1. The Social Use of Space 37 



will increase its probability of encountering at least one member of the 

 alpha species. About each such home range center a smaller circle was 

 drawn (Fig. 16). This smaller circle represents the same proportion of the 

 beta species home range as does the larger circle for the alpha species. 



Examination of Fig. 16 shows that according to this formulation there 

 will be in an ideal steady state exactly twice as many individuals of the 

 subordinate beta species as there are of the dominant alpha species. This 

 is because there are twice as many interstices between uniformly distributed 

 alpha home ranges as there are alpha home ranges. 



Fig. 16. Spatial distribution of a dominant and a subordinate species. Large circles 

 represent a uniform distribution of one sigma radius portions of the home ranges of a 

 dominant, alpha, species, while the smaller circles represent a similar proportion of the 

 home range for members of a subordinate, beta, species. See text for other details, 

 Section VII, A. 



Now, suppose that a few traps are placed at random within a habitat 

 characterized by inhabitation by such an alpha and a beta species. The 

 fifteen dots in Fig. 16 represent such random points. It is readily seen that 

 there is an alpha individual exposed to nearly every trap, but few in- 

 dividuals of the beta species are exposed to traps. 



Now suppose we do set traps in such a system and remove the individuals 

 caught. It is the general experience in continuous removal trapping that 

 25-50% of the members of the alpha species which are taken during 30 

 days are actually taken during the first 3 days. 



This can only mean that by the end of 3 days there must be many mem- 

 bers of the beta species whose neighbors of the alpha species are then no 



