In the second stage, we solve the transcendental equation 

 P = F[p.T^.{p,...,p)] 



(2.5: 



for p. In accordance with what we said above, the community at climax 

 corresponds to the set U={iipc(3ii} of limiting values, corresponding to 

 the permissible set Wg={pc(3( .,...,.) ^ of the functional transforms 

 Pu3( .,...,.) . We note that a portion of the functions p^^p^l .,...,. ) may 

 be independent of p. 



Let us analyze an explicit solution of the equations presented for 

 the model of the community, based on the characteristics of birth and 

 death of a-indi viduals . These characteristics, as resultant indices of 

 interactions of the components of the community among themselves and 

 with the environment, are widely used, primarily for the description of 

 the higher trophic levels of community. 



Let us introduce the conditional probability of birth 

 conditional probability ii^ of death of an ct-indi vidual of 

 corresponding age in one time step. 



It can then be shown that : 



4s ' 

 the 



and the 



/ Pn 



^'= 







pUi \ 



Paa + l 



"aa Paa+l 



.Pa*n    Pa.ia    Pa^^a Pa^t.a^x 

 pLxa - (K, 0,  . ., 0). p^^,^^^^ = 1 - i A^ 



P'aa 







^aba-l Kba,-l^'ah^-i 



(2.6) 



~^'„ 



"''a-l 



f'ah„ 



344 



