Z. The Social Use of Space 



171 



Since the rank, Ra, of the omega individual is A^;,: 



Va = 



Nt 





(123) 



Since Vn is the lowest velocity achieved in the normal Nb selected by evolu- 

 tion, Vq most likely also represents v,n. Given a v,„ observed, y£°^^ we may 

 calculate a v^J^'p^ appropriate to Nb. Recall that from Eq. (108) v^'^^^ in 

 relative terms = 1.0 and the relative velocity, v^'^^\ of any other ranked 

 individual is by this equation represented as proportions of the alpha's 

 velocity, v^^^^^ or v^^^''^ from Fig. 38 is 12. Therefore 



12 = v^'^^^ 



i(exp) 



And thus at Nb, and utilizing Eq. (123) : 



yCexpat.Vft) = ^(obs) /y (rel) — y(obs) ^ jy^ 



(124) 



However, solving Eq. (124) requires that Nb be known. The rats used were 

 a domesticated albino strain, Osborne-Mendel. Nb still might be 12, as we 

 can expect it to be for the wild type, but we have no way of knowing 

 directly how domestication has altered Nb. Furthermore, the artificial 

 environment imposed possible changes on the area. A, factor in fj. = dv/A. 

 So all that can be expected is that there is some optimum A^, No, har- 

 monious with the existing spatial structure of the environment and any 

 changes arising through domestication. Now, using Nb in the sense of A'',,, 

 values in relative (rel) terms become: 



For N ^ Nb, R = l:v„ = 1 



For A^ = A^6 or iV < or > Nb, R = Nb or A^: vq = Vm = l/Nb 



'N - Nb 



For N > Nb, R = I: vj'^^^ = 1 - 



A^ 



(1 - v„,) 



(125) 



When A^ = oo : y„ = t;^ = 1/A^6 



The general equation for v, where v„ = 1/A^6, and R = velocity rank 

 becomes: 



_ {1 _ [(jV - A^,)/A^](l - vj] 

 A^ - 1 



,(rel) 



R - N 



+ v„, (126) 



