A mathematical approach to territorial pattern formation

Territorial behaviour is widespread in the animal kingdom, with creatures seeking to gain parts of space for their exclusive use. It arises through a complicated interplay of many different behavioural features. Extracting and quantifying the processes that give rise to territorial patterns requires both mathematical models of movement and interaction mechanisms, together with statistical techniques for rigorously extracting parameters from data. Here, we give a brisk, pedagogical overview of the techniques so far developed to tackle the problem of territory formation. We give some examples of what has already been achieved using these techniques, together with pointers as to where we believe the future lies in this area of study. This progress is a single example of a major aim for 21st century science: to construct quantitatively predictive theory for ecological systems.