7. The Social Use of Space 125 



bearing on our understanding of the course of evolution involving change 

 in group size. It will mean that gradual changes in heredity or culture will 

 rarely have transpired. Rather, from the pool of gene variability accumu- 

 lated in the species, there will be rapid shifts in gene frequencies of many 

 genes, thus resulting in a new phenotype. In so long as environmental 

 conditions facilitate maintenance of its Nb by a species, its gene pool may 

 become quite diverse through the accumulation of mutant genes. Then, 

 once environmental circumstances force the species to maintain an ele- 

 vated A'' near its tolerance level for dd or 9/, an extreme selection pressure 

 will arise for reducing the frequency of all genes except those which adapt 

 the species to its new N. A genetically variable A^^^^ species will thus 

 rapidly be transformed into a genetically rigid Nl"^^ species. 



On the cultural level such a process of saltatorial change in basic group 

 size demands that the value system which dictates acceptable roles of 

 action and communication be preserved even after the usual group size 

 has far exceeded the Nb appropriate for that value system. At the same 

 time, under the pressure of increases in 6d and 6/, small segments of the 

 closed system will develop values divergent from the main group. At the 

 tolerance limit of dd and 6/, when A^ has so diverged from Nl^\ there will 

 arise a marked and rapid shift to the prevalence of those newer values 

 appropriate to d^'"^ and 9f"'^ at N^'^K Value frequencies and gene frequencies 

 become isomorphic in these two avenues through which there can be a 

 saltatorial evolution from one basic group size to another. 



Basic group size for adults only in the primary steps of human cultural 

 evolution seem to include the 10-16 range, 50, 200, and 2,000. This series 

 resembles neither of the hypothetical saltatorial group size series except in 

 its saltatorial character. The hypothetical series merely demonstrated the 

 kind of changes following from stated assumptions. The exact series 

 followed by any line of change depends upon the threshold tolerance limit 

 for dd and 6/ as well as three factors ignored in our discussion up to the 

 present. Discussion up to this point assumes /x = (dv/A) = 1.0, where 

 d represented the target diameter of other individuals, A the area inhabited 

 by the N individuals, and v the velocity of movement of individuals. In 

 essence, m represented the likelihood in time t of one individual encounter- 

 ing another. 



It can readily be shown from Eqs. (52) and (60) that da, the satiation 

 from social interaction, i.e., afaa, can remain constant regardless of changes 

 in fjL. At least this is so if the physiology and behavior of the species is com- 

 pletely adjustive. From the general form of Eq. (60) where n' = 1.0, 

 a = 1/[m(A^ — 1 ) ], it follows that each doubling of /x, that is doubling the 

 likelihood of one indi\'idual meeting another, necessitates a halving of 

 a, and thus reduces intensity of interaction from (a)^'^ to (a)^/-/2. If we 



