A complex systems approach to the emergence of animal territoriality

A PhD study in Compexity Science by Jonathan R. Potts, funded by the EPSRC and supervised by Dr. Luca Giuggioli and Prof. Stephen Harris.

space-use model
Territorial dynamics emerging from an agent-based model


In many animal populations, space-use patterns emerge as a consequence of the animals' movements and interactions. For example, insects form swarms, fish form schools and birds form flocks. Typically, these patterns do not arise from centralised control but due to natural self-organisation of the system of interacting animals.

Territorial formation also arises from collective animal behaviour. However, unlike flocking or swarming, the key interaction is one of conspecific avoidance rather than attraction. We have constructed a movement and interaction model based on random walk patterns with a scent mediated avoidance interaction and shown how this gives rise to natural subdivisions of the terrain into territories1. Due to the transient nature of the scent marks, the resulting patterns do not settle to a steady state. Rather the territory boundaries ebb and flow causing overlapping home ranges to arise as the utilisation distribution is measured over time.


In order to understand the emergence of "macroscopic" space-use patterns from "microscopic" individual actions, we have built a model with each individual as a seperate agent. This allows us to input individual animal-movement data into the model. In this project, we use an extensive data-set on the movement of red foxes (Vulpes vulpes) gathered from more than 30 years of studies by the Mammal group at Bristol. This gives us a fantastic opportunity to verify both the movement and interaction mechnisms in our model, as well as the emergent space-use patterns.

On the theory side, the "microscopic" description of the animal behaviour allows us to use the well-developed tools of statistical physics in order to aim towards a mathematical derivation of the emergent properties of the model.


Having built a model of territorial emergence, the aim of my thesis is twofold: Firstly, to formulate and begin a programme of mathematical analysis of our model in order to create a predictive theory of territory formation and dynamics2,3. Secondly, to examine the effect of different movement processes, such as correlated random walks4, Levy walks and central place foraging5, on the territorial geometry and animal space use distributions.


1. Giuggioli L, Potts JR, Harris S (2011) Animal interactions and the emergence of territoriality PLoS Comput Biol 7(3) (featured research) doi:10.1371/journal.pcbi.1002008

2. Giuggioli L, Potts JR, Harris S (2011) Brownian walkers in subdiffusing territorial boundaries Phys. Rev. E 83, 061138

3. Potts JR, Harris S, Giuggioli L (2011) An anti-symmetric exclusion process for two particles on an infinite 1D lattice J. Phys. A: Math. Theor. 44, 485003

4. Giuggioli L, Potts JR, Harris S (2012) Predicting oscillatory dynamics in the movement of territorial animals J. Roy. Soc. Interface 9(72):1529-43. doi:10.1098/rsif.2011.0797

5. Potts JR, Harris S, Giuggioli L (2012) Territorial dynamics and home range formation for central place foragers PLoS One 7(3) doi:10.1371/journal.pone.0034033

Prize and public engagement

Bristol Art of Science 2010 winner, featured in the Daily Telegraph and the Changing perpectives exhibition.

MRes project: Animal social interactions and the emergence of home range

For more information on foxes visit our website:

Logo and link to The Fox Website

Contact details

Jonathan R. Potts
Mammal Research Unit
School of Biological Sciences
University of Bristol
Woodland Road
Bristol BS8 1UG, U.K.

Telephone: 0117 9288918
Email: Jonathan R. Potts