A review of attraction and repulsion models of aggregation: Methods, findings and a discussion of model validation

Animal aggregates (sparrow flocks, anchovy schools, caribou herds) are complex systems made up of potentially thousands of individuals moving in a coordinated mass. While such aggregates are difficult to study in the field, models of aggregation offer researchers a way to investigate how the interplay of individual behaviour makes aggregation possible and leads to different aggregate-level behaviour. This paper reviews the findings of models of aggregation, both mathematical and computer-based, with a focus on the means used to validate these models. In the context of this review it is argued that the existing de facto modelling framework, the Attraction Repulsion (AR) framework, does not allow for an adequate representation of the properties of individuals required to create validatable models of natural aggregation. However, it is further argued that the increasing use of information or perceptual fields in AR models provides a promising direction for future research.