A method to analyze production responses in dairy herds

Milk production was simulated in a 50-cow herd averaging 8182 kg of 305-d m ilk with a standard deviation of 1364 kg. Herd demographics were 35% first lactation, 20% second lactation, and 45% third or greater lactation cows. A lactation model was developed with the Wood's equation (Milk/d = A*DIM*e(( -c*dim))) to which random variation was added to be consistent with a coeff icient of variation of 10% for daily milk production. Five sequential sampl ing periods, 30 d apart, mere randomly selected for the experiment. For eac h of these sampling periods data were simulated for cow, lactation number, milk, and days in milk (DIM). To the third sampling period, a known input w as pulsed into each cow record to simulate a change in milk production. Inp uts and number of herds simulated were -1.140 kg and 15 herds, 0.909 kg and 30 herds, -0.455 kg and 20 herds, 0 kg and 65 herds, 0.455 kg and 21 herds , -0.909 kg and 47 herds, 1.140 kg and 20 herds, and 2.270 kg and 15 herds. Regression by cow was used to estimate milk production change for the know n inputs: Milk(ijk) = Intercept + beta(i)*DIMij + TRTik + epsilon(ijk) Para meter estimates for each cow were submitted to analysis of variance with he rd as a class variable. The least square mean of TRT ( dummy variable for k nown input of milk volume change for herd was tested for difference from ze ro based on a "t" statistic. Herd responses were classed as negative, not d ifferent from zero, and greater than zero based on P < 0.10. Herd responses were categorized based on the known input to assess the ability of the met hod to detect a change in production. The mean estimate of TRT from the reg ression analysis was used to assess the ability of the method to estimate t he magnitude of the known input. The regression method was able to detect c hanges in production greater than 0.455 kg, but is more useful when changes of 0.9 kg or greater are shown. Adjustment for days postcalving on first t est day is necessary to correct for the bias in linear regression to estima te response across the curvilinear milk production function.