1. The Social Use of Space 45 



sigma apart. However, by the time home range centers are uniformly dis- 

 tributed at 2.1 sigma apart, all portions of the environment are approxi- 

 mately equally utilized although every point is more intensively utilized 

 than when home range centers were farther apart. Every further increase 

 in density, as represented by home range centers coming closer together, 

 merely increases the intensity of usage of every part of the environment and 

 all parts continue to be equally utilized. 



These curves (Fig. 19) are particularly instructive in gaining an insight 

 into an "ideal" interval between home range centers. It is logical to assume 

 that portions of the environment which are less utilized than others serve 

 as a trap to catch wandering individuals who have not yet established a 

 home range. As long as the process of eciualizing distance between adjoining 

 home range centers continues, no remaining pockets of less utilized habitat 

 will occur by the time adjoining home range centers are nearly 2.1 sigma 

 apart. 



Any increase in density, that is any shortening of the interval between 

 home range centers below 2.1 sigma, will merely increase the probability 

 that available objects will be overutilized. 



At the maximum interval between HRC's at which uniform utilization 

 of the environment arises, aggressi^'e actions exhibited by individuals with 

 resident home ranges may be expected to prevent excess members of the 

 populations from settling down within such an established area. Such 

 wandering individuals may be expected to wander through and out of such 

 established areas and into marginal habitats. 



Thus, if minimizing the opportunity for aggressive encounters and the 

 development of a uniform utilization of resources represent forces affecting 

 evolution, we may anticipate development of capacities for communication 

 which will most readily assure that the members of a population of a single 

 species will be able to distribute themselves uniformly through space with 

 an approximate 2.0 home range sigma distance intervening between any 

 two adjoining home range centers. 



G. Contacting Neighbors 



The product of the density functions of any two individuals at a particu- 

 lar point determines the relative probability that these individuals will 

 meet by chance. Similarly, the product of the density function of any one 

 individual at a point with the sum of the density functions of all other 

 individuals determines the relative probability that this one individual 

 will contact neighbors at that point. Such latter calculations were made 

 for uniformly distributed home range centers at 2.7, 2.1, and 1.5 sigma 



