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Title:   Author  item
                                            DEMATAWEWA, C.M.B. - VPI & SUitem
                                            PEARSON, R. - VPI & SUitem
                                            Vanraden, Paul
  Submitted to: Journal of Dairy Science
                                    Publication Type: Peer Reviewed Journal
                                    Publication Acceptance Date: 3/28/2007
                                    Publication  Date: 8/1/2007
                                    Citation: Dematawewa, C., Pearson, R.E., Van Raden, P.M. 2007.  Modeling Extended Lactations of Holsteins. Journal of Dairy Science. 90(8):3924-3936.Interpretive Summary: Understanding of the lactation curve of dairy cows is important for efficient management, breeding and profit maximization of dairy enterprises.  Currently majority of the US Holstein cows produce milk beyond the standard 305 days.   Many formulas have been developed to model the standard 305 day lactations.  This study compares a set of nine widely used lactation curves on their ability to predict 305 day as well as 999 day lactations, and finds that some of the simple formulas are more favorable than the complicated ones since the computational difficulties associated with complicated formulas outweigh their marginal superiority in prediction accuracy.
                                Technical Abstract: Modeling extended lactations for the US Holsteins is useful as a majority (>55%) of the cows in the present population produce lactations longer than 305 d.  In this study nine empirical and mechanistic models were compared on their suitability for modeling 305-d and 999-d lactations of US Holsteins.  A pooled data set of 4266,597 test day yields from 427,657 (305-d complete) lactation records from the AIPL-USDA database were used for model fitting.  The empirical models included Wood (WD), Wilmink (WIL), Rook (RK), Monophasic (MONO), Diphasic (DIPH), and Lactation Persistency (LPM) functions while Dijkstra (DJ), Pollott (POL), and New-Multiphasic (MULT) models comprised the mechanistic counterparts.  Each model was separately tested on 305-d (>280 DIM) and 999-d (>800 DIM) lactations for cows in first parity and those in third and greater parities, as those four scenarios showed distinctly different lactation curve shapes. All models were found to produce a significant fit for all four cases.  However, the resulting parameter estimates were unique to each case.  All except MONO, DIPH and LPM models yielded residuals with absolute values smaller than 2kg for the entire period of the 305-d lactations.  For the extended lactations, the prediction errors were larger.  However, RK, DJ, POL and MULT models were able to predict daily yield within ±3 kg range for the entire 999 d period.  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 others models were small.  Conversely, POL and MULT were often associated with poor convergence and highly correlated, unreliable and/or biologically atypical parameter estimates.  Considering the computational problems of large mechanistic models and 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.  All models considered were also satisfactory in describing fat and protein yields of 305-d and 999-d lactations of all parities.


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