I. The Social Use of Space 121 



this line in Fig. 35. Further elaboration of such saltatorial series of Nb is 

 given in Section XIII, B, 3. 



It must be kept in mind that a basic assumption underlying this general 

 formulation of social interaction is that the mean free path of an individual 

 must be large in comparison with the target diameter represented by any 

 other individual. That is, animals must not be so crowded that one in- 

 dividual becomes so physically hemmed in or surrounded by a few others 

 that opportunity to contact many of its associates becomes markedly re- 

 duced. When an experimental study violates this condition, what has been 

 said in the above statements will not apply. 



2. The Buddixg Off of Social Groups 



As the group size increases beyond Nb both the deficit in satiation, dd, 

 and the amount of frustration, 9f, increase in so long as intensity of inter- 

 action remains constant. Members of the group will find participation in 

 it both less and less satisfactory and more and more stressful. The question 

 arises, "At what point will members find conditions so unbearable that 

 they will leave or at which the group will split?" Changes in da, or da, as a 

 consequence of changes in A^, are proportional to /„„. Therefore, we would 

 like to know if there is some N from which any given change in N brings 

 about a greater change in faa than a similar change from any other N. The 

 second derivative, f^'a = 0, occurs when: A^ = 1 + 2/(a6Mo) [see Eq. 

 (81) ]. This N shall be referred to as Ni. 



For Nb = 12.11 this arithmetic inflection point comes &t N = 23.22. 

 As may be seen from the inset graph in Fig. 35 this N marks the point of 

 maximal change in da with a given change in N. At this point an increase 

 in N produces a greater decrease in da than a similar change at any other 

 N greater than Nb. Furthermore, at Ni, dd, as calculated by Eq. (86), for 

 any N will always be 0.0278, which represents an 11% deficit in do. 



For howler monkeys and man, where the basic A'' appears to be about 12 

 adults, the social group size rarely exceeds 2Nb unless, as in the case with 

 man, the next well-defined larger group is much larger. It is for this reason 

 that I suspect that N will split or bud off another group when N approaches 

 (2Nb — 1) , the point of maximal rate of change in satiation deficit as given 

 by Eq. (85). In essence, this line of reasoning says that by the time a 

 group nearly doubles in size from its basic A^, its members will begin to feel 

 uncomfortable in the sense that they do not find participation in the group 

 sufficiently satisfactory. This will lead to enough members leaving the 

 former group so that within each of the two new groups interaction will 

 produce near optimal results. 



