FISHERY BULLETIN: VOL. 79, NO. 2 



djmamic parameters generated in this manner 

 PCX) is calculated for X from to 100 m. For each 

 set of parameters the constant k in Equation (16) is 

 determined according to the condition expressed 

 by Equation (15) by numerically integrating the 

 integral 



Vk 



-f 



Xe 



-2(a + bc)/(c+XO 



ic+X')'''''' 



dX. 



(23) 



Using Simpson's rule for integration \/k is 

 evaluated within a few percent accuracy with a 

 1 m integration step and X* = 300 m. 



The response of P(X) to variations in the 

 dynamic parameters is illustrated in Figures 4-8, 



15 t 



05  



8 



20 40 60 80 100 



Figure 4.— Probability distribution (P) vs. school diameter (X), 

 in meters, for relative schooling density parameter values p' = 

 0.1, 1, and 10. 



15 T 



05  



(e; 



' <^' t ''^ I 1 1 h- 



. 1 



I I I I 



fi 2 4 6 8 10 



X 



Figure 6. — Probability distribution (P) vs. school diameter (X) 

 for relative exit rate parameter values /3' = 0.1, 1, and 10. 



15 T 



. 1 



05 -l 



80 100 



FIGURE 7.— Probability distribution (P) vs. school diameter (X) 

 for relative shrinkage rate standard deviation values a' = 0.1, 1, 

 and 10. 



15 t 



1 •• 



6 



. 1 



'' 1\^ 





10 







2 4 



<. « y 



6 S 10 



15 t 



. 1 



. 05  



. 1 



.::...) 







20 40 60 80 100 



FIGURE 5.— Probability distribution (P) vs. school diameter (X) 

 for relative entrance rate values a' = 0.1, 1, and 10. 



FIGURE 8. — Probability distribution (P) vs. school diameter (X) 

 for relative expansion rate standard deviations values a'i = 0.1, 

 1, and 10. 



320 



