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. Resumen El uso de datos extensivos, pero de baja resolución, de la abundancia es una práctica común en la evaluación del estado de riesgo de una especie con base en los criterios cuantitativos de declinación establecidos por la Unión Internacional para la Conservación de la Naturaleza (UICN) y la legislación nacional sobre especies en peligro extinción. Dicha información puede ser problemática por tres razones: primero, e