Stochastic modelling of seasonal migration using rewriting systems with spatiality

Seasonal migration is the long-distance movement of a large number of animals belonging to one or more species that occurs on a seasonal basis. It is an important phenomenon that often has a major impact on one or more ecosystem(s). It is not fully understood how this population dynamics phenomenon emerges from the behaviours and interactions of a large number of animals. We propose an approach to the modelling of seasonal migration in which dynamics is stochastically modelled using rewriting systems, and spatiality is approximated by a grid of cells. We apply our approach to the migration of a wildebeest species in the Serengeti National Park, Tanzania. Our model relies on the observations that wildebeest migration is driven by the search for grazing areas and water resources, and animals tend to follow movements of other animals. Moreover, we assume the existence of dynamic guiding paths. These paths could either be representations of the individual or communal memory of wildebeests, or physical tracks marking the land. Movement is modelled by rewritings between adjacent cells, driven by the conditions in the origin and destination cells. As conditions we consider number of animals, grass availability, and dynamic paths. Paths are initialised with the patterns of movements observed in reality, but dynamically change depending on variation of movement caused by other conditions. This methodology has been implemented in a simulator that visualises grass availability as well as population movement.