If we show graphically the changes of the rate of increase, 

 represented as weight^increaSe^per^yearj by increasing fishing 

 intensity and thus lowering density, then it ensues from the fore- 

 going explanation that we must find an optimtun curve (figo 1, 

 curve l) o The rate of increase is at first gradual and after 

 reaching a maximum, it declines againo From curve I, we can 

 construct curve II which shows the density of the stock by changed 

 fishing intensityo For instance, if a practically emptied sea 

 (to M in figo 1) re^populates itself without being fished, after 

 one year this stock will have increased with the amount M M o This 

 amount is regulated by the speed of increase during the first year 

 of recovery and represented by curve I in the illustrationo 

 (it is tabulated in the illustration that the average rate of 

 increase during the first year is equal to the rate of increase 

 at a period 6 months after the start of the protections) Continu- 

 ing in the same way,, the strength of the fish stock may be tabulated 

 from year to year with the aid of curve lo The result is the S-shaped 

 curve IIo This shows, from right to left, how in a sparsely populated 

 sea the fish stock grows if there is no fishingo From left to right, 

 it shows how a fish stock decreases when fished with steadily= 

 increasing intensity© The rate of increase (or increase°per=unit- 

 of-time) is shown for each density value of the fish s tock by a 

 point on curve I, vertically below these values o 



From the curves, it appears that the rate of increase has a 

 maximum value at density P of the fish stocko If one starts to 

 fish th© untouched stock and if, for instance, during one year one 

 catches less than the yearly increase at strength P, then an 

 equilibrium will appear at a density somewhere between P and the 

 limit, whereby the stock remains constant but cannot deliver the 

 largest possible catch annuallye 



One may speak here of a state of overfishingo If one increases 

 the fishing intensity in such a way that annually more than the 

 increase at strength P is taken from the stock, then, besides this 

 increase, a part of the fish stock is also removed annuallyo The 

 stock will decrease and as soon as the point of maximum annual 

 increase is passed this decline will go faster because the rate of 

 increase or the productive capacity of the fish stock diminishes 

 at an increasing rate© This is the state of overfishingo Only if 

 the fishing intensity is regulated in such a way that the fish 

 stock remains at strength P will it be possible to harvest a 

 maximum catch from year to yearo We shall call this optimum 

 catch and the accessory strength of the stock, the optimum strength© 

 The catch which may be taken at each arbitrary strength of the 

 stock, without changing its strength, we shall call the allowable 

 catcho 



