APPROXIMATIONS FOR SOLVING THE CATCH EQUATION WHEN IT INVOLVES A PLUSGROUP

Virtual population and cohort analyses are sometimes conducted with an age category known as the ''plus group.'' This category is used to ke ep track of the abundance and catches of older fish that cannot be ass igned individual ages accurately. In this study we present a procedure for solving the catch equation backwards in time when it involves a p lus group. The procedure consists of an initial analytical approximati on, followed by a correction function based on an empirical analysis, followed by the application of Newton's Method. The results indicate t hat the procedure works well for a wide range of natural and fishing m ortality values. For comparison, we also applied the same procedure to the basic catch equation (without a plus group) and found that adequa te approximation to the true fishing mortality value is achieved even before application of Newton's Method.