Assessing conservation status with extensive but low-resolution data: Application of frequentist and Bayesian models to endangered Athabasca River rainbow trout

Use of extensive but low-resolution abundance data is common in the assessment of species at-risk status based on quantitative decline criteria under International Union for Conservation of Nature (IUCN) and national endangered species legislation. Such data can be problematic for 3 reasons. First, statistical power to reject the null hypothesis of no change is often low because of small sample size and high sampling uncertainty leading to a high frequency of type II errors. Second, range-wide assessments composed of multiple site-specific observations do not effectively weight site-specific trends into global trends. Third, uncertainty in site-specific temporal trends and relative abundance are not propagated at the appropriate spatial scale. A common result is the propensity to underestimate the magnitude of declines and therefore fail to identify the appropriate at-risk status for a species. We used 3 statistical approaches, from simple to more complex, to estimate temporal decline rates for a designatable unit (DU) of rainbow trout in the Athabasca River watershed in western Canada. This DU is considered a native species for purposes of listing because of its genetic composition characterized as >0.95 indigenous origin in the face of continuing introgressive hybridization with introduced populations in the watershed. Analysis of abundance trends from 57 time series with a fixed-effects model identified 33 sites with negative trends, but only 2 were statistically significant. By contrast, a hierarchical linear mixed model weighted by site-specific abundance provided a DU-wide decline estimate of 16.4% per year and a 3-generation decline of 93.2%. A hierarchical Bayesian mixed model yielded a similar 3-generation decline trend of 91.3% and the posterior distribution showed that the estimate had a >99% probability of exceeding thresholds for an endangered listing. We conclude that the Bayesian approach was the most useful because it provided a probabilistic statement of threshold exceedance in support of an at-risk status recommendation.