Modeling standard and extended lactation curves of cows in pasture-based systems using Legendre polynomials

New Zealand's pasture-based dairy systems typically utilize a seasonal 12-mo calving interval with standard lactations (SL) of less than or equal to 305 d. However, there is growing interest in extended lactation systems (EL: ≥400 DIM), with limited studies exploring EL curve models in grazing dairy cows. Lactation curves are useful for characterizing cow milk and milk component yields and could be used to select cows suitable for different farm management systems, such as EL. These models could support the development of a method to predict an animal's suitability for EL. This study aimed to (1) evaluate the suitability of a range of SL and EL lactation curve models (Wood, Wilmink, Dijkstra, and Legendre polynomials) for modeling individual lactations of pasture-based dairy cows and (2) describe daily milk, milksolids (fat + protein), fat, and protein data for spring-calving, pasture-based dairy cows completing either a SL or EL using the most suitable model. In total, 35 commercial herds across 101 production herd-years in New Zealand were identified in the national database as having cows with EL due to intentionally delayed seasonal breeding. From those herds, 6,135 SL and 2,387 EL curves were modeled across a range of breeds and parities using third- and fifth-order Legendre polynomials, respectively. Legendre polynomials were chosen due to their average lower percent relative predictive error of predicted daily yields for EL (8.0%) than Wood (15.5%), Wilmink (14.4%), and Dijkstra (14.5%). Standard lactation cows produced, on average, 6,814 kg of milk, 512 kg of milksolids, 272 kg of fat, and 240 kg of protein per lactation (301 DIM). Cows in EL produced 9,581 kg of milk, 763 kg of milksolids, 410 kg of fat, and 353 kg of protein per lactation (510 DIM). The mean persistency for milk, milksolids, fat, and protein was similar between SL and EL. All breeds and parities had a second peak in yield at approximately 375 DIM during an EL. For both SL and EL, the total yields increased, and lactation persistency decreased with the proportion of Holstein-Friesian genetics relative to Jersey and with increased parity number. Holstein-Friesian cows produced, on average, 747 kg more milk and 8 kg more milksolids than Friesian-Jersey cows across an entire EL. Modeling pasture-based lactations using Legendre polynomials has enabled the variability in curve shapes for EL to be captured, allowing for a more accurate modeling of milk and milk component yields relative to other commonly selected parametric lactation curve methods. Future research should explore environmental-, cow-, and farm-level factors and their interactions not captured in this dataset that influence a cow's lactation characteristics.