1. The Social Use of Space 105 



which defines the probability of a contact being socially "perceived'' shall 

 be called n'. 



ria == number of contacts made while the given animal is in the "re- 

 sponsive" state. 



fa = (ria/t) is the frequency of responsive contacts when the animal in 

 question is in the "responsive" state over all time. 



Since each contact between two individuals, at least one of whom is in 

 the responsive state, is followed by a refractory period a, characteristic of 

 each of the responsive individuals, and since there are ?ia such contacts in 

 time t, then the individual is in the refractory state for a total time ana. 

 Clearly, the total time ta in which the individual is in a responsive state 

 is t — an'Ua. 



Since na = tfa then 



ta = t - aix'Ua = t - afx'tfa = t{l - OCuJa) (38) 



In this sum of refractory intervals, ta, contacts will be made at frequency 

 /c, but all such contacts are made while the animal is responsive so that 



Ua = fda = fct{l — CXIl'fa) = tfa 



or, since /a = ria/t 



fa = /.(I - V/a) (39) 



Thus 



1 — anja 

 It will also be helpful to rearrange Eq. (39) to obtain /„ as a function of /d 

 /. = /„ + ccn'fafc =/«(!+ an%) 



So 



/« = , / ., (41) 



We may also define the frequency of refractory contacts by each in- 

 dividual over all time 



fp =fc-fa (42) 



Contacts between individuals will be of three kinds: (a) both individuals 

 responsive; (b) both refractory; and (c) one individual responsive and 

 the other refractory. A given individual meets fc other individuals in unit 



