A Biological Approach to Lactation Curve Analysis for Milk Yield

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Abstract
Lactation records of milk yield are commonly analyzed with empirical mathematical models. A family of new models is described based on the known biology of the mammary gland during pregnancy and lactation. The new models fit two logistic curves representing secretory cell differentiation and cell death (apoptosis) throughout lactation. A further function describes secretion rate changes. Both additive and multiplicative forms of the new models are described. Additional terms in the model can account for factors that alter the course of milk yield during the lactation, either by new cell differentiation, a change in the rate of milk secretion loss, or both. The new models were compared with three widely used empirical functions and another biologically based function using weekly records of milk yield taken from 40 dairy cows. The new models fitted the data with a lower residual mean square than the other functions. In addition, the parameters of the new models have a biological interpretation and can be used to discuss key characteristics of lactation. The application of the new models to monthly lactation records is possible, although a reduction in the number of parameters is likely to be required. Some parameters in the cell differentiation function of the models will be poorly estimated from monthly records and can be replaced with average or standard values.