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We propose a (time) multiscale method for the coarse-grained analysis ofself--propelled particle models of swarms comprising a mixture of `na\"{i}ve'and `informed' individuals, used to address questions related to collectivemotion and collective decision--making in animal groups. The method is based onprojecting the particle configuration onto a single `meta-particle' thatconsists of the group elongation and the mean group velocity and position. Thecollective states of the configuration can be associated with the transient andasymptotic transport properties of the random walk followed by themeta-particle. These properties can be accurately predicted by anadvection-diffusion equation with memory (ADEM) whose parameters are obtainedfrom a mean group velocity time series obtained from a single simulation run ofthe individual-based model.

Multiscale analysis of collective motion and decision-making in swarms: An advection-diffusion equation with memory approach