170 John B. Calhoun 



the effects of increased levels of vitamin A on behavior, it suffices to note 

 that increases in vitamin A above normal levels acts as a kind of "tran- 

 quilizer" which reduces fighting but increases the prevalence of abnormal 

 behavior (i.e., females become poorer mothers while males increase the 

 frequency of exhibiting inappropriate sexual behavior) . 



Previously we have seen (Section XIV, A) that in an A'' = 11 the ob- 

 served velocities for mice, as calculated by Eq. (113), closely approximated 

 the theoretical. We may ask the same equation of the present data. For 

 2A the sum of velocity indices [^iLi^i"*"^^] foi' IG hours of observation 

 was 1089.2, and for lA it was 804.7. Let v^^''^^ and v^^^p^ represent the 

 velocities of the alpha, Ist-ranked, individual and the omega, A^th ranked, 

 individual, as calculated by Eq. (113). For lA, v^^^p^ = 48.77 and v^f^'P^ = 

 1.52; while for 2A, yj^^p) = 66.01 and yjj^^p) = 2.06. 



Had all the intermediate v^^^p'> been calculated, as would have been 

 represented by a straight line connecting these extremes on Fig. 38, it is 

 quite obvious that the observed w^ould differ significantly from the ex- 

 pected. One could drop the inquiry at this point and conclude that veloci- 

 ties for rats do not accord with theory as for the mice cited in Section 

 XIV, A. However, there are two reasons for not dropping the inquiry at 

 this stage. First, 32 males represent an V almost three times the theoretical 

 basic N, Nb = 12 while the A" = 11 for the mice closely approximated this 

 Nb. Second, the regression curve of velocity for the lA and 2A males con- 

 verge at the omega-ranked individual. Furthermore, this convergence is 

 at a velocity 6 to 8 times that anticipated by Eq. (113) . This fact suggests a 

 minimum velocity, Vm, below which rats cannot reduce their velocity and 

 long survive. Two such individuals with excessively reduced velocity are 

 shown on Fig. 38. I can only say that, on the basis of the very few individ- 

 uals which did develop such unusually low velocities, such individuals 

 usually become bloated and usually shortly died. 



Accepting the indication of the reality of Vm, is there a logical basis for 

 recognizing its relative value? In the course of evolution, where the group 

 becomes adjusted to an Nb, there will in any stabilized group be an Nb- 

 ranked omega individual. In terms of Eq. (107) it is readily apparent that, 

 where R = rank in the sense used in Table XIII: 



Ni = 1 -\- (N - R) (121) 



Therefore, for any ith. individual where i is equivalent to its rank R, Kq. 

 (108) becomes 



