Distribution of time to first postpartum estrus in beef cattle

The function of a distribution that describes postpartum interval (PPI) under any experimental treatment is useful for simulation modeling, understanding the effects of stimuli on the endocrine system, and estimating the average PPI in experiments terminated before all animals have expressed estrus. This study was undertaken to compare the fit of three statistical distributions, the Weibull, the log-normal, and the linear hazard rate (LHR), to the empirical distribution of PPI for five treatment regimens: no bull exposure postpartum, bull exposure from 53 d postpartum, bull exposure from 3 d postpartum, and bull exposure from an average of 63 d postpartum for 2-yr-old cows and for mature cows. The Weibull and the log-normal distributions deviated considerably from the empirical distribution. The LHR distribution with parameters changing over three different regions gave an excellent fit. The resulting hazard rate (instantaneous probability of a cow expressing her first estrus at time t postpartum) revealed a low probability of expressing estrus within 27 d postpartum (43 d for 2-yr-olds). For cows not exposed to bulls, the hazard rate increased slowly with time. For cows exposed to bulls after 3 d postpartum, the hazard rate increased rapidly between d 27 and d 50. For cows exposed to bulls after 53 d postpartum, the hazard rate increased instantaneously approximately 12 d after initial exposure to bulls. This increase was also seen when cows were exposed to bulls beginning at a constant date (at an average of 63 d postpartum). Because of lack of fit, the Weibull and the log-normal distributions should not be used in survival analysis of PPI.(ABSTRACT TRUNCATED AT 250 WORDS)