During the summer of 2022, I completed a project named “Information Transfer in Collectively Moving Animal Groups” at IISc, Bangalore under Dr. Vishwesha Guttal, Center of Ecological Sciences, IISc. One of the most foundational models of collective movement is Couzin’s model, presented in his iconical paper “Collective Memory and Spatial Sorting in Animal Groups”. [1] The existence of major group-level behavioural transitions generated by minor changes in individual-level interactions are observed through Couzin's model. Physical and/or motivational differences among individuals may influence the spatial positions of individuals within animal aggregations. In this paper, they presented a flocking model in three dimensions which was based on the principle that simple local interactions, in collectively moving animal groups, add up to produce complex, emergent properties.They proposed three assumptions which gave way to three zones around each “boid” (Here, a boid can be any object that is part of the collectively moving animal group). The assumptions and zones were as follows –

1. At any given moment, the boid will follow an avoidance maneuver at a certain distance(say, dr) around the boid such that if the distance between two boids is less than dr then the boid repels the other boid. This is the Zone of Repulsion.
2. If there is no other boid in the Zone of Repulsion, then it either attracts towards the average position of the other boids and/or aligns itself according to the average velocities of other boids and this forms the Zone of Attraction and Zone of Orientation.

According to the model, we made a working simulation through agent-based modelling in Python using AgentPy and matplotlib where we programmed each rule through its mathematical formulation. We also calculated the values of polarization and angular momentum at each timestep. We observed different types of collective behaviors like swarming, dynamic parallel group, and highly parallel group in the simulations on varying the parameters(distance of zone of attraction, distance of orientation zone, distance of repulsion zone, noise, number of individuals, maximum turning angle, etc.). We could not observe the torsion behaviour through our simulations -- the reason might be that we produced the model in 2D as opposed to 3D.

Workflow followed:

[1] Couzin ID, Krause J, James R, Ruxton GD, Franks NR. 2002 Collective memory and spatial sorting in animal groups. J. Theor. Biol. 218, 1-11