106 John B. Calhoun 



time. Of these J\ contacts, fa are with individuals in a responsive state. 

 Hence, the probabiHty pa that any given encounter will be with a responsive 

 individual will be 



Pa = (fa/f.) (43) 



Therefore, of all the encounters /„ in unit time which the given individual 

 makes while it is responsive, the number 



faa = Pa fa (44) 



will be with other responsive animals. Thus, /„<, may be considered the 

 (absolute) frecjuency of responsive-responsive encounters. Substituting 

 (43) into (44) we obtain 



faa = y (45) 



Using Eq. (41) 



•^'"' ^ /.(I + an%r ^ (1 + «M7e)2 ^^^^ 



In like manner we can define fpp as the frequency of contacts of individuals 

 both of whom are refractory and of fap for the freciuency of contacts in 

 which one individual is responsive and the other refractory. 



By an argument analogous to that given above we arrive at the 

 formulation 



fr>.='^ = ^^^^-^ (47) 



Je Je 



Using Eq. (41) 

 J pp ~ 



^' Vl + V/JJ/ -^ -^ \ l+V/e / 



(1 -^an%y 



Again: 



(48) 



/.. = -^ = ?^^^I^ (49) 



