Modeling lactation curves: classical parametric models re-examined and modified

A large number of methods for modeling lactation curves have been proposed – parametric and nonparametric, mathematically or biologically oriented. The most popular of these are methods that express the milk yield in terms of time via a parametric nonlinear functional equation. This is intuitive and allows for relatively easy mathematical and biological interpretations of the parameters involved. Interestingly, as far as we are aware, all such models generate nonzero milk yields on the whole positive time half-line, even though real lactation curves always have finite range, with spans of approximately 300 days for dairy cows. For this reason, we re-examine a number of existing parametric models, and modify them to produce finite-range lactation curves that fit remarkably well to data of milk yields from New Zealand cows. The use of daily or weekly yields rather than the monthly yields normally considered reveals considerable variation that is usually suppressed. Both individual and herd lactation curves are examined in the present paper, and median-based procedures explored as alternatives to the usual average-based methods. These suggestions offer further insights into the existing literature on modeling lactation curves.