Chap. III. J GEOMETRICAL RATIO OF INCUEASE. 51 



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. Linnseus 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 animals, 

 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, descended from the first pair. 



But we have better evidence on this subject than mere theoretical 

 calculations, namely, the numerous recorded cases of the astonish- 

 ingly rapid increase of various animals in a state of nature, when 

 circumstances have been favourable to them during two or three 

 following seasons. Still more 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 Australia, 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 throughout whole 

 islands in a period of less than ten years. Several of the plants, 

 such as the cardoon and a tall thistle, which are now the com- 

 monest over the wide plains of La Plata, clothing square leagues 

 of surface almost to the exclusion of every other plant, have been 

 introduced from Europe ; and there are plants which now range in 

 India, as I hear from Dr. Falconer, from Cape Comorin to the 

 Himalaya, which have been imported from America since its dis- 

 covery. In such cases, and endless others could be given, no one 

 supposes, that the fertility of the animals or plants has been suddenly 

 and temporarily increased in any sensible degree. The obvious 

 explanation is that the conditions of life have been highly favourable, 

 and that there has consequently been less destruction of the old and 

 voung, and that nearly all the young have been enabled to breed. 

 Their geometrical ratio of increase, the result of which never fails to 

 be surprising, simply explains their extraordinarily rapid increase 

 and wide diffusion in their new homes. 



e 2 



