Fig 1.
a.) Example of a focal agent (blue) with three visible agents (green) exploiting resource patches (light grey). Agents’ heading angle is depicted as a white line. The focal agent’s visual field (here: 360° field of view) is shown as a surrounding black dotted circle, with thick areas indicating regions where other agents are visible. Visibility is also represented by a cone projecting from the focal to the exploiting agents. The visual projection field V(ϕ, t) of the focal agent is unfolded below. Note that visual projections conform to the laws of optics with nearer agents (e.g., agent 2) causing wider projections than farther agents (e.g., agent 1). b.)-c.) Scenario where an agent joins another agent exploiting a patch. The colors of agents and their movement paths correspond to their current behavioral states (blue for exploration, pink for social relocation and green for exploitation). Panel c.) shows corresponding individual and social integrator values of the focal agent with time points of the snapshots indicated by vertical lines. Initially, the focal agent is exploring its environment (A). An exploiting agent is visible and the individual’s social integrator w(t) increases proportionally to the successful agent’s projection on the focal agent’s retina (i.e. distance) until reaching its threshold (grey dotted line). The focal agent then switches to social relocation (pink) and approaches the social cue (B). When reaching the patch, the agent’s individual integrator u(t) receives a large novelty component from the newly discovered patch and crosses its threshold. The focal agent starts exploiting the found patch immediately. Agents keep receiving private information proportional to the patch quality and they exploit the patch (C) until depleted. After depletion, another patch is generated at a random location in the arena and both agents start exploring their environment again (D). d.) Example of the resulting collective behavior for different values of the social excitability parameter ϵw for NA = 100 agents. Moving from left to right, agents become more sensitive to social information.
Fig 2.
Optimal social information use.
Collective search efficiency E normalized by columns (i.e. relative search efficiency, first row), mean inter-individual distance (, second row) and average fraction of time agents spent in social relocation state (Tsoc, third row) for different group sizes (NA; columns), environments (x-axis) and social excitability values (ϵw; y-axis). Environments change from more patchy (few but rich patches) on the left to more uniform (many but poor patches) on the right. Agents become more sensitive to social information as we go from bottom to top on the y-axis. The environment shapes the optimal social information use. Social information is valuable when the resource landscape is scarce and patchy. High ϵw in uniform environments causes maladaptive herding, especially in large groups.
Fig 3.
The left panel shows the absolute search efficiency (including standard deviations across simulation runs) for different social excitability values (ϵw), separately for idealized vision without occlusions (solid yellow) and for more realistic vision with visual occlusions (blue). Results are shown for different group sizes in rows and resource distributions in columns. The right panel shows demonstrative simulation frames to illustrate single scenarios (A-D) with large groups (NA = 100) and large ϵw where the difference between idealized and realistic vision is largest. In case of idealized vision (B, D), agents tend to stay closer together and fail to explore the environment sufficiently. More realistic visual occlusion (A, C) prevents the over-exploitation of social information and maintains high levels of foraging efficiency even in highly social groups.
Fig 4.
Effects of limited field of view (FOV).
The illustration on the top right shows an exploring agent with a FOV limited to ϕ = [−L, L]. Agent 2 is fully visible, agent 3 is only partially visible and agent 1 is fully out of view. The resulting visual projection V(ϕ, t) is shown in black for visible parts of other agents and in grey for invisible parts. The left panel shows the absolute foraging efficiency (including standard deviations across simulation runs) for different FOVs, and for different levels of social excitability (ϵw). Results are shown for different group sizes in rows and resource distributions in columns. The bottom right panel shows demonstrative simulation frames for single scenarios (A-C) with ϵw = 2 in intermediate environments. Different FOVs are labeled in the corresponding plot on the left. In patchy and intermediate environments, typically there exists an optimal intermediate FOV that maximizes search efficiency. In uniform environments, “blind” agents are the most effective.
Fig 5.
Effects of physical collisions.
The right panel shows the absolute foraging efficiency (including standard deviations across simulation runs) for different patch sizes (containing the same amount of resource units) and social excitability values (ϵw) in different environments (columns). The first row shows results for simulations where overlaps are allowed and vision is idealized. In the second row, overlaps are impossible but vision is still idealized. In the third row, agents cannot overlap and can visually occlude social information. The left panel shows exemplary simulation frames for single scenarios (A-F) in patchy environments. Different constellations of social excitability, overlap and occlusion are labeled in the corresponding plots on the right. In general, collisions reduce the value of social information, making more social groups less efficient. Introducing additional visual occlusions can recover efficiency of social groups through the visual shielding of inaccessible social information.
Table 1.
Fixed and varied (v) parameters of the simulation framework during large-scale experimentation.
Unit px denotes pixels, ts simulation timesteps and R denotes resource unit. Variable names for data and code provided in [26] and [28].