Levy flight search patterns of marine predators not questioned: a reply to Edwards et al

Edwards et al question aspects of the methods used in two of our published papers that report results showing Levy walk like and Levy flight movement patterns of marine predators.The criticisms are focused on the applicability of some statistical methodologies used to detect power law distributions.We reply to the principal criticisms levelled at each of these papers in turn including our own reanalysis of specific datasets and find that neither of our papers conclusions are overturned in any part by the issues raised.Indeed, in addition to the findings of our research reported in these papers there is strong evidence accumulating from studies worldwide that organisms show movements and behaviour consistent with scale invariant patterns such as Levy flights.

[1]  A. M. Edwards,et al.  Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer , 2007, Nature.

[2]  B. Brembs,et al.  Order in Spontaneous Behavior , 2007, PloS one.

[3]  Jayanth R Banavar,et al.  Scale invariance in the dynamics of spontaneous behavior , 2012, Proceedings of the National Academy of Sciences.

[4]  A. M. Edwards,et al.  Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals. , 2011, Ecology.

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

[6]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[7]  Frederic Bartumeus,et al.  The Effects of Spatially Heterogeneous Prey Distributions on Detection Patterns in Foraging Seabirds , 2011, PloS one.

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

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

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

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

[12]  Nicolas E. Humphries,et al.  Foraging success of biological Lévy flights recorded in situ , 2012, Proceedings of the National Academy of Sciences.

[13]  Sabrina Fossette,et al.  High activity and Lévy searches: jellyfish can search the water column like fish , 2012, Proceedings of the Royal Society B: Biological Sciences.

[14]  Nicolas E. Humphries,et al.  Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics. , 2012, The Journal of animal ecology.

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

[16]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[17]  Sepideh Bazazi,et al.  Intermittent Motion in Desert Locusts: Behavioural Complexity in Simple Environments , 2012, PLoS Comput. Biol..

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

[19]  T. Geisel,et al.  The scaling laws of human travel , 2006, Nature.

[20]  N. Masuda,et al.  Dopamine Modulates the Rest Period Length without Perturbation of Its Power Law Distribution in Drosophila melanogaster , 2012, PloS one.

[21]  A. Barabasi,et al.  Human dynamics: Darwin and Einstein correspondence patterns , 2005, Nature.

[22]  A. M. Edwards,et al.  Incorrect Likelihood Methods Were Used to Infer Scaling Laws of Marine Predator Search Behaviour , 2012, PloS one.

[23]  G. Viswanathan,et al.  Lévy flights and superdiffusion in the context of biological encounters and random searches , 2008 .

[24]  Andrea J. Liu,et al.  Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells , 2012, Nature.

[25]  Vincent Bretagnolle,et al.  Fishery Discards Impact on Seabird Movement Patterns at Regional Scales , 2010, Current Biology.

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

[27]  A. Reynolds Olfactory search behaviour in the wandering albatross is predicted to give rise to Lévy flight movement patterns , 2012, Animal Behaviour.

[28]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[29]  Albert-László Barabási,et al.  Limits of Predictability in Human Mobility , 2010, Science.

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

[31]  Gonzalo G. de Polavieja,et al.  The Origin of Behavioral Bursts in Decision-Making Circuitry , 2011, PLoS Comput. Biol..

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