This isn’t a true story. I wrote it to show that we should view predictions based on scientific observations with extreme caution.

A biologist decided to study the rabbit population on a small farm. So he decided on a reasonably reliable way to assess the number of wild rabbits living on the farm at the beginning of his study (year 0) and at the end of each year, for a total of 5 years. His results are shown in the table below.

When he plotted a graph of the number of rabbits against time (in years), he found that his data points were very close to being on a straight line. So he extrapolated his result, meaning that he extended this line, to estimate what the rabbit population would be in 20 years’ time. The result is shown below.

From this graph, he predicted that there would be over 1 000 rabbits on the farm in 20 years’ time and that they would be a serious pest. So he recommended killing most of the rabbits to prevent the problem.

The owner of the farm decided that she wouldn’t kill any rabbits until there really were too many of them. To find out what was happening, she continued the biologist’s work, using exactly the same methods. Her results are shown below.

The biologist’s prediction was completely wrong! After 20 years, the number of rabbits was the same as at the beginning – much less than the predicted number of about 1 000. The number never exceeded 400 which was not enough for the rabbits to be a serious pest.

She also drew a graph of her results. Here it is:

You can see that the number of rabbits doesn’t continue to increase. Instead, it increases for about 8 years and then decreases again. After 17 years, there are hardly any rabbits left. But the number then starts to increase again.

What’s happening?

The farmer noticed that, after about 5 years, foxes started to appear on her farm. Foxes like to eat rabbits. So she supposed that the increasing rabbit population was attracting foxes who then started to eat them. As a result, the number of rabbits declined. Some years later, she noticed that the foxes were beginning to move away. Presumably because there were not enough rabbits for them to eat. Eventually, she stopped seeing any foxes and the rabbit population started to increase again.

Notice that the results oscillate up and down. Oscillatory results, like this, are much more common in real life than you might expect from reading most science textbooks. The reason is that textbooks usually deal with simple systems in which whatever is being measured depends on a small number of variables in a very simple way. Real life isn’t always like that!

It is always dangerous to extrapolate results, in the way that the biologist did, without having a clear idea of all the mechanisms that could have an important influence on the results and what their effects might be.

Unfortunately, some scientists do extrapolate results without thinking carefully about all the mechanisms involved!

Related posts

16.5 Exponential growth: bacteria

16.6 Exponential decay: radioactivity

Follow-up posts

16.42 Keep it simple
16.43 Test before you predict
17.1 It’s obvious
19.2 Real gases
22.17 Coupled differential equations