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Title:   Author  item
                                            DEMATAWEWA, C - VPI & SUitem
                                            PEARSON, R - VPI & SUitem
                                            Vanraden, Paul
  Submitted to: Journal of Dairy Science
                                    Publication Type: Abstract Only
                                    Publication Acceptance Date: 2/17/2006
                                    Publication  Date: 7/9/2006
                                    Citation: Dematawewa, C., Pearson, R.E., Van Raden, P.M. 2006. Modeling extended lactations in Holsteins [abstract]. Journal of Dairy Science. 89(Suppl. 1):96-97(abstr. 35).Interpretive Summary:
                                Technical Abstract: The objective of this study was to develop an equation for predicting average yield of cows still in milk from 1 to 999 days.  Test day yields (kg/d) of 903,529 lactations of 305,202 Holstein cows calved between 1997 and 2003 were used.  Average daily yield (Y) for each 30-d interval of lactation was calculated for each parity (9 parities), based on cows which were in milk during the month considered.  Various lactation models available in literature (i.e. Wood’s model and other variants of incomplete Gamma function, inverse polynomials and, mono-, di-, and multi-phasic curves) were tested, before and after a modification made by including a new additive parameter, k. Nonlinear regression procedures in SAS were carried out between Y (34 30-d means) and respective days in milk (DIM), within and across parities.  R-squared value, mean square error, Bayesian information criteria, and autocorrelation of errors were considered as the model selection criteria.  Standard models underestimated yields in later stages of lactation for every parity, but improved when modified to include constant k.  The modified Dijkstra model (i.e. Y= k + a[exp(b(1-exp(-c*DIM))/c – d*DIM)]) fitted best (R squared = 0.99), both within and across parities, with the lowest estimates of mean square error and Bayesian information criteria (BIC=59.6). The parameter estimates for a, b, c, d, and k were 12.9088, 0.0183, 0.00806, and 0.00925, and 20.1303, respectively, for across parities.  Durbin-Watson statistic showed that the first order autocorrelations of errors were negligible for the above model for both within and across parities (DW=1.412, N=34).  The modified mono-phasic curve (i.e. Y = k + ab[1- tanh2 (b(DIM-c))]) provided the second best fit for both within and across parities.  These results show that modified Dijkstra formula stated above can be effective in modeling the mean yield of cows remaining in milk through lactations well beyond 305 days.


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