Using saturation rational function models to calculate yield adjustment factors across varied milking frequencies

Area of Science:

• Animal Science
• Dairy Science
• Mathematical Modeling

Background:

• Milking frequency is a key factor influencing milk yield in dairy cows.
• Yield response to milking frequency is nonlinear, exhibiting saturation.
• Accurate prediction of yield adjustment factors is crucial for optimizing dairy farm management.

Purpose of the Study:

• To introduce and evaluate a novel polynomial rational function model for deriving milk yield adjustment factors.
• To compare the performance of the polynomial model against an existing exponential rational function model.
• To assess the utility of using 2x milking data for predicting yield across frequencies.

Main Methods:

• Development of a polynomial rational function model (ratio of 2 polynomials with 3 parameters).
• Comparison of model performance using root mean square error (RMSE) and R-squared (R²) metrics.
• Evaluation of model accuracy in predicting yield adjustment factors for unobserved milking frequencies.

Main Results:

• The polynomial rational function model showed higher accuracy (RMSE = 0.004, R² = 0.999) than the exponential model (RMSE = 0.011, R² = 0.994).
• Both models fit data well up to 10x milking frequency and predicted factors for absent data.
• The exponential model was more robust with limited milking frequency data coverage.

Conclusions:

• The polynomial rational function model offers enhanced flexibility and accuracy for predicting milk yield adjustments across diverse milking frequencies.
• While accurate, extrapolation of yield factors far beyond observed data requires caution.
• The study provides valuable insights into modeling dairy cow lactation yields based on milking frequency.