6.2 Modeling Lactations Longer than 305-d

The original implementation of BP was limited to 305-d lactations, although longer lactations can be accommodated by calculating breed- and lactation-specific standard lactation curves ($ \mu$ ) longer than 365-d and estimating covariances among test days for DIM $ >$ 365-d. Additionally, $ \mu$ were constructed using the test interval method [Sargent, Lytton, and WallSargent et al.1968], which uses simple linear interpolation that assumes incorrectly that yields change at a constant rate in the interval between successive test days. Dematawewa et al. DematawewaPVR2007 used data from long lactations to fit a number of lactation curves to test day data for M, F, and P, concluding that Wood's Wood1967 curves best described yield out to 999-d. Standard curves are now calculated using the "smooth" Wood's curves, although the test interval curves are still available (see: INTmethod). However, new curves for SCS yield, as well as SD of M, F, P, and SCS yield, were needed for a complete implementation of smooth curves in BESTPRED. Standard deviations of M, F, and P were modeled using Wood's Wood1967 curves, but there is little work in the literature describing lactation curves for SCS.

Rodriguez-Zas et al. RodriguezZasGS2000 used non-linear mixed effects models which included cow-specific lactation curves to study SCS. A number of functions were fit to SCS yield data for long lactations [Dijkstra, France, Dhanoa, Maas, Hanigan, Rook, and BeeverDijkstra et al.1997,Morant and GnanasakthyMorant and Gnanasakthy1989,NelderNelder1966,Rook, France, and DhanoaRook et al.1993,WilminkWilmink1987,WoodWood1967], and a four-parameter function (C4) described by Morant and Gnanasakthy MorantG1989 provided the best fit (Cole, 2007, unpublished data). As in Rodriguez-Zas et al.'s RodriguezZasGS2000 paper the C4 model overestimated mean SCS early and late in lactation and underestimated it in the middle. However, the other models provided much poorer fits to the data, asymptoting to positive infinity as DIM increased. The C4 function also was used to develop curves for SD of SCS yield.

Curves describing the mean and SD of all traits were developed for each of the major U.S. dairy breeds (Ayrshire, Brown Swiss, Guernsey, Jersey, Holstein, Milking Shorthorn).

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