DETERMINISTIC COMPARTMENTAL MODEL FOR THE EASTERN KING PRAWN (PENAEUS-PLEBEJUS) FISHERY IN NEW-SOUTH-WALES

Eastern king prawns (Penaeus plebejus) migrate north from estuaries al ong the eastern coast of New South Wales and are subject to fishing du ring this migration. A constant-parameter deterministic compartmental model of the northward migration is described in which the compartment s are zones of constant latitudinal width. Assumptions made for each z one are similar to those made for the Baranov catch equation, in which the population decays exponentially through constant instantaneous ra tes of natural mortality, fishing mortality and emigration. However, i n addition to these assumptions, emigration from each zone is assumed to replenish the population in the next zone to the north. This result s in the dynamics of the population being described by a system of con stant-coefficient linear first-order differential equations. The solut ions of this system and of equations for cumulative catch are given in a form that allows the model to be generalized to other migration pat terns as a multizone analogue of the Baranov catch equation. A discret ized form of the model with a restricted parameterization is used to a nalyse tag-return data from four tag releases. Estimated parameters ar e used in a yield-per-recruit analysis of prawns recruited to the ocea n fishery from Botany Bay.