Population and environment – what's the connection?
Box 2 | Exponential growth
Suppose you wanted to keep some bacteria alive in a test tube. You would supply them with everything they need and watch them, with a microscope, to make sure they didn’t get too crowded. With plenty of food and the right temperature, bacteria can divide into two about every 20 minutes. If you had started with just one bacterium, you might decide that there’s little chance of overcrowding with such tiny creatures in a large test tube. (A bacterium is about 1 micrometre in length; that’s one-thousandth of a millimetre.)
After 40 minutes you would see only four bacteria. Twenty minutes later, there would be just eight. Not much chance of any rapid overcrowding – so you decide to go out and come back the next day. Twenty-four hours later, how many bacteria might you find?
About 1,000,000,000,000,000,000,000,000 (1024), or one million billion billion! Their initial rate of growth (doubling every 20 minutes), although it seems slow at first, is actually frighteningly fast, as you can see on the graph. This growth rate produces a curve with a characteristic shape, sometimes known as a J-curve.
Once the population reaches about 1000 bacteria, which takes ten doublings, or 3 hours and 20 minutes, we start to deal with large numbers and doubling has dramatic results. For example, in just the final 20 minutes of a 24-hour period, the same number of bacteria were created as were made in the previous 23 hours and 40 minutes.
Geometric and arithmetic increase
This sort of growth rate – where the number added depends on how much is already there – is called exponential growth or geometric increase. The same principle applies in the calculation of compound interest, when a sum is deposited in a bank and the interest is reinvested. It is different from arithmetic (or additive) increase, where the same absolute amount is added in each time interval. In exponential growth the same percentage is added each time but, because the percentage is calculated from a growing base, it represents a greater absolute number per unit of time.
Limits to bacterial growth
Of course, in reality, after 24 hours you would only find a test tube of bacteria, their food run out and many of them dead. Fortunately for us, and for everything else in the world, bacteria can’t keep up their maximum growth rate for long. It can only happen under the best of circumstances (what scientists call the optimal environment). Think of the factors that act to limit the growth of bacteria. Obviously, food starts running out, waste accumulates, and so the reproductive rate of the bacteria falls. For example, suppose poor conditions mean that a quarter of the bacteria die during the course of each 20 minutes (the doubling time). Is the population still growing exponentially? The answer is yes – even though it is not at the fastest rate of growth that the bacteria are capable of. The population will take longer to double, but the shape of the J-curve remains much the same.
Human population growth
The story of the human population is similar in some respects to the bacteria in the test tube. We are, for the foreseeable future, confined to a large test tube – the Earth – where we find the conditions necessary for our survival. The human population is currently doubling every 53 years. That is much more slowly than the bacteria, but unless something changes, it is still only a matter of time before we could find ourselves in the same situation – resources running out, waste products accumulating, and a high death rate.
Boxes
Box 1. Trends in world population
Box 3. Immigration and population growth
Related sites
Eliminating the zeroes (Box 1 of Nova topic, Harnessing direct solar energy)
Modelling exponential growth – using logarithms (Department of Mathematics and Statistics, University of Saskatchewan, Canada)
Posted April 2005.