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ABSTRACT: Dairy cow fertility is a complex trait that depends on the cow's physiological status, the farm's environmental and management conditions, and their interactions. Already the slightest improvement in fertility can positively impact a farm's profitability and sustainability. In research, milk progesterone (P4) has often been used as an accurate and feasible way to identify a dairy cow's reproduction status. Moreover, in Europe and Canada, it has been used to improve fertility management on commercial farms as it allows to accurately identify reproduction issues, pregnancy, and the optimal insemination window. An on-farm P4 device (OPD) automatically samples, measures, and monitors the milk P4 concentration of individual cows. To this end, the P4 data are smoothed to be robust for measurement errors and outliers, and fixed thresholds are used to estimate the time of luteolysis preceding ovulation, thereby generating a luteolysis alert (LA). By smoothing the P4 data, the OPD introduces a time lag on the LA. Variation in this time lag is not considered in the estimation of the optimal insemination window that is advised to the farmer. Ignoring this variation might decrease the accuracy of the optimal insemination window and, therefore, decreases the likelihood of conception. We hypothesize that considering the length of the time lag and adapting the advice accordingly improves the conception rate. This observational retrospective study uses an extensive dataset from 17 commercial dairy farms that are equipped with an OPD. We estimated the time lag on the alerts and evaluated their relationship with the interval from LA to insemination for successful (n = 3,721) and unsuccessful inseminations (n = 3,896) separately. Results showed that the probability of conception increases when a longer LA time lag is compensated with a shorter interval from LA to insemination and vice versa. In addition, for successful inseminations, we found a clear negative relation between the time lag and the interval from LA to insemination and the interval was significantly shorter when the time lag of the LA was longer. This negative relation between time lag and interval from LA to insemination was less pronounced for unsuccessful inseminations. Additionally, we evaluated the conception rates for inseminations that are performed too early, in time, or too late with respect to the optimal insemination window advised by the OPD, in function of their associated time lags. We found that, for inseminations that were preceded by a short time lag (

Early predictions of cows' probability of survival to different lactations would help farmers in making successful management and breeding decisions. For this purpose, this research explored the adoption of joint models for longitudinal and survival data in the dairy field. An algorithm jointly modelled daily first-lactation sensor data (milk yield, body weight, rumination time) and survival data (i.e., time to culling) from 6 Holstein dairy farms. The algorithm was set to predict survival to the beginning of the second and third lactations (i.e., second and third calving) from sensor observations of the first 60, 150, and 240 days in milk of cows' first lactation. Using 3-time-repeated 3-fold cross-validation, the performance was evaluated in terms of Area Under the Curve and expected error of prediction. Across the different scenarios and farms, the former varied between 45% and 76%, while the latter was between 3.5% and 26%. Significant results were obtained in terms of expected error of prediction, meaning that the method provided survival probabilities in line with the observed events in the datasets (i.e., culling). Furthermore, the performances were stable among farms. These features may justify further research on the use of joint models to predict the survival of dairy cattle.