MAJKOWSKI and HAMPTON: CATCH STABILIZING PARENTAL BIOMASS 



alytically. The determination of the age composition 

 which results in the absolute maximum stabilizing 

 catch weight requires a standard computer program 

 from a linear programming package. The system of 

 equations associated with methods II and III cannot 

 be solved analytically; a computer program which 

 finds the zeros of a function has to be used. 



Data requirements for the methods are not exten- 

 sive. They are usually available from an established 

 and well- documented fishery. Data required for 

 method I may be more easily obtained than those for 

 methods II or III. This is the major advantage of 

 method I. 



Assumptions associated with methods II and III are 

 more realistic for most fisheries than those related to 

 method I. Therefore, if the data for methods II and III 

 are available, these methods will be superior in the 

 majority of cases. However, the example presented 

 clearly indicates that methods I and II, at least for 

 southern bluefin tuna, provide nearly identical re- 

 sults if the present age specific pattern of fishing is 

 considered. 



The example also suggests that the methods, at 

 least in the case examined, are relatively robust with 

 respect to uncertainties in the input parameters. 

 This is a very important consideration because many 

 population and fisheries parameters are frequently 

 poorly known. 



Because of their deterministic nature and the as- 

 sumptions involved, none of the methods will be com- 

 pletely realistic in their description of the fishery and 

 population. However, they should provide managers 

 with a valuable tool for gaining an impression of the 

 level of sustainable catch and for assessing the rela- 

 tive merits of harvesting alternatives. 



ACKNOWLEDGMENTS 



We are grateful to Geoffrey P. Kirkwood (CSIRO 

 Division of Fisheries Research, Cronulla, NSW, Aus- 

 tralia), Ron Sandland (CSIRO Division of Mathe- 

 matics and Statistics, Cronulla, NSW, Australia), 

 Robin L. Allen (Ministry of Agriculture and Fish- 

 eries, Fisheries Research Division, Wellington, New 

 Zealand), and Patrick K. Tomlinson (Inter- American 

 Tropical Tuna Commission, La Jolla, Calif., USA) for 

 suggestions for improvements to an earlier version of 

 this paper. 



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