Differential smoothing of time-series measurements to identify disturbances in performance and quantify animal response characteristics: An example using milk yield profiles in dairy cows

Recent advances in on-farm technology now provide us with multiple time-series of reliably measured indicators of animal performance and status at the level of the individual. This paper presents a smoothing approach for extracting biologically meaningful features from such time series using bovine milk yield data as an example. The main goal of this study was to illustrate how the method can be used to detect production deviations, extract quantifiable features of the deviation profiles, and thus provide means to examine hypotheses concerning the nature of the deviations. The effectiveness of the method was assessed with complete lactation curves from 47 Holstein cows. Within their lactations, the cows were each subjected to 1 nutritional challenge for a period of 4 d (their standard diet: a maize silage-based total mixed ration was diluted with 60% wheat straw), which provoked a decline in the milk yield in all cows. The challenge was imposed between the same calendar days for all cows. Thus, the cows were at different stages of lactation: early (n = 14), mid (n = 15), and late (n = 18). Each milk-yield curve was decomposed into components that capture the short-term deviations of the cow such as the response to the nutritional challenge and describe the phenotypic potential yield function of that cow throughout its lactation. The difference between the 2 components gives a measure of the milk loss. In all, 480 deviations were detected from the complete lactations of 47 cows. The milk loss provoked by the feeding challenge (n = 47) was significantly related to the milk yield immediately before the challenge (r = 0.86, P < 0.01). The correlation between the rate of recovery and milk loss was (r = 0.94, P < 0.01). Further, there was no significant slope (P > 0.1) to the relationship between the ratio (rate of recovery/milk loss) and days from calving, indicating that the force of recovery was unaffected by stage of lactation. These results suggest that differential smoothing can be a useful tool for quantifying biological disturbances in animal performance and for extracting features that relate to the potential and robustness of an animal.