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



that the difference in a^'s is more an effect than a 

 cause of their positions. 



Figure 2b makes an important point. Although, 

 in the absence of fishing, the anomalous cells (the 

 "hot spots") act as a net source of fish to the entire 

 region of the model, there is still much mixing of 

 fish into these sources. The importance of mixing 

 depends upon the rate of dispersal of fish, mortal- 

 ity rate, and the distance involved. In this case, it 

 is clear that it would be foolhardy, having divided 

 the region into "substock areas", to then try to 

 manage these areas in isolation. 



The effect, seen in Figures 2c and 2d, that fishing 

 has of creating a minimum in the abundance close 

 to the maximum, needs to be explained further. 

 Figure 2a shows the steady-state abundance before 

 any extraction of fish; the net flux through each cell 

 is zero. The probability that a given individual with- 

 in each cell migrates must be inversely proportional 

 to the number of others within that cell, as other- 

 wise the total emigrating would not be constant for 

 all cells. Let us suppose that fishing starts in just 

 one cell, that with most fish. The balance of migra- 

 tion is temporarily disturbed. Fish move in at the 

 same rate as before but, because there are now 

 fewer fish inside than there were, there is less 

 emigration from that cell. This causes a net flow 

 towards the cell that is being fished despite the fact 

 that this cell still contains more fish; the variability 

 of a^ allows flow "uphill", against the gradient in 

 abundance. The flow to the cell being fished causes 

 the abundance to drop in its neighbors, which then 

 stimulate a net flow from cells more distant from 

 the fishing. A dynamic equilibrium is established 

 when the amount removed by fishing is met by a 

 balance of local production and net immigration to 

 the cell of exploitation. This immigration is fed by 

 the rest of the region, where carrying capacity is 

 constant and flow is "downhill". The transport of 

 fish towards exploitation is maintained by a gradient 

 of abundance and amplified by the differences in 

 a~ created by that gradient. Fishing at the places 

 of highest capacity makes them sinks for the 

 entire region, drawing fish in from everywhere. 

 The ability of a fishery to mold the topography 

 of the abundance may lead to a founder effect 

 in (model) fisheries. An established fishery will 

 depress the abundance in the surrounding region, 

 which may make fishing uneconomical. This might 

 not have been so if fishing had started simultane- 

 ously. 



There is no clear evidence, as far as I am aware, 

 that abundance minima surround areas of exploit- 

 ation. It is the bane of fisheries science that little 



information is obtainable from marginal areas; most 

 of our information comes from fishermen who do 

 not generally choose to work where they expect 

 fewer fish. In a more realistic model, with habitats 

 changing realistically (time-scales of a few hours), 

 the system may rarely be near equilibrium. This, and 

 the fact that there is variability on very different 

 scales in space as well as time, make it unlikely that 

 the simple topography illustrated here would be seen 

 in practice. Indeed, most fishermen would suggest 

 that the spatial and temporal topography of abun- 

 dance is extremely complicated. The variability of 

 q, the notional catchability coefficient, may be due 

 to changes in the degree of aggregation of the fish. 

 Too disperse and the fish may not be economic to 

 catch. Too aggregated and a few boats might be for- 

 tunate, but they would be overwhelmed and unable 

 to fully exploit what they had found. 



Migration of fish between different fishing areas 

 tends to diminish the attraction of catch reduction 

 as a management tool to a manager responsible for 

 just one of those areas; high rates of exploitation 

 effectively enlarge the range of the fishery. With 

 a ' a function of the immediate environment, the ef- 

 fect is enhanced; reducing the catch reduces immi- 

 gration and enhances emigration. 



Within the Schaefer (1954) model, biological pro- 

 duction is highest at half the carrying capacity. 

 Figure 2a shows that the abundance at the hot spots, 

 while higher than elsewhere, is less than 40% of the 

 carrying capacity of those spots. In this sense the 

 populations offish at the "hot spots" are below op- 

 timum, even before any fishing takes place. Fish are 

 exported to the surrounding region, increasing the 

 abundance there to more than the local carrying 

 capacity. Thus the surrounding region has negative 

 net production. Maximizing local production every- 

 where is impossible, and working out the distribu- 

 tion of effort that would lead to maximum overall 

 production would be difficult. Harvesting outside of 

 the hot spots would reduce the abundance of fish 

 at these hot spots and so reduce the productivity 

 there still further. Regardless, it is unrealistic to sup- 

 pose that a total ban on fishing where catch rates 

 are highest is feasible, or even desirable. The eco- 

 nomic portion of this model allows us to investigate 

 the effects of intrinsic change and less intrusive 

 management. 



Table 1 indicates that the effects of an increase 

 in power of the fishery may not be positive in a 

 region where the fishery is viable before the change. 

 Here power denotes the technology that allows 

 fishing to be viable at a particular index of abun- 

 dance of fish. Reducing the cost, as was done ex- 



360 



