Darwin and the Elephants

The basic idea underlying Charles Darwin theory of evolution is that the number of individuals in a given species would grow exponentially, in the absence of pressures against population growth. Only selective pressures may curb this exponential growth, and select some species over the others.

In Charles Darwin’s own words, in the Origin of the Species:

“There is no exception to the rule that every organic being 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 a few thousand years, there would literally not be standing room for his progeny. Linnaeus 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 to be 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 under the mark to assume that it breeds when thirty years old, and goes on breeding till ninety years old, bringing forth three pairs of young in this interval; if this be so, at the end of the fifth century there would be alive fifteen million elephants, descended from the first pair.”

elephants

Even though Charles Darwin got his numbers wrong, as pointed out by William Thomson, later to become Lord Kelvin, the idea is entirely correct. The number of elephants at generation n is given by the formula a(n) = 2 × a(n-1) – a(n-3). 

This succession of numbers converges rapidly to a ratio of 1.618 between the number of elephants at generation n and the number at generation n-1.

If one plugs the numbers in, one realizes that even though only 14 elephants are alive after one hundred years and 8360 after five hundred years (not 15 million, as Darwin stated), there would be almost 30 million elephants alive after a thousand years. After three thousand years, there would be a billion trillion elephants, which would have a combined mass equal to that of planet Earth. Assuming they can grow indefinitely, after only seven thousand years, the solid sphere of roughly 10 to the 50th elephants, by that time with a diameter of 200 light-years, would expand outward faster than the speed of light.

 

 

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2 thoughts on “Darwin and the Elephants”

  1. May I ask for the reference that Lord Kelvin pointed out Darwin’s numbers were wrong? I have seen this claimed but have never seen a historical reference for it.

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    1. I am sorry to let you know that I have also obtained this information from secondary sources (a number of them) but did not check the primary source. I will let you know if I manage to find it out. There was extensive correspondence between William Thomson and Charles Darwin, but I did not find, in the sources I have, the explicit reference to this particular issue.

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