1. The Social Use of Space 103 



Since d, v, and A will be considered constants for this presentation, we set 



(dv/A) = n so that /. = m(A^ - 1) ('^^i 



fjL reflects the ease of communication in the sense of contacts per unit ot 

 time. Basically, d, v and A may be specified in terms of linear unit, L. 

 Therefore, 



dv L • Lt~^ 1 ..,_, 



" = 1^-6^ = 7 ''•^' 



The symbol ^ is here used in the sense of ''dimensionally equivalent to." 

 So by selecting appropriate units of time, n can be made equal to 1.0. In 

 following discussions n will be considered equal to 1.0 in this sense whenever 

 the basic A^, Nb, of a species is in an evolutionarily steady state. 



We will assume that the population of individuals can be divided into 

 two classes: [Na], those individuals who are in a responsive state, and 

 [Np] those individuals who are in a refractory state. We further assume 

 that the individuals in [Na] will be rendered refractory either after a 

 contact with a member of the same class or with a member of [Np]. After 

 any such contact, an individual will remain in the refractory state for a 

 length of time, a, the refractory period, and after this time has elapsed 

 return to membership in [N^]. It is also assumed that any contact that 

 an individual undergoes while it is in the refractory state has no influence 

 on the duration of its refractory period. 



The duration of such refractory periods must be a function of the be- 

 havior of each member of the contacting pair toward the other. It is as- 

 sumed that the critical aspect of this behavior is its intensity. At the steady 

 state of an Nb we shall first consider every individual to be identical with 

 reference to the intensity of its behavior toward others. 



Let: 



la be the intensity of action of any member of [A^„] toward every associ- 

 ate it encounters. 



ip be the intensity of action of any member of [Np] toward every associ- 

 ate it encounters. 



It is further assumed that the most likely way that the duration of the 

 refractory period, a, becomes a function of the behavior of two individuals 

 toward each other is that it results from the product of the intensities of 

 their behaviors. Furthermore, there must be some factor, which will be 

 called B, which governs whether a refractory period will result from the 

 interaction. 



