?HE SPRING GRAIN-APHIS OR " GREEN BUG.'' 73 
FECUNDITY OF VIVIPAROUS FEMALE. 
The average person, unfamiliar with the habits of the Aphididse, 
would scarcely think it possible for such small creatures to become 
sufficiently numerous to devastate vast areas of grainfields, destroy- 
ing millions of dollars' worth of property within the space of a few 
weeks. When one becomes familiar with their powers of reproduc- 
tion, however, the problem seems very simple. 
Prof. Huxley * states that the tenth generation alone of a single 
rose aphis, were all of its members to survive the perils to which they 
are exposed, would contain more substance than 500,000,000 stout 
men. Buckton, 2 commenting on Prof. Huxley's figures, states that 
he much underestimates the real quantity of animal matter capable 
of elaboration from a single aphis in a year, and goes on to say: 
Basing the calculation, for simplicity, upon the supposition that every aphis lives 
twenty days, and that at the expiration of that period each aphis shall have pro- 
duced twenty young and no more, then at the expiration of three hundred days only, 
the living individuals would be represented by the following figures: 
Aphides. Days. Aphides. 
1 produces in 20 20 = a 
a produces in 40=20 2 400 = b 
b produces in 100=20 5 3, 200, 000 = c 
c produces in 200=20 10 10, 240, 000, 000, 000 = d 
d produces in 300=20 15 =32, 768, 000, 000, 000, 000, 000 = e 
Again, if 1,000 aphides weigh 1 grain, and 
1 man weighs 2,000,000 grains 
1 man weighs 2,000,000,000 aphides, 
■p 
•'• 2 000 000 000 =1 >638,400,000 men; equal, perhaps, to the population of China seven- 
fold! 
To quote further: 
But a mathematical friend remarks that this calculation even does not express the 
real rate of increase, since it supposes the progeny of the first aphis to be produced at 
once, and not to commence producing until the expiration of the first twenty days. 
To this same friend I am indebted for the annexed calculation. 
If we suppose the progeny of the first aphis to equal 20 in twenty days, and this 
progeny to begin producing when five days old 20 young, each of which again on 
attaining the age of five days begins the propagation of 20 young, and completes also 
that number in 20 days: 
Then at Jhe end of 20 days from the commencement of first aphis production 
* there would be direct issue = 20a 
At the end of fifth day, progeny a begin to produce, which at the end of first 20 
days will altogether equal 154-14+134-12, &C.+2+1 =1206 
At the end of tenth day, progeny b begin to produce, which at the end of the 
first 20 days will altogether equal 10+9+8, &c. +2+1 = 55c- 
At the end of the fifteenth day, progeny c begin to produce, which at the end of 
the first 20 days will altogether equal 5+4+3+2+1 = 15c? 
Total at the end of 20 days equals a+b+c+d =210 
The amount, therefore, at the end of 300 days (or 20X15) would not be les3 than the 
fifteenth power of 210, which is almost impossible to express in figures. There would 
be room in the world for nothing else but aphides. 
i Trans. Linn. Soc, vol. 22, p. 215 (part 3, 1858). » Monograph of British Aphides, vol. 1, p. 80. 
