where y— , A is the extreme value of y with fixed yand X, while X— is the 

 extreme^ value of x with fixed y and X. ^ 



Of primary significance is the function: 



obtained by replacing in M (X, y- , X)the extreme value of x = x- with 



X y^ y^ 



the extreme value of X = X- (y^^y,). This function, as in the theory 



of Statistical selection among hypotheses (Basharinov, Fleishman, 1962) 

 will be called the operative characteristic. Using the method of 

 multipliers, we find its expression: 



m(z^, z^) = uCx^) + y(x^, X2) "^v'lz^) v'fz^) (z^ - z^), (2.20) 

 where the function v(Y) is the solution of the transcendental equation: 



i = Urr^) + v-1] (2.21) 



while the function X(z., z^) is: 



y=y(z, ,z.)= \Lll^ I \y^ , (2.22) 



^ ^ '''v'(i^) Vv'(I^) 



while the expression Vq(z) is defined as follows. 



Equation (2.21) has a solution if the structure of the community is 

 "linear," in which case: 



1 - 2x^ a - 1 



- = C + A T" ( a = 1 , a) , 



1 - X ^ " ^"^"T 



1-2x1 xi-Xa 



where C = ^j and the quantity a = ,, „ \/i ^ \ characterizes the 



1-xi ^ ^ (l-xi)(l-Xa) 



"standardized difference" of mortality of components of the community. 



349 



