Fig 2 -

Changes in direction of motion, Δθ/Δt (in degrees per second), as a function of the distance to a neighbour, di,j (in unspecified spatial units), and angular difference in directions of motion, φi,j (in degrees), for exact pairwise interactions from the alignment only (panels A to E) and zonal (panel K) models, and as inferred via force mapping for simulations of the alignment only model in an unbounded domain (panels F to J), zonal model (panels L and M) and ODE model (panels N and O). For all plots, positive turns are anticlockwise (redder regions) and negative turns are clockwise (bluer regions). Panels A to E illustrate the exact turning response of a focal individual to a single neighbour for interaction/orientation zones of increasing radius for the alignment-only model (see equation (S2.9) and its derivation in Section S2.1.1 of the S1 File); panels F to J illustrate force maps for groups of N = 10 individuals in an unbounded domain for the same increasing sequence of interaction radii. White regions in panels A to E correspond to regions where no interaction applies, whereas white regions in panels F to J coincide with empty bins/no data. Panel K illustrates the exact turning response of an individual to a single neighbour in its zone of orientation for the zonal model, with a repulsion zone radius rr = 1, orientation zone width Δro = 5 and attraction zone width Δra = 8 (such that the orientation zone extends between 1 and 6 units from a focal individual, and the attraction zone extends from 6 to 14 units; see equation (S2.21), SI Section S2.2.3). White regions in panel K correspond to regions where no orientation interaction applies. Panels L and M show force maps for simulations of the zonal model with groups of N = 10 individuals for the same zone sizes as panel K, for groups that exhibited cohesive but non-parallel motion (panel L) or parallel motion (panel M). The particular simulations used to generate panels L and M also applied a blind zone that extended across the zones of orientation and attraction (but not repulsion). Panels N and O illustrate force map inferred turning responses from simulations of the ODE model with N = 10 individuals where parallel motion (panel N) or swarming emerged.