The study of an insect population which live on summer to disappear on winter after the egg-laying is
much simple and nevertheless as much revealing. The example of bombyx is perfect. Let’s begin with a
little colony.

Let's suppose that the same percentage of bombyx's eggs hatches and survives each year, the number of larva during a year is function of the number of larva which was transformed into bombyx and has laid eggs the previous year. Let's suppose a colony of 100 bombyx which double each year. The colony will have 200 elements the second year and 400 the next year.

It is very easy to establish a general formula to calculate the population of a year in function of that of the previous year.

In fact populations do not all double. Some of them can grow faster or slower. If we call N the birth-rate, each colony is this year N times more sizeable than the previous year.

This equation is quite good for populations which are reduced or spread and with a lot of food and a large vital space. In fact the growth do not continue indefinitely because each population depends on others within food chain. There are relations between these populations which make that the number of elements in a population is function of all the environment.