A Strike Limit Algorithm based on Adaptive Kalman Filtering with an application to aboriginal whaling of bowhead whales

Abstract

A full and detailed description of a Strike Limit Algorithm (SLA) based on Adaptive Kalman Filtering techniques with an application to the Bering-Chukchi-Beaufort (B-C-B) Seas stock of bowhead whales is presented in this paper. Extended Kalman filters are used to estimate the present stock size and posterior probability distributions for MSY-rate (MSYR) and the pre-exploitation stock size K. A catch control law selected from a one-parameter family of such rules is then used on the conditional estimates of stock size. These conditional strike limits together with the posterior distributions of the various combinations of MSYR and K, give a cumulative distribution function for the strike limit. The eventual strike limit is then determined as a pre-specified percentile of this distribution. The SLA can be tuned to varying degrees of risk by the choice of the parameter characterising the catch control law and the percentile of the distribution for the strike limit. The procedure is tested on the Evaluation Trials set by the Standing Working Group on Aboriginal Whaling Management Procedures.