## 1. Introduction

The growth of organisms in a favourable environment is typically modeled by a simple exponential function, in which the population size increases at an ever-increasing rate. This is because the models, at their most simple, assume a fixed net 'birth' rate per individual. This means that as the number of individuals increases, so does the number of individuals added to the population (see the resource on exponential models). This description of population change pre-supposes that resources for growth are always adequate, even in the face of an ever-increasing population.

In the real world, resources become limiting for growth, so that the rate of population growth declines as population size increases. There are several numerical models that simulate this behaviour, and here we will explore a model termed 'logistic' growth.