1. The Social Use of Space 



meaningful from an ecological standpoint because it states in comparative 

 terms the amount of time spent by an animal in a small standard area at 

 any position in the home range. However, for the initial mathematical 

 manipulation, it was found more convenient to express the density func- 

 tion in terms of polar coordinates. Then the probability of finding the 

 animal between the radii r and r -\- dr about the true center of the home 

 range is: 



2 



f{r)dr = — - exp ( — r~/2a'^) rdr 



If Eq. (3) is integrated over the range to o- we have 



r 2r 



/ T- exp (-rV2(r2) rfr = 1 - g-'/^ = 0.3940 



'o -^0- 



(3) 



(4) 



In the above eciuations a, the standard deviation of the normal distribu- 

 tion function, is the value of a radius within w^hich the probability of the 

 animal being present is 39.4%, if its movements can be described by a 

 bivariate normal density function. 



Similarly, integrating Eq. (3) over the range to 2o- gives 



1 - e-4/2 ^ 0.8645 (5) 



Similarly, integrating Eq. (3) over the range to 3o- gives 



1 _ p-9/2 = 0. 



f6) 



The above sigma thus delineates a single distance term by which home 

 range may be described. The term "home range sigma" will be so utilized 

 in following sections. 



Although this sigma may be calculated from a series of coordinate points 

 of capture by equations presented in the original paper, use of recapture 

 radii provide a more direct means, adequate for most purposes. Calculate 

 the mean coordinate point of capture, the approximate home range center. 

 Then on a large scale grid map of the study area measure recapture radii, 

 r, from this mean coordinate point of capture. Unbiased estimates of sigma, 

 s and Si may be calculated by the following equations: 



s = 



&i = 



(7) 



(8) 



