The mathematical analysis of biological aggregation and dispersal: Progress, problems and perspectives

Motile organisms alter their movement in response to signals in their environment for a variety of reasons, such as to find food or mates or to escape danger. In populations of individuals this often this leads to large-scale pattern formation in the form of coherent movement or localized aggregates of individuals, and an important question is how the individual-level decisions are translated into population-level behavior. Mathematical models are frequently developed for a population-level description, and while these are often phenomenological, it is important to understand how individual-level properties can be correctly embedded in the population-level models. We discuss several classes of models that are used to describe individual movement and indicate how they can be translated into population-level models.