CLARK and MANGEL AGGREGATION AND FISHERY DYNAMICS 



1 



bExo 



{bExo)^ 



(B44) 



Consequently, if overfishing is occurring, the 

 number of complexes with two tuna schools is 

 much less than the number of complexes with one 

 school. As effort increases further, the fishery will 

 find more and more attractors without any as- 

 sociated tuna schools. Such observations should 

 act as a warning that the tuna are being over- 

 exploited. We note that it is possible that CPUE 

 will not decrease, even though the number of tuna 

 schools per complex is decreasing (see Figure 7). 

 A host of complex solutions and bifurcations can 



be determined if the values of y, , y.^ are not 1 . Since 

 y, > 1, y., > 1 do not have an immediately obvious 

 interpretation for fishery dynamics, we will not 

 consider those cases here. 



In this Appendix, we have taken an approach to 

 modelling the fishery that is substantially dif- 

 ferent from the approach in the main part of the 

 paper. The results obtained here complement the 

 main results, and extend them. We have shown 

 that models A and B presented in the paper arise 

 as special cases of the kinetic models in this Ap- 

 pendix. It is clear that these models could be 

 greatly elaborated and many other details 

 explored. 



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