JJ4 John B. Calhoun 



A core aspect of this thesis is that whenever ju increases above m6 there 

 will be compensatory shifts in m' such that mm' will again eciual 1.0. There- 

 fore, a and i will gradually become a function of N„„ or we might rather 

 say that the members of the group attempt to adjust their intensities of 

 interaction to make any existing A'', regardless of how much it has diverged 

 from Nb, become A„,. Thus, Eqs. (60) and (68) become: 



Oim — 



N - 1 



(69) 



(70) 



At Nb it follows from Eqs. (56) and (69) that the maximum frequency 

 of interaction of one responsive individual with other responsive ones 

 becomes : 



Hrn) ^ ^f - 1 (71) 



J aa A 



Accepting the logic above that in time all individuals will attempt to ad- 

 just their intensity of interaction compatible with any existing N, it 

 follows that: 



A — 1 



fm) ^ f! i (72) 



Jaa ^ ^ ^ 



It further follows from Eqs. (02) and (69), where mm' tend to adjust to 

 1.0 and i adjusts to maximize <?„ regardless of change in N, that: 



.(.) . ^(^ - 1) = ^(^ - '^ (73) 



•''"' [1 + a(N - i)y 4 



And similarly at/i"'\ it follows from Eqs. (51), (59), and (69) that: 



^ a,HN - 1)^ ^ ,HN - 1) 

 •'"^ [1 + a(N - l)y 4 



Equations (73) and (74) must be kept in mind while reading Section 

 XIII, B. It has already been pointed out in the discussion following Eq. 

 (66) that in the evolutionary steady state dj"'^ = di'"\ Here [see Eq. 

 (63)], f^a^ = fai'"\ This is a major premise of this paper, that animals 

 "strive" to experience equal amounts of satisfaction and frustration from 

 social interaction. But note what happens according to Eqs. (73) and 

 (74) when ju varies. If m increases and the members attempt to optimize 



