Curve TRAILS 
A a TOTAL number of FEET OF TRAILS 
B □ NUM8ER OF FEET OF TRAILS PER IOOO GRAMS 
OF RATS 
C. o NUMBER OF FEET OF TRAILS PER RAT 
Figure 60. — The growth of trailway systems. All curves are 
empirically drawn to approximate the observed points. 
A. Increase in total feet of trails. The apparent contin- 
uous increase in the total feet of trails results from the fact 
that peripheral expansion was still possible. From figure 61 
it is probable that the trails would have become stabilized 
at about 2,100 feet. B. This curve probably would have 
stabilized at approximately 34.3 feet (see remarks under 
C.) per 1 ,000 grams of rats on each following March 1 , on 
and following March 1, 1950. March 1 marks the ap- 
proximate initiation of the breeding season. C. Number 
of feet of trails per rat. Note that this curve becomes es- 
sentially stable at 1 5 feet per rat. On March 1 , 1 949, there 
were 1 27 rats with an average weight of 437 grams or 2.288 
rats per 1,000 grams. If the same sex-weight-age rela- 
tionship continued to exist at the initiation of future breed- 
ing seasons, we can calculate the expected level at which 
the number of feet per 1,000 grams of rats becomes con- 
stant. Fifteen feet per rat X 2.288 rats per 1,000 grams 
= 34.3 feet per 1,000 grams of rats. 
rat. This naturally raised the question: “What 
contributed to this decline in rate?” For one 
thing it is quite apparent that as neighboring 
goals become connected with trails there is less 
need for the construction of new trails. New rats 
born into the population could then utilize and 
maintain preexisting trails. But this leads to 
greater contacts along trails. The rats’ solution 
of this situation was the construction of alternate 
routes. 
If one examines those sections of the pen in which 
systems of alternate routes of travel had already 
been developed by November 1947 (fig. 59B), it 
may be noted that during the succeeding year 
(fig. 14) essentially no increase in amount of trails 
had occurred in these regions, although there had 
been slight alterations of position. Reflection upon 
this point suggested that failure to develop more 
trails in a given region is related to intolerances 
of rats to close proximity with other rats. The 
network of trails formed irregular-shaped polygonal 
cells whose centers were devoid of trails. Now let 
us assume that the distance across these cells is 
limited by a certain distance that one rat will 
tolerate the approach of another. Transects taken 
in a random direction across these cells will approx- 
imate the distribution of distances between rats on 
opposite sides of cells. Since the long axes of cells 
appear to have no regular compass orientation 
transects taken in fixed directions should closely 
approximate random directions. Therefore tran- 
sects were taken for the survey of November 1 948 
(fig. 14) at 5-foot intervals in both NE to SW, and 
SE to NW directions. For the 554 measurements 
thus taken the mean was 5.90 ft. (cr = 4.05 ft.). 
In a crude way this may represent an “approach 
tolerance distance.” It is this inferred approach 
tolerance distance that constitutes the environ- 
mental resistance to the continued growth of trails. 
An attempt was also made to approximate the 
average diameter of cells for this November 1948 
survey. Two measurements were made of each 
cell: (a) the greatest distance across it, and (b) the 
greatest distance across the cell at right angles to 
this first measurement. The mean of these 245 
measurements was 7.95 ft. (a-=5.61 ft.). There 
still existed a few areas of the pen where the 
typical pattern of cell development of trails had 
not yet been completed. Even were these to 
develop trails in a similar fashion, and even if 
some of the larger cells were to be divided by in- 
tervening trails it is unlikely that the approach 
tolerance distance characteristic of rats would have 
permitted more than 3,000 feet of trails to develop 
in the pen even if the colony had been maintained 
after 1949. Curve C in figure 60 suggests that as 
the population began to grow rapidly (see also 
fig. 146) at least 15 feet of trails are required per 
rat. Thus this method of viewing the data suggests 
that the colony would never have exceeded 200 
rats. 
There was actually a decline in the number 
of feet of trails between November 1948 and the 
beginning of the breeding season in March 1949. 
61 
