1. The Social Use of Space 113 



df approaches 0.25 at Nb 



df approaches 1.0 as A^ approaches infinity with 



reference to Nb- 

 Of represents the consequences of negatively affective 

 interactions. 

 0<»') = amfi":^^ = maximal da = 0.25; see Eq. (57). 

 j^(m) ^ That A^ at which S^"'^ results. In other words, at N"" 

 satisfaction from social interaction is maximized, but 

 at A'"^'"^ df"^ = d^"'\ that is, there is as much frustra- 

 tion as satisfaction from social interaction. 

 A^6 = The basic group size of a species living under those 

 conditions to which it is most adapted. A^6 is a special 

 case of N^'"\ 0f \ e^/\ ab, u, ixb, and Mb' represent values 

 appropriate to Nb- Here 6^^^ and df^ always = 0.25, 

 as may be seen from Eqs. (57) and (63). At Nb both 

 Mb and nb must equal 1.0. d^J"\ dj'"^ represent values 

 appropriate to A^c-) in which ^i'"> - ^f ^ and 0)'"> = 



However, a^"'^ i^"'\ m^""^ and m'^'"^ at A^^'") may all 

 differ from comparable values appropriate to Nb. 

 Q(o) _ Q{m) £q^. ^ij ^ Q^j^gj. ^j^g^j^ ^^^ although quantitatively 



9^^°\ d^J"\ and da'"^ all = 0.25. 

 No = Any A^ when da = d^°\ No may equal Nb, but when it 

 differs from Nb, some alteration in n, ij.', or a permits 

 attainment of the optimum 6 a, that is dj . 



2. Interaction P'unctioxs Stated in Terms of A^ 



The number of indi\iduals inhabiting an area is more readily measured 

 than any other function relating to this model of social interaction. There- 

 fore, it will be helpful to state all other functions in terms of A^: 



/. = n{N - 1) (34) 



If intensity of interaction is labile to the point that 0^'"* can always be 

 attained, then 



^ (60) 



which means that : 



jlmlJ-m {N m — 1) 



\n,ny^n^'{Nm " 1)/ 



(68) 



