Uncertainty and the Assessment of Extinction Probabilities

A proper assessment of the probability of early collapse or extinction of a population requires consideration of our uncertainty about crucial parameters and processes. Simple simulation approaches to assessment consider only a single set of parameter values, but what is required is consideration of all more or less plausible combinations of parameters. Bayesian decision theory is an appropriate tool for such assessment. I contrast standard (frequentist) and Bayesian approaches to a simple regression problem. I use these results to calculate the probability of early population collapse for three data sets relating to the Palila, Laysan Finch, and Snow Goose. The Bayesian results imply much higher risk of early collapse than maximum likelihood methods. This difference is due to large probabilities of early collapse for certain parameter values that are plausible in light of the data. Because of simplifying assumptions, these results are not directly applicable to assessment. Nevertheless they imply that maximum likelihood and similar methods based upon point parameter estimates will grossly underestimate the risk of early collapse.