South African Journal of Science
On-line version ISSN 1996-7489
Animal groups in motion, examples being fish schools, bird flocks, insect swarms and mammal herds, can exhibit spectacular collective behaviour. Attempts at formalizing the basic individual behaviour that accounts for the complex dynamics of an animal group began over 50 years ago. Numerous models of these dynamics have since been published. We review this information, starting with an overview of various approaches that have arisen from mathematical, physical, and computer-modelling methods. Our focus is on individual-based models of animal groups. Individuals are assumed to exert three types of local interactions with their neighbours in these models, namely attraction, alignment, and repulsion. We review these models according to their main objectives: to compare modelled results with observational data; to analyse the influence of model parameters on simulated group properties; and to investigate group response to any change in environment, or to divergent behaviour of some of the group members.