A computational study of density-dependent individual movement and the formation of population clusters in two-dimensional spatial domains

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Colleges, School and Institutes


The patterns of collective behaviour in a population emerging from individual animal movement have long been of interest to ecologists, as has the emergence of heterogeneous patterns among a population. In this paper we will consider these phenomena by using an individual-based modelling approach to simulate a population whose individuals undergo density-dependent movement in 2D spatial domains. We first show that the introduction of density-dependent
movement in the form of two parameters, a perception radius and a probability
of directed movement, leads to the formation of clusters. We then show that the properties of the clusters and their stability over time are different between populations of Brownian and non-Brownian walkers and are also dependent on the choice of parameters. Finally, we consider the effect of the probability of directed movement on the temporal stability of clusters and show that while clusters formed by Brownian and non-Brownian walkers may have similar
properties with certain parameter sets, the spatio-temporal dynamics remain different.


Original languageEnglish
Article number110421
JournalJournal of Theoretical Biology
Early online date28 Jul 2020
Publication statusPublished - 21 Nov 2020


  • Animal movement, Brownian motion, Density-dependence, Individual-based modelling, Pattern formation