A Model of Catchability of Developing Fishery

Abstract

This paper proposes a mathematical model correlating the realized catchability coefficient with the theoretical one in random operation and stock abundance, based on the assumption that fishery preferentially exploits stocks in abundant areas. The catchability coefficient in year t, qt, is given by qt = q(μt/λ0)(N0/Nt) or q(μt/λt)(N′t,/Nt). Here, q, μt, λt, Nt, and N′t are respectively the theoretical catchability coefficient, stock density exploited at t, mean density of stock at the beginning of the fishing season at t, stock size at t, and stock size at the beginning of t. Assuming gamma distributions for the initial stock density, the functional relationship between (μt/λ0) and N0/Nt and that between (μt/λt) and N′t/Nt are derived. Numerical examinations showed that the initial geographic distribution of the stock density and its changes due to fluctuation of the stock abundance caused the variability in the catchability coefficient. The model was applied to the Japanese longline fishery which exploits the southern bluefin tuna, Thunnus maccoyii. The estimations were conducted under each of five different conditions. The values of the coefficient of determination from the qt estimates using the first equation of qt ranged from 0.82 to 0.92. The applications and the modifications for the model were discussed.