Inferring individual rules from collective behavior

Abstract

Social organisms form striking aggregation patterns, displaying cohesion, polarization, and collective intelligence. Determining how they do so in nature is challenging; a plethora of simulation studies displaying life-like swarm behavior lack rigorous comparison with actual data because collecting field data of sufficient quality has been a bottleneck. Here, we bridge this gap by gathering and analyzing a high-quality dataset of flocking surf scoters, forming well-spaced groups of hundreds of individuals on the water surface. By reconstructing each individual's position, velocity, and trajectory, we generate spatial and angular neighbor-distribution plots, revealing distinct concentric structure in positioning, a preference for neighbors directly in front, and strong alignment with neighbors on each side. We fit data to zonal interaction models and characterize which individual interaction forces suffice to explain observed spatial patterns. Results point to strong short-range repulsion, intermediate-range alignment, and longer-range attraction (with circular zones), as well as a weak but significant frontal-sector interaction with one neighbor. A best-fit model with such interactions accounts well for observed group structure, whereas absence or alteration in any one of these rules fails to do so. We find that important features of observed flocking surf scoters can be accounted for by zonal models with specific, well-defined rules of interaction.

Fig. 1.

A typical flock of M. perspicillata (surf scoter) moving on the water surface showing a raw image (A) and an image filtered and thresholded to isolate individuals and eliminate noise (B). (C) Validation of objects by overlay on original image; centers of mass for individuals were calculated. (D) Correction for perspective and transformation to ”real” positions, calculated velocities (gray lines), and correction for drift currents.

Fig. 2.

Results of data analysis: Density maps for position and orientation of neighbors relative to a typical individual (central white disk, with ”beak” in front) based on pooled data excluding flock edges. Radial distances of 1, 2, and 3 BL are superimposed. (A) Density of neighbor positions (normalized to have an average value of 1) showing a preference for frontal neighbors. (B) Relative neighbor orientation showing high deviation in front/behind versus low at left/right flanks. Deviation increases radially outwards, indicating local alignment interaction (as distinct from alignment to common goal).

Fig. 3.

Results of model predictions: Neighbor distribution plots (as in Fig. 2A) for a sequence of models (details in SI Text). Simple attraction-repulsion (A/R) (A), with alignment (A/R/A) (B), A/R/A with 45° blind angle in back (C), A/R/A with angle-dependent weighting exp(w cos(θ_ij))/ exp(w), where θ_ij is the relative angle between neighbors, and w = 2 is a weighting parameter (D), A/R/A model with additional frontal interaction, (θ ± 30) (E). Each distribution was calculated from 20 model simulations of 100 individuals, with random initial conditions. Radial distances of 1, 2, and 3 BL are superimposed.

Fig. 4.

Individual behavior inferred by matching model to data. Individuals obey a hierarchy of repulsion, alignment, and attraction to neighbors in zones shown in A, supplemented by A/R with one neighbor in a frontal interaction sector. (B) Relative magnitudes of repulsion, attraction, alignment, and frontal forces (ω_k) obtained by optimizing the model fit to data (logarithmic scale). (B Inset) Evidence for optimality shown by varying each parameter about its best-fit value. Ranges explored were −50% to +50% of the optimal parameter set (ω_rep = 8.5, ω_att = 1.2, ω_al = 0.74, ω_front = 0.08, and ω_ξ = 0.37). (C) Density of neighbors vs. angle −90° ≤ θ ≤ 90° at 1.5 BL (the preferred distance) showing good agreement between model (solid) and data (dotted) (0° is to the front). (D) A comparison of radial neighbor density for data (dotted) and model (solid).