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

Authors: WU, XIAO-LIN - Council On Dairy Cattle Breeding; COLE, JOHN - Council On Dairy Cattle Breeding; Miles, Asha; Van Raden, Paul

Submitted to: Journal of Dairy Science Communications
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 8/5/2025
Publication Date: 11/1/2025
Citation: Wu, X., Cole, J., Miles, A.M., Van Raden, P.M. 2025. Using saturation rational function models to calculate yield adjustment factors across varied milking frequencies. Journal of Dairy Science Communications. 6(6):786–791. https://doi.org/10.3168/jdsc.2024-0720.
DOI: https://doi.org/10.3168/jdsc.2024-0720

Interpretive Summary: Milking frequency significantly impacts milk yield in dairy cows, with higher frequency generally increasing lactation yields. However, such differences are due to environmental or management factors, requiring adjustments in genetic evaluations to ensure fair comparisons among cows with different milking patterns. The study compared new adjustment functions, polynomial vs. exponential, and both accurately predicted responses to varying milking frequencies. The polynomial function was more flexible, whereas the exponential function was more robust with limited data. The study also used standard 2X milking data to predict adjustment factors for higher frequencies but caution against extending this too far beyond available data. This research can improve genetic evaluations and cow management by more precisely adjusting yields from cows with unequal milking frequencies.

Technical Abstract: Milking frequency significantly impacts milk yield in dairy cows, with higher frequency generally leading to increased lactation yields. The increase follows a non-linear pattern, showing diminishing returns as milking frequency rises and eventually reaching saturation at elevated milking frequencies. This study introduces a polynomial rational function model to derive yield adjustment factors across different milking frequencies. Formulated as a ratio of two polynomials, this model has three 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 10X and successfully predicted yield adjustment factors for milking frequencies where data were absent. The polynomial, rational function model exhibited a higher R^2 accuracy, achieving greater accuracy across a broader range of varied milking frequencies, while the exponential rational function model proved more robust to limited data coverage of milking frequencies. This study also evaluated a strategy leveraging 2X milking data to derive yield adjustment factors across different frequencies. However, caution is advised when extrapolating far beyond the data-supported frequency range.