The reduction in milk yield (RMY) due to impaired health of dairy cows is a common parameter used in economic modelling. Hortet et al. (1999) showed the association between RMY and somatic cell count (SCC) levels in French Holstein cows and proposed a polynomial model to estimate the expected average lossOn the individual cow level RMY can differ, but so far no estimates for the variation around the average RMY are available. Additionally, estimates are based on only one breed. The aim of our study is to investigate the expected variation around the average RMY and to examine the influence of different breeds on the RMY estimation. Combining DHI data from over 900,000 cows from two German federal states (Bavaria and North Rhine Westphalia) over the course of two years yields more than 10 million measurements with high representation of the four most common breeds (Brown Swiss, German Fleckvieh, Holstein-Fresian, Red-Holstein). A quantile regression model with 10%, 50% and 90% bounds stratified for breed was used. Milk yield was calculated using the estimated lactation curve based on laction number, days in milk (DIM) and SCC of all animals, while adjusting for farm size and seasonal effects. Similar to Hortet et al., the SCC was set to 50,000 cells/ml to calculate unimpaired milk yield as a reference. The quantile regression was performed as a generalized additive model with penalized cubic splines using the package "qgam" (Fasiolo et al., 2017) for R (version 3.53). The High Performance Cluster of ZEDAT (Freie Universität Berlin) kindly provided us with computing time. Our results show the absolute reduction in milk yield is dependent on the breed. The highest performing breed “Holstein-Friesian” has a comparably low median absolute RMY at 100 DIM and in the first and second lactation. In contrast the variation is one of the highest of all breeds, with a 90% quantile which is one of the lowest compared to the other breeds and a 10% quantile which shows high losses especially for higher lactation numbers. The relative milk loss curves are shaped similarly for all breeds. Especially at the beginning of the lactation the median RMY closely tracks the 90% quantile with most of the variation within the lower 50% of cows. Towards the end of the lactation the relative RMY increases since healthy milk yield is dropping and absolute RMY is rising. The observed milk loss and it’s variation is similar and only slightly higher for 500,000 and 1 Mio. SCC/ml. Quantile regression allows us to quantify the variation around the estimated median RMY depending on the SCC. We can show that the variation in RMY at 300,000 SCC/ml can be higher than 1.5 liters for Holstein cows. It has already been shown that different pathogens can result in highly different RMY (Gröhn et al., 2010). Further investigation is needed to determine how much of the variation can be explained by a combination of SCC and pathogen. Our model assumes that individual cows stay on their respective milk yield quantiles with increasing SCC. This implies that low performing cows on the 10% quantile will experience the highest RMY, while high performing cows (90% quantile) will experience the lowest RMY. We believe this is unrealistic. If the model assumption is not true and cows change their respective quantiles due to rising SCCs, the observed variation in RMY can only be higher. Our approach therefore provides a lower limit for the total variation of the RMY. We hope to improve the estimation of uncertainty of RMY in the future by better modelling the disease-free milk performance of individual cows.

{"references": ["Hortet, P., Beaudeau, F., Seegers, H., & Fourichon, C. (1999). Reduction in milk yield associated with somatic cell counts up to 600 000 cells/ml in French Holstein cows without clinical mastitis. Livestock Production Science, 61(1), 33\u201342. https://doi.org/10.1016/S0301-6226(99)00051-2", "Fasiolo, M., Goude, Y., Nedellec, R., & Wood, S. N. (2017). Fast calibrated additive quantile regression. Arxiv Preprint, (2000). https://doi.org/10.1097/MD.0000000000007529", "Gr\u00f6hn, Y. T., Wilson, D. J., Gonz\u00e1lez, R. N., Hertl, J. A., Schulte, H., Bennett, G., & Schukken, Y. H. (2010). Effect of Pathogen-Specific Clinical Mastitis on Milk Yield in Dairy Cows. Journal of Dairy Science, 87(10), 3358\u20133374. https://doi.org/10.3168/jds.s0022-0302(04)73472-4", "R Core Team. (2019). R: A Language and Environment for Statistical Computing. Vienna, Austria. Retrieved from https://www.r-project.org/"]}