1. The Social Use of Space 165 



regard to home range, Mr. James U. Casby (see Calhoun and Casby, 

 1958, pp. 16-17) derived a function, K/'Iira^-. He called this term "visita- 

 tion frequency." It describes the relative frequency of visiting a particular 

 place in the environment. Later, though published earlier (Calhoun, 1957), 

 Dr. Murray Eden derived the function, ^l = dv/A to represent a communi- 

 cation function defining the relative probability of one individual meeting 

 another. K/2Ta~ concerns arrival at a stationary point, while dv/A con- 

 cerns arrival at a moving point. It was only after I began this elaboration 

 of concepts concerning social use of space that I realized the isomorphism 

 of these two functions. A and 2ira^ become equivalent expressions as like- 

 wise do K and dv. d here is used in the sense of S'~''\ Eq. (107). 



I have already pointed out in the discussion pertaining to Eqs. (35), 

 (80), and (88) to (91) that when a group is in a steady state in harmony 

 with its heredity and environment, m = 1.0, provided appropriate units of 

 time are considered. It followed that v, S^'^ and A also have relative 

 values of 1.0 at Nb, the harmonious steady state TV. Therefore 



t;*S(^V27rc72 = 1.0 (117) 



Given this relationship, can it assist us in determining relative home range 

 0-? We have already seen in Sections VI-VIII that contractions and ex- 

 pansions result from both intraspecific and interspecific interactions. Let 

 us consider home range of members of a constellation as discussed in Sec- 

 tion VIII, C. 



On the average the constellation consists of one alpha, 6 beta, and 5 

 gamma individuals, ranked in this order: 



Nb = N. + N0^ Ny, 



where N^ = 1, N^ = Q, Ny = o. The a individual represents the ideal 

 prototype. Each beta diverges an equivalent amount from the alpha. Like- 

 wise, each gamma also diverges from the alpha, but more so than the beta. 

 By analogy to the discussion pertaining to Table XIII, the rf-genotypes of 

 the 12 individuals in a constellation will be represented as shown in Table 

 XVIII. as in the table denotes alteration in the home range a resulting 

 from the individual's S'-''\ 



The Ni for the alphas, betas, and gammas, according to the formula- 

 tion of Section XIII, B, 5 become respectively 12, 11, and 5. From Eq. 

 (107) it follows that their S^''^ are, respectively, 1.0, 1.091, and 2.40. 

 This increase in response-evoking capacity, S^''\ among beta and gamma 

 individuals will lead to their reduction of velocity, v, respectively to 0.9167 

 and 0.4167, as given by Eq. (108), when compared with v = 1.0 for the 

 alpha member. 



