Statistical Power of Trends in Fish Abundance

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Abstract
Estimation errors inherent in stock assessment methods may make it difficult to estimate time trends in fish abundances correctly. Our objective was to quantify the probability that trends in abundance of recruits will be successfully identified. For this analysis, we used an empirically based simulation model of English sole (Parophrys vetulus) off the west coast of North America. The unique wealth of data and past analyses of this population permitted us to include deterministic and stochastic components of growth, mortality, and reproduction in a realistic manner. Errors were also included in two simulated stock assessment methods: a trawl survey and cohort analysis. Under various conditions, we calculated the probability (analogous to statistical power) that these methods will meet three management objectives concerning time trends in recruitment. Monte Carlo simulations showed that although power depends on the objective, under most realistic conditions the probability of correctly detecting recruitment time trends may be unacceptably low. These results suggest new management guidelines for fisheries.

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