Persistency of lactation yield: A novel approach

The objectives of our study were to propose a new, simple, and easy-to-understand definition for persistency of lactation yield and to develop a new mathematical model to describe a lactation curve, one that includes a measure for persistency of lactation yield according to the proposed definition. Our definition of persistency is the number of days during which the level of constant yield is maintained. No lactation model exists that includes a measure of persistency in terms of duration of time or that allows this measure of persistency to be derived from model parameters. It was necessary,therefore, to develop a new model to describe the lactation curve: Y_t = Y_P/t₁ t - Y_P/t₁ Ln [e^t + e^t1/1^t + e^t1] + b₃ Ln[e^t + e^{t1 + P}/1^t + e^{t1 + P}] where y_t = yield at time t, t₁ = time at transition from increased yield to constant yield, y_p = level of constant yield, b₃ = rate of decline in yield from the end of constant yield to the end of lactation, and P = persistency of constant yield. These four parameters measured directly the important biological characteristics of a lactation curve. Two test day data sets, one for individual records from a high-producing cow and one for average records from 17,607 cows, were used to illustrate the model and to estimate persistency. The proposed measure of persistency should be important for genetic selection because it might be desirable to select for increased persistency (e.g., for extended lactations) without increasing peak yield and, hence, subjecting the cow to undesirable stress.