19$ K. E. F. WATT 



It is not necessary to outline here in detail how equation (2) can be ex- 

 panded, since I have discussed the structure of such equations and components 

 thereof in considerable detail elsewhere (Watt, 1955, 1956, 1959^, K 1960a, 

 b). Only enough of the symbolic statement of the problem will be given 

 here to indicate the general form of such equations. Again, in so far as 

 possible I shall use the notation proposed by Holt et al. (i959)- 



The number of individuals of the I'th year class surviving to the jth birthday 

 may be written as 



Nij = N,o . 5,1 .5,2 ... Sij (3) 



= N,o n s,j, 



where N,o represents the number of the ith year-class hatched, spawned, 

 born or germinated, say. 



Where G^p fractional growth increment of the /th year-class during itsjth 

 year of life is defined by 



we may similarly write 



^^ij = ^io • Qi • Q2 • • • ^ij 



= WiQ n Gy. (4) 



Hence 





Pin = ^in ^in 



n 



= Nio n 5,; w,, n G,,. (5) 



The total biomass present in the relevant universe at any time consists of the 

 sum of the P,^'s for all relevant year-classes. 



Enough is known now to make a rather reasonable attempt at the detailed 

 form of equation (5) for various kinds of organisms. For example, for sexual 

 animals in a stable environment, where only population density regulates 

 fecundity rate, the best equation we can write for N^q (Watt, 1960a) is as 

 follows. 



Where N^^^^ is the total number of fecund individuals in the population, 

 and we assume a 50 : 50 sex ratio, 



