Modeling extended lactations of Holsteins

Modeling extended lactations for the US Holsteins is useful because a majority (>55%) of the cows in the present population produce lactations longer than 305 d. In this study, 9 empirical and mechanistic models were compared for their suitability for modeling 305-d and 999-d lactations of US Holsteins. A pooled data set of 4,266,597 test-day yields from 427,657 (305-d complete) lactation records from the AIPL-USDA database was used for model fitting. The empirical models included Wood (WD), Wilmink (WIL), Rook (RK), monophasic (MONO), diphasic (DIPH), and lactation persistency (LPM) functions; Dijkstra (DJ), Pollott (POL), and new-multiphasic (MULT) models comprised the mechanistic counterparts. Each model was separately tested on 305-d (>280 days in milk) and 999-d (>800 days in milk) lactations for cows in first parity and those in third and greater parities. All models were found to produce a significant fit for all 4 scenarios (2 parity groups and 2 lactation lengths). However, the resulting parameter estimates for the 4 scenarios were different. All models except MONO, DIPH, and LPM yielded residuals with absolute values smaller than 2 kg for the entire period of the 305-d lactations. For the extended lactations, the prediction errors were larger. However, the RK, DJ, POL, and MULT models were able to predict daily yield within a +/- 3 kg range for the entire 999-d period. The POL and MULT models (having 6 and 12 parameters, respectively) produced the lowest mean square error and Bayesian information criteria values, although the differences from the other models were small. Conversely, POL and MULT were often associated with poor convergence and highly correlated, unreliable, or biologically atypical parameter estimates. Considering the computational problems of large mechanistic models and the relative predictive ability of the other models, smaller models such as RK, DJ, and WD were recommended as sufficient for modeling extended lactations unless mechanistic details on the extended curves are needed. The recommended models were also satisfactory in describing fat and protein yields of 305-d and 999-d lactations of all parities.