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 The Elephant Problem 
All organisms produce more offspring than can survive in the world. Charles Darwin used elephants to illustrate this point:
Source: Corel

There is no exception to the rule that every organic being naturally increase at so high a rate that if not destroyed, the earth would soon be covered by the progeny of a single pair .... 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
- (Darwin, 1859 p.64)

Shortly after this, the eminent physicist William Thompson (later Lord Kelvin) pointed out that Darwin got the math wrong. After about 500 years, there should only be about 16 thousand elephants, not 15 million. Indeed, the engineer Fleeming Jenkin referred to another of Darwin's calculations as guessing at the half and multiplying by two (fide Burchfield, 1990 p.74). The basic problem, however, remains, a few elephants can produce lots of elephants. But how many?

    Let's make some simple assumptions:
  1. Elephants live about 90 years
  2. Elephants become sexually mature and can reproduce at about age 30
  3. Thus, an elephant has a reproductive lifetime of about 60 years
  4. A pair of elephants produce about 6 offspring in their lifetimes
  5. An elephant has a volume of about 5 cubic meters

    Now let us suppose that all elephants grew up to a ripe old age of about 90 years. Given a pair (one male and one female) of elephants, how many elephants would there be after 120 years? 1000 years? 5000 years? Enter a number of years in the form below, and it will calculate how many elephants there are...

    If we let these elephants breed for years (enter a number and press tab),
    which is equivalent to generations.
    We get elephants (alive at that time).
    These elephants have a total volume of cubic meters,
    or times the volume of the earth.
    If these elephants were formed into a spherical herd,
    it would have a radius of meters,
    or a diameter of light years.
    The surface of this sphere of solid elephants would
    expand outward at a rate of meters per second in all directions,
    or at warp where warp 1 = speed of light.

    Note: (2000 Nov 20) an observant reader noticed an error in the calculation of Earth Volumes in this calculator (the volume of the earth had been entered in cubic km rather than cubic m making the earth volumes 10^9 too small). This has been fixed. Numbers may display in scientific notation. For example: 1.48e12 means 1,480,000,000,000 or 1.48 trillion. Numbers have been rounded to three significant digits, but browsers vary in how they display these numbers.

    You may repeat this calculation with any organism you desire. The results, while they may take a bit longer, are the same. Without some sort of limits to population growth, any organism will rapidly produce far more offspring than there are available resources. All organisms overproduce.

    Sources: Burchfield, 1990 Darwin, 1859
    Part of the Athro, Limited web site.
    Copyright © 1997-2000 Athro, Limited. All Rights Reserved.
    Written by Paul J. Morris
    Maintained by Athro Limited Date Created: 2 Dec 1997
    Last Updated: 21 Nov 2000