Heterogeneous populations in a network model of collective motion

Biological systems are typically heterogeneous as individuals vary in their response to the external environment and each other. Here, the effect of heterogeneity on the properties of collective motion is studied analytically in the context of a simple network models of collective motion. We consider a population that is composed of two or more sub-groups, each with different sensitivities to external noise. We find that within a mean-field model, in which particles are sampled uniformly, the dynamics in the heterogeneous case is equivalent to an effective homogeneous model with a noise term that is obtained analytically. This is different than recent simulation results with the well-known Vicsek model of collective motion, in which sub-populations with different noise interact non-additively. In particular, if one of the sub-populations is sufficiently ”cold”, it dominates the dynamics of the group as a whole. By introducing an ad-hoc bias in the sampling of neighbors, it is shown that the differences between the mean-field and Vicsek dynamics can be explained by the tendency of colder particles to cluster and partially separate from hotter ones. It is analytically shown that, provided the clustering property is sufficiently strong, the mixed system can become ordered regardless of the noisier populations.