Spatial populations

Many biological systems depend not only on how many individuals are present but also on where they are located. Spatial models therefore describe population density as a function of both space and time.

In one spatial dimension, a density may be written as

where \(x\) is position and \(t\) is time.

Why space matters

Movement, local crowding, environmental variation, habitat boundaries and local interactions can all make population behaviour depend on location.

Continuous and discrete space

Space may be represented continuously, using partial differential equations, or divided into patches, sites or network nodes.