Research Document - 2014/096

Hierarchical Bayesian modeling for Cambridge Bay Arctic Char, Salvelinus alpinus (L.), incorporated with precautionary reference points

By Xinhua Zhu, A. Chris Day, Theresa J. Carmichael, and Ross F. Tallman

Abstract

In response to growing concerns over fisheries sustainability and the vulnerability to climate changes, precautionary reference points have become central priorities for maintaining the healthy status of fish populations and fisheries. In the present study, we applied a hierarchical Bayesian state-space formulation of surplus production models to assessments of Arctic Char biomass dynamics in the Cambridge Bay area and to estimates of a set of precautionary reference points (PRPs) with uncertainties for evaluation processes. Four kinds of probability distribution functions (pdfs), uniform (UKR), lognormal (LNKR), half-Cauchy lognormal (HCLNKR), and random walk with lognormal (LNKRWQ), were structured to specify priors on model parameters, K, r, and q in a Markov chain Monte Carlo (MCMC) framework. We employed deviance information criterion (DIC) and multimodel inference (MMI) to evaluate model performance and model selection. The model considered the best fit has the smallest DIC value, leading to the recognition that the model LNKRWQ was identified as the best among the candidate models. Model UKR produced next lowest DIC value, with a substantial difference (5.18) from LNKRWQ. Models LNKR and HCLNKR did not substantially support the model averaging of MMI. Given two better model scenarios, the populations for all years under model LNKRWQ, 93% DIC weight, had experienced somewhat lower targeted exploitation rate (FMSY=0.1761±0.1098 per year) and the population biomass remained in the healthy zone. Under model UKR, 7% DIC weight, the targeted exploitation rate seemed to be slightly higher (FMSY=0.2390±0.1182 per year) but were never exceeded. The results from both models demonstrated that Cambridge Bay Arctic Char populations were in the Cautious Zone of the Precautionary Approach Framework at the start of the time series. Under the current exploitation strategy, the populations are in the Healthy Zone. With the data currently available it was not possible to estimate these reference points for individual stocks (i.e., waterbodies). This does not imply that there should be a change to the current management units or methods of the collection of fishery statistics. However, additional information, proportional contributions from river-based stocks and river-specific catch-per-unit-effort (CPUE), should be collected that would facilitate definition of individual stock reference points.

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