Order–Disorder Phase Transition in Heterogeneous Populations of Self-propelled Particles

Biological systems are typically heterogeneous as individuals vary in their characteristics, their response to the external environment and to each other. For example, cell diversity plays a crucial role in the successful survival of many biological systems. Phenotypic heterogeneity is associated with cellular response to intercellular communications, the response to external environmental cues, motility modes, and proliferation rates. Here we study the effect of phenotypic diversity on the properties of collective motion in the context of the scalar noise model of collective migration. For simplicity, we study a population that is composed of two sub-populations, each with different sensitivities to external noise. We find that the two sub-populations interact non-additively: Within a large range of parameters, the dynamics of the system can be described by an equivalent homogeneous system with an effective temperature that depends on the average circular mean of the phenotypes. However, if one of the sub-populations is sufficiently “cold”, it dominates the dynamics of the group as a whole.