes of New Forage Digestibility, New Milk Energy, and New EBG Equation.

^{3}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; Sd = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 12.**Comparison of adjusted models using 5 forage intake equations to predict forage intake and body weight simultaneously in the beef calf intake and body weight dataset using the combination of new forage digestibility, milk energy concentration, and empty body weight gain equation.

Item | Eq91 ^{1} | Eq67 | Eq25 | Eq17 | Eq21 |
---|---|---|---|---|---|

Forage Intake | |||||

CCC ^{2} | 0.822 | 0.670 | 0.434 | 0.686 | 0.380 |

Cb | 0.956 | 0.951 | 0.546 | 0.842 | 0.628 |

MB (SD), kg/d | −0.149 (0.674) | −0.107 (0.879) | 0.783 (0.925) | 0.281 (0.809) | 0.233 (1.078) |

MB, % | −7.01 | −5.08 | 39.87 | 13.24 | 10.96 |

Intercept ± SE | −0.4464 ± 0.1063 | −0.1010 ± 0.1427 | −0.4021 ± 0.1337 | −0.4482 ± 0.1263 | −1.0047 ± 0.2712 |

Slope ± SE | 1.1309 ± 0.0429 | 0.9969 ± 0.0588 | 1.8840 ± 0.0924 | 1.3958 ± 0.0634 | 1.6545 ± 0.1391 |

Pr > F | <0.0001 | 0.1603 | <0.0001 | <0.0001 | <0.0001 |

Body Weight | |||||

CCC | 0.935 | 0.938 | 0.896 | 0.926 | 0.886 |

Cb | 0.978 | 0.985 | 0.972 | 0.98 | 0.956 |

MB (SD), kg/d | −8.173 (11.663) | −6.918 (12.128) | −0.104 (16.267) | −5.956 (13.310) | −10.486 (14.937) |

MB, % | −7.34 | −6.21 | −0.09 | −5.35 | −9.41 |

Intercept ± SE | −6.6719 ± 2.1851 | −3.2861 ± 2.2109 | −19.3587 ± 3.2651 | −13.6285 ± 2.6198 | −16.0307 ± 3.0696 |

Slope ± SE | 0.9875 ± 0.0174 | 0.9693 ± 0.0178 | 1.1727 ± 0.0282 | 1.0654 ± 0.0214 | 1.0455 ± 0.0242 |

Pr > F | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

^{1}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{2}CCC = concordance correlation coefficient; Cb = bias correction factor; MB = mean bias; SD = standard deviation; Intercept = intercept coefficient of linear regression of observed on predicted values; SE = standard error; Slope = slope coefficient of linear regression of observed on predicted values; and Pr > F = p-value for linear hypothesis test.

**Table 13.**Effect of birth period with the covariate of forage intake on deviation between observed and predicted forage intake from the adjusted model using the combination of new forage digestibility, milk energy concentration, and empty body weight gain equation in the beef calf intake and body weight dataset.

Birth Period ^{1} | p-Value ^{2} | |||||||
---|---|---|---|---|---|---|---|---|

Equation ^{3} | Covariate Level | 1 | 2 | 3 | SEM | BP | Cov | BP × Cov |

Eq91 | 0.75 kg/d | −0.62 ^{a} | −0.46 ^{a} | −0.06 ^{b} | 0.09 | 0.01 | 0.01 | 0.01 |

1.50 kg/d | −0.37 ^{a} | −0.22 ^{a} | 0.02 ^{b} | 0.06 | ||||

2.25 kg/d | −0.11 | 0.02 | 0.10 | 0.06 | ||||

3.00 kg/d | 0.15 | 0.26 | 0.19 | 0.07 | ||||

3.75 kg/d | 0.40 | 0.50 | 0.27 | 0.10 | ||||

Eq67 | 0.75 kg/d | −1.08 ^{a} | −0.75 ^{a} | −0.22 ^{b} | 0.10 | 0.01 | 0.01 | 0.01 |

1.50 kg/d | −0.61 ^{a} | −0.39 ^{a} | 0.02 ^{b} | 0.07 | ||||

2.25 kg/d | −0.13 ^{a} | −0.03 ^{a} | 0.27 ^{b} | 0.07 | ||||

3.00 kg/d | 0.34 | 0.34 | 0.52 | 0.08 | ||||

3.75 kg/d | 0.82 | 0.70 | 0.76 | 0.11 | ||||

Eq25 | 0.75 kg/d | −0.72 ^{a} | −0.55 ^{ab} | −0.32 ^{a} | 0.10 | 0.47 | 0.01 | 0.05 |

1.50 kg/d | −0.37 | −0.26 | −0.13 | 0.07 | ||||

2.25 kg/d | −0.02 | 0.03 | 0.06 | 0.07 | ||||

3.00 kg/d | 0.33 | 0.32 | 0.25 | 0.08 | ||||

3.75 kg/d | 0.66 | 0.61 | 0.44 | 0.11 | ||||

Eq17 | 0.75 kg/d | −0.64 ^{a} | −0.55 ^{a} | −0.24 ^{b} | 0.09 | 0.17 | 0.01 | 0.08 |

1.50 kg/d | −0.34 | −0.27 | −0.07 | 0.07 | ||||

2.25 kg/d | −0.03 | 0.01 | 0.09 | 0.07 | ||||

3.00 kg/d | 0.27 | 0.29 | 0.26 | 0.08 | ||||

3.75 kg/d | 0.58 | 0.57 | 0.43 | 0.11 | ||||

Eq21 | 0.75 kg/d | −1.11 ^{a} | −1.02 ^{a} | −0.54 ^{b} | 0.09 | 0.01 | 0.01 | 0.01 |

1.50 kg/d | −0.50 ^{a} | −0.54 ^{a} | −0.20 ^{b} | 0.07 | ||||

2.25 kg/d | 0.10 | −0.05 | 0.14 | 0.07 | ||||

3.00 kg/d | 0.71 ^{a} | 0.43 ^{b} | 0.47 ^{ab} | 0.08 | ||||

3.75 kg/d | 1.31 ^{a} | 0.92 ^{b} | 0.81 ^{b} | 0.11 |

^{1}Birth Period 1 = March 1 to March 20; Birth Period 2 = March 21 to March 31; and Birth Period 3 = April 1 to May 2.

^{2}BP = p-value for birth period effect; Covariate = p-value for forage intake covariate effect; and BP × Cov = p-value for birth period × covariate interaction.

^{3}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{ab}Mean deviations without a common superscript within a row differ at p ≤ 0.05.

**Table 14.**Effect of birth period with covariate of body weight on deviation between observed and predicted body weight from the adjusted model using the combination of new forage digestibility, milk energy concentration, and empty body weight gain equation in the beef calf intake and body weight dataset.

Birth Period ^{1} | p-Value ^{2} | |||||||
---|---|---|---|---|---|---|---|---|

Equation ^{3} | Covariate Level | 1 | 2 | 3 | SEM | BP | Cov | BP × Cov |

Eq91 | 60 kg | −11.6 ^{a} | −6.1 ^{a} | 2.2 ^{b} | 1.7 | 0.01 | 0.01 | 0.01 |

90 kg | −5.8 ^{a} | −3.5 ^{a} | 2.2 ^{b} | 1.2 | ||||

120 kg | −0.1 | −0.8 | 2.3 | 1.1 | ||||

150 kg | 5.6 | 1.9 | 2.3 | 1.5 | ||||

Eq67 | 60 kg | −11.7 ^{a} | −6.4 ^{a} | 1.6 ^{b} | 1.7 | 0.01 | 0.01 | 0.01 |

90 kg | −5.8 ^{a} | −3.6 ^{a} | 2.1 ^{b} | 1.2 | ||||

120 kg | 0.1 | −0.8 | 2.5 | 1.1 | ||||

150 kg | 5.9 | 1.9 | 3.0 | 1.6 | ||||

Eq25 | 60 kg | −15.3 ^{a} | −10.5 ^{a} | 0.8 ^{b} | 2.1 | 0.01 | 0.01 | 0.01 |

90 kg | −6.3 ^{a} | −6.1 ^{a} | 1.4 ^{b} | 1.5 | ||||

120 kg | 2.7 | −1.7 | 2.1 | 1.5 | ||||

150 kg | 11.7 ^{a} | 2.7 ^{b} | 2.7 ^{b} | 1.9 | ||||

Eq17 | 60 kg | −12.7 ^{a} | −7.8 ^{a} | 1.7 ^{b} | 1.9 | 0.01 | 0.01 | 0.01 |

90 kg | −5.6 ^{a} | −4.6 ^{a} | 1.8 ^{b} | 1.3 | ||||

120 kg | 1.5 | −1.4 | 1.9 | 1.2 | ||||

150 kg | 8.6 ^{a} | 1.8 ^{b} | 2.0 ^{b} | 1.7 | ||||

Eq21 | 60 kg | −18.5 ^{a} | −8.2 ^{b} | 1.7 ^{c} | 2.1 | 0.01 | 0.01 | 0.01 |

90 kg | −8.9 ^{a} | −4.4 ^{a} | 1.9 ^{b} | 1.4 | ||||

120 kg | 0.7 | −0.7 | 2.1 | 1.4 | ||||

150 kg | 10.3 ^{a} | 3.0 ^{b} | 2.3 ^{b} | 1.8 |

^{1}Birth period 1 = March 1 to March 20; Birth Period 2 = March 21 to March 31; and Birth Period 3 = April 1 to May 2.

^{2}BP = p-value for birth period effect; Cov = p-value for body weight covariate effect; and BP × Cov = p-value for birth period × covariate interaction.

^{3}Eq91 = Equation (3); Eq67 = Equation (4); Eq25 = Equation (5); Eq17 = Equation (6a–c); and Eq21 = Equation (7).

^{ab}Mean deviations without a common superscript within a row differ at p ≤ 0.05.

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**MDPI and ACS Style**

Baldin, G.C.; Hildebrand, C.; Larson, R.L.; Lancaster, P.A.
Evaluation and Development of a Nutrition Model to Predict Intake and Growth of Suckling Calves. *Ruminants* **2024**, *4*, 47-78.
https://doi.org/10.3390/ruminants4010004

**AMA Style**

Baldin GC, Hildebrand C, Larson RL, Lancaster PA.
Evaluation and Development of a Nutrition Model to Predict Intake and Growth of Suckling Calves. *Ruminants*. 2024; 4(1):47-78.
https://doi.org/10.3390/ruminants4010004

**Chicago/Turabian Style**

Baldin, Geovana Camila, Caleb Hildebrand, Robert L. Larson, and Phillip A. Lancaster.
2024. "Evaluation and Development of a Nutrition Model to Predict Intake and Growth of Suckling Calves" *Ruminants* 4, no. 1: 47-78.
https://doi.org/10.3390/ruminants4010004