Role of projection in the control of bird flocks

Supporting Information

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• Download Movie_S01 (AVI) - Movie S1. The behavior of a swarm of n = 100, 10:1 anisotropic (long and thin) individuals within our hybrid projection model. This movie shows the distinct behavioral phenotypes observed with the parameters ϕp and ϕa, highlighted in Fig. S16. Each frame is a single timestep. This movie is obtained for ϕp = 0.1, ϕa = 0.75, point B in Fig. S16; this shows a phenotype displaying a high level of orientational order, similar to that seen in migratory animals.
• Download Movie_S02 (AVI) - Movie S2. The behavior of a swarm of n = 100, 10:1 anisotropic (long and thin) individuals within our hybrid projection model. This movie shows the distinct behavioral phenotypes observed with the parameters ϕp and ϕa, highlighted in Fig. S16. Each frame is a single timestep. This movie is obtained for ϕp = 0.45, ϕa = 0.45, point F in Fig. S16; this shows a phenotype displaying a high swarm vorticity, much like the milling behavior observed in fish.
• Download Movie_S03 (AVI) - Movie S3. The behavior of a swarm of n = 100, 10:1 anisotropic (long and thin) individuals within our hybrid projection model. This movie shows the distinct behavioral phenotypes observed with the parameters ϕp and ϕa, highlighted in Fig. S16. Each frame is a single timestep. This movie is obtained for ϕp = 0.175, ϕa = 0.45, point I in Fig. S16; this shows a phenotype with lower order, in which there is a higher variation in the density of the swarm, reminiscent of the swarming behavior observed in insects.
• Download Movie_S04 (AVI) - Movie S4. The introduction of a “blind angle” behind each individual means that the projection term does not respond in any way to individuals within a π/8 cone directly behind them. This movie shows simulations with the exact same parameters as those in Movie S5 and highlights the modest effect of the blind angle on behavior.
• Download Movie_S05 (AVI) - Movie S5. The introduction of a blind angle behind each individual means that the projection term does not respond in any way to individuals within a π/8 cone directly behind them. This movie shows simulations with the exact same parameters as those in Movie S6 and highlights the modest effect of the blind angle on behavior.
• Download Movie_S06 (AVI) - Movie S6. The introduction of a blind angle behind each individual means that the projection term does not respond in any way to individuals within a π/8 cone directly behind them. This movie shows simulations with the exact same parameters as those in Movie S7 and highlights the modest effect of the blind angle on behavior.
• Download Movie_S07 (AVI) - Movie S7. Starling flocks shown in the red traces of Fig. 3B. This movie was taken at Brighton, East Sussex, United Kingdom, on November 14, 2011, between 1530 and 1630 hours. It is typical of the footage captured of starling flocks. Two movies are available to give examples of the type of data on real starling flocks used in this study and the qualitative behavior of swarms generated by the hybrid projection model.
• Download Movie_S08 (AVI) - Movie S8. Starling flocks shown in the black traces of Fig. 3B. This movie was taken at Brighton, East Sussex, on November 14, 2011, between 1530 and 1630 hours. It is typical of the footage captured of starling flocks.
• Download Movie_S09 (AVI) - Movie S9. The robustness of the hybrid projection model under attack by a simple predator trying to split up the swarm. Because of the global nature of the interactions among individuals, the flock can always re-form after the predator’s attacks. This movie features n = 100 individuals with ϕp = 0.2, ϕa = 0.7. The predator travels at a speed of vp = 2 * v0 and is attracted to the center of mass of the swarm. The individuals react to the predator when it is within rp = 10 * dt * v0, and their response is to travel directly away from it at vresponse = 1.5 * v0.
• Download Movie_S10 (AVI) - Movie S10. Swarm response to the same predator as shown in Movie S9 when the interactions among individuals have a limited range, which enables the predator to sever interaction completely between two regions of the swarm. The result is a far less cohesive swarm, with no guarantee it will re-form after becoming scattered. This movie features n = 100 individuals with ϕp = 0.2, ϕa = 0.7. The predator travels at a speed of vp = 2 * v0 and is attracted to the center of mass of the swarm. The individuals react to the predator when it is within rp = 10 * dt * v0, and their response is to travel directly away from it at vresponse = 1.5 * v0. In this movie, individuals react only to other members of the swarm within rlimit = 30 * dt * v0.