FISHERY BULLETIN: VOL. 81, NO. 4 



limited control over age composition of catches, this 

 maximum catch is usually not attainable. Method III 

 allows the determination of stabilizing catches when 

 relative fishing effort in one or more of the com- 

 ponents of the fishery is changed. This enables the 

 selection of a fishing strategy that is most suitable for 

 achieving a management objective (e.g., the attain- 

 able maximum catch weight). 



Maximization of catch weight using methods I and 

 III can be regarded as an improved yield-per- recruit 

 analysis. The advantage of this approach in com- 

 parison with the classical one (Beverton and Holt 

 1957) is the explicit incorporation of the condition of 

 constant parental biomass and, as a consequence of 

 other assumptions inherent in the methods, of con- 

 stant recruitment. The condition of constant recruit- 

 ment must be assumed in the classical analysis to 

 make the interpretation of results practically usefuL 

 However, the difficulty in the classical approach is 

 that the effect of changing the fishing strategy upon 

 the recruitment level is not considered. As pointed 

 out by Dunning et al. (1982), this may result in long- 

 term yield losses if the reproductive potential of the 

 population is reduced. 



The three methods differ in their data require- 

 ments. Method I requires the relative catch age com- 

 position to be specified, while methods II and III can 

 be used if estimates of age class- specific catchability 

 coefficients (defined as the fraction of all fish in the 

 age class caught using one unit of fishing effort) are 

 available. These catchability coefficients in the case 

 of method III have to be known for all components of 

 the fishery being investigated. Also, the three meth- 

 ods require estimates of recruitment, natural mor- 

 tality, weights at age, proportions of sexually mature 

 fish in each age class, and present parental biomass. 



Although few fisheries will exactly comply with all 

 the assumptions underlying the use of these 

 methods, fisheries scientists and managers, knowing 

 the characteristics of their fisheries and the data 

 available, should be able to decide which method 

 best suits their particular cases. The consequences 

 of incomplete compliance with the assumptions 

 inherent in the methods and their management 

 implications are discussed. The methods are illus- 

 trated by their application to southern bluefin tuna, 

 Thunnus maccoyii (Castlenau), population and 

 fishery data collected prior to 1981. 



METHODS 



Theoretical Background 



A population satisfying the following assumptions 

 724 



is considered: 



(a) Both recruitment to the fishable portion of the 

 population and spawning are discrete events with 

 respect to time and take place once per year at the 

 same time each year. 



(b) The magnitude of recruitment is dependent only 

 upon the magnitude of parental biomass. 



(c) Instantaneous rate of natural mortality may be 

 dependent on age class only. 



(d) Average weight of fish in the population at the 

 time of spawning is a function of age only. 



(e) Average weight of caught fish from any age class 

 does not change from year to year. 



If 1) these assumptions are satisfied, 2) both the 

 magnitudes of yearly catches decomposed into age 

 classes and their variability within a year do not 

 change from year to year, and 3) a catch level is being 

 maintained which ensures that the magnitude of 

 parental biomass at spawning is constant, the pop- 

 ulation is in a regime referred to in this paper as a 

 steady- state. 



The question posed is what level of yearly catch 

 would lead to the maintenance of parental biomass, 

 P, at a specific level PS at the time of spawning over 

 an infinite number of years. If a steady- state exists, 

 only a single cohort need be considered to address 

 this question. 



The catch determination methods to be presented 

 are based on the Pope (1972) catch equation: 



C = No, exp(-0.5M,) - Ne, exp(0.5M,) 



(1) 



where C, is the yearly catch (in number) offish from 

 age class i (age class i is defined as a group of fish at 

 age i — 1 to i years), No, and Ne, are, respectively, the 

 initial and final abundances of fish in age class i, i.e., 

 at age i — 1 and i years of age (in steady-state Ne, = 

 No, +1 ), and M, is the instantaneous rate of natural 

 mortality for age class i. This equation was derived 

 assuming that the entire yearly catch is taken in the 

 middle of the year and M, is constant during the year. 

 It is a modification of the equation (Ricker 1975) 



C = 



No,(l - exp(- Z,)) 



(2) 



where Z, and F, are the yearly average rates of total 

 and fishing mortalities, respectively, for age class i. 

 Both equations are equally effective in the majority 

 of cases, but the use of Equation (2) is complicated 

 from the computational point of view (see dis- 

 cussions in Pope 1972; Ricker 1975). Therefore, 



