Fig 1.
Attention trade-off in collective behavior.
a: Schematic visualization of attention trade-off in collective behavior in complex environments. The focal individual can only pay attention to k = 3 nearest objects—other agents or non-social environmental features—simultaneously. b: Visualization of different situations that may occur in the model. The arrows indicate the velocity vectors of the different agents. The small black circles indicate the location of danger sites l and l′ with their repulsion zones shown in blue. Agent i (red) reacts to the danger site (DS) l as two conditions are met simultaneously: DS l is in i’s kNO, and agent i is also within the corresponding repulsion zone. Agent j (magenta) does not react to DS l′ since it’s attention slot is already filled with three other agents (one blue and two gray). Agent k (blue) perceives DS l′ but does not react to it, because it is outside of the repulsion zone. It only reacts to two other neighbors (gray and magenta) and aligns with them.
Fig 2.
Emergent interaction networks.
a,b: Examples of social interaction networks for k = 3 (a) and k = 12 (b) at ρDS = 0.25. The black symbols indicate socially interacting agents, whereas the red symbols indicate agents responding to a DS. The lines indicate the (non-directed) interaction network. Filled circles represent uninformed agents, empty circles indicate agents informed about the preferred direction of migration. The DS positions shown by blue dots, are surrounded by a disc-like repulsion zones (light blue). For clarity, only a portion of the respective simulation box is represented here, see S1 Fig. for the full snapshots. c,d: In-out degree distributions for the emergent social interaction networks for low attention limit k = 3 (c) and high attention limit k = 12 (d) at low and high DS densities (ρDS = 0.05, and ρDS = 0.25). The vertical dashed lines are for visual guidance to distinguish the subpopulations with Dout = 0 corresponding to agents responding to DSs (left of the vertical line). At high density of DSs this distribution is clearly bimodal with two peaks at Dout = 0 and Dout = k. By increasing DS density number of agents with Dout = 0 increases. These agents have a lower in-degree compared to non-responders, which contributes to the self-isolation of the collective from environmental cues at low k values. For all panels: Rinf = 0.1.
Fig 3.
Collective accuracy C of migration along the preferred direction versus the ratio of informed individuals for different attention limits k, for environments with no danger sites ρDS = 0 (a), and environments with high DS density ρDS = 0.2 (b). The red arrows show the direction of increasing k. c: Collective accuracy C versus attention limit k for different DS densities ρDS at Rinf = 0.1.
Fig 4.
Collective response to environmental cues.
a: The fraction of agents responding to DS directly rd (direct responders, solid lines), or indirectly via social interactions with direct responders ri (indirect responders, dashed lines), for k = 2 (blue) and k = 24 (red) versus DS density ρDS. b: DS avoidance A versus attention limit k for different DS densities ρDS. A = 1 corresponds to the DS avoidance of solitary (non-interacting) agents. c: Global fitness versus attention limit k and relative benefits of DS avoidance β at ρDS = 0.25. Red (blue) regions correspond to better (worse) performance of a collective than isolated individuals according to the fitness function used. d and e: Example snapshots of emergent collective behavior in structured environments with a circular, DS-free path. For low attention capacity (k = 1, e), individuals ignore the structure of the environment and align with the preferred direction of migration. At high attention capacity (k = 16, f), the collective behavior is dominated by the environmental structure and collective migration breaks down. f: DS avoidance A for the structured environment depicted in d, e versus attention limit k. A = 1 is the DS avoidance of solitary agents in the same environment. For all panels: Rinf = 0.1.