The Malthusian parameter

For many types of branching process in which the expected number of offspring of each individual exceeds one, the expected population at large times t is of the form

This type of exponential growth is typically observed for microbiological populations provided steps are taken to minimise competition for space and nutrients, by diluting cultures periodically.

The parameter , which determines the exponential rate of growth is called the Malthusian parameter.

Simple explicit formulae for are available both for the age-dependent branching process and for Green's model of asymmetrical cell division. To see these formulae, follow the links on the right.

As part of our project, we have developed some new approximations to the Malthusian parameter.