some years there are lots of frogs in the pond, and some years there are very few. And if
you drew a graph of how many frogs there were in the pond, it would look like this
(but this graph
is what’s called hypothetical, which means that the numbers aren’t the real numbers, it is just an
illustration):
And if you looked at the graph you might think that there was a really cold winter in 1987 and
1988 and 1989 and 1997, or that there was a heron which came and ate lots of the frogs (sometimes
there is a heron who comes and tries to eat the frogs, but there is chicken wire over the pond to stop
it).
But sometimes it has nothing to do with cold winters or cats or herons. Sometimes it is just
maths.
Here is a formula for a population of animals:
N new = λ(N old)(1 – N old)
And in this formula N stands for the population density. When N = 1 the population is the
biggest it can get. And when N = 0 the population is extinct. N new is the population in one year,
and N old is the population in the year before. And λ is what is called a constant.
When λ, is less than 1, the population gets smaller and smaller and goes extinct. And when λ,
is between 1 and 3, the population gets bigger and then it stays stable like this (and these graphs are
hypothetical, too):
And when λ is between 3 and 3.57 the population goes in cycles like this:
But when λ, is greater than 3.57 the population becomes chaotic like in the first graph.
This was discovered by Robert May and George Oster and Jim Yorke. And it means that
sometimes things are so complicated that it is impossible to predict what they are going to do next,
but they are only obeying really simple rules.
And it means that sometimes a whole population of frogs, or worms, or people, can die for no
reason whatsoever, just because that is the way the numbers work.