THE ESTIMATION OF A CATCH LEVEL WHICH STABILIZES THE 

 PARENTAL BIOMASS OF AN EXPLOITED FISH STOCK 



J. Majkowski and J. Hampton 1 



ABSTRACT 



This paper addresses the problem of determining a catch level which stabilizes the parental biomass of a fish 

 population at its present level. Initially, two methods are presented, both based on a simple catch equation 

 and requiring estimates of recruitment, natural mortality, weights at age, proportions of sexually mature fish 

 in each age class, and present parental biomass. Method I deals with a fishery assumed to have complete con- 

 trol overage composition of catches and requires age composition to be specified. Estimation of the catch age 

 composition which results in the absolute maximum catch weight while holding parental biomass constant is 

 also demonstrated. In method II no control over catch age composition is assumed; this composition is deter- 

 mined by catchability coefficients and the age structure of the population. Then, a simple modification of 

 method II, method III, is presented for a fishery' which has limited control over catch age composition through 

 selective allocation of relative fishing effort among components of the fishery, the age composition of each 

 component being different but not controllable by the fishery. This allows the determination of catches 

 stabilizing the parental biomass for different allocations of relative fishing effort Maximization of catch 

 weight using methods I and III can be regarded as an improved yield per recruit analysis having the explicitly 

 incorporated conditions of constant parental biomass and, as a consequence of other assumptions inherent 

 in the methods, of constant recruitment. Consequences of incomplete compliance with assumptions inherent 

 in these methods and their management implications are discussed. These methods are applied to southern 

 bluefin tuna, Thunnus maccoyii, population and fishery data collected prior to 1981, and indicate that a total 

 stabilizing catch of about 30,000 t per year is possible under the existing pattern of fishing. 



Management of many commercial fisheries involves 

 the determination of the maximum sustainable yield 

 (MSY), (see reviews in Ricker 1975; Gulland 1977) 

 and the imposition of restrictions which ensure that 

 catches do not exceed this MSY. The estimation of 

 MSY is usually made with the aid of production mod- 

 els which typically require historical catch per unit 

 fishing effort data (Ricker 1975; Gulland 1977). Even 

 if such data are available, assumptions underlying 

 the use of these models are often violated or at least 

 poorly complied with in real fisheries situations. 

 Models taking account of the population age struc- 

 ture such as those reviewed by Getz (1979) are, in 

 many cases, more appropriate for determining the 

 MSY, but, in addition to estimates of natural mor- 

 tality and growth rate, they also require information 

 on the stock-recruitment relationship. 



It is often the case that the stock- recruitment 

 relationship for an exploited population is poorly 

 known and the production models cannot be used 

 for the reasons outlined. In this situation, a sensi- 

 ble management strategy is to stabilize the pa- 

 rental biomass at its present level which, through 

 experience, is known to provide an adequate recruit- 



' Division of Fisheries Research, CSIRO Marine Laboratories, P.O. 

 Box 21, Cronulla, NSW 2230, Australia. 



Manuscript accepted May 1983. 



FISHERY BULLETIN: VOL. 81, NO. 4. 1983. 



ment. As well as the assurance of reproductive suc- 

 cess, the stabilization of parental biomass (and, as a 

 consequence of the approach to be applied, of the 

 entire age structure of the population) may be 

 desired for completely different reasons, e.g., the 

 preservation of a certain ecological equilibrium in a 

 community of interacting species in which the 

 exploited species is a member. 



The objective of this paper is to demonstrate how a 

 level of yearly catch that will stabilize the parental 

 biomass of a population at its present level can be 

 determined. This catch is hereafter referred to as the 

 stabilizing catch. Initially, two methods developed 

 for this purpose are presented. Method I deals with a 

 fishery which has complete control over age composi- 

 tion of catches, while method II is relevant to a fishery 

 having no such control. Method III, a simple mod- 

 ification of method II, is then presented for a fishery 

 having limited control over catch age composition. It 

 is assumed that this fishery can be divided into com- 

 ponents, the catch age composition of each being dif- 

 ferent but not controllable by the fishery. 



An estimation of stabilizing catch based on method 

 I can be made for nearly any age composition of 

 catches. This method allows also the determination 

 of an age composition which results in the absolute 

 maximum stabilizing-catch weight. If a fishery has 



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