Modelling lactation curves of dairy cows with emphasis on individual variability

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Abstract
Five published equations were compared on their ability to adjust different patterns of lactation curves. The equation y(t) = a exp(b1t'2/2 + b2/t – c(l + t'/2)t') with t' = (t – 21·4)/l00 (i) was retained because of the quality of the adjustment and the absence of convergence problems when applied on individual curves. Including an effect of season (SE) and an effect of pregnancy (PE) improved the quality of individual adjustments (no. = 339). The final equation was equal to (i) + SE + PE with SE = a + b cos (2π(wc+ w - l)/52) + c sin(2n(wc+ w - 1)/52), with wc= week of the year at calving, w = week after calving and a = 0·0065, b = -1·26 and c = 0·374, and PE = a (wp–18) e-bwp, with wp= week of pregnancy and a, b fixed parameters. Individual cow characteristics were used to analyse equation (i) parameters. The predictions obtained with this equation and several predictive functions of the equation (i) parameters, which differed in the way they included or not the potential of production, were compared. With no indication of this potential, the prediction was very poor. With the initial production (mean production of the 4th, 5th and 6th days of lactation) as an estimate of this potential, 75% of the lactations had the median of absolute values of errors less than 2·95 kg/day. The results were highly improved by using the yield during the 5th week of lactation. The threshold of 2·95 was reduced to about 2 kg/day. The quality of the individual prediction was better for primiparous than for multiparous cows, and for French Friesian and Montbeliarde cows than for pure or crossbred Holstein cows. Although individual predictions were not always satisfactory, they provided excellent agreement when averaged per group (20 cows).