FISHERY BULLETIN: VOL. 87, NO. 2, 1989 



abundance of fish in the absence of movement, A*, 

 would be ^* = cipq. If, say, the cost of fishing, c, 

 is reduced by half, it becomes profitable to increase 

 the effort until the concentration of fish is half of 

 what it was (Fig. 2d). Note also that this reduction 

 in cost allows parts of the region with lower carry- 

 ing capacities to be exploited. The term A * deter- 

 mines the maximum equilibrium concentration of 

 fish, and effort increases locally until the abundance 

 of fish is reduced to that level. Effort has a level- 

 ling effect upon abundance; it is greatest in the cells 

 with the greatest capacity. In the area immediate- 

 ly surrounding these cells of high capacity, which 

 contain the maximum density, the abundance of fish 

 falls to a minimum because of movement to the cells 

 of high capacity. At this minimum fishing is un- 

 profitable (less than A*), so there is no exploitation 

 in this area. 



It was suggested earlier that regions surrounding 

 islands might consist of enhanced habitat. Cells of 

 higher carrying capacities may contain an island or 

 group of islands with economic conditions signifi- 

 cantly different from the rest of the region. The 

 economic parameters need to be different for these 

 cells. This is simply done; the model allows con- 

 sideration of the effects of economic changes, both 

 local and global, upon the fishery throughout the 

 whole region. 



A single island was considered; the island and its 

 waters were assumed to be synonymous with a 

 single cell having a capacity 10 times that of any 

 other cell within the entire 20 x 20 cell region. 

 Three regimes of fishing were considered: low ex- 

 ploitation with the cost of a unit of effort set at 

 $24,000; a regime twice as intensive as a result of 

 halving the cost of effort; and a mixed regime where 

 the single cell of high capacity was exploited accord- 

 ing to the parameters of low exploitation, while 

 elsewhere the parameters were as for high exploit- 

 ation. This could be thought of as a paradigm of 

 development of the fishery if one is careful to en- 

 sure that units of effort from different types of fish- 

 ing are comparable in that they have an equivalent 

 effect upon the target population. It takes many 

 days for a trolling boat to equal the impact a purse 

 seiner has in one day. 



The first regime might represent a relatively low 

 level of technological development where further 

 fishing becomes uneconomical while fish are still 

 relatively abundant. Changes in technology might 

 reduce the cost of effort, leading to the second 

 regime with the cost cut by half. The model is such 

 that effort increases everywhere while the abun- 

 dance of fish is more than half of the previous 



maximum, and continues to increase until the abun- 

 dance falls to that level. The mixed regime might 

 represent the case where the higher technology 

 could not be used close to the island because of 

 technical considerations, such as lack of depth 

 for purse seiners, or political ones, such as the 

 prohibition of such fishing to protect artisanal 

 fishermen. 



Table 1 shows the effect on catches and sustain- 

 able effort of these changes in technology or policy. 

 Technological advancement temporarily increases 

 profits, which leads to greater effort and a decHne 

 in catch per unit effort (CPUE). For the parameters 

 used here, the long-term effect of higher technology 

 is to increase the effort expended within the island's 

 waters by 20%, but the CPUE is halved; hence the 

 local catch decreases substantially. Effort is sustain- 

 able offshore with the change to the model, and the 

 catch from the newly exploited area is much higher 

 than the total catch which was previously taken only 

 from the island's waters. If the new technology were 

 kept from the island's waters, then the original 

 CPUE could be maintained only by halving the 

 original local effort. Thus, if the new technology 

 were introduced to the high seas, one would expect 

 half as many artisanal boats to be viable, and these 

 boats would catch about half of what had been taken 

 from their waters. If the managers of the island's 

 waters chose to maximize catch by allowing access 

 to the new technology, they could still only stabil- 

 ize the catch at 60% of what it had been before the 

 advent of the high-seas fleet. 



Table 1 . — Effort and catches at equilibrium under different eco- 

 nomic conditions. CPUE at higfi exploitation is half that at low 

 exploitation. 



Low rate of High rate Mixed rates 



exploitation of exploitation of exploitation 



Effort/catch 

 within hot spot 



Total effort/catch 

 elsewhere 



2.03/40.6 



0.0/0.0 



2.43/24.3 



38.53/385.3 



1.01/20.2 



39.29/392.9 



DISCUSSION 



Although I feel certain that constant diffusivity 

 is an inappropriate model for tunas, there may other 

 models at least as appropriate as that presented 

 here. (See Okubo (1980) for an extensive review of 

 diffusion within models of ecology.) If the basic 

 structure of the model were correct; the assump- 

 tion that a- is a linear function of local saturation 

 might not be. The structure of the model is testable; 



358 



