1. The Social Use of Space 



63 



The probability, Pa{i), that i number of the six a individuals will be at- 

 tracted to the given alpha will be : 



Pa(i) 



(A /I 



(28) 



Similarly the probability, pb(i), that i number of the six b individuals will 

 be attracted to the given alpha wdll be: 



Pb(i) = 



il \3/ \3 



' /9\^— * 



(29) 



Therefore, the probability, p{m), where m = to 12, of m members of 

 the 12 next-nearest neighbors joining any given alpha and its six nearest 

 neighbors to form a constellation will be: 



p{m) = ^ Paii) ' Pbim - i) 



(30) 



For example, if m = 4 this becomes: 



P(4) = PaiO) ' Pbi^) + Pail) ' Pt(:i) + Pa{'2) ' p,{2) + p„(3) 



• P5(l) +p„(4) . PbiQ) (31) 



p(S)) • • • p{12) were calculated and are shown in Table VIII as p{7 + 0) 



Table VIII 

 Expected ^'ARIABILITy ix the Number of Individuals Formixg a Constellation 



Xumbor of animals in group 



Prol:)abilit3' of group developing 



9 

 10 

 11 

 12 

 13 

 14 

 15 

 16 

 17 

 18 

 19 



0.00137200 

 0.01234568 

 0.05041152 

 0.12345679 

 0.20190329 

 0.23225308 

 0.19266546 

 0.11612654 

 0.05047582 

 0.01543210 

 0.00315072 

 0.00038580 

 0.00002143 



Z 1.00000023 



