The Emergence of Lines of Hierarchy in Collective Motion of Biological Systems

The emergence of large scale structures in biological systems, and in particular the formation of lines of hierarchy, is observed in many scales, from collections of cells to groups of insects to herds of animals. Motivated by phenomena in chemotaxis and phototaxis, we present a new class of alignment models which exhibit alignment into lines. The spontaneous formation of such ``fingers" can be interpreted as the emergence of leaders and followers in a system of identically interacting agents. Various numerical examples are provided, which demonstrate emergent behaviors similar to the ``fingering'' phenomenon observed in some phototaxis and chemotaxis experiments; this phenomenon is generally known as a challenging pattern to capture for existing models. The novel pairwise interactions provides a fundamental mechanism by which agents may form social hierarchy across a wide range of biological systems.