20 JoJui B. Calhoun 



one in that in a two-dimensional field the area available at successive radial 

 distances from home increases with radius. Considering this fact, will the 

 behavior exhibited by rats in a one-dimensional field lead to an equation 

 for home range closely resembling the bivariate normal distribution 

 [Eq. (3)]? 



When Casby and I originally found that the bivariate normal distribution 

 did conform with the observed home range resulting from captures, we 

 were merely culminating a search for a means of describing the distribution 

 of captures about the mean coordinate point of capture. This conformity 

 revealed nothing about the biological mechanisms involved. We shall now 

 inquire whether the phenomena of (a) decreasing frequency of arriving at 

 successively greater distances from home, and (b) the probability of 

 wandering increasing with distance from home suffice to explain the origin 

 of the bivariate normal type home range. 



A critical issue concerns the origin of the observation or "capture." Two 

 types of observation are possible. First, the observer may record the 

 physical presence of the animal at successive points independent of the 

 activities of the individual. Second, the observation may arise as a conse- 

 quence of the animal responding to an object placed by the investigator. 

 Captures in traps represent this type of observation. 



An assumption is made regarding where responses, such as entering 

 baited traps, will be made. This is that such responses to continuously 

 present and unvarjdng stimuli occur only during the period of wandering 

 at the end of trips. This assumption implies that the animal remains in a 

 perceptually blind state during the outward and return phases of a trip. 

 The circumstantial evidence suggesting this assumption will not be con- 

 sidered here. 



Let : Pi = probability of terminating a trip at radius r. 

 t = time spent wandering at r if it stops there. 

 C = probability of capture at r, which equals tPi times geometry 

 factor of two-dimensional space. 



Then: 



Pi(r) = Ae-^'-^ (19) 



t{r) = Br (20) 



These two equations, in which .4, B, and a are constants, represent the 

 two basic assiunptions regarding use of one-dimensional space. Then 

 considering the geometry factor: 



C = Kre-'i" ' rdrde (21) 



