Modeling daily energy balance of dairy cows in the first three lactations

Daily energy balance was calculated for 111 Holstein cows in their first 3 lactations, based on combinations of smoothed preadjusted phenotypic records for milk yield, feed intake, live weight, and body condition score. Two energy balance traits were defined: one based on milk yield and feed intake (EB1) and the other on live weight and body condition score change (EB2). Bessel functions (BF), Legendre polynomials ( LP), sinusoidal functions ( SF), and cubic splines ( CS) were used to model energy balance within and across lactations. Models with BF or LP fitted fixed regressions of order 1 to 6 and random regressions of order 1 to 10. Cubic splines were fitted at 5 to 30 equally spaced knot points. In within-lactation analyses with BF and LP models, likelihood ratio tests revealed that the fit improved significantly up to random regression order of 5 for EB1 and 4 for EB2, independently of the fixed regression order. For EB1 analyses with LP, improvement was marginal albeit significant even for higher random regression order. For CS models, optimal number of knot points was 13 and 12 for EB1 and EB2, respectively. Residual variance and comparisons between actual and predicted energy balance showed that LP of minimum order 8 and 5 modeled, respectively, EB1 and EB2 better than the other 3 functions. In across-lactation analyses with BF and LP models, likelihood ratio tests were significant as the random regression order increased, for any order of the fixed regression. For CS models, optimal number of knot points was 14 and 16 for EB1 and EB2, respectively. Residual variance and comparisons between actual and predicted energy balance showed that models fitting CS and high (>8) random order BF or LP provided the best fit to both traits. However, in an across-lactation analysis, even higher order of LP or BF will be required to provide as good a fit as within-lactation analyses.