THE SMALL-MAMMAL PROBLEM 739 



In 191 1, between i6th 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, R in the following equation represents the number of rats living in 

 any given month for each 100 rats living in the next preceding month. 



/? = 54.5 +45.5 - 10 + ±§i2i? = 90+ 10-91 = 100-91. 

 4 

 Applying the formula given for compound interest, where 



t = °^i^~ p^ • 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. 



