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Multiphasic analysis of lactation curves in dairy cattle.

Abstract A multiphasic function that considers milk yield to result from an accumulation from more than one phase of lactation was used to describe a lactation curve. Estimated mean milk yields from purebred Dutch Friesian Black and White cows for 15 test d with 20-d intervals, starting from 10 d in milk, were fitted by nonlinear regression using the sum of logistic functions: yt = ∑ i = 1 n { aibi \[ 1 − tan h 2 \( bi \( t − ci \) \) \] } where y t is milk yield (kg) at time t (t = days in milk); n is number of lactation phases (n = 1, 2, 3); tanh is the hyperbolic tangent; for each phase i, a function of parameters a i b i is maximum (peak) yield, c i is time of peak yield, and 2b i −1 is duration, defined as days required to attain about 75% of asymptotic total yield during that phase. Initial yield and 305-d yield were additional functions of parameters. The diphasic function (n = 2) was chosen to estimate parameters for lactation curves for purebred Dutch Friesian Black and White and purebred Meuse-Rhine-Yssel Red and White cows. Effects of breed, parity, and length of lactation on functions of estimates for these parameters were analyzed. Relationships between the two phases of lactation were examined using correlations between functions of estimates for parameters within and between phases.