MAJKOWSKI and HAMPTON: CATCH STABILIZING PARENTAL BIOMASS 



species is highly migratory and spawns in waters off 

 the south coast of Java. Juveniles migrate to waters 

 off the coast of Australia, passing Western and South 

 Australia and New South Wales. The general direc- 

 tion of their movement within the 200 mi Australian 

 Fishing Zone (AFZ) is from west to east; however, 

 some fish also move in the reverse direction. Schools 

 of juveniles within the AFZ support the most impor- 

 tant and valuable Australian finfish fishery. The fish- 

 ing methods used are pole and line, purse seining, 

 and, to a small extent, trolling. Southern bluefin tuna 

 passing Australia gradually leave the nearshore fish- 

 ing areas and become available to the Japanese long- 

 line fishery. 



The parental biomass of this population, present- 

 ly (i.e., in 1980) equal to about one- third of the pre- 

 exploitation level, has been continuously and signi- 

 ficantly reduced over the period of exploitation 

 (Murphy and Majkowski 1981). Recruitment to the 

 fishable portion of the stock has been quite stable 

 over the same period, although reliable recruitment 

 estimates are available only to 1976. Due to the ab- 

 sence of accurate information on the southern bluefin 

 tuna stock- recruitment relationship and the lag in 

 evaluation of the recruitment level, a conservative 

 approach to fisheries management is most appro- 

 priate at this stage. Therefore, it is recognized by 

 scientists of Australia, Japan, and New Zealand, the 

 countries involved in the southern bluefin tuna fish- 

 ery, that the present level of parental biomass should 

 not be reduced further. This scenario provided the 

 impetus for this paper. 



Determination of Input Parameters 



The input values required for the application of 

 method I, their symbols, descriptions, and reference 

 sources are presented in Table 1. The values of No r 

 and PS were estimated by cohort analysis while the f, 

 values were derived from the 1980 catch-at-age data. 

 The catchability coefficients (calculated by using 

 No,'s from cohort analysis), required for the applica- 

 tion of methods II and III, are presented in Table 

 2. 



Results 



Results from several applications of methods I and 

 II are presented in Table 3. Values of CB calculated 

 on the basis of method I using the catch age composi- 

 tion specified in Table 1 and calculated on the basis 

 of method II using the global catchability coefficients 

 (see Table 2) are almost identical (30,01 2 and29,013 

 t, respectively). The associated age structures of 



both population and catch produced by the two 

 methods are also very similar (Table 4). 



Estimates of CB derived using method I are depen- 

 dent on the specified values off,. CB is maximized at 

 52,690 t/yr under the condition that only age classes 

 10 and 11 are fished. This fishing strategy requires 



catches of 123, 100 fish from age class 10 and 688, 100 

 fish from age class 1 1. The result is obtained using a 

 linear programming computer program from the 

 Numerical Algorithm Group Library, utilizing the 

 contracted simplex method (McMillan 1970). 



Within method II it is possible to examine the effect 

 of various fishing regimes on CB simply by varying 

 the values of q. Examples are presented in Table 3. 

 The catchability coefficients used in these examples 

 reflect the operation of 1) single components of the 

 southern bluefin tuna fishery (Le., the Australian 

 fisheries off the coasts of Western Australia, South 

 Australia, or New South Wales, or the Japanese fish- 

 ery), or 2) the entire fishery with the exclusion of a 

 selected component. The range of CB's estimated in 

 this way was 12,523-44,695 t, These extreme values 

 of CB corresponded to the lone operation of the West- 

 ern Australian and Japanese fisheries, respectively. 



Method III allows calculations of various com- 

 binations of stabilizing catches by the components of 

 the global fishery. Examples of possible catch com- 

 binations are given in Table 5. These catch values are 

 generated by specifying combinations of E's asso- 

 ciated with the Western Australian, South Aus- 

 tralian, and New South Wales fisheries, then cal- 

 culating the Japanese fishing effort index and all 

 related catches which would enable the stabilization 

 of parental biomass. These results show that, as the 

 fishing efforts of the Western Australian, South Aus- 

 tralian, and New South Wales components increase, 

 the Japanese and global stabilizing catches decrease. 

 The minimum and maximum CB values generated by 

 using method III are equivalent to the values in Table 

 3, relating to the lone operation of the Western Aus- 

 tralian and Japanese fisheries, respectively. 



Sensitivity Analysis 



The sensitivity analysis technique used is referred 

 to as ordinary sensitivity analysis (Majkowski and 

 Bramall 1980; Majkowski and Waiwood 1981; Maj- 

 kowski 1982, in press). The procedure consists in 

 individually perturbing input parameters by various 

 relative amounts and observing the resultant 

 changes in CB. 



The results of ordinary sensitivity analyses of the 

 CB estimates of 3 0,0 1 2 and 29,0 1 3 t derived by using 

 methods I and II, are presented in Tables 6 and 7, re- 



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