How the Spatial Position of Individuals Affects Their Influence on Swarms: A Numerical Comparison of Two Popular Swarm Dynamics Models

Abstract

Schools of fish and flocks of birds are examples of self-organized animal groups that arise through social interactions among individuals. We numerically study two individual-based models, which recent empirical studies have suggested to explain self-organized group animal behavior: (i) a zone-based model where the group communication topology is determined by finite interacting zones of repulsion, attraction, and orientation among individuals; and (ii) a model where the communication topology is described by Delaunay triangulation, which is defined by each individual's Voronoi neighbors. The models include a tunable parameter that controls an individual's relative weighting of attraction and alignment. We perform computational experiments to investigate how effectively simulated groups transfer information in the form of velocity when an individual is perturbed. A cross-correlation function is used to measure the sensitivity of groups to sudden perturbations in the heading of individual members. The results show how relative weighting of attraction and alignment, location of the perturbed individual, population size, and the communication topology affect group structure and response to perturbation. We find that in the Delaunay-based model an individual who is perturbed is capable of triggering a cascade of responses, ultimately leading to the group changing direction. This phenomenon has been seen in self-organized animal groups in both experiments and nature.

Collective response to perturbations in a data-driven fish school model

“…Previous works [13,26] had already studied the impact of perturbations in fish schools, but they focused on punctual or instantaneous perturbations, while we looked into the long-term changes that result from the perturbation. These analyses were also mainly related to changes in the school trajectory, and did not focus on the main behavioural changes undergone by the school.…”

Data-driven modelling of social forces and collective behaviour in zebrafish

“…i.e. where points of intersection are on the boundaries of both Voronoi cells [57,58]. The corresponding interaction network is given by the dual representation, know as the Delaunay triangulation [59], where individuals sharing a Voronoi boundary are connected by a Delaunay Edge.…”

Leadership emergence in a data-driven model of zebrafish shoals with speed modulation

“…Its motion is driven by the same equations in (3), with speed U 0 (t), but where Ω 0 (t) = 0 and σ u dW (t) = 0, ∀t. A compatible interaction network between all agents is chosen based on a periodic equivalent to the non-metric Voronoi neighbourhood used in related models [8,13,33,45]. A more detailed description and a diagram of the construction of this topology is shown in Fig.…”