The lag response of daily milk yield to heat stress in dairy cows

Previous studies suggest that there exists a lag relationship between daily milk yield and heat stress. The values of heat stress indicators (e.g., temperature-humidity index and ambient temperature) before test day have a simple correlation with daily milk yield on test day. However, the simple correlation might not be the best description because daily milk yield and heat stress indicators have a nature of time series in common, and their correlations are cross correlations that could be affected by autocorrelations. We hope to give a more reliable estimation on the lag relationship of daily milk yield via excluding autocorrelations with transfer function modeling. In this study, we found a lag relationship between daily milk yield and heat stress indicators based on transfer function modeling. Heat stress indicators included ambient temperature and temperature-humidity index. The daily milk yield data from 123 cows were obtained during a consecutive 63-d period (July 10-September 10, 2016). The mean daily milk yield (MY) and the maximum daily ambient temperature (TA_max) satisfied the stationary hypothesis, and the cross correlation between them was calculated. Before excluding autocorrelation, MY at 0 to 4 d after test day had significant cross correlations with TA_max on test day. After excluding the influence of autocorrelations, MY at 1 to 3 d after the test day had significant cross correlations with TA_max on test day. This result suggested that MY would respond to TA_max 1 d after the test day. In addition, the strength of cross correlations between MY and TA_max decreased from 1 to 3 d in sequence, implying a declining lag response of MY that would last for 3 d. The transfer function model for MY and TA max is written as: MYt = 16.90 + 0.74MY(t -1) - 0.25 Til_mar(t-1) + N-t, where N-t is white noise. This model can be used to track and predict the dynamic response of MY to TA_max.

Automated summary

Through transfer function modeling, a lag relationship between daily milk yield and heat stress indicators was identified, with daily milk yield responding to the maximum ambient temperature 1 day after the test day and lasting for 3 days. The strength of cross correlations between daily milk yield and maximum ambient temperature decreased gradually from 1 to 3 days, suggesting a declining lag response of daily milk yield. A transfer function model was established to track and predict the dynamic response of daily milk yield to maximum ambient temperature.