[1] Adamic, L. A., Lukose, R. M., Puniyani, A. R., and Huberman, B. A. 2001. Search in power-law networks. Physical Review E, 64, 046135.CrossRefGoogle ScholarPubMed

[2] Aldana, M., Dossetti, V., Huepe, C., Kenkre, V. M., and Larralde, H. 2007. Phase transitions in systems of self-propelled agents and related network models. Physical Review Letters, 98, 095702.CrossRefGoogle ScholarPubMed

[3] Allegrini, P., Bellazzini, J., Bramanti, G., et al. 2002. Scaling breakdown: A signature of aging. Physical Review E, 66, 015101.CrossRefGoogle Scholar

[4] Alves-Pereira, A. R., Nunes-Pereira, E. J., Martinho, J. M. G., and Berberan-Santos, M. N. 2007. Photonic superdiffusive motion in resonance line radiation trapping: Partial frequency redistribution effects. Journal of Chemical Physics, 126, 154505.CrossRefGoogle ScholarPubMed

[5] Amaral, L. A. N., Cizeau, P., Gopikrishnan, P., et al. 1999. Econophysics: Can statistical physics contribute to the science of economics? Computer Physics Communications, 122, 145–152.CrossRefGoogle Scholar

[6] Amaral, L. A. N., Scala, A., Barthelemy, M., and Stanley, H. E. 2000. Classes of small-world networks. Proceedings of the National Academy of Sciences of the United States of America, 97, 11 149–11 152.CrossRefGoogle ScholarPubMed

[7] Angelico, R., Ceglie, A., Olsson, U., Palazzo, G., and Ambrosone, L. 2006. Anomalous surfactant diffusion in a living polymer system. Physical Review E, 74, 031403.CrossRefGoogle Scholar

[8] Anteneodo, C., and Morgado, W. A. M. 2007. Critical scaling in standard biased random walks. Physical Review Letters, 99, 180602.CrossRefGoogle ScholarPubMed

[9] Anteneodo, C., Dias, J. C., and Mendes, R. S. 2006. Long-time behavior of spreading solutions of Schrodinger and diffusion equations. Physical Review E, 73, 051105.CrossRefGoogle ScholarPubMed

[10] Ares, J. O., Dignani, J., and Bertiller, M. B. 2007. Cost analysis of remotely sensed foraging paths in patchy landscapes with plant anti-herbivore defenses (Patagonia, Argentina). Landscape Ecology, 22, 1291–1301.CrossRefGoogle Scholar

[11] Atkinson, R. P. D., Rhodes, C. J., Macdonald, D. W., and Anderson, R. M. 2002. Scale-free dynamics in the movement patterns of jackals. Oikos, 98, 134–140.CrossRefGoogle Scholar

[12] Austin, D., Bowen, W. D., and McMillan, J. I. 2004. Intraspecific variation in movement patterns: Modeling individual behaviour in a large marine predator. Oikos, 105, 15–30.CrossRefGoogle Scholar

[13] Baeumer, B., Kovács, M., and Meerschaert, M. M. 2007. Fractional reproduction-dispersal equations and heavy tail dispersal kernels. Bulletin of Mathematical Biology, 69, 2281–2297.CrossRefGoogle ScholarPubMed

[14] Bak, P. 1996. How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus.CrossRefGoogle Scholar

[15] Barabási, A. L. 2003. Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life. New York: Plume.Google Scholar

[16] Barabási, A. L., and Stanley, H. E. 1995. Fractal Concepts in Surface Growth. Cambridge: Cambridge University Press.CrossRefGoogle Scholar

[17] Bartumeus, F. 2007. Lévy processes in animal movement: An evolutionary hypothesis. Fractals – Complex Geometry Patterns and Scaling in Nature and Society, 15, 151–162.Google Scholar

[18] Bartumeus, F., and Catalan, J. 2009. Optimal search behavior and classic foraging theory. Journal of Physics A, 42, 434002.CrossRefGoogle Scholar

[19] Bartumeus, F., Catalan, J., Fulco, U. L., Lyra, M. L., and Viswanathan, G. M. 2002. Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Physical Review Letters, 88, 097901.CrossRefGoogle ScholarPubMed

[20] Bartumeus, F., Peters, F., Pueyo, S., Marrase, C., and Catalan, J. 2003. Helical Lévy walks: Adjusting searching statistics to resource availability in microzooplankton. Proceedings of the National Academy of Sciences of the United States of America, 100, 12 771–12 775.CrossRefGoogle ScholarPubMed

[21] Bartumeus, F., da Luz, M. G. E., Viswanathan, G. M., and Catalan, J. 2005. Animal search strategies: A quantitative random-walk analysis. Ecology, 86, 3078–3087.CrossRefGoogle Scholar

[22] Bartumeus, F., Fernandez, P., da Luz, M. G. E., et al. 2008. Superdiffusion and encounter rates in diluted, low dimensional worlds. European Physical Journal – Special Topics, 157, 157–166.CrossRefGoogle Scholar

[23] Bartumeus, F., Catalan, J., Viswanathan, G. M., Raposo, E. P., and da Luz, M. G. E. 2008. The influence of turning angles on the success of non-oriented animal searches. Journal of Theoretical Biology, 252, 43–55.CrossRefGoogle ScholarPubMed

[24] Bartumeus, F., Giuggioli, L., Louzao, M., et al. 2010. Fishery discards impact on seabird movement patterns at regional scales. Current Biology, 20, 215–222.CrossRefGoogle ScholarPubMed

[25] Beggs, J. M., and Plenz, D. 2003. Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23, 11167–11177.CrossRefGoogle ScholarPubMed

[26] Belik, V. V., and Brockmann, D. 2007. Accelerating random walks by disorder. New Journal of Physics, 9, 54.CrossRefGoogle Scholar

[27] Benhamou, S. 2004. How to reliably estimate the tortuosity of an animal's path: Straightness, sinuosity, or fractal dimension? Journal of Theoretical Biology, 229, 209–220.CrossRefGoogle ScholarPubMed

[28] Benhamou, S. 2007. How many animals really do the Lévy walk? Ecology, 88, 1962–1969.CrossRefGoogle ScholarPubMed

[29] Benhamou, S. 2008. How many animals really do the Lévy walk? Reply. Ecology, 89, 2351–2352.CrossRefGoogle Scholar

[30] Bénichou, O., Coppey, M., Moreau, M., Suet, P.-H., and Voituriez, R. 2005. A stochastic model for intermittent search strategies. Journal of Physics – Condensed Matter, 17, S4275–S4286.CrossRefGoogle Scholar

[31] Bénichou, O., Coppey, M., Moreau, M., Suet, P.-H., and Voituriez, R. 2005. A stochastic theory for the intermittent behaviour of foraging animals. Physica A, 356, 151–156.CrossRefGoogle Scholar

[32] Bénichou, O., Coppey, M., Moreau, M., and Voituriez, R. 2006. Intermittent search strategies: When losing time becomes efficient. Europhysics Letters, 75, 349–354.CrossRefGoogle Scholar

[33] Bénichou, O., Loverdo, C., Moreau, M., and Voituriez, R. 2006. Two-dimensional intermittent search processes: An alternative to Lévy flight strategies. Physical Review E, 74, 020102.CrossRefGoogle ScholarPubMed

[34] Bénichou, O., Loverdo, C., Moreau, M., and Voituriez, R. 2007. A minimal model of intermittent search in dimension two. Journal of Physics – Condensed Matter, 19, 065141.CrossRefGoogle Scholar

[35] Berg, H. C. 1993. Random Walks in Biology. Princeton, NJ: Princeton University Press.Google Scholar

[36] Berkolaiko, G., and Havlin, S. 1997. Territory covered by N Lévy flights on d-dimensional lattices. Physical Review E, 55, 1395–1400.CrossRefGoogle Scholar

[37] Berkolaiko, G., and Havlin, S. 1998. Number of distinct sites visited by Lévy flights injected into a d-dimensional lattice. Physical Review E, 57, 2549–2552.CrossRefGoogle Scholar

[38] Bertiller, M. B., and Ares, J. O. 2008. Sheep spatial grazing strategies at the arid Patagonian Monte, Argentina. Rangeland Ecology and Management, 61, 38–47.CrossRefGoogle Scholar

[39] Bertrand, S., Burgos, J. M., Gerlotto, F., and Atiquipa, J. 2005. Lévy trajectories of Peruvian purse-seiners as an indicator of the spatial distribution of anchovy (Engraulis ringens). ICES Journal of Marine Science, 62, 477–482.CrossRefGoogle Scholar

[40] Bertrand, S., Bertrand, A., Guevara-Carrasco, R., and Gerlotto, F. 2007. Scaleinvariant movements of fishermen: The same foraging strategy as natural predators. Ecological Applications, 17, 331–337.CrossRefGoogle Scholar

[41] Bovet, J., and Bovet, P. 1993. Computer-simulations of rodent homing behaviour, using a probabilistic model. Journal of Theoretical Biology, 161, 145–156.CrossRefGoogle Scholar

[42] Bovet, P., and Benhamou, S. 1988. Spatial analysis of animals' movements using a correlated random walk model. Journal of Theoretical Biology, 131, 419–433.CrossRefGoogle Scholar

[43] Bovet, P., and Benhamou, S. 1991. Optimal sinuosity in central place foraging movements. Animal Behaviour, 42, 57–62.CrossRefGoogle Scholar

[44] Boyer, D., and Larralde, H. 2005. Looking for the right thing at the right place: Phase transition in an agent model with heterogeneous spatial resources. Complexity, 10, 52–55.CrossRefGoogle Scholar

[45] Boyer, D., and Lopez-Corona, O. 2009. Self-organization, scaling and collapse in a coupled automaton model of foragers and vegetation resources with seed dispersal. Journal of Physics A, 42, 434014.CrossRefGoogle Scholar

[46] Boyer, D., Miramontes, O., Ramos-Fernández, G., Mateos, J. L., and Cocho, G. 2004. Modeling the searching behavior of social monkeys. Physica A, 342, 329–335.CrossRefGoogle Scholar

[47] Boyer, D., Ramos-Fernández, G., Miramontes, O., et al. 2006. Scale-free foraging by primates emerges from their interaction with a complex environment. Proceedings of the Royal Society B, 273, 1743–1750.CrossRefGoogle ScholarPubMed

[48] Boyer, D., Miramontes, O., and Ramos-Fernández, G. 2007. Evidence for biological Lévy flights stands. arXiv:0802.1762v1 [q-bio.PE].

[49] Boyer, D., Miramontes, O., and Larralde, H. 2009. Levy-like behaviour in deterministic models of intelligent agents exploring heterogeneous environments. Journal of Physics A, 42, 434015.CrossRefGoogle Scholar

[50] Bradshaw, C. J. A., Sims, D. W., and Hays, G. C. 2007. Measurement error causes scale-dependent threshold erosion of biological signals in animal movement data. Ecological Applications, 17, 628–638.CrossRefGoogle ScholarPubMed

[51] Brantingham, P. J. 2006. Measuring forager mobility. Current Anthropology, 47, 435–459.CrossRefGoogle Scholar

[52] Brockmann, D. 2008. Anomalous diffusion and the structure of human transportation networks. European Physical Journal – Special Topics, 157, 173–189.CrossRefGoogle Scholar

[53] Brockmann, D., and Geisel, T. 2000. The ecology of gaze shifts. Neurocomputing, 32, 643–650.CrossRefGoogle Scholar

[54] Brockmann, D., and Hufnagel, L. 2007. Front propagation in reaction-superdiffusion dynamics: Taming Lévy flights with fluctuations. Physical Review Letters, 98, 178301.CrossRefGoogle Scholar

[55] Brockmann, D., and Sokolov, I. M. 2002. Lévy flights in external force fields: From models to equations. Chemical Physics, 284, 409–421.CrossRefGoogle Scholar

[56] Brockmann, D., Hufnagel, L., and Geisel, T. 2006. The scaling laws of human travel. Nature, 439, 462–465.CrossRefGoogle ScholarPubMed

[57] Brown, C. T., Witschey, W. R. T., and Liebovitch, L. S. 2005. The broken past: Fractals in archaeology. Journal of Archaeological Method and Theory, 12, 37–78.CrossRefGoogle Scholar

[58] Brown, C. T., Liebovitch, L. S., and Glendon, R. 2007. Lévy flights in Dobe Ju/'hoansi foraging patterns. Human Ecology, 35, 129–138.CrossRefGoogle Scholar

[59] Buchanan, M. 2008. Ecological modelling: The mathematical mirror to animal nature. Nature, 453, 714–716.CrossRefGoogle ScholarPubMed

[60] Buendía, G. M., Viswanathan, G. M., and Kenkre, V. M. 2008. Multifractality of random walks in the theory of vehicular traffic. Physical Review E, 78, 056110.CrossRefGoogle ScholarPubMed

[61] Buiatti, M., Papo, D., Baudonniere, P.-M., and Van Vreeswijk, C. 2007. Feedback modulates the temporal scale-free dynamics of brain electrical activity in a hypothesis testing task. Neuroscience, 146, 1400–1412.CrossRefGoogle Scholar

[62] Buldyrev, S. V., Havlin, S., Kazakov, A. Y., et al. 2001. Average time spent by Lévy flights and walks on an interval with absorbing boundaries. Physical Review E, 6404, 041108.Google Scholar

[63] Buldyrev, S. V., Gitterman, M., Havlin, S., et al. 2001. Properties of Lévy flights on an interval with absorbing boundaries. Physica A, 302, 148–161.CrossRefGoogle Scholar

[64] Bunde, A., and Havlin, S. (eds.). 1991. Fractals and Disordered Systems. Berlin: Springer.CrossRefGoogle Scholar

[65] Bunde, A., and Havlin, S. (eds.). 1994. Fractals in Science. Berlin: Springer.Google Scholar

[66] Bunimovich, L. A. 2003. Walks in rigid environments: Symmetry and dynamics. Asterisque, 286, 231–248.Google Scholar

[67] Bunimovich, L. A. 2004. Deterministic walks in random environments. Physica D, 187, 20–29.CrossRefGoogle Scholar

[68] Burrell, K. H., Isely, J. J., Bunnell, D. B., Van Lear, D. H., and Dolloff, C. A. 2000. Seasonal movement of brown trout in a southern Appalachian river. Transactions of the American Fisheries Society, 129, 1373–1379.2.0.CO;2>CrossRefGoogle Scholar

[69] Cabrera, J. L., and Milton, J. G. 2004. Human stick balancing: Tuning Lévy flights to improve balance control. Chaos, 14, 691–698.CrossRefGoogle ScholarPubMed

[70] Cabrera, J. L., Bormann, R., Eurich, C., Ohira, T., and Milton, J. 2004. State-dependent noise and human balance control. Fluctuation and Noise Letters, 4, L107–L117.CrossRefGoogle Scholar

[71] Cabrera, J. L., Luciani, C., and Milton, J. 2006. Neural control on multiple time scales: Insights from human stick balancing. Condensed Matter Physics, 9, 373–383.CrossRefGoogle Scholar

[72] Cao, X.-Q., Zend, J., and Yan, H. 2009. Physical signals for protein-DNA recognition. Physical Biology, 6, 036012.CrossRefGoogle ScholarPubMed

[73] Cascetta, E., and Russo, F. 1997. Calibrating aggregate travel demand models with traffic counts: Estimators and statistical performance. Transportation, 24, 271–293.CrossRefGoogle Scholar

[74] Chambers, R., Bickel, W. K., and Potenza, M. N. 2007. A scale-free systems theory of motivation and addiction. Neuroscience and Biobehavioral Reviews, 31, 1017–1045.CrossRefGoogle ScholarPubMed

[75] Charnov, E. L. 1976. Optimal foraging: Attack strategy of a mantid. American Naturalist, 110, 141–151.CrossRefGoogle Scholar

[76] Charnov, E. L. 1976. Optimal foraging: The marginal value theorem. Theoretical Population Biology, 9, 129–136.CrossRefGoogle ScholarPubMed

[77] Chechkin, A. V., Metzler, R., Gonchar, V. Y., Klafter, J., and Tanatarov, L. V. 2003. First passage and arrival time densities for Lévy flights and the failure of the method of images. Journal of Physics A, 36, L537–L544.CrossRefGoogle Scholar

[78] Chechkin, A. V., Gonchar, V. Y., Klafter, J., Metzler, R., and Tanatarov, L. V. 2004. Lévy flights in a steep potential well. Journal of Statistical Physics, 115, 1505–1535.CrossRefGoogle Scholar

[79] Chechkin, A. V., Gonchar, V. Y., Klafter, J., and Metzler, R. 2005. Natural cutoff in Lévy flights caused by dissipative nonlinearity. Physical Review E, 72, 010101.CrossRefGoogle ScholarPubMed

[80] Chechkin, A. V., Gonchar, V. Y., Gorenflo, R., Korabel, N., and Sokolov, I. M. 2008. Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights. Physical Review E, 78, 021111.CrossRefGoogle ScholarPubMed

[81] Chechkin, A. V., Metzler, R., Klafter, J., and Gonchar, V. Y. 2008. Introduction to the theory of Lévy flights. In: Anomalous Transport. Berlin: Wiley-VCH, 129–162.CrossRefGoogle Scholar

[82] Cheung, A., Zhang, S., Stricker, C., and Srinivasan, M. V. 2007. Animal navigation: The difficulty of moving in a straight line. Biological Cybernetics, 97, 47–61.CrossRefGoogle Scholar

[83] Cheung, A., Zhang, S., Stricker, C., and Srinivasan, M. V. 2008. Animal navigation: General properties of directed walks. Biological Cybernetics, 99, 197–217.CrossRefGoogle ScholarPubMed

[84] Codling, E. A., Plank, M. J., and Benhamou, S. 2008. Random walk models in biology. Journal of the Royal Society Interface, 5, 813–834.CrossRefGoogle ScholarPubMed

[85] Cole, B. J. 1995. Fractal time in animal behaviour: The movement activity of Drosophila. Animal Behavior, 50, 1317–1324.CrossRefGoogle Scholar

[86] Condat, C. A., Rangel, J., and Lamberti, P. W. 2002. Anomalous diffusion in the nonasymptotic regime. Physical Review E, 65, 026138.CrossRefGoogle ScholarPubMed

[87] Coppey, M., Bénichou, O., Klafter, J., Moreau, M., and Oshanin, G. 2004. Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium. Physical Review E, 69, 036115.CrossRefGoogle ScholarPubMed

[88] Cressoni, J. C., da Silva, M. A. A., and Viswanathan, G. M. 2007. Amnestically induced persistence in random walks. Physical Review Letters, 98, 070603.CrossRefGoogle ScholarPubMed

[89] Crook, J. H. (ed.). 1970. Social Behaviour in Birds and Mammals. London: Academic Press.Google Scholar

[90] da Luz, M. G. E., Buldyrev, S. V., Havlin, S., et al. 2001. Improvements in the statistical approach to random Lévy flight searches. Physica A, 295, 89–92.CrossRefGoogle Scholar

[91] da Luz, M. G. E., Grosberg, A., Raposo, E. P., and Viswanathan, G. M. (eds.). 2009. The random search problem: Trends and perspectives [special issue]Journal of Physics A, 42, no. 43.Google Scholar

[92] Dahirel, V., Paillusson, F., Jardat, M., Barbi, M., and Victor, J.-M. 2009. Nonspecific DNA-protein interaction: Why proteins can diffuse along DNA. Physical Review Letters, 102, 228101.CrossRefGoogle ScholarPubMed

[93] Dahl, O. C. 1991. Migration from Kalimantan to Madagascar. Oslo: Norwegian University Press.Google Scholar

[94] Dai, X., Shannon, G., Slotow, R., Page, B., and Duffy, K. J. 2007. Short-duration daytime movements of a cow herd of African elephants. Journal of Mammalogy, 88, 151–157.CrossRefGoogle Scholar

[95] Davies, P. 1989. The New Physics. Cambridge: Cambridge University Press.Google Scholar

[96] Dawkins, R. 1986. The Blind Watchmaker. Harlow, UK: Longman.Google Scholar

[97] De Knegt, H. J., Hengeveld, G. M., van Langevelde, F., de Boer, W. F., and Kirkman, K. P. 2007. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology, 18, 1065–1072.CrossRefGoogle Scholar

[98] Denisov, S. I., Horsthemke, W., and Haenggi, P. 2008. Steady-state Lévy flights in a confined domain. Physical Review E, 77, 061112.CrossRefGoogle Scholar

[99] Diamond, J. M. 2000. Linguistics: Taiwan's gift to the world. Nature, 403, 709–710.CrossRefGoogle Scholar

[100] Doi, M. 1989. Introduction to Polymer Physics. Oxford: Oxford University Press.Google Scholar

[101] Doran, E. B. 1981. Wangka: Austronesian Canoe Origins. College Station: Texas A&M University Press.Google Scholar

[102] Dubkov, A., and Spagnolo, B. 2007. Langevin approach to Lévy flights in fixed potentials: Exact results for stationary probability distributions. Acta Physica Polonica B, 38, 1745–1758.Google Scholar

[103] Dybiec, B. 2008. Random strategies of contact tracking. Physica A, 387, 4863–4870.CrossRefGoogle Scholar

[104] Ebert, L. A., Schaerli, P., and Moser, B. 2005. Chemokine-mediated control of T cell traffic in lymphoid and peripheral tissues. Molecular Immunology, 42, 799–809.CrossRefGoogle ScholarPubMed

[105] Edwards, A. M., Phillips, R. A., Watkins, N. W., et al. 2007. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature, 449, 1044–1048.CrossRefGoogle ScholarPubMed

[106] Eilazar, I., and Klafter, J. 2003. On the extreme flights of one-sided Lévy processes. Physica A, 330, 8–17.CrossRefGoogle Scholar

[107] Eliazar, I., Koren, T., and Klafter, J. 2007. Searching circular DNA strands. Journal of Physics – Condensed Matter, 19, 065140.CrossRefGoogle Scholar

[108] Eliazar, I., Koren, T., and Klafter, J. 2008. Parallel search of long circular strands: Modeling, analysis, and optimization. Journal of Physical Chemistry B, 112, 5905–5909.CrossRefGoogle Scholar

[109] Emlen, J. M. 1966. The role of time and energy in food preference. American Naturalist, 100, 611–617.CrossRefGoogle Scholar

[110] Engbert, R. 2006. Microsaccades: A microcosm for research on oculomotor control, attention, and visual perception. Progress in Brain Research, 154, 177–192.CrossRefGoogle ScholarPubMed

[111] Fauchald, P. 1999. Foraging in a hierarchical patch system. American Naturalist, 153, 603–613.CrossRefGoogle Scholar

[112] Fauchald, P., and Tveraa, T. 2003. Using first-passage time in the analysis of arearestricted search and habitat selection. Ecology, 84, 282–288.CrossRefGoogle Scholar

[113] Fauchald, P., Erikstad, K. E., and Skarsfjord, H. 2000. Scale-dependent predatorprey interactions: The hierarchical spatial distribution of seabirds and prey. Ecology, 81, 773–783.Google Scholar

[114] Faure, P., Neumeister, H., Faber, D. S., and Korn, H. 2003. Symbolic analysis of swimming trajectories reveals scale invariance and provides a model for fish locomotion. Fractals – Complex Geometry Patterns and Scaling in Nature and Society, 11, 233–243.Google Scholar

[115] Faustino, C. L., da Silva, L. R., da Luz, M. G. E., Raposo, E. P., and Viswanathan, G. M. 2007. Search dynamics at the edge of extinction: Anomalous diffusion as a critical survival state. Europhysics Letters, 77, 30002.CrossRefGoogle Scholar

[116] Felisberto, M. L., da Luz, M. G. E., Bartumeus, F., Raposo, E. P., and Viswanathan, G. M. 2009. Correlated Lévy walk. In Abstracts of the Latin American Workshop on Nonlinear Phenomena, Búzios, 05–09 October. Curitiba-PR, Brazil: Editora Universidade Federal do Paraná, p. 27.Google Scholar

[117] Fenchel, T. 2004. Orientation in two dimensions: Chemosensory motile behaviour of Euplotes vannus. European Journal of Protistology, 40, 49–55.CrossRefGoogle Scholar

[118] Figueiredo, A., Gléria, I., Matsushita, R., and da Silva, S. 2006. Nonidentically distributed variables and nonlinear autocorrelation. Physica A, 363, 171–180.CrossRefGoogle Scholar

[119] Filfillan, S. L. 2001. An ecological study of a population of Pseudantechinus macdonnellensis (Marsupialia: Dasyuridae) in central Australia. II. Population dynamics and movements. Wildilife Research, 28, 481–492.CrossRefGoogle Scholar

[120] Fisher, M. E. 1998. Renormalization group theory: Its basis and formulation in statistical physics. Reviews of Modern Physics, 70, 653.CrossRefGoogle Scholar

[121] Focardi, S., Montanaro, P., and Pecchioli, E. 2009. Adaptative Lévy walks in foraging fallow deer. PLoS ONE, 4, e6587.CrossRefGoogle Scholar

[122] Forester, J. D., Ives, A. R., Turner, M. G., et al. 2007. State-space models link elk movement patterns to landscape characteristics in Yellowstone National Park. Ecological Monographs, 77, 285–299.CrossRefGoogle Scholar

[123] Freitas, J. F. L., and Lyra, M. L. 2003. Optimal transition rate and stochastic resonance in a bistable system driven by power-law noise. International Journal of Modern Physics C, 14, 303–310.CrossRefGoogle Scholar

[124] Freund, H., and Grassberger, P. 1992. The Red Queen's walk. Physica A, 190, 218–237.CrossRefGoogle Scholar

[125] Fritz, H., Said, S., and Weimerskirch, H. 2003. Scale-dependent hierarchical adjustments of movement patterns in a long-range foraging seabird. Proceedings of the Royal Society B, 270, 1143–1148.CrossRefGoogle Scholar

[126] Gale, D., Propp, J., Sutherland, S., and Troubetzkoy, S. 1995. Further travels with my ant. Mathematical Intelligencer, 17, 48–56.CrossRefGoogle Scholar

[127] Gao, J. B., Hu, J., Tung, W. W., and Cao, Y. H. 2006. Distinguishing chaos from noise by scale-dependent Lyapunov exponent. Physical Review E, 74, 066204.CrossRefGoogle ScholarPubMed

[128] Garcia, R., Moss, F., Nihongi, A., et al. 2007. Optimal foraging by zooplankton within patches: The case of Daphnia. Mathematical Biosciences, 207, 165–188.CrossRefGoogle ScholarPubMed

[129] Garoni, T. M., and Frankel, N. E. 2002. d-dimensional Lévy flights: Exact and asymptotic. Journal of Mathematical Physics, 43, 5090–5107.CrossRefGoogle Scholar

[130] Garoni, T. M., and Frankel, N. E. 2002. Lévy flights: Exact results and asymptotics beyond all orders. Journal of Mathematical Physics, 43, 2670–2689.CrossRefGoogle Scholar

[131] Gautestad, A. O., and Mysterud, I. 2005. Intrinsic scaling complexity in animal dispersion and abundance. American Naturalist, 165, 44–55.CrossRefGoogle ScholarPubMed

[132] Gautestad, A. O., and Mysterud, I. 2006. Complex animal distribution and abundance from memory-dependent kinetics. Ecological Complexity, 3, 44–55.CrossRefGoogle Scholar

[133] Geisel, T., Nierwetberg, J., and Zacherl, A. 1985. Accelerated diffusion in Josephson junctions and related chaotic systems. Physical Review Letters, 54, 616.CrossRefGoogle ScholarPubMed

[134] Gibbons, A. 2001. The peopling of the Pacific. Science, 291, 1735–37.CrossRefGoogle ScholarPubMed

[135] Giuggioli, L., Viswanathan, G. M., Kenkre, V. M., Parmenter, R. R., and Yates, T. L. 2007. Effects of finite probing windows on the interpretation of the multifractal properties of random walks. Europhysics Letters, 77, 40004.CrossRefGoogle Scholar

[136] Giuggioli, L., Sevilla, F. J., and Kenkre, V. M. 2009. A generalized master equation approach to modelling anomalous transport in animal movement. Journal of Physics A, 42, 434004.CrossRefGoogle Scholar

[137] González, M. C., Hidalgo, C. A., and Barabási, A.-L. 2008. Understanding individual human mobility patterns. Nature, 453, 779–782.CrossRefGoogle ScholarPubMed

[138] Goss-Custard, J. D. 1970. Feeding dispersion in some overwintering wading birds. In Social Behavior in Birds and Mammals, ed. J. H., Crook, pp. 3–35. London: Academic Press.Google Scholar

[139] Goss-Custard, J. D. 1980. Competition for food and interference among waders. Ardea, 68, 31–52.Google Scholar

[140] Gray, R. D., Drummond, A. J., and Greenhill, S. J. 2009. Language phylogenies reveal expansion pulses and pauses in Pacific settlement. Science, 323, 479–483.CrossRefGoogle ScholarPubMed

[141] Grima, R. 2008. Multiscale modeling of biological pattern formation. In Multiscale Modeling of Developmental Systems, ed. S., Schnellet al. London: Academic Press, pp. 435–460. Current Topics in Developmental Biology 81.CrossRefGoogle Scholar

[142] Gu, W., Regens, J. L., Beier, J. C., and Novak, R. J. 2006. Source reduction of mosquito larval habitats has unexpected consequences on malaria transmission. Proceedings of the National Academy of Sciences of the United States of America, 103, 17560–17563.CrossRefGoogle ScholarPubMed

[143] Gupta, H. M., and Campanha, J. R. 2000. The gradually truncated Lévy flight: Stochastic process for complex systems. Physica A, 275, 531–543.CrossRefGoogle Scholar

[144] Gupta, H. M., and Campanha, J. R. 2002. Tsallis statistics and gradually truncated Lévy flight – distribution of an economical index. Physica A, 309, 381–387.CrossRefGoogle Scholar

[145] Guy, A. G., Bohan, D. A., Powers, S. J., and Reynolds, A. M. 2008. Avoidance of conspecific odour by carabid beetles: A mechanism for the emergence of scale-free searching patterns. Animal Behaviour, 76, 585–591.CrossRefGoogle Scholar

[146] Haefner, J. W., and Crist, T. O. 1994. Spatial model of movement and foraging in harvester ants (Pogonomyrex)(I): The role of memory and communication. Journal of Theoretical Biology, 166, 299–313.CrossRefGoogle Scholar

[147] Hapca, S., Crawford, J. W., MacMillan, K., Wilson, M. J., and Young, I. M. 2007. Modelling nematode movement using time-fractional dynamics. Journal of Theoretical Biology, 248, 212–224.CrossRefGoogle ScholarPubMed

[148] Harnos, A., Horvath, G., Lawrence, A. B., and Vattay, G. 2000. Scaling and intermittency in animal behaviour. Physica A, 286, 312–320.CrossRefGoogle Scholar

[149] Havlin, S., and Benavraham, D. 1987. Diffusion in disordered media. Advances in Physics, 36, 695–798.CrossRefGoogle Scholar

[150] Hays, G. C., Hobson, V. J., Metcalfe, J. D., Righton, D., and Sims, D. W. 2006. Flexible foraging movements of leatherback turtles across the North Atlantic Ocean. Ecology, 87, 2647–2656.CrossRefGoogle ScholarPubMed

[151] Heisenberg, M. 2009. Is free will an illusion?Nature, 459, 164–165.CrossRefGoogle ScholarPubMed

[152] Herrmann, H. J. 1999. Statistical models for granular materials. Physica A, 263, 51–62.CrossRefGoogle Scholar

[153] Herrmann, H. J., and Roux, S. (eds.). 1990. Statistical Models for the Fracture of Disordered Media. Amsterdam: North-Holland.Google Scholar

[154] Hobbs, N. T. 2003. Challenges and opportunities in integrating ecological knowledge across scales. Forest Ecology and Management, 181, 223–238.CrossRefGoogle Scholar

[155] Hobbs, N. T., Gross, J. E., Shipley, L. A., Spalinger, D. E., and Wunder, B. A. 2003. Herbivore functional response in heterogeneous environments: A contest among models. Ecology, 84, 666–681.CrossRefGoogle Scholar

[156] Horn, D. J., Stairs, G. R., and Mitchell, R. D. (eds.). 1979. Analysis of Ecological Systems. Columbus: Ohio State University Press.Google Scholar

[157] Houston, A. I., and McNamara, J. M. 1999. Models of Adaptive Behaviour: An Approach Based on State. Cambridge: Cambridge University Press.Google Scholar

[158] Hoyle, M., and Cresswell, J. E. 2007. A search theory model of patch-to-patch forager movement with application to pollinator-mediated gene flow. Journal of Theoretical Biology, 248, 154–163.CrossRefGoogle ScholarPubMed

[159] Hu, L., Grosberg, A. Y., and Bruinsma, R. 2009. First passage time distribution for the 1D diffusion of particles with internal degrees of freedom. Journal of Physics A, 42, 434011.CrossRefGoogle Scholar

[160] Huet, S., Karatekin, E., Tran, V. S., et al. 2006. Analysis of transient behavior in complex trajectories: Application to secretory vesicle dynamics. Biophysical Journal, 91, 3542–3559.CrossRefGoogle ScholarPubMed

[161] Huettmann, F. 2004. Computing foraging paths for shore-birds using fractal dimensions and pecking success from footprint surveys on mudflats: An application for red-necked stints in the Moroshechnaya River Estuary, Kamchatka – Russian Far East. In Computational Science and ITS Applications – ICCSA 2004, PT 2, ed. M. L., Gavrilovaet al., pp. 1117–1120. Lecture Notes in Computer Science 3044. Berlin: Springer.CrossRefGoogle Scholar

[162] Huey, R. B., and Planka, E. R. 1981. Ecological consequences of foraging mode. Ecology, 62, 991–999.CrossRefGoogle Scholar

[163] Humphries, N. E., Queiroz, N., Dyer, J. R. M., et al. 2010. Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature, 465, 1066–1069.CrossRefGoogle ScholarPubMed

[164] Hurst, H. E., Black, R. P., and Simaika, Y. M. 1965. Long-Term Storage: An Experimental Study. London: Constable.Google Scholar

[165] Imkeller, P., and Pavlyukevich, I. 2006. Lévy flights: Transitions and meta-stability. Journal of Physics A, 39, L237–L246.CrossRefGoogle Scholar

[166] Jennings, H. D., Ivanov, P. C., Martins, A. M., Silva, P. C., and Viswanathan, G. M. 2004. Variance fluctuations in nonstationary time series: A comparative study of music genres. Physica A, 336, 585.CrossRefGoogle Scholar

[167] Jespersen, S., Metzler, R., and Fogedby, H. C. 1999. Lévy flights in external force fields: Langevin and fractional Fokker-Planck equations and their solutions. Physical Review E, 59, 2736–2745.CrossRefGoogle Scholar

[168] Johnson, C. J., Boyce, M. S., Mulders, R., et al. 2004. Quantifying patch distribution at multiple spatial scales: Applications to wildlife-habitat models. Landscape Ecology, 19, 869–882.CrossRefGoogle Scholar

[169] Johnson, S. N., Crawford, J. W., Gregory, P. J., et al. 2007. Non-invasive techniques for investigating and modelling root-feeding insects in managed and natural systems. Agricultural and Forest Entomology, 9, 39–46.CrossRefGoogle Scholar

[170] Kabatiansky, G., and Oshanin, G. 2009. Finding passwords by random walks: how long does it take? Journal of Physics A, 42, 434016.CrossRefGoogle Scholar

[171] Kamil, A. C., and Sargent, T. D. (eds.). 1981. Foraging Behavior: Ecological, Ethological, and Psychological Approaches. New York: Garland.Google Scholar

[172] Kamil, A. C., Drebs, J. R., and Pulliam, H. R. (eds.). 1987. Foraging Behavior. New York: Plenum Press.CrossRefGoogle Scholar

[173] Kareiva, P. M., and Shigesada, N. 1983. Analyzing insect movement as a correlated random walk. Oecologia, 56, 234–238.CrossRefGoogle ScholarPubMed

[174] Katori, H., Schlipf, S., and Walther, H. 1997. Anomalous dynamics of a single ion in an optical lattice. Physical Review Letters, 79, 2221–2224.CrossRefGoogle Scholar

[175] Kenkre, V. M. 1977. The generalized master equation and its applications. In Statistical Mechanics and Statistical Methods in Theory and Application, ed. U., Landman, pp. 441–461. New York: Plenum.CrossRefGoogle Scholar

[176] Kenkre, V. M. 2003. Memory formalism, nonlinear techniques, and kinetic equation approaches. In Modern Challenges in Statistical Mechanics: Patterns, Noice, and the Interplay of Nonlinearity and Complexity, ed. V. M., Kenkre and K., Lindenberg, pp. 63–102. Melville, NY: American Institute of Physics.Google Scholar

[177] Kenkre, V. M. 2007. Analytic formulation, exact solutions, and generalizations of the elephant and the Alzheimer random walks. arXiv:0708.0034v2 [cond-mat.statmech].

[178] Kenkre, V. M., and Knox, R. S. 1974. Generalized-master-equation theory of excitation transfer. Physical Review B, 9, 5279–5290.CrossRefGoogle Scholar

[179] Kenkre, V. M., and Lindenberg, K. (eds.). 2003. Modern Challenges in Statistical Mechanics: Patterns, Noise and the Interplay of Nonlinearity and Complexity [Proceedings of the Pan American Advanced Studies Institute, Bariloche, Argentina]. Melville, NY: American Institute of Physics.Google Scholar

[180] Kenkre, V. M., Montroll, E. W., and Shlesinger, M. F. 1973. Generalized master equations for continuous-time random walks. Journal of Statistical Physics, 9, 45–50.CrossRefGoogle Scholar

[181] Khinchin, A. I. 1949. Mathematical Foundations of Statistical Mechanics. New York: Courier Dover.Google Scholar

[182] Kinouchi, O., Martinez, A. S., Lima, G. F., Lourenço, G. M., and Risau-Gusman, S. 2002. Deterministic walks in random networks: An application to thesaurus graphs. Physica A, 315, 665–676.CrossRefGoogle Scholar

[183] Kiorboe, T., Grossart, H. P., Ploug, H., and Tang, K. 2002. Mechanisms and rates of bacterial colonization of sinking aggregates. Applied and Environmental Microbiology, 68, 3996–4006.CrossRefGoogle ScholarPubMed

[184] Kish, D. 2009. Echo vision: The man who sees with sound. New Scientist, 202(2703), 31–33.CrossRefGoogle Scholar

[185] Klafter, J., Blumen, A., and Shlesinger, M. F. 1987. Stochastic pathway to anomalous diffusion. Physical Review A, 35, 3081.CrossRefGoogle ScholarPubMed

[186] Kleiber, M. 1947. Body size and metabolic rate. Physiological Reviews, 27, 511–541.CrossRefGoogle ScholarPubMed

[187] Kleinberg, J. M. 2000. Navigation in a small world. Nature, 406, 845.CrossRefGoogle Scholar

[188] Kölzsch, A., and Blasius, B. 2008. Theoretical approaches to bird migration. European Physical Journal – Special Topics, 157, 191–208.CrossRefGoogle Scholar

[189] Korobkova, E., Emonet, T., Vilar, J. M. G., Shimizu, T. S., and Cluzel, P. 2004. From molecular noise to behavioural variability in a single bacterium. Nature, 428, 574–578.CrossRefGoogle Scholar

[190] Krebs, J. R. 1978. Optimal foraging: decision rules for predators. In Behavioural Ecology: An evolutionary Approach, ed. J. R., Krebs and N. B., Davies, pp. 34–63. Oxford: Blackwell.Google Scholar

[191] Krebs, J. R., and Davies, N. B. (eds.). 1978. Behavioral Ecology: An Evolutionary Approach. Oxford: Blackwell.Google Scholar

[192] Krebs, J. R., Kacelnik, A., and Taylor, P. 1978. Test of optimal sampling by foraging great tits. Nature, 275, 27–31.CrossRefGoogle Scholar

[193] Kumar, N., Viswanathan, G. M., and Kenkre, V. M. 2009. Hurst exponents for interacting random walkers obeying nonlinear Fokker-Planck equations. Physica A, 388, 3687–3694.CrossRefGoogle Scholar

[194] Kutner, R. 1999. Hierarchical spatio-temporal coupling in fractional wanderings. (I) – Continuous-time Weierstrass flights. Physica A, 264, 84–106.CrossRefGoogle Scholar

[195] Kutner, R., and Maass, P. 1998. Lévy flights with quenched noise amplitudes. Journal of Physics A, 31, 2603–2609.CrossRefGoogle Scholar

[196] Lacasta, A. M., Sancho, J. M., Romero, A. H., Sokolov, I. M., and Lindenberg, K. 2004. From subdiffusion to superdiffusion of particles on solid surfaces. Physical Review E, 70, 051104.CrossRefGoogle ScholarPubMed

[197] Lamine, K., Lambin, M., and Alauzet, C. 2005. Effect of starvation on the searching path of the predatory bug Deraecoris lutescens. BioControl, 50, 717–727.CrossRefGoogle Scholar

[198] Landman, U. (ed.). 1977. Statistical Mechanics and Statistical Methods in Theory and Application. New York: Plenum.CrossRefGoogle Scholar

[199] Larralde, H., Trunfio, P., Havlin, S., Stanley, H. E., and Weiss, G. H. 1992. Territory covered by N diffusing particles. Nature, 355, 423–426.CrossRefGoogle Scholar

[200] Latora, V., Rapisarda, A., and Tsallis, C. 2001. Non-Gaussian equilibrium in a long-range Hamiltonian system. Physical Review E, 64, 056134.CrossRefGoogle Scholar

[201] Lauzon-Guay, J. S., Scheibling, R. E., and Barbeau, M. A. 2006. Movement patterns in the green sea urchin, Strongylocentrotus droebachaensis. Journal of the Marine Biological Association of the United Kingdom, 86, 167–174.CrossRefGoogle Scholar

[202] Lee, S. H., Bardunias, P., and Su, N. Y. 2007. Optimal length distribution of termite tunnel branches for efficient food search and resource transportation. Biosystems, 90, 802–807.CrossRefGoogle ScholarPubMed

[203] Lee, S. H., Bardunias, P., and Su, N. Y. 2008. Two strategies for optimizing the food encounter rate of termite tunnels simulated by a lattice model. Ecological Modelling, 213, 381–388.CrossRefGoogle Scholar

[204] Leggett, K. E. A. 2006. Home range and seasonal movement of elephants in the Kunene region, northwestern Namibia. African Zoology, 41(1), 17–36.CrossRefGoogle Scholar

[205] Levandowsky, M., Klafter, J., and White, B. S. 1988. Feeding and swimming behavior in grazing zooplankton. Journal of Protozoology, 35, 243–246.CrossRefGoogle Scholar

[206] Levandowsky, M., Klafter, J., and White, B. S. 1988. Swimming behavior and chemosensory responses in the protistan microzooplankton as a function of the hydrodynamic regime. Bulletin of Marine Science, 43, 758–763.Google Scholar

[207] Levandowsky, M., White, B. S., and Schuster, F. L. 1997. Random movements of soil amebas. Acta Protozoologica, 36, 237–248.Google Scholar

[208] Levina, A., Herrmann, J. M., and Geisel, T. 2007. Dynamical synapses causing self-organised criticality in neural networks. Nature Physics, 3, 857–860.CrossRefGoogle Scholar

[209] Lévy, P. 1937. Théorie de l'addition des Variables Aléatoires. Paris: Gauthier-Villars.Google Scholar

[210] Libet, B. 2004. Mind Time: The Temporal Factor in Consciousness. Cambridge: Harvard University Press.Google Scholar

[211] Lima, G. F., Martinez, A. S., and Kinouchi, O. 2001. Deterministic walks in random media. Physical Review Letters, 8701, 010603.Google Scholar

[212] Lomholt, M. A., Ambjornsson, T., and Metzler, R. 2005. Optimal target search on a fast-folding polymer chain with volume exchange. Physical Review Letters, 95, 260603.CrossRefGoogle ScholarPubMed

[213] Lomholt, M. A., Koren, T., Metzler, R., and Klafter, J. 2008. Lévy strategies in intermittent search processes are advantageous. Proceedings of the National Academy of Sciences of the United States of America, 105, 11 055–11 059.CrossRefGoogle Scholar

[214] Lomholt, M. A., van den Broek, B., Kalisch, S.-M. J., Wuite, G. J. L., and Metzler, R. 2009. Facilitated diffusion with DNA coiling. Proceedings of the National Academy of Sciences of the United States of America, 106, 8204–8208.CrossRefGoogle ScholarPubMed

[215] Luque, B., Miramontes, O., and Lacasa, L. 2008. Number theoretic example of scale-free topology inducing self-organized criticality. Physical Review Letters, 101, 158702.CrossRefGoogle ScholarPubMed

[216] Lutz, C., Kollmann, M., and Bechinger, C. 2004. Single-file diffusion of colloids in one-dimensional channels. Physical Review Letters, 93, 026001.CrossRefGoogle ScholarPubMed

[217] Maass, P., and Scheffler, F. 2002. Lévy field distributions and anomalous spin relaxation in disordered magnetic systems. Physica A, 314, 200–207.CrossRefGoogle Scholar

[218] MacArthur, R. H. 1972. Geographical Ecology: Patterns in the Distribution of Species. New York: Harper and Row.Google Scholar

[219] MacArthur, R. H., and Pianka, E. R. 1966. On the optimal use of a patchy environment. American Naturalist, 100, 603–609.CrossRefGoogle Scholar

[220] Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. San Francisco: Freeman.Google Scholar

[221] Mantegna, R. N., and Stanley, H. E. 1994. Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. Physical Review Letters, 73, 2946.CrossRefGoogle ScholarPubMed

[222] Mantegna, R. N., and Stanley, H. E. 2000. An Introduction to Econophysics. Cambridge: Cambridge University Press.Google Scholar

[223] Marchal, P., Poos, J.-J., and Quirijns, F. 2007. Linkage between fishers' foraging, market and fish stocks density: Examples from some North Sea fisheries. Fisheries Research, 83, 33–43.CrossRefGoogle Scholar

[224] Mårell, A., Ball, J. P., and Hofgaard, A. 2002. Foraging and movement paths of female reindeer: Insights from fractal analysis, correlated random walks, and Lévy flights. Canadian Journal of Zoology, 80, 854–865.CrossRefGoogle Scholar

[225] Martin, J. R., Faure, P., and Ernst, R. 2001. The power law distribution for walkingtime intervals correlates with the ellipsoid-body in Drosophila. Journal of Neurogenetics, 15, 205–219.CrossRefGoogle Scholar

[226] Martinez, A. S., Kinouchi, O., and Risau-Gusman, S. 2004. Exploratory behavior, trap models, and glass transitions. Physical Review E, 69, 017101.CrossRefGoogle ScholarPubMed

[227] Martinez-Conde, S., Macknik, S. L., Troncoso, X. G., and Dyar, T. A. 2006. Microsaccades counteract visual fading during fixation. Neuron, 49, 297–305.CrossRefGoogle ScholarPubMed

[228] Martinez-Conde, S., Macknik, S. L., Martinez, L. M., Alonso, J. M., and Tse, P. U. (eds.). 2006. Visual Perception, Part 1, Fundamentals of Vision: Low and Mid-level Processes in Perception. Progress in Brain Research 154. Amsterdam: Elsevier.Google Scholar

[229] Martins, M. L., Ceotto, G., Alves, S. G., et al. 2000. Cellular automata model for citrus variegated chlorosis. Physical Review E, 62, 7024–7030.CrossRefGoogle ScholarPubMed

[230] Mashanov, G. I., and Molloy, J. E. 2007. Automatic detection of single fluorophores in live cells. Biophysical Journal, 92, 2199–2211.CrossRefGoogle ScholarPubMed

[231] Mason, O., and Verwoerd, M. 2007. Graph theory and networks in biology. IET Systems Biology, 1, 89–119.CrossRefGoogle ScholarPubMed

[232] Masson, J.-B., Bechet, M. B., and Vergassola, M. 2009. Chasing information to search in random environments. Journal of Physics A, 42, 434009.CrossRefGoogle Scholar

[233] Matsunaga, Y., Li, C.-B., and Komatsuzaki, T. 2007. Anomalous diffusion in folding dynamics of minimalist protein landscape. Physical Review Letters, 99, 238103.CrossRefGoogle ScholarPubMed

[234] Matthiopoulos, J. 2003. The use of space by animals as a function of accessibility and preference. Ecological Modelling, 159, 239–268.CrossRefGoogle Scholar

[235] Mazzoni, A., Broccard, F. D., Garcia-Perez, E., et al. 2007. On the dynamics of the spontaneous activity in neuronal networks. PloS ONE, 5, e439.CrossRefGoogle Scholar

[236] Meats, A., and Edgerton, J. E. 2008. Short- and long-range dispersal of the Queensland fruit fly, Bactrocera tryoni and its relevance to invasive potential, sterile insect technique and surveillance trapping. Australian Journal of Experimental Agriculture, 48, 1237–1245.CrossRefGoogle Scholar

[237] Melloni, L., Schwiedrzik, C. M., Rodriguez, E., and Singer, W. 2009. (Micro)Saccades, corollary activity and cortical oscillations. Trends in Cognitive Sciences, 13, 239–245.CrossRefGoogle ScholarPubMed

[238] Meroz, Y., Eliazar, I., and Klafter, J. 2009. Facilitated diffusion in a crowded environment: from kinetics to stochastics. Journal of Physics A, 42, 434012.CrossRefGoogle Scholar

[239] Metzler, R. 2000. Generalized Chapman-Kolmogorov equation: A unifying approach to the description of anomalous transport in external fields. Physical Review E, 62, 6233.CrossRefGoogle ScholarPubMed

[240] Metzler, R., and Compte, A. 2000. Generalized diffusion-advection schemes and dispersive sedimentation: A fractional approach. Journal of Physical Chemistry B, 104, 3858–3865.CrossRefGoogle Scholar

[241] Metzler, R., and Klafter, J. 2000. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Physics Reports, 339, 1–77.CrossRefGoogle Scholar

[242] Metzler, R., and Klafter, J. 2001. Lévy meets Boltzmann: Strange initial conditions for Brownian and fractional Fokker-Planck equations. Physica A, 302, 290–296.CrossRefGoogle Scholar

[243] Metzler, R., and Klafter, J. 2004. The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. Journal of Physics A, 37, R161–R208.CrossRefGoogle Scholar

[244] Metzler, R., and Nonnenmacher, T. F. 2002. Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation. Chemical Physics, 284, 67–90.CrossRefGoogle Scholar

[245] Metzler, R., and Sokolov, I. M. 2002. Superdiffusive Klein-Kramers equation: Normal and anomalous time evolution and Lévy walk moments. Europhysics Letters, 58, 482–488.CrossRefGoogle Scholar

[246] Metzler, R., Ambjornsson, T., Hanke, A., Zhang, Y., and Levene, S. 2007. Single DNA conformations and biological function. Journal of Computational and Theoretical Nanoscience, 4, 1–49.Google Scholar

[247] Metzler, R., Koren, T., van den Broek, B., Wuite, G. J. L., and Lomholt, M. A. 2009. And did he search for you, and could not find you? Journal of Physics A, 42, 434005.CrossRefGoogle Scholar

[248] Meysman, F. J. R., Malyuga, V. S., Boudreau, B. P., and Middelburg, J. J. 2008. A generalized stochastic approach to particle dispersal in soils and sediments. Geochimica et Cosmochimica Acta, 72, 3460–3478.CrossRefGoogle Scholar

[249] Mirny, L., Slutsky, M., Wunderlich, Z., et al. 2009. How a protein searches for its site on DNA: The mechanism of facilitated diffusion. Journal of Physics A, 42, 434013.CrossRefGoogle Scholar

[250] Montroll, E. W., and Weiss, G. 1965. Random walks on lattices. II. Journal of Mathematical Physics, 6, 167–181.CrossRefGoogle Scholar

[251] Moore, N. T., and Grosberg, A.Y. 2006. The abundance of unknots in various models of polymer loops. Journal of Physics A, 39, 9081–9092.CrossRefGoogle Scholar

[252] Morales, J. M., Haydon, D. T., Frair, J., Holsiner, K. E., and Fryxell, J. M. 2004. Extracting more out of relocation data: Building movement models as mixtures of random walks. Ecology, 85, 2436–2445.CrossRefGoogle Scholar

[253] Moreau, M., Bénichou, O., Loverdo, C., and Voituriez, R. 2007. Intermittent search processes in disordered medium. Europhysics Letters, 77, 20006.CrossRefGoogle Scholar

[254] Moreau, M., Bénichou, O., Loverdo, C., and Voituriez, R. 2009. Dynamical and spatial disorder in an intermittent search process. Journal of Physics A, 42, 434007.CrossRefGoogle Scholar

[255] Morse, P. M., and Kimball, G. E. 1951. Methods of Operations Research. New York: John Wiley.Google Scholar

[256] Morse, P. M., and Kimball, G. E. 1956. How to Hunt a Submarine, vol. 4, The world of Mathematics. New York, Simon and Schestor.Google Scholar

[257] Mueller, T., and Fagan, W. F. 2008. Search and navigation in dynamic environments – from individual behaviors to population distributions. Oikos, 117, 654–664.CrossRefGoogle Scholar

[258] Nara, S., Davis, P., and Totsuji, H. 1993. Memory search using complex dynamics in a recurrent neural network model. Neural Networks, 6, 963.CrossRefGoogle Scholar

[259] Nec, Y., Nepomnyashchy, A. A., and Golovin, A. A. 2008. Oscillatory instability in super-diffusive reaction-diffusion systems: Fractional amplitude and phase diffusion equations. Europhysics Letters, 82, 58003.CrossRefGoogle Scholar

[260] Nepomnyashchikh, V. A. 2003. The conflict between optimization and regularity in building behaviour of the caddisfly, Chaetopteryx villosa Fabr. (Limnephilidae: Prichoptera), larvae. Zhurnal Obshchei Biologii, 64, 45–54.Google Scholar

[261] Nepomnyashchikh, V. A., and Podgornyj, K. A. 2003. Emergence of adaptive searching rules from the dynamics of a simple nonlinear system. Adaptive Behavior, 11, 245–265.CrossRefGoogle Scholar

[262] Newlands, N. K., Lutcavage, M. E., and Pitcher, T. J. 2004. Analysis of foraging movements of Atlantic bluefin tuna (Thunnus thynnus): Individuals switch between two modes of search behaviour. Population Ecology, 46, 39–53.CrossRefGoogle Scholar

[263] Newman, J. R. 1956. The World of Mathematics. New York: Simon and Schuster.Google Scholar

[264] Nowak, M. A. 2006. Evolutionary Dynamics: Exploring the Equations of Life. Cambridge, MA: Harvard University Press.Google Scholar

[265] Okubo, A., and Levin, S. A. (eds.). 2001. Diffusion and Ecological Problems: Modern Perspectives. New York: Springer.CrossRefGoogle Scholar

[266] Onsager, L. 1944. Crystal statistics. I. A two-dimensional model with an order disorder transition. Physical Review, 65, 117–149.CrossRefGoogle Scholar

[267] Orians, G. H., and Pearson, N. E. 1979. On the theory of central place foraging. In Analysis of Ecological Systems, ed. D. J., Hornet al., pp. 155–177. Columbus: Ohio State University Press.Google Scholar

[268] Oshanin, G., Wio, H. S., Lindenberg, K., and Burlatsky, S. F. 2007. Intermittent random walks for an optimal search strategy: One-dimensional case. Journal of Physics – Condensed Matter, 19, 065142.CrossRefGoogle Scholar

[269] Oshanin, G., Lindenberg, K., Wio, H. S., and Burlatsky, S. 2009. Efficient search by optimized intermittent random walks. Journal of Physics A, 42, 434008.CrossRefGoogle Scholar

[270] Pagurek, B., Dawes, N., and Kaye, R. 1992. A multiple paradigm diagnostic system for wide area communication networks. Lecture Notes in Computer Science, 604, 256–265.CrossRefGoogle Scholar

[271] Parashar, R., and Cushman, J. H. 2008. Scaling the fractional advective-dispersive equation for numerical evaluation of microbial dynamics in confined geometries with sticky boundaries. Journal of Computational Physics, 227, 6598–6611.CrossRefGoogle Scholar

[272] Pasternak, Z., Blasius, B., and Abelson, A. 2004. Host location by larvae of a parasitic barnacle: Larval chemotaxis and plume tracking in flow. Journal of Plankton Research, 26, 487–493.CrossRefGoogle Scholar

[273] Pasternak, Z., Blasius, B., Abelson, A., and Achituv, Y. 2006. Host-finding behaviour and navigation capabilities of symbiotic zooxanthellae. Coral Reefs, 25, 201–207.CrossRefGoogle Scholar

[274] Pasternak, Z., Bartumeus, F., and Grasso, F. W. 2009. Lévy-taxis: A novel search strategy for finding odor plumes in turbulent flow-dominated environments. Journal of Physics A, 42, 434010.CrossRefGoogle Scholar

[275] Patterson, T. A., Thomas, L., Wilcox, C., Ovaskainen, O., and Matthiopoulos, J. 2008. State-space models of individual animal movement. Trends in Ecology and Evolution, 23, 87–94.CrossRefGoogle ScholarPubMed

[276] Pauly, D., Christensen, V., Dalsgaard, J., Froese, R., and Torres, F. Jr., 1998. Fishing down marine food webs. Science, 279, 860–863.CrossRefGoogle ScholarPubMed

[277] Penrose, R. 1994. Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford: Oxford University Press.Google Scholar

[278] Pepin, D., Adrados, C., Mann, C., and Janeau, G. 2004. Assessing real daily distance traveled by ungulates using differential GPS locations. Journal of Mammalogy, 85, 774–780.CrossRefGoogle Scholar

[279] Pereira, E., Martinho, J. M. G., and Berberan-Santos, M. N. 2004. Photon trajectories in incoherent atomic radiation trapping as Lévy flights. Physical Review Letters, 93, 120201.CrossRefGoogle ScholarPubMed

[280] Peruani, F., and Morelli, L. G. 2007. Self-propelled particles with fluctuating speed and direction of motion in two dimensions. Physical Review Letters, 99, 010602.CrossRefGoogle ScholarPubMed

[281] Peters, R. 2005. Translocation through the nuclear pore complex: Selectivity and speed by reduction-of-dimensionality. Traffic, 6, 421–427.CrossRefGoogle ScholarPubMed

[282] Peterson, I. 1997. The Jungles of Randomness: A Mathematical Safari. New York: John Wiley.Google Scholar

[283] Petrovskii, S., Morozov, A., and Li, B.-L. 2008. On a possible origin of the fat-tailed dispersal in population dynamics. Ecological Complexity, 5, 146–150.CrossRefGoogle Scholar

[284] Phillips, R. A., Croxall, J. P., Silk, J. R. D., and Briggs, D. R. 2007. Foraging ecology of albatrosses and petrels from South Georgia: Two decades of insights from tracking technologies. Aquatic Conservation – Marine and Freshwater Ecosystems, 17, S6–S21.CrossRefGoogle Scholar

[285] Pinaud, D., and Weimerskirch, H. 2007. At-sea distribution and scale-dependent foraging behaviour of petrels and albatrosses: A comparative study. Journal of Animal Ecology, 76, 9–19.CrossRefGoogle ScholarPubMed

[286] Pirolli, P., and Card, S. 1995. Information foraging in information access environments. Proceedings of the 1995 Conference on Human Factors in Computing Systems, ed. G. C., vonder Veer and C., Gale p. 381. New York: ACM Press.Google Scholar

[287] Pirolli, P. L. T. 2007. Information Foraging Theory: Adaptive Interaction with Information. New York: Oxford University Press.CrossRefGoogle Scholar

[288] Plank, M. J., and James, A. 2008. Optimal foraging: Lévy pattern or process? Journal of the Royal Society Interface, 5, 1077–1086.CrossRefGoogle ScholarPubMed

[289] Plotnick, R. E. 2007. Chemoreception, odor landscapes, and foraging in ancient marine landscapes. Palaeontologia Electronica, 10, 1A.Google Scholar

[290] Porto, M., and Roman, H. E. 2002. Autoregressive processes with exponentially decaying probability distribution functions: Applications to daily variations of a stock market index. Physical Review E, 65, 046149.CrossRefGoogle ScholarPubMed

[291] Radons, G., Klages, R., and Sokolov, I. M. (eds.) 2008. Anomalous Transport. Berlin: Wiley-VCH.Google Scholar

[292] Ramos-Fernández, G., Mateos, J. L., Miramontes, O., et al. 2004. Lévywalk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behavioral Ecology and Sociobiology, 55, 223–230.Google Scholar

[293] Randon-Furling, J., Majumdar, S. N., and Comtet, A. 2009. Convex hull of N planar Brownian motions: Exact results and an application to ecology. Physical Review Letters, 103, 140602.CrossRefGoogle ScholarPubMed

[294] Raposo, E. P., Buldyrev, S. V., da Luz, M. G. E., et al. 2003. Dynamical robustness of Lévy search strategies. Physical Review Letters, 91, 240601.CrossRefGoogle ScholarPubMed

[295] Raposo, E. P., Buldyrev, S. V., da Luz, M. G. E., Viswanathan, G. M., and Stanley, H. E. 2009. Lévy flights and random searches. Journal of Physics A, 42, 434003.CrossRefGoogle Scholar

[296] Reynolds, A. 2008. How many animals really do the Lévy walk? Comment. Ecology, 89, 2347–2351.CrossRefGoogle ScholarPubMed

[297] Reynolds, A. M. 2006. On the intermittent behaviour of foraging animals. Europhysics Letters, 75, 517–520.CrossRefGoogle Scholar

[298] Reynolds, A. M. 2006. Optimal scale-free searching strategies for the location of moving targets: New insights on visually cued mate location behaviour in insects. Physics Letters A, 360, 224–227.CrossRefGoogle Scholar

[299] Reynolds, A. M. 2007. Preprint.

[300] Reynolds, A. M. 2007. Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy. Europhysics Letters, 79, 30006.CrossRefGoogle Scholar

[301] Reynolds, A. M. 2008. Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey. Physical Review E, 78, 011906.CrossRefGoogle ScholarPubMed

[302] Reynolds, A. M. 2008. Optimal random Lévy-loop searching: New insights into the searching behaviours of central-place foragers. Europhysics Letters, 82, 20001.CrossRefGoogle Scholar

[303] Reynolds, A. M. 2009. Scale-free animal movement patterns: Lévy walks outperform fractional Brownian motions and fractional Lévy motions in random search scenarios. Journal of Physics A, 42, 434006.CrossRefGoogle Scholar

[304] Reynolds, A. M., and Frye, M. A. 2007. Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLoS ONE, 2(4), e354.CrossRefGoogle ScholarPubMed

[305] Reynolds, A. M., Reynolds, D. R., Smith, A. D., Svensson, G. P., and Lofstedt, C. 2007. Appetitive flight patterns of male Agrotis segetum moths over landscape scales. Journal of Theoretical Biology, 245, 141–149.CrossRefGoogle ScholarPubMed

[306] Reynolds, A. M., Smith, A. D., Menzel, R., et al. 2007. Displaced honey bees perform optimal scale-free search flights. Ecology, 88, 1955–1961.CrossRefGoogle ScholarPubMed

[307] Reynolds, A. M., Smith, D., Reynolds, D. R., Carreck, N. L., and Osborne, J. L. 2007. Honeybees perform optimal scale-free searching flights when attempting to locate a food source. Journal of Experimental Biology, 210, 3763–3770.CrossRefGoogle ScholarPubMed

[308] Reynolds, A. M. 2005. Scale-free movement patterns arising from olfactory-driven foraging. Physical Review E, 72, 041928.CrossRefGoogle ScholarPubMed

[309] Reynolds, A. M. 2006. Cooperative random Lévy flight searches and the flight patterns of honeybees. Physics Letters A, 354, 384–388.CrossRefGoogle Scholar

[310] Rhee, I., Shin, M., Hong, S., Lee, K., and Chong, S. 2008. On the Lévy-walk nature of human mobility. In IEEE INFOCOM 2008 Proceedings. Phoenix, Arizona: Curran Associates.Google Scholar

[311] Rhodes, C. J., and Anderson, R. M. 1997. Epidemic thresholds and vaccination in a lattice model of disease spread. Theoretical Population Biology, 52, 101–118.CrossRefGoogle Scholar

[312] Rhodes, T., and Turvey, M. T. 2007. Human memory retrieval as Lévy foraging. Physica A, 385, 255–260.CrossRefGoogle Scholar

[313] Riggs, T., Walts, A., Perry, N., et al. 2008. A comparison of random vs. chemotaxisdriven contacts of T cells with dendritic cells during repertoire scanning. Journal of Theoretical Biology, 250, 732–751.CrossRefGoogle ScholarPubMed

[314] Risau-Gusman, S., Martinez, A. S., and Kinouchi, O. 2003. Escaping from cycles through a glass transition. Physical Review E, 68, 016104.CrossRefGoogle ScholarPubMed

[315] Ritchie, M. E. 1998. Scale-dependent foraging and patch choice in fractal environments. Evolutionary Ecology, 12, 309–330.CrossRefGoogle Scholar

[316] Roman, H. E., and Porto, M. 2001. Self-generated power-law tails in probability distributions. Physical Review E, 6303, 036128.Google Scholar

[317] Romero, P. D., and Candela, V. F. 2008. Blind deconvolution models regularized by fractional powers of the Laplacian. Journal of Mathematical Imaging and Vision, 32, 181–191.CrossRefGoogle Scholar

[318] Roshier, D. A., Doerr, V. A. J., and Doerr, E. D. 2008. Animal movement in dynamic landscapes: Interaction between behavioural strategies and resource distributions. Oecologia, 156, 465–477.CrossRefGoogle ScholarPubMed

[319] Royer, F., Fromentin, J. M., and Gaspar, P. 2005. A state-space model to derive bluefin tuna movement and habitat from archival tags. Oikos, 109, 473–484.CrossRefGoogle Scholar

[320] Santos, M. C., Raposo, E. P., Viswanathan, G. M., and da Luz, M. G. E. 2004. Optimal random searches of revisitable targets: Crossover from superdiffusive to ballistic random walks. Europhysics Letters, 67, 734–740.CrossRefGoogle Scholar

[321] Santos, M. C., Viswanathan, G. M., Raposo, E. P., and da Luz, M. G. E. 2005. Optimization of random searches on regular lattices. Physical Review E, 72, 046143.CrossRefGoogle ScholarPubMed