Application of a Strike Limit Algorithm based on adaptive Kalman filtering to the eastern North Pacific stock of gray whales

Abstract

The application of a Strike Limit Algorithm (SLA) based on Adaptive Kalman Filtering techniques to the eastern North Pacific (ENP) stock of gray whales is described. This SLA is a modification of an earlier one which was designed for the Bering-Chukchi-Beaufort Seas stock of bowhead whales. Extended Kalman filters are used to estimate the present stock size and posterior probability distributions for Maximum Sustainable Yield (MSY) and MSY-rate (MSYR). 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 MSY, 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 internal model parameters – so-called tuning parameters. The procedure is tested based on a set of trials specified by the IWC Scientific Committee Standing Working Group on Aboriginal Whaling Management Procedures, designed to test the performance of potential SLAs for the ENP gray whale stock.