GEOMETRICAL RATIO OF INCREASE. 57 



country could support the product. Hence, as more in- 

 dividuals are produced than can possibly survive, there 

 must in every case be a struggle for existence, either one 

 individual with another of the same species, or with the 

 individuals of distinct species, or with the physical con- 

 ditions of life. It is the doctrine of Malthus applied with 

 manifold force to the whole animal and vegetable king- 

 doms ; for in this case there can be no artificial increase of 

 food, and no prudential restraint from marriage. Although 

 some species may be now increasing, more or less rapidly, 

 in numbers, all cannot do so, for the world would not hold 

 them. 



There is no exception to the rule that every organic being 

 naturally increases at so high a rate, that, if not destroyed, 

 the earth would soon be covered by the progeny of a single 

 pair. Even slow-breeding man has doubled in twenty-five 

 years, and at this rate, in less than a thousand years, there 

 would literally not be standing-room for his progeny. Lin- 

 naeus has calculated that if an annual plant produced only 

 two seeds — and there is no plant so unproductive as this — 

 and their seedlings next year produced two, and so on, then 

 in twenty years there would be a million plants. The 

 elephant is reckoned the slowest breeder of all known ani- 

 mals, and I have taken some pains to estimate its probable 

 minimum rate of natural increase ; it will be safest to 

 assume that it begins breeding when thirty years old, and 

 goes on breeding till ninety years old, bringing forth six 

 young in the interval, and surviving till one hundred years 

 old ; if this be so, after a period of from 740 to 750 years 

 there would be nearly nineteen million elephants alive de- 

 scended from the first pair. 



But we have better evidence on this subject than mere 

 theoretical calculations, namely, the numerous recorded cases 

 of the astonishingly rapid increase of various animals in 

 a state of nature, when circumstances have been favorable 

 to them during two or three following seasons. Still moie 

 striking is the evidence from our domestic animals of many 

 kinds which have run wild in several parts of the world ; 

 if the statements of the rate of increase of slow-breeding 

 cattle and horses in South America, and latterly in Aus- 

 tralia, had not been well authenticated, they would have 

 been incredible. So it is with plants ; cases could be given 

 of introduced plants which have become common through- 

 out whole islands in a period of less than ten years, §ey 



