CLARK and MANGEL AGGREGATION AND FISHERY DYNAMICS 



FIGURE 8— Simulaion results. Model 

 B, noncatastrophic case. In this case, 

 CPUE (catch per unit effort) seriously 

 overestimates the decline in tuna abun- 

 dance. SDF = standardized days 

 fishing. 



EFFORK SDF ) 



E5CAPEMENTI TONS! 



CATCH I T0N5 ) 



CPUE I TONS/SOF) 



Q* = 50 tons 



6 = 2 X lO""" per vessel day 



r„ =1.5 per annum 



N = 10« tons. 



In the first simulation (Figure 7) we set a = 10 '', 

 implying an intrinsic schooling rate of 5'7f per day. 

 Since this is well in excess of the intrinsic growth 

 rateofO.ll'X per day, a catastrophe is observed. In 

 the second simulation (Figure 8) we set a = 1.5 ^ 

 10 ', implying an intrinsic schooling rate of 

 0.075% per day, which is below the intrinsic 

 growth rate. 



In Figure 7, effort is fixed at 6,000 vessel days for 

 years 1-4, then 12,000 vessel days for years 5-8, 

 and finally 18,000 vessel days for all later years. 

 The escapement population stabilizes at about 

 890.000 tons by year 4, and stabilizes again at 

 about 735,000 tons by year 8. However in years 

 9-17 the effort level is above £, s 15,000 vessel 

 days, and the population is steadily reduced, ulti- 

 mately to a level <100 tons. Although the popula- 

 tion decline itself occurs gradually, neither catch 

 nor CPUE shows any marked decline until the 

 tuna population has crashed. For example, the 

 decline in catch (and CPUE) in year 14 is 2.5'^f 

 relative to the level for year 1, and in year 15 is 

 5.4'^ relative to the .same level. Even in year 16, 

 when the tuna population is virtually destroyed, 

 the catch (and CPUEl falls by only 20'7, . 



The same effort profile was used in the simula- 

 tion shown in Figure 8, except for an additional 



increase in effort at year 12. In this simulation, 

 CPUE declines significantly, but the population 

 level is only slightly reduced. The biological ex- 

 planation lies in the low rate of schooling in com- 

 parison with the first simulation. Because of this 

 low schooling rate, increased effort mainly has the 

 effect of reducing the surface population, and (at 

 the levels shown here) has little effect on the sub- 

 surface population. This also explains why CPUE 

 is much lower, at any fixed E. than in the first 

 simulation. 



Finally, Figure 9 shows the results of a simula- 

 tion based on submodel A, using the same parame- 

 ter values as for Figure 7. This simulation indi- 

 cates that, as expected, submodel A behaves quite 

 similarly to traditional fishery models. 



MANAGEMENT IMPLICATIONS 



The models described above, and in the appen- 

 dices, indicate that traditional methods of fishery 

 management may be inappropriate in cases where 

 aggregation processes significantly affect the 

 fishery. On the one hand, such processes may be 

 the source of bias in CPUE indices of stock abun- 

 dance. On the other hand, these processes may 

 also lead to a catastrophic relationship between 

 fishing effort and sustainable yield. The latter 

 situation will be especially serious in the event 

 that CPUE underestimates declines in abun- 

 dance. 



In addressing the management implications of 



327 



