Evaluation of Two Approaches to Defining Extinction Risk under the U.S. Endangered Species Act.

The predominant definition of extinction risk in conservation biology involves evaluating the cumulative distribution function (CDF) of extinction time at a particular point (the "time horizon"). Using the principles of decision theory, this article develops an alternative definition of extinction risk as the expected loss (EL) to society resulting from eventual extinction of a species. Distinct roles are identified for time preference and risk aversion. Ranges of tentative values for the parameters of the two approaches are proposed, and the performances of the two approaches are compared and contrasted for a small set of real-world species with published extinction time distributions and a large set of hypothetical extinction time distributions. Potential issues with each approach are evaluated, and the EL approach is recommended as the better of the two. The CDF approach suffers from the fact that extinctions that occur at any time before the specified time horizon are weighted equally, while extinctions that occur beyond the specified time horizon receive no weight at all. It also suffers from the fact that the time horizon does not correspond to any natural phenomenon, and so is impossible to specify nonarbitrarily; yet the results can depend critically on the specified value. In contrast, the EL approach has the advantage of weighting extinction time continuously, with no artificial time horizon, and the parameters of the approach (the rates of time preference and risk aversion) do correspond to natural phenomena, and so can be specified nonarbitrarily.