Quantifying nonlinear dynamics and key drivers of herd-level milk yield and losses under meteorological and physiological stressors in Holstein cattle.

Meteorological and physiological stressors significantly impair dairy farm productivity and profitability. Although their impacts on individual cows have been extensively analyzed, macroscopic herd-level dynamics require further investigation to inform farm-wide decision-making. Therefore, the main objective of this study was to quantify the nonlinear effects of various stressors on herd-level performance and identify the key drivers of herd productivity and variability from a population perspective. We collected high-frequency milk yield records from 45,148 Holstein cows across 5 large-scale commercial farms from 2020 to 2024. Using the herd-day as the evaluation unit, the cow-level records were aggregated into herd-level features (the mean and standard deviation of milk yields and milk losses across all cows per herd-day). By integrating statistical analyses, causal inference modeling, and predictive machine learning algorithms, this study evaluated the nonlinear impact of the temperature-humidity index (THI), daily variation of THI, incidences of 5 diseases (udder health; reproductive, metabolic, and digestive disorders; and hoof health), and the proportions of estrus and artificial insemination (AI) on herd-level features. From a population perspective, increased THI and specific disease incidences were identified as drivers of herd-level milk losses. The herd-level features showed robust stability during periods of low meteorological and physiological stresses. When critical thresholds were exceeded (7-d average THI >68.4, 7-d average incidence of udder health >0.36%, or 7-d average incidence of metabolic disorders >1.30%), the rapid increases in herd-level milk losses were attributable to these stressors, culminating in maximum increases of 1.61%, 1.59%, and 2.90%, respectively. Crucially, elevated disease incidence destabilized the herd, driving significant increases in herd-level variability of both milk yield and milk losses, thereby widening the production gap between healthy and stressed subpopulations. Furthermore, the XGBoost models captured the complex nonlinear dynamics for all herd-level features, explaining 89.3% to 95.2% of the variance for milk yield features and 52.4% to 62.3% for milk loss features. The 7-d average THI and the 7-d average incidence of udder health were the primary risk factors impacting the herd-level milk yield and milk losses. Notably, the 7-d average udder health incidence contributed significantly to all milk loss features, accounting for 8.98% to 17.87% of the total feature importance. Overall, this study highlights the adverse impacts of various stressors on herd-level milk yield and milk loss features, facilitating the improvement of population-centric targeted management practices to mitigate milk losses and enhance the overall resilience of commercial dairy farms.