MAJKOWSKI and HAMPTON: CATCH STABILIZING PARENTAL BIOMASS 



TABLE 2.— The catchability coefficients characterizing the 

 global southern bluefin tuna fishery and its major components, 

 the Australian fisheries off the coasts of Western Australia 

 (WA), South Australia (SA), and New South Wales (NSW), and 

 the Japanese fishery. 



Table 3. — Estimates of CB and fishing effort index associated with 

 various fishing strategies. WA = Western Australia, SA = South 

 Australia, NSW = New South Wales, aa. = not available. 



Method 



Specification of f/s or q,' 



CB 



(t) 



Effort 

 index 



fy s from Table 1 



f/s corresponding to the 



absolute' maximum catch weight 



Global q/s 



WA q/s 



SA q/s 



NSW q/s 



Japanese q/s 



WA q/s subtracted from global q/s 



SA q/s subtracted from global q/s 



NSW q/s subtracted from global q/s 



Japanese q/s subtracted from global q/s 



30,012 



TABLE 4. — The estimated age composition of the southern 

 bluefin tuna population and its catches (C,) associated with 

 the fishing strategies determined by the f, values from Table 

 1 and the q, values for the global fishery from Table 2. 



spectively. Several facts are evident from these 

 results: 



1) Both estimates of CB are most sensitive to per- 

 turbations of M, and N r . 



2) Approximately linear relationships exist between 

 CB and No r , M„ PS, and W, (but not Ws,) in the case of 

 both CB estimates. 



3) Perturbing all q, values (method II) by the same 

 percentage has no effect on CB, but does produce 

 changed values of E. 



4) Method II appears slightly more robust than 

 method I in that CB (Method II) is less sensitive to 

 changes in No,, M„ PS, and Ws, than CB (Method 

 I). 



The results of sensitivity analysis presented in 

 Tables 6 and 7 reflect the sensitivity of the CB esti- 

 mates to changes in the individual input parameters. 

 In the case of southern bluefin tuna, the input para- 

 meter estimates are related and this complicated the 

 interpretation of the results. The effect of such inter- 

 relationships upon the CB estimates is illustrated by 

 examining the dependence of No r and PS upon M,. 

 These three parameters are probably subject to the 

 greatest estimation error. 



In the presented example, No r and PS are estimated 

 on the basis of cohort analysis for which M, is an input 

 parameter. Therefore, both No r and PS values are 

 dependent on the M, estimate in which a relative 

 error of up to ±50% may have existed. Table 8 shows 

 the effects of perturbations in M„ and the conse- 

 quent changes in No r and PS, upon the CB estimates 

 of 30,012 and29,013 t Here, the percentage changes 

 in CB in both cases are much smaller than the corres- 

 ponding changes brought about by perturbations in 

 M, only (Tables 6, 7). This mostly results from the 

 fact that No r estimated on the basis of cohort analysis 

 is a strongly increasing function of M, and the effects 

 of No r and M, on the CB estimates are antagonistic. 

 Therefore, if No r is estimated from cohort analysis, 

 the results of both methods are considerably less sen- 

 sitive to perturbations in M, than in the case when No r 

 and M, are independently estimated. If, however, M, 

 and No r for southern bluefin tuna are independently 

 estimated, a high degree of accuracy is necessary to 

 confidently evaluate CB. Note that the degree of sen- 

 sitivity of a CB estimate to changes in M, is dependent 

 also on the age composition of CB. For example, the 

 sensitivity of the CB estimate of 52,690 t (age classes 

 10 and 1 1 only are fished), derived by using method I, 

 to changes in M, is much higher than that of 30,012 t 

 (age classes 2-20 are fished). More extensive sen- 

 sitivity examinations are beyond the scope of this 



729 



