THE SMALL-MAMMAL PROBLEM 739 
In 1911, between 16th January and 14th February, these 
observers examined 6071 individuals, collected in Suffolk and 
Essex during the period specified. Of these rats 3273 were 
males, 2724 females, and of 74 the sex was not recorded; 290, 
or 10.6 per cent. of the females were pregnant, the average 
number of embryos in each being 9. Had the count been 
made in warmer months of the year a higher percentage of 
pregnant females would doubtless have been observed. It is 
clear from these statistics that many more rats are born than 
can possibly survive; limitations of space and food ensure 
that a large proportion of all the young born must perish 
before attaining sexual maturity. If from any cause the 
mortality among the adult rats is increased, competition for 
food and space is diminished and the chances possessed by 
the young of reaching sexual maturity are increased propor- 
tionately. From the data cited it is possible to form an 
idea of the maximum monthly loss which the rat population 
can sustain without fear of extinction. We are thus able 
to gain a rough notion of the magnitude of the task of rat 
extermination, and to realize the necessity of following up each 
campaign by another. For, assuming Petrie and Macalister’s 
results to apply throughout Britain at all seasons, it may be 
shown that, provided there is sufficient food and space, the 
rat population can double itself in about seven years, even 
although we assess the monthly mortality among the sexually 
mature individuals at 10 per cent., and assume that 75 per 
cent. of all the young born perish without reaching sexual 
maturity. High mortality among the young can only be 
1 The calculation upon which this statement is based is as follows :—Of 5997 
rats 3273 or 54:5 per cent. are males, 2724 or 45-5 per cent. females. Of the females, 
290 or 4:85 per cent. of the total stock give birth to litters of 9. Assuming a 
mortality of 10 per cent, among adults and 75 per cent. among the immature in 
each month, #& in the following equation represents the number of rats living in 
any given month for each 1oo rats living in the next preceding month. 
gs 2 Be 
R= 54:5+45:5-10 + wey = 90+10-91 = 100-91. 
Applying the formula given for compound interest, where 
oe log. a—log. ; ; 
> Shae we find that the rat population doubles in 79-5 months. 
The equation shows that, with the rates of mortality assumed, the rat population 
would increase if 4-45 per cent. of the population gave birth to young in each 
month ; while if less than 4-4 per cent. gave birth to young it would decline. 
