Multifractal random walk in copepod behavior

A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the field of turbulence and anomalous diffusion in natural sciences. We show that the walk belongs to “multifractal random walks”, characterized by a nonlinear moment scaling function for the distance versus time. To our knowledge, this is the first experimental study of multifractal anomalous diffusion in natural sciences. We then propose a new type of stochastic process reproducing these multifractal scaling properties. This can be directly used for stochastic numerical simulations, and is thus of important potential applications in the field of animal movement study, and more generally of anomalous diffusion studies.

[1]  R. Hughes,et al.  Foraging by mobile predators on a rocky shore: underwater TV observations of movements of blennies Lipophrys pholis and crabs Carcinus maenas , 1999 .

[2]  K. Johannesson,et al.  Microdistribution of the polymorphic snail Littorina saxatilis (Olivi) in a patchy rocky shore habitat , 1997 .

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

[4]  P. Tiselius,et al.  Foraging behaviour of six calanoid copepods: observations and hydrodynamic analysis , 1990 .

[5]  J. Costello,et al.  Grazing in a turbulent environment: behavioral response of a calanoid copepod, Centropages hamatus. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[6]  James G. Mitchell,et al.  Foraging kinematics of barramundi during early stages of development , 2000 .

[7]  R. Daan.  Factors controlling the summer development of copepod populations in the Southern Bight of the North Sea , 1989 .

[8]  L. Legendre,et al.  Biogenic carbon cycling in the upper ocean: effects of microbial respiration. , 2001, Science.

[9]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[10]  D. Sims,et al.  Selective foraging behaviour of basking sharks on zooplankton in a small-scale front , 1998, Nature.

[11]  E. Bacry,et al.  Multifractal random walk. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[13]  W. Peterson,et al.  Seasonal contrasts in the diel vertical distribution, feeding behavior, and grazing impact of the copepod Temora longicornis in Long Island Sound , 1993 .

[14]  Anomalous diffusion of particles in regular fields , 1990 .

[15]  L. Seuront,et al.  Multiscale patchiness of the calanoid copepod Temora longicornis in a turbulent coastal sea , 2001 .

[16]  P. Jönsson,et al.  Swimming behaviour, patch exploitation and dispersal capacity of a marine benthic ciliate in flume flow , 1997 .

[17]  M J Weissburg,et al.  The fluid physics of signal perception by mate-tracking copepods. , 1998, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[18]  H. Weimerskirch,et al.  Exploitation of distant Antarctic waters and close shelf-break waters by white-chinned petrels rearing chicks , 2000 .

[19]  P. Turchin.  Quantitative Analysis Of Movement , 1998 .

[20]  B. Roitberg.  Searching Behavior: the Behavioral Ecology of Finding Resources , 1992 .

[21]  D. Bellwood,et al.  Development of swimming abilities in reef fish larvae , 2000 .

[22]  Serge Frontier,et al.  Applications of Fractal Theory to Ecology , 1987 .

[23]  Zbigniew S. Kolber,et al.  Contribution of Aerobic Photoheterotrophic Bacteria to the Carbon Cycle in the Ocean , 2001, Science.

[24]  John J. Videler,et al.  Swimming behaviour of developmental stages of the calanoid copepod Temora longicornis at different food concentrations , 1995 .

[25]  D E Newman,et al.  Anomalous diffusion in a running sandpile model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  N. Nibbelink,et al.  Diel vertical migration and global climate change: A dynamic modeling approach to zooplankton behavior , 1993 .

[27]  C R Gallistel,et al.  Computations on metric maps in mammals: getting oriented and choosing a multi-destination route. , 1996, The Journal of experimental biology.

[28]  Peter Turchin,et al.  Translating Foraging Movements in Heterogeneous Environments into the Spatial Distribution of Foragers , 1991 .

[29]  Andrea Mazzino,et al.  On strong anomalous diffusion , 1998, chao-dyn/9811012.

[30]  J. Videler,et al.  The trade-off between feeding, mate seeking and predator avoidance in copepods: behavioural responses to chemical cues , 1996 .

[31]  G. Davoren,et al.  Differences in prey selection and behaviour during self-feeding and chick provisioning in rhinoceros auklets , 1999, Animal Behaviour.

[32]  G. Pyke.  Optimal foraging in hummingbirds: Rule of movement between inflorescences , 1981, Animal Behaviour.

[33]  J. A. Schaefer,et al.  Caribou movement as a correlated random walk , 2000, Oecologia.

[34]  J. Strickler,et al.  Observing free-swimming copepods mating , 1998 .

[35]  G. Hays,et al.  The diving behaviour of green turtles at Ascension Island , 2000, Animal Behaviour.

[36]  E. Josse,et al.  Movement patterns of large bigeye tuna (Thunnus obesus) in the open ocean, determined using ultrasonic telemetry , 2000 .

[37]  M. Brewer.  Mating behaviours of Daphnia pulicaria, a cyclic parthenogen: comparisons with copepods , 1998 .

[38]  Paul A. Garber,et al.  On the move : how and why animals travel in groups , 2000 .

[39]  Y. Cherel,et al.  Benthic and pelagic dives: a new foraging behaviour in rockhopper penguins , 2000 .

[40]  Pikovsky.  Statistical properties of dynamically generated anomalous diffusion. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[41]  John A. Wiens,et al.  Fractal patterns of insect movement in microlandscape mosaics , 1995 .

[42]  D. B. Siniff,et al.  A Simulation Model of Animal Movement Patterns , 1969 .

[43]  F. Schmitt,et al.  Copepod diffusion within multifractal phytoplankton fields , 1998 .

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

[45]  Sims,et al.  Filter-feeding and cruising swimming speeds of basking sharks compared with optimal models: they filter-feed slower than predicted for their size. , 2000, Journal of experimental marine biology and ecology.

[46]  F. S. Jacoff.  Advances in marine environmental research , 1979 .

[47]  P. Tiselius.  Behavior of Acartia tonsa in patchy food environments , 1992 .

[48]  C. Meneveau,et al.  Numerical study of the feeding current around a copepod , 1999 .

[49]  J. Yen,et al.  Advertisement and concealment in the plankton: what makes a copepod hydrodynamically conspicuous? , 1996 .

[50]  Jensen,et al.  Multidiffusion in critical dynamics of strings and membranes. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[51]  Mercedes Pascual,et al.  Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability , 1995 .

[52]  K. H. Andersen,et al.  Simple stochastic models showing strong anomalous diffusion , 2000, cond-mat/0004070.

[53]  P. Cheng,et al.  Focus on multidimensional microscopy , 1999 .

[54]  Guido Boffetta,et al.  MIMICKING A TURBULENT SIGNAL : SEQUENTIAL MULTIAFFINE PROCESSES , 1997, chao-dyn/9711006.

[55]  Shaun Lovejoy,et al.  Multifractal Cascade Dynamics and Turbulent Intermittency , 1997 .

[56]  J. Yen,et al.  Following the invisible trail: kinematic analysis of mate-tracking in the copepod Temora longicornis. , 1998, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[57]  W. J. Bell.  Searching Behaviour: The Behavioural Ecology of Finding Resources , 1991 .

[58]  Shaun Lovejoy,et al.  Universal multifractal analysis as a tool to characterize multiscale intermittent patterns : example of phytoplankton distribution in turbulent coastal waters , 1999 .

[59]  Peter A. Burrough,et al.  Using fractal dimensions for characterizing tortuosity of animal trails , 1988 .

[60]  D. Coughlin,et al.  Swimming and search behaviour in clownfish, Amphiprion perideraion, larvae , 1992, Animal Behaviour.

[61]  J. Titelman,et al.  Swimming and escape behavior of copepod nauplii: implications for predator-prey interactions among copepods , 2001 .

[62]  U. Frisch.  Turbulence: The Legacy of A. N. Kolmogorov , 1996 .

[63]  P. Legendre,et al.  Developments in Numerical Ecology , 1988 .

[64]  F. Schmitt,et al.  Turbulence intermittency, small-scale phytoplankton patchiness and encounter rates in plankton: where do we go from here? , 2001 .

[65]  Jiang‐Shiou Hwang,et al.  Copepod grazing in turbulent flow: elevated foraging behavior and habituation of escape responses , 1994 .

[66]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[67]  M. Cody.  Finch flocks in the Mohave desert. , 1971, Theoretical population biology.

[68]  P. Jonsson,et al.  Effects of copepod foraging behavior on predation risk: An experimental study of the predatory copepod Pareuchaeta norvegica feeding on Acartia clausi and A. tonsa (Copepoda) , 1997 .

[69]  V. V. Ballenberghe,et al.  Extraterritorial Movements and Dispersal of Wolves in Southcentral Alaska , 1983 .

[70]  A. Mazzino,et al.  Numerical study of strong anomalous diffusion , 2000 .

[71]  Jr Strickler,et al.  Matched spatial filters in long working distance microscopy of phase objects , 1999 .

[72]  Andrew W. Leising,et al.  Copepod vertical distribution within a spatially variable food source : a simple foraging-strategy model , 2000 .

[73]  Carsten J. Loose.  Daphnia diel vertical migration behavior: Response to vertebrate predator abundance , 1993 .

[74]  C. Guinet,et al.  Foraging habitat and diving activity of lactating Subantarctic fur seals in relation to sea-surface temperatures at Amsterdam Island , 2000 .

[75]  J. Costello,et al.  Grazing in a turbulent environment: energy dissipation, encounter rates, and efficacy of feeding currents in Centropages hamatus. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[76]  Alan R. Johnson,et al.  Diffusion in Fractcal Landscapes: Simulations and Experimental Studies of Tenebrionid Beetle Movements , 1992 .

[77]  William R. Young,et al.  Strongly and weakly self-similar diffusion , 2001 .