36 John B. Calhoun 



A. A Two-Species System 



The relationship between Clethrionomys and Sorex on the Rich Lake 

 Island (Section VI, A, Fig. 9) and between Peronujscus and Blarina in 

 the Chadwick Woods study (Section VI, B, Fig. 10) form the basic data 

 leading to this formulation. The shrews — Sorex and Blarina, respectively, — 

 in these two studies exhibited a delay in entering traps until many of the 

 mice, Clethrionomys or Peromyscus, had been removed. Yet despite this 

 slowness of entering traps, twice as many shrews as mice were taken during 

 the 30 days of trapping in each study. 



These data pose two questions : 



1. Why were there twice as many shrews as mice? 



2. In what way (and why) did the behavior of the shrews change so 

 that after se\'eral days of trapping they were more exposed to traps 

 than initially? 



The first assumption will be that the larger the home range the greater 

 the likelihood an animal will encounter a trap and be caught. Since during 

 the first few days of trapping many mice but few shrews were taken, despite 

 the greater abundance of shrews, the mice must have had considerably 

 larger home ranges than the shrews. Furthermore, since the number of 

 shrews taken per daj^ increased during the first 10 days of trapping, it 

 follows that their home range expanded as the mice were killed off. This 

 leads to the conclusion that the mice in some way inhibited the extent of 

 home range of these shrews. We may now designate the mice as being 

 dominant or alpha species and the shrews as subordinate or beta species. 



Formulation of a theory depicting the social and spatial aspects of such 

 a two-species system recjuires the assumption of a uniform distribution of 

 centers of home range for the alpha species. This represents the simplest 

 assumption leading to a 1:2 ratio of number of alpha and beta species. 

 In the preparation of Fig. 16, a field of uniformly spaced dots (not showTi 

 in Fig. 16) was plotted. These dots represented home range centers for 

 members of the alpha species. A circle of radius half the distance between 

 centers was drawn about each center. Each of the larger circles in Fig. 16 

 encompasses some portion of an alpha individual's home range. 



Now w^e can ask : Where is it most logical to find the home range centers 

 of beta species? They should be located at points minimizing encounter 

 by members of the beta species with members of the alpha species. The 

 interstices formed by juncture of each set of three neighboring home ranges 

 of alpha species represent such locations. 



Here a beta individual is equidistant from three alpha individuals. Dis- 

 placement of the home range of a beta species member from such a point 



