J. The Social Use of Space 



43 



to the amount of time per unit area it spends at successive distance from 

 its home. This relative impact is described by the bivariate normal dis- 

 tribution function (Fig. 2). For any particular animal this means that at 

 3 sigma distance from its home its impact per unit area will be only 0.011 

 of what it was adjacent to its home. We may visualize the impact of any 

 one animal upon its enviroimient as having a mountain-shaped topography. 

 Where home range centers are at least 6 sigma apart, there lies between 

 them a "valley" where neither animal has a significant effect on the en- 



IMPACT ON THE ENVIRONMENT 

 (PER UNIT AREA) 



>- 

 z 

 < o 



o °^. 



I- I 



Ul to 



> K 



-I < 



UJ UJ 



Q: z 



i< 

 "* 1 



> z 



CD < 



5 



0.4 I — 



-• /.5tr 



• • » » 



-• • 2./<r 



3.0 



0.6 1.2 1.8 2.4 



o- DISTANCE FROM ANY H.R.C. 



Fig. 19. Impact on the environment (per unit area). The value 1.0 represents the 

 effect one individual will have near its home range center. Since home ranges increasingly 

 overlap as their centers approach each other, i.e., density increases, the summated 

 impact of all animals on any one point not only increases, but the relative impact on 

 all points becomes more nearly equivalent. 



vironment. As soon as home range centers get closer than 6 sigma to each 

 other, the home ranges overlap and neighbors can both affect those por- 

 tions of the environment falling within both neighbor's home ranges. As 

 soon as home range centers become less than 3 sigma apart, some portion 

 of the environment can be affected by more than two individuals. 



At any point in the environment, the impact of all animals which can 

 arrive at that point during this normal ranging about their home is pro- 

 portional to the sum of their separate density functions at that point. 

 Utilizing the normative data of density function as a function of the sigma 

 radius from home, given in Table 2 of Calhoun and Casby (1958), several 

 curves of summated density function were calculated (Fig. 19). 



