1. The Social Use of Space 39 



identification of the means is unessential to the general argument; only- 

 recognition of the existence of some effective means of communication is 

 necessary. 



C. The Learning of Signals 



There exists the possibility that the response of one individual to a 

 signal emitted by another has become through evolutionary processes 

 one which does not require a learned association between the signal and 

 some act on the part of the emitter for its development. In the prior history 

 of such species there must have been the opportunity for associating the 

 signal with its emitter and there must have been survival value in the re- 

 ceptor developing an innate response to detection of the signal. However, 

 until such responses to signals are demonstrated to be innate, it shall be 

 assumed that they are learned. 



We may now ask, "How may the members of a species learn a signal 

 when the individuals are characterized by fixed home ranges which may be 

 described by the bivariate normal distribution function?" In order to gain 

 insight into this question, we shall consider two neighbors, A and B. A's 

 home range center is fixed whereas B, who lives some distance away, 

 gradually shifts its home range center toward that of A. When the home 

 range centers are six home range sigma or more apart, it is apparent that 

 the probability of their meeting by chance will be extremely remote. This 

 relative probability of meeting is proportional to the product of their 

 density functions at any particular point (see Table 2 in Calhoun and 

 Casby, 1958). 



However, as the home range center of B approaches that of A, these 

 two individuals will meet by chance on very rare occasions. Three examples 

 of the relative probability of A and B contacting are given in Fig. 17. 

 When the home range centers (HRC's) are 3.9 sigma apart, one peak is 

 1.5 sigma from ^'s HRC and the other is 1.5 sigma from B's HRC. In 

 examining Fig. 17 it is well to keep in mind that we are considering the 

 probability of contact at points along the line connecting the two home 

 range centers. At all distances intervening between home range centers, 

 from slightly over 3 sigma up to 6 sigma, there are always two peaks in 

 this curve of probability of contact between two neighbors. As the home 

 range center of B approaches 3 sigma to that of A , these two peaks approach 

 each other until at 3 sigma they coincide for the first time. This single peak 

 of highest probability of contact of two neighbors, which lies exactly half- 

 way between the two home range centers, characterizes all distances less 

 than 3 sigma intervening between the home range centers. 



