On the mathematical description of lactation curves

Publisher Website
Google Scholar
Abstract
SUMMARY: The lactation curve may be represented mathematically by the general equation Y = Aϕ1(t)ϕ2(t), where A is a positive scalar, ϕ1,(t) is a positive monotonically increasing function with an asymptote at ϕ1 = 1, and ϕ2 is a monotonically decreasing function with an initial value of unity and an asymptote at ϕ2 = 0. Functions considered as candidates for ϕ1 were: (Mitscherlich), (Michaelis-Menten), (generalized saturation kinetic), 1/(1 + b0 (logistic), b0 exp (Gompertz) and [1+ tanh(b0 + b1t)]/2 (hyperbolic tangent). Candidates for ϕ2 were e–ct (exponential) and 1/(1 + ct) (inverse straight line). The 12 models thus obtained and Y = Atb e–ct (Wood's model) were fitted to whole-lactation data from 23 animals. Mitscherlich x exponential, Michaelis-Menten x exponential, logistic x exponential, logistic × inverse straight line and Wood's model all fitted well. For these models, expressions for time to peak, maximum yield, total yield over a finite lactation and relative decline at the midway point of the declining phase were obtained. The Mitscherlich x exponential model generally fitted better than Wood's model and, unlike Wood's model, gives simple algebraic formulae for all these summary statistics.