A method to analyze production responses in dairy herds

Milk production was simulated in a 50-cow herd averaging 8182 kg of 305-d milk 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 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 -1.140 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 known inputs: Milk(ijk) = Intercept + beta(i)*DIM(ij) + TRT(ik) + epsilon(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 < 0.10. Herd responses were categorized based on the known input to assess the ability of the method to detect a change in production. The mean estimate of TRT from the regression analysis was used to assess the ability of the method to estimate the magnitude of the known input. The regression method was able to detect changes 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 test day is necessary to correct for the bias in linear regression to estimate response across the curvilinear milk production function.