Modeling Vortex Swarming In Daphnia

Based on experimental observations in Daphnia, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for Daphnia, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single Daphnia. To simulate vortex swarming of many Daphnia, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance—as a special form of asymmetric repulsion between animals—leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in Daphnia is provided by comparing experimental and simulation results for two animals.

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

[2]  A. Ōkubo,et al.  MODELLING SOCIAL ANIMAL AGGREGATIONS , 1994 .

[3]  L. Edelstein-Keshet,et al.  Complexity, pattern, and evolutionary trade-offs in animal aggregation. , 1999, Science.

[4]  Alf H Øien.  Daphnicle dynamics based on kinetic theory: An analogue-modelling of swarming and behaviour of Daphnia , 2004, Bulletin of mathematical biology.

[5]  O. Kleiven,et al.  Diel horizontal migration and swarm formation in Daphnia in response to Chaoborus , 2004, Hydrobiologia.

[6]  Werner Ebeling,et al.  Directed motion of Brownian particles with internal energy depot , 1999 .

[7]  Frank Schweitzer,et al.  Aggregation Induced by Diffusing and Nondiffusing Media , 1997 .

[8]  Werner Ebeling,et al.  COLLECTIVE MOTION OF BROWNIAN PARTICLES WITH HYDRODYNAMIC INTERACTIONS , 2003 .

[9]  Philip S. Lobel,et al.  Swarming behavior of the hyperiid amphipod Anchylomera blossevilli , 1986 .

[10]  W. Rappel,et al.  Self-organization in systems of self-propelled particles. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Steven V. Viscido,et al.  Self-Organized Fish Schools: An Examination of Emergent Properties , 2002, The Biological Bulletin.

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

[13]  Andreas Huth,et al.  THE SIMULATION OF FISH SCHOOLS IN COMPARISON WITH EXPERIMENTAL DATA , 1994 .

[14]  P. Lenz.  Zooplankton: sensory ecology and physiology , 2021 .

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

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

[17]  C. S. Wardle,et al.  Predator evasion in a fish school: test of a model for the fountain effect , 1986 .

[18]  G. Johnsen,et al.  Behavioural response of the water flea Daphnia pulex to a gradient in food concentration , 1987, Animal Behaviour.

[19]  A. Mikhailov,et al.  Noise-induced breakdown of coherent collective motion in swarms. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  A. Deutsch.  Principles of biological pattern formation: swarming and aggregation viewed as selforganization phenomena , 1999, Journal of Biosciences.

[21]  F. Schweitzer.  Brownian Agents and Active Particles , 2003, Springer Series in Synergetics.

[22]  Thomas Caraco,et al.  Avian flocking in the presence of a predator , 1980, Nature.

[23]  Werner Ebeling,et al.  Noise-induced transition from translational to rotational motion of swarms. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Frank Schweitzer,et al.  Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences , 2003 .

[25]  Andreas Deutsch,et al.  Dynamics of cell and tissue motion , 1997 .

[26]  Eshel Ben-Jacob,et al.  Bacterial self–organization: co–enhancement of complexification and adaptability in a dynamic environment , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  I D Couzin,et al.  Self-organized lane formation and optimized traffic flow in army ants , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  Swarm location in zooplankton as an anti-predator defence mechanism , 1994, Animal Behaviour.

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

[30]  Werner Ebeling,et al.  Complex Motion of Brownian Particles with Energy Depots , 1998 .

[31]  B L Partridge,et al.  The structure and function of fish schools. , 1982, Scientific American.

[32]  W. Ebeling,et al.  Active Brownian particles with energy depots modeling animal mobility. , 1999, Bio Systems.

[33]  Petter Larsson,et al.  Ideal free distribution in Daphnia? Are daphnids able to consider both the food patch quality and the position of competitors? , 1997, Hydrobiologia.

[34]  J. Strickler,et al.  Size and structure of 'footprints' produced by Daphnia: impact of animal size and density gradients , 1999 .

[35]  H. Chaté,et al.  Active and passive particles: modeling beads in a bacterial bath. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Werner Ebeling,et al.  Swarms of particle agents with harmonic interactions , 2001, Theory in Biosciences.

[37]  Julia K. Parrish,et al.  Animal Groups in Three Dimensions: Analysis , 1997 .

[38]  C. Aris Chatzidimitriou Dreismann.  New frontiers in theoretical biology , 1996 .

[39]  Petter Larsson,et al.  Direct distributional response in Daphnia pulex to a predator kairomone , 1996 .

[40]  Frank Moss,et al.  Pattern formation and stochastic motion of the zooplankton Daphnia in a light field , 2003 .

[41]  F. Schweitzer,et al.  Brownian particles far from equilibrium , 2000 .

[42]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

[43]  W Ebeling,et al.  Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  O. Kleiven,et al.  Diel horizontal migration and swarm formation in Daphnia in response to Chaoborus. , 1995 .

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

[46]  Vicsek,et al.  Formation of complex bacterial colonies via self-generated vortices. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[47]  The social organisation of fish schools , 2001 .

[48]  G. F.,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[49]  F Schweitzer,et al.  Active random walkers simulate trunk trail formation by ants. , 1997, Bio Systems.

[50]  Charlotte K. Hemelrijk,et al.  Artificial Fish Schools: Collective Effects of School Size, Body Size, and Body Form , 2003, Artificial Life.

[51]  Neha Bhooshan,et al.  The Simulation of the Movement of Fish Schools , 2001 .

[52]  Werner Ebeling,et al.  Self-Organization, Active Brownian Dynamics, and Biological Applications , 2002, cond-mat/0211606.