A Bayesian approach for characterizing uncertainty in declaring a population collapse

Detecting rapid and substantial population declines (collapses) is of considerable importance to many applied ecological fields. Published definitions of a population collapse describe a decline in abundance over time (e.g., 90% decline within 10 years or less). We develop a flexible, rigorous method to account for uncertainty in the magnitude and period of a collapse, and provide a way to estimate the probability of a collapse having occurred. Using Bayesian approaches we quantify uncertainty in the maximum abundance obtained in a time series and the time step in which this maximum is realized. We then use this estimate of uncertainty as a way to set a confidence interval around a specified percentage decline from the maximum, and as a way to acknowledge uncertainty in how many time steps it took for the decline to occur. We apply this method to evaluate the prevalence of collapses among 12 declining native Hawaiian birds, and show a high probability that six of these 12 have declined by ≥90% within 10 years. Our procedure advances current methods for identifying collapses within time series of abundance data by explicitly and transparently accounting for uncertainty in the key component of any definition of a collapse; the maximum abundance.