Scale-free correlations in starling flocks

From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations.

[1]  J. T. Emlen.  Flocking Behavior in Birds , 1952 .

[2]  L. Ryder,et al.  Quantum Field Theory , 2001, Foundations of Modern Physics.

[3]  J. Buck,et al.  Mechanism of Rhythmic Synchronous Flashing of Fireflies , 1968, Science.

[4]  P. Anderson.  More is different. , 1972, Science.

[5]  K. Wilson.  Problems in Physics with many Scales of Length , 1979 .

[6]  A. Ōkubo.  Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[7]  HERBERT A. SIMON,et al.  The Architecture of Complexity , 1991 .

[8]  W. Cresswell,et al.  Flocking is an effective anti-predation strategy in redshanks, Tringa totanus , 1994, Animal Behaviour.

[9]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[10]  Yuhai Tu,et al.  SOUND WAVES AND THE ABSENCE OF GALILEAN INVARIANCE IN FLOCKS , 1998 .

[11]  J. Hutchinson.  Animal groups in three dimensions , 1999 .

[12]  T. Vicsek,et al.  Collective behavior of interacting self-propelled particles , 2000, cond-mat/0611742.

[13]  T. Vicsek,et al.  Self-organizing processes: The sound of many hands clapping , 2000, Nature.

[14]  Tamás Viczek,et al.  Fluctuations and Scaling in Biology , 2001 .

[15]  R. R. Krausz.  Living in Groups , 2013 .

[16]  Iain D. Couzin,et al.  Self‐Organization in Biological Systems.Princeton Studies in Complexity. ByScott Camazine,, Jean‐Louis Deneubourg,, Nigel R Franks,, James Sneyd,, Guy Theraulaz, and, Eric Bonabeau; original line drawings by, William Ristineand, Mary Ellen Didion; StarLogo programming by, William Thies. Princeton (N , 2002 .

[17]  I. Couzin,et al.  Self-Organization and Collective Behavior in Vertebrates , 2003 .

[18]  H. Chaté,et al.  Onset of collective and cohesive motion. , 2004, Physical review letters.

[19]  R. Goldstein,et al.  Self-concentration and large-scale coherence in bacterial dynamics. , 2004, Physical review letters.

[20]  S. L. Lima,et al.  Determinants of predation risk in small wintering birds: the hawk’s perspective , 2006, Behavioral Ecology and Sociobiology.

[21]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[22]  J. Toner,et al.  Hydrodynamics and phases of flocks , 2005 .

[23]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[24]  Joseph J. Hale,et al.  From Disorder to Order in Marching Locusts , 2006, Science.

[25]  I. Couzin.  Collective minds , 2007, Nature.

[26]  Uovo Cimento,et al.  Field Theories with ( ( Superconductor * * Solutions , 2007 .

[27]  I. Aranson,et al.  Concentration dependence of the collective dynamics of swimming bacteria. , 2007, Physical review letters.

[28]  R. Cortez,et al.  Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations , 2007 .

[29]  S. Taraskin,et al.  Temporal and dimensional effects in evolutionary graph theory. , 2006, Physical review letters.

[30]  Giorgio Parisi,et al.  The STARFLAG handbook on collective animal behaviour: Part I, empirical methods , 2008, 0802.1668.

[31]  Giorgio Parisi,et al.  The STARFLAG handbook on collective animal behaviour: 2. Three-dimensional analysis , 2008, Animal Behaviour.

[32]  G. Parisi,et al.  The STARFLAG handbook on collective animal behaviour: Part II, three-dimensional analysis , 2008, 0802.1674.

[33]  G. Parisi,et al.  Empirical investigation of starling flocks: a benchmark study in collective animal behaviour , 2008, Animal Behaviour.

[34]  Giorgio Parisi,et al.  The STARFLAG handbook on collective animal behaviour: 1. Empirical methods , 2008, Animal Behaviour.

[35]  G. Parisi,et al.  An empirical study of large, naturally occurring starling flocks: a benchmark in collective animal behaviour , 2008, 0802.1667.

[36]  G. Parisi,et al.  Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study , 2007, Proceedings of the National Academy of Sciences.

[37]  Christian A. Yates,et al.  Inherent noise can facilitate coherence in collective swarm motion , 2009, Proceedings of the National Academy of Sciences.

[38]  I. Couzin.  Collective cognition in animal groups , 2009, Trends in Cognitive Sciences.

[39]  M. Magnasco,et al.  Self-tuned critical anti-Hebbian networks. , 2009, Physical review letters.

[40]  V. Isaeva.  Self-organization in biological systems , 2012, Biology Bulletin.

[41]  L. Leon,et al.  The sound of many hands clapping , 2022 .