State Key Laboratory of Animal Nutrition, Institute of Animal Science, Chinese Academy of Agricultural Sciences, Beijing 100193, P. R. China.
State Key Laboratory of Animal Nutrition, Institute of Animal Science, Chinese Academy of Agricultural Sciences, Beijing 100193, P. R. China.
J Dairy Sci. 2021 Jan;104(1):981-988. doi: 10.3168/jds.2020-18183. Epub 2020 Oct 31.
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: MY = 16.90 + 0.74MY - 0.25TA_max + N, where N is white noise. This model can be used to track and predict the dynamic response of MY to TA_max.
先前的研究表明，奶牛的日产量与热应激之间存在滞后关系。在测试日之前，热应激指标（如温湿度指数和环境温度）的值与测试日的日产量呈简单相关。然而，这种简单的相关性可能不是最好的描述，因为日产量和热应激指标具有时间序列的共同性质，它们的相关性是交叉相关，可能受到自相关的影响。我们希望通过传递函数建模排除自相关来更可靠地估计日产量的滞后关系。在这项研究中，我们发现基于传递函数建模的日产量与热应激指标之间存在滞后关系。热应激指标包括环境温度和温湿度指数。从 2016 年 7 月 10 日至 9 月 10 日连续 63 天期间，获得了 123 头奶牛的日产量数据。每日牛奶产量（MY）和最大日环境温度（TA_max）满足平稳性假设，并计算了它们之间的交叉相关。在排除自相关之前，测试日后 0 到 4 天的 MY 与测试日的 TA_max 具有显著的交叉相关性。在排除自相关的影响后，测试日后 1 到 3 天的 MY 与测试日的 TA_max 具有显著的交叉相关性。这一结果表明，MY 会在测试日之后的第 1 天对 TA_max 做出反应。此外，MY 和 TA_max 之间的交叉相关强度从第 1 天到第 3 天依次降低，表明 MY 的滞后响应呈下降趋势，持续 3 天。MY 和 TA_max 的传递函数模型为：MY = 16.90 + 0.74MY - 0.25TA_max + N，其中 N 为白噪声。该模型可用于跟踪和预测 MY 对 TA_max 的动态响应。
