APPLICATION OF MATHEMATICAL MODELS TO FISH POPULATIONS 217 



and consumption by the young fish. This may be done for the North Sea 

 stock of plaice. Shelbourne (1957) has shown that, especially during the 

 probably vulnerable stage during and after the absorption of the yolk sac a 

 major food of the young plaice is Oikopleura sp., and that probably mortality 

 of plaice larvae at this stage is high when this food is scarce. From Shel- 

 bourne's Tables i and 3, the abundance offish and food on his patch of 

 denser food is, Oikopleura 37,000 from 30 hauls and 3,153 plaice larvae, of 

 stages id and 2a, from 156 hauls; the relative abundance in terms of numbers 

 per haul being 1,200 : 20 = 60 : i. It seems well within the power of a 

 single young plaice to eat a large proportion of these sixty Oikopleura 

 within a few days. There are therefore all the necessary stages for density 

 dependent control by food. The exact mechanism and fmal effect will 

 depend on the dynamics of the food population ; if there is no reproduction 

 and recruitment into it, then a very abundant plaice population might well 

 wipe out the food and itself die out shortly after. This would give a maxi- 

 mum, perhaps pronounced, in the stock recruitment relation. Alterna- 

 tively there might be more or less constant recruitment of young Oikopleura 

 which would tend to give a rather flat stock-recruitment curve. 



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