Deterministic compartmental model for the eastern king prawn (Penaeus plebejus) fishery in New South Wales

Abstract

Eastern king prawns (Penaeus plebejus) migrate north from estuaries along the eastern coast of New South Wales and are subject to fishing during this migration. A constant-parameter deterministic compartmental model of the northward migration is described in which the compartments are zones of constant latitudinal width. Assumptions made for each zone are similar to those made for the Baranov catch equation, in which the population decays exponentially through constant instantaneous rates of natural mortality, fishing mortality and emigration. However, in addition to these assumptions, emigration from each zone is assumed to replenish the population in the next zone to the north. This results in the dynamics of the population being described by a system of constant-coefficient linear first-order differential equations. The solutions of this system and of equations for cumulative catch are given in a form that allows the model to be generalized to other migration patterns as a multi- zone analogue of the Baranov catch equation. A discretized form of the model with a restricted parameterization is used to analyse tag-return data from four tag releases. Estimated parameters are used in a yield-per-recruit analysis of prawns recruited to the ocean fishery from Botany Bay.