On assessment of the Bering-Chukchi-Beaufort Seas stock of bowhead whales (Balaena mysticetus) using a Bayesian approach

Abstract

This paper explores a number of issues surrounding the current assessment of the Bering-Chukchi-Beaufort (B-C-B) Seas stock of bowhead whales and provides a ‘preferred’ set of specifications for this assessment. A Bayesian approach appears to be preferable. However, the Bayesian Synthesis method is subject to the Borel paradox. Reverting to a ‘standard’ Bayesian approach which places all ‘indirect’ nformation in priors (rather than representing this information as likelihoods) would overcome this problem. The basis for the prior distributions used should be documented clearly, and the sources of information for the B-C-B bowhead stock divided into ‘indirect’ and ‘direct’. Simulation results and ‘in principle” arguments support the choice of a current population size rather than the pre-exploitation equilibrium size for the parameter to scale the population size (i.e. a *backwards’ rather than a ‘forwards’ approach). Arguments are presented that the most appropriate choice for a productivity-related parameter, for which a prior has to be specified, is the maximum steady rate of increase. A method for treating the Ny/P, estimates as relative indices of abundance, allowing for prior information about the relationship between absolute abundance and those estimates, and accounting for the correlation among the indices of relative abundance ‘derived from the N, and P, data is developed. Two ‘preferred approaches’ for assessing the resource both lead to estimates for the lower 5 percentile of the replacement yield that are greater than the current annual strike limit of 67 for the B-C-B stock.