APPLICATION OF MATHEMATICAL MODELS TO FISH POPULATIONS 215 



Table 2 of the number of immatures (the recruits) have been plotted against 

 the corresponding number of adults in the preceding period. (For the un- 

 exploited populations C and D the mean number of immature fish has 

 been plotted.) This stock-recruitment curve, though the points are somewhat 

 scattered, definitely has a maximum. A Hkely curve has been drawn by eye. 

 Straight lines have also been drawn giving the approximate relation between 

 recruitment and stock for the various levels of exploitation. The likely 



50r 



40- 



« 30 



20 



10 



25% Exploitation 



iO% Exploitation 



No exploitation 



Adultj 



100 



ISO 



Fig. 4. — Stock-recruitment relationship for guppies (data from Silliman & Outsell, 1958), 

 showing adult stock and numbers of immatures three weeks later. Large points are means 

 of several observations. Curve is fitted by eye. Straight lines give the recruitment-stock 

 relation for various levels of exploitation. 



equihbrium states for 10 per cent and 25 per cent exploitation he on the steep 

 descending part of the curve, while the unexploited state is not on so steep a 

 part. The oscillations and their differing amplitude for these varying exploita- 

 tion rates seem well explained by the stock-recruitment relation, as is the fact 

 that at 75 per cent (and possibly also at 50 per cent) exploitation rate the stock 

 goes to extinction. 



This population is perhaps not typical of most marine fish in that a major 

 cause of the stock-recruitment relation lies in the direct predation of the 

 adults on the young. However similar predation, though perhaps on 

 relatively older fish, also occurs in hake {Merluccius merluccius) and to a lesser 

 extent in cod {Gadus morhud). 



