## Introduction

This session introduces the concept of a stable population and aims to provide an intuitive understanding of the properties of model stable populations. Examples of the uses of stable population models in the study of real populations are outlined briefly. The mathematical relationship between growth rate and age structure within a stable population will be explored, as will methods for calculating the rate of growth. Finally, we will explore the variations in stable population age structure that arise from different combinations of fertility and mortality schedules.

### Definition

A stationary population is a special example of a stable population with a zero growth rate, neither growing nor shrinking in size, and is equivalent to a life table population.

Stable populations are theoretical models widely used by demographers to represent and understand the structure, growth and evolution of human populations. By definition, stable populations have age-specific fertility and mortality rates that remain constant over time. It can be proved mathematically that populations with unchanging fertility and mortality patterns grow (or shrink) at a constant rate and acquire a characteristic age structure that does not change over time.