A population can be described by how many individuals it contains and how those individuals are distributed in space.

The population size $N$ is the number of individuals. Population density is the number of individuals per unit area or volume. Two populations can have the same $N$ but very different densities if they occupy different amounts of space.

Population size changes through four demographic processes:

• births add individuals;
• deaths remove individuals;
• immigration adds individuals arriving from elsewhere;
• emigration removes individuals leaving the population.

Over a time interval,

$$\Delta N = B + I - D - E,$$

where $B$, $I$, $D$ and $E$ are the numbers of births, immigrants, deaths and emigrants.

Example

A bird population begins with 500 individuals. During one year there are 120 births, 80 deaths, 30 immigrants and 50 emigrants. Then

$$\Delta N=120+30-80-50=20,$$

so the new population size is

$$N_{\text{new}}=500+20=520.$$

This bookkeeping separates how population size changed from why each demographic rate had its value. Food availability, disease, predation, climate and age structure can all affect births, deaths or movement, but the demographic balance equation remains the accounting identity connecting those causes to abundance.