1. The Social Use of Space 59 



such a low frequency of communication with the selected individual that 

 mutual effects will be of little significance. 



Examination of the spatial distribution of home range centers in a uni- 

 formly distributed population reveals that one-twelfth of the members 

 each have six nearest neighbors whom they can influence without competi- 

 tive influence being exerted by any other individuals in this one-twelfth 

 population. Such individuals will hereafter be designated as alpha indi- 

 viduals. Home range centers for these alpha individuals are designated by 

 small open circles in Fig. 26. It will further be noted that two such alpha 

 individuals, who live closest to each other, share next-nearest neighbors. 



Antagonistic relations, uniform utilization of the environment, and 

 attainment of uniform sign and signal fields approximating in intensity 

 the sign and signal intensity expressed by an individual at its own home 

 range center, and eciualization of contact rate with all neighbors throughout 

 any one individual range, all serve as forces leading to a uniform distribu- 

 tion of home range centers at near 2.0 sigma between centers (Section 



VII, K) . Yet, we may anticipate an opposing force of attraction between 

 members in close communication with each other. This will lead to all 

 nearest neighbors shifting the centers of their home ranges slightly toward 

 their single alpha associate. Such nearest neighbors will hereafter be 

 designated as beta individuals. 



Now we can turn our attention to the alpha's next-nearest neighbors. 

 It may be seen from Fig. 26 that in each group of twelve next-nearest 

 neighbors, six are eciuidistant to two neighboring alphas. Therefore, since 

 the probability of each of these six nearest neighbors is 0.5 of being at- 

 tracted to either of two alpha individuals to which they are eciuidistant, 

 each alpha on the average will have attracted to it three of these next- 

 nearest neighbors. The remaining six next-nearest neighbors to any alpha 

 are ecjuidistant to three alphas. It similarly follows that on the average 

 any one alpha will have attracted to it two of six such next-nearest neigh- 

 bors. Next-nearest neighbors w^hich so move toward an alpha associate 

 will hereafter be designated as gamma individuals. Thus, each alpha will 

 have attracted toward it six beta individuals and on the average five 

 gamma individuals. This process leads to a clumping of the population 

 into groups ranging in size from 7 to 19, with a mean of 12 (see Section 



VIII. D). 



The central alpha indi\'idual because of its more favored position in the 

 communication network may be assumed to be dominant to both its beta 

 and gamma associates. Gamma individuals, because of their peripheral 

 location in the developing clump, here designated a constellation, will be 

 subordinate to both the beta and alpha associates. Now let us consider the 



