xi YIELD EQUATION 293 



way to fish. However, the theoretical equation derived by Beverton 

 and Holt gives us the yield Y w in terms of the parameters already 

 discussed with in addition the maximum weight W^ and a factor K 

 related to the catabolism 



d ^ = FN l W. (1) 



The number N t at the time t is given by 



N t = R^F+MXt-t,^ ( 2 ) 



and the weight W t by 



W t = W^i-e-w- 1 *?). (3) 



This last is best handled as a cubic of the form 



W t = W^2 Q -n e ' UK(l - tti) - 

 n = 



Substituting (2) for N t in (1), and (3) for W t we obtain 



at ri=o 



This provides the basic equation with which forecasts of effects of 

 changing the various factors are made. 



Empirical values can be obtained for the yield per recruit (Y W I R ) 

 for various values of F, with a mesh of 70 mm. Such a yield/intensity 

 curve of North Sea plaice is shown in Fig. 171c. The graph shows that 

 with infinite effort all fish would be caught at recruitment and would 

 yield their initial weight of 123 g. At the pre-war fishing mortality of 

 0-73 the yield was 200 g. But the curve has a clear maximum at over 

 250 g, with a fishing mortality of only 0-22. Therefore if these pre- 

 dictions are correct, a lesser intensity of fishing should provide a 

 greater yield. 



One possible way of reducing fishing intensity is to increase the 

 size of the mesh of the cod net. If the age at recruitment were in- 

 creased to ten years the yield per recruit would be as high as 400 g 

 (Fig. 17 id, curve a). Beyond this maximum, the yield falls because of 

 the death of fish by natural causes before entering the exploited phase. 

 However, this curve assumes that the growth-rate is independent 

 of density and it ignores the complex problem of the competition of 

 old and young fishes for a limited supply of raw materials. Curve b 

 of Fig. 17 id has assumed a reduced growth-rate with increasing 

 density and it will be seen that the advantage of increasing mesh size 

 is much reduced. 



