A neural coding scheme reproducing foraging trajectories

The movement of many animals may follow Lévy patterns. The underlying generating neuronal dynamics of such a behavior is unknown. In this paper we show that a novel discovery of multifractality in winnerless competition (WLC) systems reveals a potential encoding mechanism that is translatable into two dimensional superdiffusive Lévy movements. The validity of our approach is tested on a conductance based neuronal model showing WLC and through the extraction of Lévy flights inducing fractals from recordings of rat hippocampus during open field foraging. Further insights are gained analyzing mice motor cortex neurons and non motor cell signals. The proposed mechanism provides a plausible explanation for the neuro-dynamical fundamentals of spatial searching patterns observed in animals (including humans) and illustrates an until now unknown way to encode information in neuronal temporal series.

[1]  A. Hofgaard,et al.  Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights , 2002 .

[2]  Ramón Huerta,et al.  Transient Cognitive Dynamics, Metastability, and Decision Making , 2008, PLoS Comput. Biol..

[3]  K. L. Montgomery,et al.  Optogenetic Control of Targeted Peripheral Axons in Freely Moving Animals , 2013, PloS one.

[4]  Karl Deisseroth,et al.  Optical inhibition of motor nerve and muscle activity in vivo , 2013, Muscle & nerve.

[5]  Andy M. Reynolds,et al.  Optimal scale-free searching strategies for the location of moving targets: New insights on visually cued mate location behaviour in insects , 2006 .

[6]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[7]  A. V. Popov,et al.  Receptor interaction and ultrastructural organization of the auditory nerve inLocusta migratoria , 1972, Neuroscience and Behavioral Physiology.

[8]  G. Buzsáki,et al.  Theta Oscillations Provide Temporal Windows for Local Circuit Computation in the Entorhinal-Hippocampal Loop , 2009, Neuron.

[9]  M. Jung,et al.  Dynamics of Population Code for Working Memory in the Prefrontal Cortex , 2003, Neuron.

[10]  R Huerta,et al.  Dynamical encoding by networks of competing neuron groups: winnerless competition. , 2001, Physical review letters.

[11]  R. May,et al.  Nonlinear Aspects of Competition Between Three Species , 1975 .

[12]  A. Reynolds,et al.  Free-Flight Odor Tracking in Drosophila Is Consistent with an Optimal Intermittent Scale-Free Search , 2007, PloS one.

[13]  Anthony J Richardson,et al.  Encounter success of free-ranging marine predator movements across a dynamic prey landscape , 2006, Proceedings of the Royal Society B: Biological Sciences.

[14]  Lutz Schimansky-Geier,et al.  Optimal foraging by zooplankton within patches: the case of Daphnia. , 2007, Mathematical biosciences.

[15]  H. Rehbein.  Auditory neurons in the ventral cord of the locust: Morphological and functional properties , 2004, Journal of comparative physiology.

[16]  M. Shlesinger,et al.  Lévy Walks Versus Lévy Flights , 1986 .

[17]  Keith Mathieson,et al.  Retinal Representation of the Elementary Visual Signal , 2014, Neuron.

[18]  Andrej Kosmrlj,et al.  How a protein searches for its site on DNA: the mechanism of facilitated diffusion , 2009 .

[19]  Gilles Laurent,et al.  Olfactory network dynamics and the coding of multidimensional signals , 2002, Nature Reviews Neuroscience.

[20]  L A González-Díaz,et al.  Winnerless competition in coupled Lotka-Volterra maps. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Zengcai V. Guo,et al.  Flow of Cortical Activity Underlying a Tactile Decision in Mice , 2014, Neuron.

[22]  Jensen,et al.  Direct determination of the f( alpha ) singularity spectrum and its application to fully developed turbulence. , 1989, Physical review. A, General physics.

[23]  R Huerta,et al.  Timing control by redundant inhibitory neuronal circuits. , 2014, Chaos.

[24]  Frederic Bartumeus,et al.  ANIMAL SEARCH STRATEGIES: A QUANTITATIVE RANDOM‐WALK ANALYSIS , 2005 .

[25]  G. Viswanathan,et al.  Amnestically induced persistence in random walks. , 2006, Physical review letters.

[26]  Alexander Borst,et al.  Information theory and neural coding , 1999, Nature Neuroscience.

[27]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[28]  Pablo Varona,et al.  Information flow dynamics in the brain. , 2012, Physics of life reviews.

[29]  Marc Timme,et al.  Nonlinear dynamics: When instability makes sense , 2005, Nature.

[30]  Laurent Seuront,et al.  Heavy-tailed distributions in the intermittent motion behaviour of the intertidal gastropod Littorina littorea , 2007 .

[31]  Frederic Bartumeus,et al.  Fractal reorientation clocks: Linking animal behavior to statistical patterns of search , 2008, Proceedings of the National Academy of Sciences.

[32]  György Buzsáki,et al.  Neural Syntax: Cell Assemblies, Synapsembles, and Readers , 2010, Neuron.

[33]  Paul Miller,et al.  Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles , 2007, Proceedings of the National Academy of Sciences.

[34]  Albert-László Barabási,et al.  Modeling bursts and heavy tails in human dynamics , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Diana H. Wall,et al.  Non‐invasive techniques for investigating and modelling root‐feeding insects in managed and natural systems , 2007 .

[36]  Mauro Copelli,et al.  Physics of psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Inés Samengo,et al.  Spike-timing precision underlies the coding efficiency of auditory receptor neurons. , 2006, Journal of neurophysiology.

[38]  Simon Benhamou,et al.  Of scales and stationarity in animal movements. , 2014, Ecology letters.

[39]  G. Laurent,et al.  Transient Dynamics versus Fixed Points in Odor Representations by Locust Antennal Lobe Projection Neurons , 2005, Neuron.

[40]  Jean-René Martin,et al.  The Power Law Distribution for Walking-Time Intervals Correlates with the Ellipsoid-Body in Drosophila , 2001, Journal of neurogenetics.

[41]  D. Boyera,et al.  Modeling the searching behavior of social monkeys , 2004 .

[42]  D. Macdonald,et al.  Scale‐free dynamics in the movement patterns of jackals , 2002 .

[43]  H. Stanley,et al.  The Physics of Foraging: An Introduction to Random Searches and Biological Encounters , 2011 .

[44]  Stefano Focardi,et al.  Adaptive Lévy Walks in Foraging Fallow Deer , 2009, PloS one.

[45]  Allen I. Selverston,et al.  Competing sensory neurons and motor rhythm coordination , 2004, Neurocomputing.

[46]  F. van Langevelde,et al.  Patch density determines movement patterns and foraging efficiency of large herbivores , 2007 .

[47]  H. Larralde,et al.  Lévy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi) , 2003, Behavioral Ecology and Sociobiology.

[48]  Z. Mainen,et al.  Speed and accuracy of olfactory discrimination in the rat , 2003, Nature Neuroscience.

[49]  B. Ronacher,et al.  Neural correlations increase between consecutive processing levels in the auditory system of locusts. , 2007, Journal of neurophysiology.

[50]  Karl Deisseroth,et al.  Optical control of neuronal excitation and inhibition using a single opsin protein, ChR2 , 2013, Scientific Reports.

[51]  F. Bartumeus,et al.  Helical Lévy walks: Adjusting searching statistics to resource availability in microzooplankton , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[52]  R. Menzel,et al.  Displaced honey bees perform optimal scale-free search flights. , 2007, Ecology.

[53]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[54]  Peter J. Gregory,et al.  A general random walk model for the leptokurtic distribution of organism movement: Theory and application , 2007 .

[55]  F. Marlowe,et al.  Evidence of Lévy walk foraging patterns in human hunter–gatherers , 2013, Proceedings of the National Academy of Sciences.

[56]  Nicolas E. Humphries,et al.  Environmental context explains Lévy and Brownian movement patterns of marine predators , 2010, Nature.

[57]  T. D. Matteo,et al.  Multi-scaling in finance , 2007 .

[58]  Gil Ariel,et al.  Swarming bacteria migrate by Lévy Walk , 2015, Nature Communications.

[59]  Nicolas E. Humphries,et al.  Scaling laws of marine predator search behaviour , 2008, Nature.