Morant SV, Gnanasakthy A. A new approach to the mathematical formulation of lactation curves. Anim Prod Sci. 1989 Oct;49(2):151-62.

Six alternative lactation curves were derived by considering the proportional rates of change in milk yield during lactation. Experimental data showed that rates of change do not necessarily fall to a constant value in mid and late lactation. This accounts for the systematic lack of fit reported by several authors using the derivative of the incomplete gamma function, whose second derivative has a horizontal asymptote. Curves whose derivatives are not restricted in this way described patterns of milk yield in first to third lactation animals more closely. Some statistical properties of their parameters have been examined. The curve loge (y) = a - bt'(1 + kt') + ct'2 + d/t, where t is days since calving, t' = t – 150, A: is a constnat and a, b, c and d are parameters to be estimated, is recommended. This curve was also fitted to yields of milk fat, protein and lactose.

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