Figure 1

An illustration of the featured factors. Pink striped area represents the frontal preference of the focal individual i. \({\mathrm{d}_\mathrm{ij}} = ||\mathbf {x_i} - \mathbf { x_j}||\) is the distance between individuals i and j (Eq. (3)); \(\mathbf {x_{ij}} = \mathbf {x_{j}} - \mathbf { x_{i}}\) is the relative position of j with respect to i (Eq. (4)); \(\mathbf {v_{j}}^{t}, \mathbf { v_{j}}^{t-1}\) are the velocity vector of individual j at time t and \(t-1\) in Eq. (5); \(\mathbf { x_{ij}}^t, \mathbf { x_{ij}}^{t-1}\) are the position vector at time t and \(t-1\) defined in Eq. (6), respectively.