Stock Reduction Analysis, Another Solution to the Catch Equations

Abstract

In fishery stock assessments, catch equations provide the critical link between stock size, natural mortality rate, fishing rate, and catch size. Catch equations are most powerful when age data are available, allowing cohorts to be followed through time using Virtual Population and Cohort Analysis. In this paper we propose a simple new method of linking catch equations when age data are not available. Assuming catches are given in biomass, catch equations are written for each year with a constant recruitment (R), based on a single parameter, added to the total biomass at the beginning of each year. In addition to the catch equations, a final equation is added describing the change in biomass caused by the years of fishing. If n years of catch data are available, n + 1 equations can be written. By conditioning on instantaneous natural mortality rate (M), initial stock size (B1) and the decline in stock size (P) (note P = Bn+1/B1), the n + 1 simultaneous nonlinear equations can be solved iteratively for instantaneous fishing mortality rates (F1, …, Fn) and recruitment (R). When properly plotted, the solution set to this system of equations was found to be a helpful tool to aid in the evaluation of stock condition. In particular, the plots provide a method for incorporating ancillary information from diverse sources such as hydroacoustic surveys, analysis of catch per unit effort data, and Virtual Population Analysis. This new method of stock assessment, which we call Stock Reduction Analysis, is applied to Pacific ocean perch (Sebastes alutus), Pacific herring (Clupea harengus pallasi), and Pacific hake (Merluccius productus) stocks being actively managed by the State of Washington.Key words: Stock Reduction Analysis, stock assessment, catch equations, computer modeling