84 John B. Calhoun 



apply to the present data with regard to captures following presumed 

 removal of all residents during the first 20 days?" If it does, we shall also 

 wish to know whether the apparent waves might reflect some basic property 

 of intraspecific social organization. 



The first problem concerns determination of the area inhabited by 

 those animals taken during the first 20 days. It must include all the rr^ 

 area delimited by the trapline. Furthermore, animals from some distance 

 outward from the trapline must also have been caught. On first thought, 

 it might be logical to anticipate that all mice whose home range centers 

 lay within 3.0 home range sigma of the circular trapline, and away from it, 

 would be the only ones to exposed. However, as we shall see, the distance 

 outward from the trapline to which animals are affected by it more likely 

 approximates the maximum distance at which they can perceive signals 

 from other mice. 



But, this is getting ahead of the analysis. For the present let us assume 

 that each wave of mice entering the traps represents the inhabitants of a 

 band of width w. Furthermore, assume that during the first 20 days mice 

 from a band of width, w, immediately outward from the trapline, get 

 caught by it in addition to those internal to the circular trapline. 



The radius from the center of the area being trapped to the trapline was 

 562 feet. Thus, the area sampled during the first 20 days equals 

 7r(562 + w)^. Since each wave of invaders is presumed to represent a band 

 of equal width, w, then the entire area sampled during the entire 80 days 

 equals 7r(o62 + ow)-. One hundred and seven mice were taken from the 

 central area, and 608 from the total area. Thus, to the extent that number 

 of mice is proportional to the area they inhabit, 5.626 as many mice in- 

 habited the total area as the central area. It follows that: 



5.626[x(562 + w)^] = 7r(562 + nwy 



Thus w = 302 feet. 



Radii to the limits of the central area and the four successive bands 

 become 864, 1166, 1468, 1770, and 2072 feet (Table IX). From these the 

 areas within the central area and the four bands may be calculated. These 

 are areas as proportions of the total within a circle having a radius of 2072 

 feet as given in Table IX. These proportions can then be utilized to calcu- 

 late the expected number of mice residing within the central area or in- 

 vading it during later successive periods. 



The assumptions force identity between observed and expected for the 

 central area, but not for the four bands. However, the observed catch for 

 the four bands will approximate that of expected only to the extent that 

 the formulation is in harmony with reality. As may be seen from Table IX, 

 observed and expected numbers approximate each other so closely as to 



