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

Milking frequency significantly affects milk yield in dairy cows, with higher frequency generally leading to greater lactation yields. The increase follows a nonlinear pattern, showing diminishing returns and eventually reaching saturation as milking frequency rises. This study introduces a polynomial rational function model to derive yield adjustment factors across different milking frequencies. Formulated as a ratio of 2 polynomials, this model has 3 parameters to capture the initial increase in yield and the saturation rate, offering enhanced flexibility across various milking frequencies. We compared its performance to a recently proposed exponential rational function model. Both models demonstrated a good fit to varying milking frequency data up to 10× and satisfactorily predicted yield adjustment factors for milking frequencies where data were absent. The polynomial rational function model exhibited a higher accuracy (root mean square error [RMSE] = 0.004; R² = 0.999), achieving greater accuracy across a broader range of varied milking frequencies, compared with the exponential rational function model (RMSE = 0.011; R² = 0.994). Nevertheless, the latter model proved more robust to limited data coverage of milking frequencies. This study also evaluated the strategy of leveraging 2× milking data to derive yield adjustment factors across different frequencies. However, caution is advised when extrapolating far beyond the data-supported frequency range.