Traditionally, 12 to 13 months has been considered to be the economically optimal calving interval for dairy cows (1, 2). Such a calving interval can maximize milk yield per cow per year, making use of peak production at the beginning of every lactation (3, 4). However, whether this yearly calving interval is the most optimal choice for every cow is now being questioned in the literature. First, cows can suffer from a negative energy balance at early lactation, especially high-producing cows (5, 6). Subsequent conception rates might therefore be low as cows may not have recovered from the metabolic problems caused by this negative energy balance (7, 8). Second, a yearly calving interval can result in cows being dried off with a relatively high milk yield at the end of the lactation. This has been described as a risk factor for poor udder health in subsequent lactations (9, 10). Third, a yearly calving interval might be an indication for more metabolic disease treatments per year (11). More costs (labor, veterinarian and insemination) may then be incurred and the cow’s health, welfare and lifespan may be impaired (12, 13).

Extending lactation has been proposed as a solution to solve the above-mentioned issues. By extending lactation, farmers deliberately delay the first insemination moment. Several advantages of extended lactation have been identified (14–16). Extended lactation could benefit cow health and production efficiency due to fewer transition periods in the lifespan of the cow. Extending the voluntary waiting period (VWP) for some cows has resulted in higher milk yield per day of calving interval (14, 17, 18). In addition, extending the VWP can lower milk yield during the last 6 weeks before dry-off and benefit udder health in the following dry period and the next lactation (10, 15, 18). Other advantages of extending lactation are that it may reduce greenhouse gas emissions per kg of milk produced, increase profitability and improve cow welfare (19–21). However, not all cows are suitable for extended lactation and the optimal VWP may vary per cow. It is therefore important to select the right cow for extended lactation (22, 23).

Maintaining milk production in late lactation is a prerequisite for extended lactation (15, 24, 25). Persistent cows decrease their milk yield at a lower rate after the peak day, resulting in a flatter lactation curve than non-persistent cows. Persistency is one of the factors that affect body condition scores at the end of the lactation, thus avoiding the risk of parturition diseases after the subsequent calving (26, 27). From an economic perspective, extending lactation of persistent cows could increase the net partial cash flow at herd level (4). Extended lactations will be more beneficial, especially in herds with more persistent cows (28). Definitions of lactation persistency differ between previous studies. Persistency was defined as the milk yield difference at selected DIMs or the declining slope of milk yield within selected intervals after peak yield (18, 29, 30). Persistency can also be determined by using lactation curve models which quantify the lactation curve based on all available milk yield data (31, 32). One of the lactation curve characteristics that defines the curve is the decay, a lactation curve characteristic that can easily be transformed into other measures of persistency as the number of days it takes to halve milk production in the declining stage of lactation (32).

When deciding on the VWP of an individual cow, it is useful to be aware of the persistency for the remainder of that lactation, especially for farmers who consider persistency in their reproduction management. Predictions of persistency for the current lactation could thus provide additional information to optimize the VWP. Currently, breeding values for persistency are calculated for dairy cows (33–35) but, to our knowledge, prediction models to accurately predict persistency at the moment of insemination are lacking.

This study aims to determine whether it is possible to predict lactation persistency for DIM 305 at different insemination moments (DIM 50, 75, 100, and 125) based on available cow and herd data (excluding breeding values).

Over all lactations the average M305 of primiparous cows (n = 11,562) varied between 6,253 (5%) and 11,390 (95%), with a mean of 8,809 kg. The average M305 of multiparous cows (n = 15,195) varied between 7,833 (5%) and 13,786 (95%), with a mean of 10,813 kg. The average decay-305 of primiparous cows was lower than that of multiparous cows (1.55 *10⁻³ vs. 2.41*10⁻³, equivalent to a persistency of 447 vs. 288 days, respectively).

Descriptive statistics for the independent variables are only shown for DIM 75 (Table 2); the statistics for the other insemination moments (DIM 50, 100, and 125) can be found in GitHub.

The model performance indicators of the prediction models for decay-305 at all selected insemination moments are summarized in Table 3A. Among all models, we found higher R² and lower RMSE, MAE and MAPE at later insemination moments. The R² of models for decay-305 range from 0.266 to 0.407, while RMSE, MAE and MAPE were slightly improved along the selected insemination moments.

Standardized coefficients of the model predicting decay-305 at all potential insemination moments are shown in Figure 3. Among all potential insemination moments, all variables had similar effects on the models. The three most influential variables affecting decay-305 were calving in autumn, daily milk yield and magnitude. However, the specific order of these variables varied across different models. Take model at DIM 75 for example, cows calving in autumn had on average 3.24 (SE = 0.14) lower decay (*10⁴) respectively than calving in winter. Increasing one unit of daily milk yield (7.90 kg) corresponded to an average 2.99 (SE = 0.17) decrease in decay (*10⁴). Increasing one unit of magnitude (9.22 kg/day) corresponded to an average 2.62 (SE = 0.18) increase in decay (*10⁴). Table 3B shows the results of the prediction models for M305, which showed much higher R².

This study aimed to predict lactation persistency for DIM 305 at insemination moments DIM 50, 75, 100, and 125. Our models have low prediction accuracy, although predictions improved at later insemination moments.

In our study, we used decay to measure persistency. The R² of all decay models was under 0.407, suggesting the bad predictive power of the model with all available information included (49). Using the same methodology, we were able to predict M305 much more accurately, thus confirming our prediction methodology to be valid for M305. Similar to previous studies (46, 47, 50), M305 was predictable at all insemination moments with R² values ranging between 0.79 and 0.92 for the different insemination moments. Other methodological approaches were explored to improve the prediction performance of the decay-305 models. First, we explored building prediction models for two parity groups separately. The results were similar (results shown in GitHub). Next to the linear regression, we built models using random forest, lasso regression and ridge regression but results were similar (results shown in GitHub). Models from lasso regression and ridge regression showed the same results to linear regression, indicating that penalization did not improve our models. In addition, adding LCC from the previous lactation did not improve the models in our study (results shown in GitHub).

In the current study, we only included cow and herd information in the prediction models that was available through the MmmooOgle herd management software. As persistency is a heritable trait and could be a target for selection (33, 51, 52) others have tried adding its breeding value to prediction models, though with little success (53). It’s worth noting that the heritability of persistency varies, influenced by factors like the definition of persistency, the breed, and the parity of the cows, with heritability values spanning the range of 0.01–0.33 (34, 52, 54). Breeding values were not available in our dataset. Persistency is furthermore influenced by feed management in herd (55, 56). We took into account this herd-level factor by including HLCC and HM305 into all of our models, rather than including herd as a random effect. This approach allows us to apply our prediction model to unknown farms and effectively consider the impact of herd-level factors on the study outcomes.

There is little existing literature to predict persistency for the mid-late lactation based on data from the beginning of lactation and herd information. We chose to predict persistency for DIM 305 because this is a classic time point for measurements like M305. Other studies chose to predict different parameters to help make insemination decisions. For example, Kjeldsen et al. predicted energy-corrected milk per day of calving interval at DIM 40 for primiparous and multiparous cows separately (53). They included the calving interval in the model while the future calving interval is actually unknown at the moment of making the insemination decision. We assumed that, in their research, predicting milk yield per day of calving interval was equivalent to predicting the milk yield. Another example, Manca et al. (57) used the threshold of daily milk yield at DIM 305 to determine whether a cow is persistent, and defining persistent cows as those with a daily milk yield at DIM 305 greater than 20 kg. Essentially, they used the lactation curve characteristics of the first DIM 90, 120, and 150 to predict the future daily milk yield at DIM 305. The results of Manca et al. (57) correspond with our results on predicting M305 as both achieved a high accuracy. It is important to note that persistency in our study primarily focuses on the slope or rate of decline in milk production over time. Consequently, persistency cannot be directly translated into the exact amount of milk that drops per day without knowledge of the initial peak milk production level. This consideration should be kept in mind when interpreting the findings and conclusions of this study.

Our prediction models could predict M305 well but could not predict persistency for DIM 305 accurately. We hypothesized that M305 is highly predictable due to its association with peak yield (42, 58). Peak yield estimation was commonly established at our insemination moments from DIM 50 onwards (59, 60). In contrast, persistency was not highly correlated with information in early lactation. Additionally, the low prediction accuracy observed in our study may be attributed to other factors that influence persistency between the insemination moments and DIM 305. One potential factor that could impact persistency is pregnancy. However, we were unable to account for the pregnancy effect in our prediction model due to several reasons. Firstly, the exact timing of pregnancy is unknown at the time of making predictions for open cows. Secondly, the quantification of the pregnancy effect on persistency is lacking in previous studies, making it difficult to incorporate it into the model. As a result, we were unable to correct for the pregnancy effect in our prediction model.

There are multiple measures of persistency, and all these measures require the transformation from raw milk data (18, 61, 62). Simple measures of persistency are typically fixed at two time points in lactation (61–63), limiting the ability to observe persistency changes throughout the lactation. To overcome this limitation, we employed lactation curve modeling using the MilkBot model, which allowed to assess persistency at any timepoint within the lactation period. This so called continuous measurement provides insights into the changes of persistency during lactation.

Our data were obtained from AMS farms and we therefore had access to milk production data for each robot visit. Such detailed data did not, however, result in high prediction values. The average M305 of the involved farms was higher than that of average dairy farms in the Netherlands and Belgium (64, 65). Higher milk production can be explained by more frequent milking on AMS farms than on conventional farms (66, 67). In our study, we deliberately only included cows with an ‘Open’ breeding status at the selected insemination moments. ‘Open’ was defined as cows which were not pregnant at the insemination moment but which could be pregnant in the future. Those open cows were the target object of our study since their insemination decisions were yet to be made. In our study, we only included lactations over 305 days, a period commonly accepted by the global standard for livestock data (68).

Our results showed that based only on cow and herd milk production information, predicting persistency for DIM 305 at different insemination moments (DIM 50, 75, 100, and 125) is challenging. The accuracy of the predictions was found to be low in our models. In order to target decision-support at the insemination moment, other information is needed to improve the accuracy in predicting persistency.

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Ethical approval was not required for the studies involving animals in accordance with the local legislation and institutional requirements because the research only involved observational data, without any direct intervention or harm to the animals involved. Written informed consent was not obtained from the owners for the participation of their animals in this study because the research relied on publicly available data from MmmooOgle programme (Puurs, Belgium) and did not involve any direct interactions with the animals or their owners, thereby not requiring explicit consent.

YC: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. WS: Conceptualization, Methodology, Supervision, Writing – review & editing. MN: Conceptualization, Methodology, Supervision, Writing – review & editing. MH: Conceptualization, Methodology, Supervision, Writing – review & editing.