A partial adjustment model to describe the lactation curve of a dairy cow

Abstract

A new model is proposed to describe the lactation curve of a dairy cow. It uses the fact that milk yield at a given stage of lactation is largely determined by the yield in the preceding stage. The model is written as: y_t = λ(m₀ – m₁t) + (1 – λ)y_t–1. t ≥ 1, 0 ≤ λ ≤ 1, where y₁, and y_t–1 are the current and preceding milk yields in kg/week, and the constant × estimates the fraction (1–λ) by which milk yield adjusts to the level at the next stage. The fraction (1–λ) by which the milk yield persists at the preceding level is used to define a measure of persistency, P = (1–λ)m₀/m₁ weeks, where m₁ is the rate of decline in kg/week and m₀ is a constant.