A spatially explicit Bayesian framework for cognitive schooling behaviours.

Social aggregations such as schools, swarms, flocks and herds occur across a broad diversity of animal species, strongly impacting ecological and evolutionary dynamics of these species and their predators, prey and competitors. The mechanisms through which individual-level responses to neighbours generate group-level characteristics have been extensively investigated both experimentally and using mathematical models. Models of social groups typically adopt a 'zone' approach, in which individuals' movement responses to neighbours are functions of instantaneous relative position. Empirical studies have demonstrated that most social animals such as fish exhibit well-developed spatial memory and other advanced cognitive capabilities. However, most models of social grouping do not explicitly include spatial memory, largely because a tractable framework for modelling acquisition of and response to historical spatial information has been lacking. Using fish schooling as a focal example, this study presents a framework for including cognitive responses to spatial memory in models of social aggregation. The framework utilizes Bayesian estimation parameters that are continuously distributed in time and space as proxies for animals' spatial memory. The result is a hybrid Lagrangian-Eulerian model in which the effects of cognitive state and behavioural responses to historical spatial data on individual-, group- and population-level distributions of social animals can be explicitly investigated.