Individual measures for heterogeneous collective motion

Abstract

: Insect swarms, fish schools and bird flocks are familiar everyday examples of collective motion. How these groups synchronize despite being made up of vastly different individuals is a fascinating question. Classical modeling of collective motion assumes homogenous individuals interacting locally to produce group-level patterns which are then classified via summary measures, usually called order parameters, such as the degree of alignment or rotation of the group. Empirical and theoretical work have pointed to the importance of individual differences (heterogeneity) driving collective behaviour. To investigate how individual differences drive collective motion, we need to understand how the different members contribute to the emergent collective motion phenomena. For this we need to shift the focus from the group to the individual and either introduce new measures or generalize the group level order parameters to the individual level. We investigated the following measures for studying heterogeneous groups: 1) the individual state (cycling, directed, random or composite trajectories) derived from applying alignment and milling order parameters to an individual’s track; 2) the individual fluidity defined as the amount of movement relative to the group centroid over a fixed p eriod; 3 ) t he d ichotomy d efined as th e lo cal di fference in he ading be tween a focal individual and its neighbours and 4) the number of neighbours an individual sees or interacts with. Using a canonical zonal (repulsion, orientation, attraction) constant speed self propelled particle model we applied the above measures to homogenous and heterogeneous groups comprised of two distinct behavioural class types to investigate key questions of multi-stability, self-sorting and state transitions. We investigated these questions in the context of hysteresis as it is a natural measure of multi-stability and the tendency of a collective motion system to exhibit a form of collective memory where current emergent group behaviour is influenced by the recent history of the system. We produced hysteresis loops for heterogeneous groups by keeping one subgroup