44 John B. Calhoun 



E. Methods of Calculating Data Relative to the Distance between 

 Neighbors 



In Fig. 16, which illustrates the uniform distribution of an alpha species 

 and of a beta species lying in the interstices between the home ranges of 

 the alpha individuals, we can select any single alpha individual and note 

 certain characteristics of the geometric distribution of its alpha neighbors. 

 One such individual, whose home range center is indicated by a triangle, 

 is shown in Fig. 16. A line drawn between the home range centers of its 

 adjoining nearest neighbors forms a hexagon about this individual. Just 

 as there are six nearest neighbors, there are twelve next-nearest neighbors. 

 Lines connecting the home range centers of these next-nearest neighbors 

 also form a hexagon. Successively more distant neighbors form concentric 

 hexagons, each containing six more indi\nduals than the next innermost 

 hexagon. For the purpose of investigating the effect of neighbors on each 

 other or upon the environment, a system of four "concentric" hexagonal 

 sets of neighbors was prepared on a large sheet of graph paper. This pro- 

 cedm'e was repeated three times, forming spatial sets in which home range 

 centers between nearest neighbors were respectively 1.5, 2.1, and 2.7 

 sigma apart. Ruler scales representing density functions (Table 2, Calhoun 

 and Casby, 1958) at successive sigma distances from the home range 

 center, as well as ruler scales representing intensity of signal (Fig. 18) 

 were prepared. Using these ruler scales, several types of events were calcu- 

 lated with regard to their changes in intensity or freciuency along a 3- 

 sigma route such as is shown by the heavy dashed line in Fig. 16. 



At each of eleven points along this typical route of travel, a sum of the 

 density functions of all neighbors whose home ranges overlapped one or 

 more of these eleven points was calculated (see Fig. 19). 



F. Further Comment on the Impact of All Individuals on the Environment 



Each of these sums of density functions were divided by 0.159, the rela- 

 tive density function of an animal near its own home range center. By so 

 doing we can obtain a fairly good idea of the impact of all individuals who 

 may arrive at any particular point with reference to the effect that one 

 individual would have near its home range center. It may be seen that 

 when home range centers are 2.7 sigma apart, considerable inequality 

 between points exists. In other words, points near home range centers are 

 relatively intensively used in comparison to distances about halfway 

 between home range centers. This inequality of usage of the environment 

 is even more pronounced when home range centers are more than 2.7 



