Prediction of Milk Yield and Lactation Curve of Dairy Cows: A Comparative Analysis of Three Mathematical Models in Tropical Smallholder Dairy Farm

Source abstract

Accurate milk yield prediction is essential for effective dairy herd management, particularly in smallholder dairy where daily milk recording is often limited. Predictive models that can estimate total milk yield during one lactation period using early-stage recording data offer a practical solution to support decision-making in such environments. This study aimed to evaluate the predictive performance of three mathematical models, i.e incomplete gamma function model , orthogonal polynomial contrast model , and non-linear regression model for estimating total milk production during lactation in dairy cows. Milk yield data were obtained from 164 Holstein-Friesian cows across five lactation parities at a dairy cooperative in East Java, Indonesia. Milk production records over the first three months (13 weeks) of lactation were used to estimate total 305-day (44 weeks) milk yield using three predictive mathematical models, each fitted with parity-specific constants (a, b, c). Model performance was evaluated by comparing predicted and actual milk yields, using absolute and percentage errors as accuracy metrics. All models demonstrated acceptable predictive ability under weekly data conditions, with average percentage errors below 10%. The incomplete gamma function model showed the highest predictive accuracy and stability with lowest deviation (average deviation: 274.67 L; 6.17%), followed by orthogonal polynomial contrast model (324.43 L; 7.29%) and non-linear regression model (346.27 L; 7.78%). Those mathematical model exhibited stronger alignment with biological lactation patterns, and more sensitive to variation across parities. Frequent data collection enhances the accuracy of milk yield predictions. The incomplete gamma function model is recommended for initial milk yield prediction in smallholder dairy systems, offering an optimal balance between flexibility and biological plausibility. These findings support the integration of predictive modeling into routine herd management practices to improve productivity and sustainability.