United By Noise How does randomness help swarms stay together? Kit Yates Centre for Mathematical Biology University of Oxford 27/10/10 - Leeds 11
Introduction to Locusts
Biblical Proportions The locusts came up over all the land of Egypt and settled in all the territory of Egypt; they were very numerous. There had never been so many locusts, nor would there be so many again. For they covered the face of the whole earth, so that the land was darkened; and they did eat every herb of the land, and all the fruit of the trees which the hail had left: and there remained not any green thing in the trees, or in the herbs of the field, through all the land of Egypt. Exodus(10:14-15) 33
Background Plagues: 60 countries 29 million square kilometers 20% of the total land surface of the world 10% of the world s population. Swarm: 1 km across 3 km long Upto 1km in the air Source: UNFAO 44
Traffic Accidents
House Eating
Locusts in the media
Back to Science
Serotonin A neurotransmitter. Mediates: Gut movements Animals perceptions of resource availability.
Gregarious vs Solitary Serotonin mediates behavioral gregarization underlying swarm formation in desert locusts. Anstey ML, Rogers SM, Ott SR, Burrows M, Simpson SJ. Science. 2009; 323(5914):627-30.
Swarming is a response to overcrowding Increased contact with other locusts causes increased serotonin Serotonin causes locust to: Change in colour Eat much more Become mutually attracted Breed more readily
Experimental Work
From Disorder to Order From Disorder to Order in Marching Locusts. Buhl, J. and Sumpter, DJT and Couzin, ID and Hale, JJ and Despland, E. and Miller, ER and Simpson, SJ Science 2006; 312:1402-1406.
Experimental Setup 1515
Experimental Results Collective motion Switching between two steady states: Clockwise and Anticlockwise Noisy/Stochastic process 30 Locusts 1717 60 Locusts
Comparison to a simple model Experimental data Model Output
Modelling
The model Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in2020 One Dimension. Czirok et al. PRL 1999; 82(1):209-212.
Inherent Noise Inherent noise can facilitate coherence in collective swarm motion. Yates, C.A. and Erban, R. and Escudero, C. and Couzin, I.D. and Buhl, J. and Kevrekidis, I.G. and Maini, P.K. and Sumpter, D.J.T. PNAS 2009; 106(14):5464.
Stochastic Differential Equations (SDEs) E 2222
Stochastic Differential Equations (SDEs) E
Corresponding time course
Equation-Free Analysis 2525
Model Results Obj100 2626 Alignment time series
Data Analysis Alignment 2727 time series
Model Revision Recall the velocity update equation, absolute value of the mean velocity. 2828
Revised Model Results Alignment time series 2929
Revised model causes locusts to stay together for longer Data time series Old model time series New model time series
Cannibalism Collective motion and cannibalism in locust migratory bands. Bazazi S, Buhl J, Hale JJ, Anstey ML, Sword GA, Simpson SJ, Couzin ID Curr. Biol. 2008; 18(10):735-9.
Cannibalism
Explanations Increased individual randomness when unaligned help the swarm stay together. Evolution - Alignment increase harvesting efficiency and reduce predation Cannibalism - Dangerous to fall out of line as sides are more vulnerable 3434
Recent Developments Ergodic directional switching in mobile insect groups. Escudero, C. and Yates, C.A. and Buhl, J. and Couzin, I.D. and Erban, R. and Kevrekidis, I.G. and Maini, P.K. PRE 2010; 82(1):11926.
Switching is a Poisson Process Fitted analytical functions to the drift and diffusion for original models and locust data. Analysed the behaviour of the SDE via a Fokker-Planck equation. Found that switching is a Poisson process: Switching times are exponentially distributed. Switching times are uncorrelated.
Order indicators Order indicators include: Well depth/barrier height. Well distance. Mean Switching time. Second moments of switching time.
Non-monotonic behaviour of order disorder transition indicators Second moments of the switching time Second moments measure the spread switching times. The smaller the second moment the closer together the switching times are and vice versa.
Conclusions Serotonin causes switch from solitary to gregarious phase. Locusts increase their individual noise in response to finding themselves unaligned. Cannibalism is a possible explanation. Switching is unpredictable. Traditional order/disorder indicators may be of no use in these sorts of models.
For more information Oxford Science Blog http://www.ox.ac.uk/media/science_blog/090427.html Physical Review Focus http://focus.aps.org/story/v26/st4
Acknowledgements Supervisors: Radek Erban, David Sumpter and Carlos Escudero. Experimentalist and Collaborators: Iain Couzin, Jerome Buhl, Yannis Keverekidis and Philip Maini. The Doctoral Training Centre, Oxford. EPSRC/BBSRC. 4141