A Bayesian Approach to Classification Criteria for Spectacled Eiders

Abstract

To facilitate decisions to classify species according to risk of extinction, we used Bayesian methods to analyze trend data for the Spectacled Eider, an arctic sea duck. Trend data from three independent surveys of the Yukon‐Kuskokwim Delta were analyzed individually and in combination to yield posterior distributions for population growth rates. We used classification criteria developed by the recovery team for Spectacled Eiders that seek to equalize errors of under‐ or overprotecting the species. We conducted both a Bayesian decision analysis and a frequentist (classical statistical inference) decision analysis. Bayesian decision analyses are computationally easier, yield basically the same results, and yield results that are easier to explain to nonscientists. With the exception of the aerial survey analysis of the 10 most recent years, both Bayesian and frequentist methods indicated that an endangered classification is warranted. The discrepancy between surveys warrants further research. Although the trend data are abundance indices, we used a preliminary estimate of absolute abundance to demonstrate how to calculate extinction distributions using the joint probability distributions for population growth rate and variance in growth rate generated by the Bayesian analysis. Recent apparent increases in abundance highlight the need for models that apply to declining and then recovering species.

Sabine's Gull (Xema sabini) Nesting Aggregations in Western Alaska

“…For delisting to occur, however, each of three spectacled eider populations (Yukon-Kuskokwim Delta, North Slope Alaska, and Arctic Russia) must show significant population growth using data from 10-15 years of annual surveys or have a population that exceeds 6,000 breeding pairs as measured by the lower 95% confidence interval bound (Taylor et al 1996; U.S. . On the Yukon-Kuskokwim Delta, the growth rate of numbers of nests (a direct surrogate to numbers of breeding pairs) using data from the most recent 15 years is 1.041 with a 95% confidence interval of 1.007 -1.075.…”

“…The Spectacled Eider Recovery Plan specifies alternative criteria for delisting that include a subpopulation exceeding 10,000 breeding pairs over three consecutive annual surveys; or a population exceeding 25,000 breeding pairs in any one survey (Taylor et al 1996; U.S. Fish Dean Demarest and Wildlife Service 1996).…”

Embracing Uncertainty: The Interface of Bayesian Statistics and Cognitive Psychology

“…Similarly, Bayesian analysts sometimes try to simplify their results by feeding them into a decision analysis that produces inferences or compares management options (e.g., Crome et al 1996, Taylor et al 1996, Wolfson et al 1996. In some ways, this simplifying tactic resembles the decision model for inferences used in classical statistics.…”

“…For instance, Wolfson et al (1996, Study 2) and Taylor et al (1996) used existing data for at least some prior estimates. In contrast, Crome et al (1996) and Wolfson et al (1996, Study 1) elicited prior probability estimates from experts.…”

“…It directly analyzes the probability of a hypothesis, allowing scientists and managers to formally update their beliefs in a variety of experimental and nonexperimental situations (Ellison 1996). To raise awareness of Bayesian analysis, several ecologists have presented strong arguments promoting its use in contexts of conservation and resource management (Crome et al 1996, Ellison 1996, Ludwig 1996, Taylor et al 1996, Wolfson et al 1996. However, despite its advantages, Bayesian analysis is not likely to become widely accepted by nonstatisticians unless its proponents make it more easily understood.…”