A method to analyze production responses in dairy herds.

Abstract Milk production was simulated in a 50-cow herd averaging 8182kg of 305-d milk with a standard deviation of 1364kg. 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 coefficient of variation of 10% for daily milk production. Five sequential sampling periods, 30 d apart, were randomly selected for the experiment. For each 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 was pulsed into each cow record to simulate a change in milk production. Inputs and number of herds simulated were –1.140kg and 15 herds, 0.909kg and 30 herds, –0.455kg and 20 herds, 0kg and 65 herds, 0.455kg and 21 herds, –0.909kg and 47 herds, 1.140kg and 20 herds, and 2.270kg and 15 herds. Regression by cow was used to estimate milk production change for the known inputs: Milk ijk = Intercept + beta i *DIM ij + TRT ik + ɛ ijk . Parameter estimates for each cow were submitted to analysis of variance with herd as a class variable. The least square mean of TRT (dummy variable for known input of milk volume change) for herd was tested for difference from zero based on a "t" statistic. Herd responses were classed as negative, not different from zero, and greater than zero based on P