Coordinated Speed Oscillations in Schooling Killifish Enrich Social Communication

We examine the spatial dynamics of individuals in small schools of banded killifish (Fundulus diaphanus) that exhibit rhythmic, oscillating speed, typically with sustained, coordinated, out-of-phase speed oscillations as they move around a shallow water tank. We show that the relative motion among the fish yields a periodically time-varying network of social interactions that enriches visually driven social communication. The oscillations lead to the regular making and breaking of occlusions, which we term “switching.” We show that the rate of convergence to consensus (biologically, the capacity for individuals in groups to achieve effective coordinated motion) governed by the switching outperforms static alternatives, and performs as well as the less practical case of every fish sensing every other fish. We show further that the oscillations in speed yield oscillations in relative bearing between fish over a range that includes the angles previously predicted to be optimal for a fish to detect changes in heading and speed of its neighbors. To investigate systematically, we derive and analyze a dynamic model of interacting agents that move with oscillatory speed. We show that coordinated circular motion of the school leads to systematic cycling of spatial ordering of agents and possibilities for enriched spatial density of measurements of the external environment. Our results highlight the potential benefits of dynamic communication topologies in collective animal behavior, and suggest new, useful control laws for the distributed coordination of mobile robotic networks.

[1]  Sheryl Coombs,et al.  The Lateral Line System , 2014, Springer Handbook of Auditory Research.

[2]  P. S. Krishnaprasad,et al.  Equilibria and steering laws for planar formations , 2004, Syst. Control. Lett..

[3]  Naomi Ehrich Leonard,et al.  Decision versus compromise for animal groups in motion , 2011, Proceedings of the National Academy of Sciences.

[4]  Colin Torney,et al.  Context-dependent interaction leads to emergent search behavior in social aggregates , 2009, Proceedings of the National Academy of Sciences.

[5]  T. Pitcher,et al.  The three-dimensional structure of fish schools , 1980, Behavioral Ecology and Sociobiology.

[6]  Ιωαννησ Τσιτσικλησ,et al.  PROBLEMS IN DECENTRALIZED DECISION MAKING AND COMPUTATION , 1984 .

[7]  Naomi Ehrich Leonard,et al.  Real-Time Feedback-Controlled Robotic Fish for Behavioral Experiments With Fish Schools , 2012, Proceedings of the IEEE.

[8]  Colin R. Twomey,et al.  Visual sensory networks and effective information transfer in animal groups , 2013, Current Biology.

[9]  Some observations on schooling in fish , 1931 .

[10]  Iztok Lebar Bajec,et al.  Organized flight in birds , 2009, Animal Behaviour.

[11]  J. Parrish,et al.  Animal Groups in Three Dimensions: Individual decisions, traffic rules, and emergent pattern in schooling fish , 1997 .

[12]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[13]  G D Ruxton,et al.  Fish shoal composition: mechanisms and constraints , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[15]  J. Hunter,et al.  Some Aspects of the Organization of Fish Schools , 1970 .

[16]  I. Couzin,et al.  Collective memory and spatial sorting in animal groups. , 2002, Journal of theoretical biology.

[17]  Naomi Ehrich Leonard,et al.  Alternating spatial patterns for coordinated group motion , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[19]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[20]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[21]  D. Weihs,et al.  Energetic advantages of burst swimming of fish. , 1974, Journal of theoretical biology.

[22]  S. Coombs,et al.  Information Encoding and Processing by the Peripheral Lateral Line System , 2013 .

[23]  Daniel T. Swain,et al.  The Role of the Dynamics of Relative Motion in Information Passing in Natural and Engineered Collective Motion , 2012 .

[24]  S. Gueron,et al.  The Dynamics of Herds: From Individuals to Aggregations , 1996 .

[25]  Naomi Ehrich Leonard,et al.  On the trajectories and coordination of steered particles with time-periodic speed profiles , 2009, 2009 American Control Conference.

[26]  Richard M. Murray,et al.  Consensus Protocols for Undirected Networks of Dynamic Agents with Communication Time-Delays , 2003 .

[27]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[28]  J. Quintanilla,et al.  Efficient measurement of the percolation threshold for fully penetrable discs , 2000 .

[29]  Animal Groups in Three Dimensions: Predicting the three-dimensional structure of animal aggregations from functional considerations: The role of information , 1997 .

[30]  Naomi Ehrich Leonard,et al.  Cooperative Filters and Control for Cooperative Exploration , 2010, IEEE Transactions on Automatic Control.

[31]  A. Barabasi,et al.  Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension , 1997, cond-mat/9712154.

[32]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion With Limited Communication , 2008, IEEE Transactions on Automatic Control.

[33]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion: All-to-All Communication , 2007, IEEE Transactions on Automatic Control.

[34]  Naomi Ehrich Leonard,et al.  Starling Flock Networks Manage Uncertainty in Consensus at Low Cost , 2013, PLoS Comput. Biol..

[35]  Frank E. Fish,et al.  Burst-and-coast swimming in schooling fish (Notemigonus crysoleucas) with implications for energy economy , 1991 .

[36]  Naomi Ehrich Leonard,et al.  Effective sensing regions and connectivity of agents undergoing periodic relative motions , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[38]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[39]  Vaibhav Srivastava,et al.  Collective Decision-Making in Ideal Networks: The Speed-Accuracy Tradeoff , 2014, IEEE Transactions on Control of Network Systems.

[40]  David J. T. Sumpter,et al.  Information transfer in moving animal groups , 2008, Theory in Biosciences.