The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations

¹ Division of Mathematics, University of Dundee, Dundee, DD1 4NR, UK
² Institut National des Sciences Appliquées de Rouen, 76800, Saint-Étienne-du-Rouvray, France

^⋆ Corresponding author. E-mail: reftimie@maths.dundee.ac.uk

Abstract

Communication forms the basis of any animal aggregation. However, not all organisms communicate the same way. Moreover, different psychological and physiological characteristics of individuals can lead to avoidance behaviours between different individuals. This can have implications on the formation and structure of large biological aggregations. In this article, we use a mathematical model to investigate the effects of avoidance behaviour by a subpopulation, on the spatial dynamics of the whole population. We show that avoidance (exhibited even by a small fraction of the population) can alter the spatio-temporal patterns of the whole groups, leading to new patterns difficult to predict from the case without avoidance. Generally, these patterns show the segregation of the populations into different aggregations (spatially separated) or inside the same aggregation. Moreover, we investigate numerically the situation where individuals can learn to tolerate their neighbours. In this case, we observe an unexpected spatial segregation inside moving aggregations of individuals that tolerate their neighbours and those that avoid their neighbours.