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 cruci al parameters and processes. Simple simulation approaches to assessmen t consider only a single set of parameter values, but what is required is consideration of all more or less plausible combinations of parame ters. Bayesian decision theory is an appropriate tool for such assessm ent. I contrast standard (frequentist) and Bayesian approaches to a si mple regression problem. I use these results to calculate the probabil ity of early population collapse for three data sets relating to the P alila, Laysan Finch, and Snow Goose. The Bayesian results imply much h igher risk of early collapse than maximum likelihood methods. This dif ference is due to large probabilities of early collapse for certain pa rameter values that are plausible in light of the data. Because of sim plifying assumptions, these results are not directly applicable to ass essment. Nevertheless they imply that maximum likelihood and similar m ethods based upon point parameter estimates will grossly underestimate the risk of early collapse.