Coarse Collective Dynamics of Animal Groups

Abstract

The coarse-grained, computer-assisted analysis of models of collective dynamics in animal groups involves (a) identifying appropriate observables that best describe the state of these complex systems and (b) characterizing the dynamics of such observables. We devise “equation-free” simulation protocols for the analysis of a prototypical individual-based model of collective group dynamics. Our approach allows the extraction of information at the macroscopic level via parsimonious usage of the detailed, “microscopic” computational model. Identification of meaningful coarse observables (“reduction coordinates”) is critical to the success of such an approach, and we use a recently-developed dimensionality-reduction approach (diffusion maps) to detect good observables based on data generated by local model simulation bursts. This approach can be more generally applicable to the study of coherent behavior in a broad class of collective systems (e.g., collective cell migration).