Short communication: Development and evaluation of equations to predict growth of Holstein dairy heifers in a tropical climate

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The objective of this study was to develop and validate equations for estimating growth of dairy heifers using measures of withers height, body weight (BW), and age. Measures of BW and withers height of 207 Holstein heifers raised in a tropical climate were taken from birth to calving, totaling to 2,047 observations. To be included in the database, the heifer had to have at least 4 measures recorded. After that, 4 models were built and evaluated as follows: (1) a linear model of BW as function of age (BW~A), (2) a linear model of the BW-to-height ratio as function of age (BW:H~A), (3) a quadratic model, adjusted for a defined plateau, to describe height as function of age (H~A), and (4) an exponential growth model of BW as function of height (BW~H). A cross-validation procedure was performed to evaluate accuracy and precision of the models. The linear relationship of BW~A and BW:H~A were estimated, respectively, by the equations: BW = 42.65 + 0.62 × A and BW:H = 0.70 + 0.0041 × A, where BW is in kilograms, BW:H = BW-to-height ratio (kg/cm), and A = age (d). Using the quadratic plateau for the model H~A, a critical "x" value of ~806 d and a height plateau of 138.6 cm were identified. Therefore, the following equations for estimating the height of animals younger and older than 806 d, respectively, were developed: H = 78.15 + 0.150 × A - 0.00009 × A2 and H = 78.15 + 0.150 × cvx - 0.00009 × cvx2, where H = height (cm) and cvx = 806 (critical "x" value; given in days). Additionally, the exponential model of W~H was estimated by the following equation: BW = 4.25 × exp(0.034 ×H), where BW is in kilograms and H = height (cm). A cross validation demonstrated that all equations had very high accuracy and precision. Overall, these models demonstrated that BW and BW-to-height ratio increase linearly as a function of age, while BW follows an exponential growth pattern as a function of height. Additionally, the H~A model predicted that heifers achieve a maximum height of 138.6 cm at 806 d of age.