Figure 9. — Simulation results: Model 

 A. The behavior of the model is similar to 

 that of traditional fishery models. SDF 

 = standardized days fishing. CPUE = 

 catch per unit effort. 



FISHERY BULLETIN VOL 77, NO, 2 

 EFFORT (SDF) 



in 862.000 



CATCH (TONS) 



ESCAPEMENT(TONS) 



CPUE ITONS/SOF) 



these theoretical results, for a particular fishery, 

 we face two main problems. First, what is the 

 likelihood that the fishery in question does involve 

 an aggregation process, and if so, that catastrophic 

 conditions may prevail? (We remark again that 

 catastrophic conditions may be the result of pro- 

 cesses other than aggregation.) Secondly, given 

 that such conditions may exist, what are the im- 

 plications for management policy? 



If an aggregation process is known to exist, our 

 models suggest that the next question that ought 

 to be addressed is whether aggregation is density 

 dependent, and if so, to what extent it depends on 

 population abundance? Also, the rate parameters 

 of the process should be determined. Unfortu- 

 nately this information may be extremely difficult 

 to obtain, and the question arises whether infer- 

 ences can be drawn from data supplied by the 

 fishery, such as catch-effort data, school size, den- 

 sity of schools, size composition of catches, and so 

 on. 



For example, if aggregation is density depen- 

 dent, then the size of the aggregated (surface) 

 population will decrease with the size of the re- 

 sidual (subsurface) population. For the case of 

 tuna, either the number or the size of schools (or 

 both) should decrease as the fishery develops. But 

 the converse implication cannot be made: school 

 size and/or number may decrease merely because 

 the surface population is reduced by fishing pres- 

 sure. Unless a direct, independent abundance es- 

 timate of the subsurface population is available. 



the interpretation of such fishery data may remain 

 ambiguous." 



The possibility that aggregation may lead to 

 catastrophic yield-effort relationships lends a 

 sense of urgency to the question of achieving a 

 fuller understanding of the dynamics of the aggre- 

 gation process. But whenever such catastrophic 

 relationships seem possible, for whatever reason, 

 a conservative approach to management appears 

 appropriate. In view of the uncertainties involved, 

 quotas should probably be established at a level 

 lower than the estimated maximum sustainable 

 yield. Furthermore, since depletion may neverthe- 

 less occur unexpectedly, emphasis should be 

 placed on achieving a high degree of controllabil- 

 ity of the fishery. To a certain extent this necessity 

 has been recognized by the Inter-American Tropi- 

 cal Tuna Commission, the Director of Investiga- 

 tions now being empowered to close the yellowfin 

 tuna fishery in the event of a sharp decline in 

 CPUE. However, if the decline were truly "catas- 

 trophic," more drastic measures, such as a 

 moratorium of some duration, might become 

 necessary. Although the possibility may seem re- 

 mote at present, we feel that further attention 



'Various alternative indicators of depletion, involving size 

 composition of the catch and the results of cohort analysis, are in 

 fact employed by the Tuna Commission and have demonstrated 

 no severe change that can be attributed to the fishery. The 

 validity of such indicators should not be affected by the presence 

 of an aggregation process, but we have not attempted to extend 

 our model to include cohort structure. 



328 



