On the relationship between fractal dimension and encounters in three-dimensional trajectories

Journal of Theoretical Biology

Volumn 247, Issue 3, 2007, Pages 480-491

  Uttieri, Marco ^a,b   Cianelli, Daniela ^a,b   Strickler, J Rudi ^c   Zambianchi, Enrico ^a  

^a UNIVERSITY OF NAPLES PARTHENOPE   (Italy)

^b Ctro Regionale di Competenza Analisi e Monitoraggio del Rischio Ambientale of the Campania district   (Italy)

^c UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Correlated random walks; Encounters; Fractal dimension; Random walks; Self avoiding random walks

Indexed keywords

ADAPTATION; BEHAVIORAL RESPONSE; EVOLUTION; PREDATOR-PREY INTERACTION; SENSORY SYSTEM; SWIMMING BEHAVIOR;

ARTICLE; CONCENTRATION (PARAMETERS); EVOLUTIONARY ADAPTATION; FRACTAL ANALYSIS; MATHEMATICAL MODEL; PREDATOR; PREY; PRIORITY JOURNAL; QUANTITATIVE STUDY; SIMULATION; STATISTICAL ANALYSIS; SWIMMING;

ADAPTATION, PHYSIOLOGICAL; ANIMALS; FRACTALS; MODELS, BIOLOGICAL; PREDATORY BEHAVIOR; SOCIAL BEHAVIOR; SWIMMING;

EID: 34250652900     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.03.026     Document Type: Article

References (79)

1. Abbott H.L., and Hanson D. A lattice path problem. Ars Combin. 6 (1978) 163-178
2. Barr R., Brender C., and Lax M. Self-avoiding walks with span limitations I. The mean square end-to-end distance. J. Chem. Phys. 72 4 (1980) 2702-2707
3. Bartumeus F., Catalan J., Fulco U.L., Lyra M.L., and Viswanathan G.M. Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88 9 (2002) 0979014
4. Benhamou S. How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity or fractal dimension?. J. Theor. Biol. 229 2 (2004) 209-220
5. Beyer, J.E., 1995. Functional heterogeneity: using the interrupted Poisson process (IPP) model unit in addressing how food aggregation may affect fish ration. ICES J. Mar. Sci., CM 1995/Q:10.
6. Bovet P., and Benhamou S. Spatial analysis of animals' movement using a correlated random walk model. J. Theor. Biol. 131 (1988) 419-433
7. Boxshall G.A., and Halsey S.H. An Introduction to Copepod Diversity (2004), The Ray Society, London
8. Boxshall G.A., Yen J., and Strickler J.R. Functional significance of the sexual dimorphism in the cephalic appendages of Euchaeta rimana Bradford. Bull. Mar. Sci. 61 2 (1997) 387-398
9. Buczkowski S., Kyriacos S., Nekka F., and Cartilier L. The modified box-counting method: analysis of some characteristic parameters. Pattern Recogn. 31 4 (1998) 411-418
10. Bundy M.H., and Paffenhöfer G.-A. Innervation of copepod antennules investigated using laser scanning confocal microscopy. Mar. Ecol. Prog. Ser. 102 (1993) 1-14
11. Buskey E.J. Swimming pattern as an indicator of the roles of copepod sensory systems in the recognition of food. Mar. Biol. 79 (1984) 165-175
12. Buskey E.J. Components of mating behavior in planktonic copepods. J. Mar. Syst. 15 (1998) 13-21
13. Carlotti F., Giske J., and Werner F. Modeling zooplankton dynamics. In: Harris R.P., Wiebe P.H., Lenz J., Skjoldal H.R., and Huntley M. (Eds). ICES Zooplankton Methodology Manual (2000), Academic Press, San Diego 571-667
14. Castiglione P., Cencini M., Vulpiani A., and Zambianchi E. Transport in finite size systems: an exit time approach. Chaos 9 4 (1999) 871-879
15. Codling E.A., and Hill N.A. Sampling rate effects on measurements of correlated and biased random walks. J. Theor. Biol. 233 4 (2005) 573-588
16. Codling E.A., Hill N.A., Pitchford J.W., and Simpson S.D. Random walk models for the movement and recruitment of reef fish larvae. Mar. Ecol. Prog. Ser. 279 (2004) 215-224
17. Cole B.J. Fractal time in animal behaviour: the movement activity of Drosophila. Anim. Behav. 50 (1995) 1317-1324
18. de Gennes P.G. Scaling Concepts in Polymer Physics (1979), Cornell University Press, Ithaca, New York
19. Doall M.H., Colin S.P., Strickler J.R., and Yen J. Locating a mate in 3D: the case of Temora longicornis. Phil. Trans. R. Soc. London B 353 (1998) 681-689
20. Doall M.H., Strickler J.R., Fields D., and Yen J. Mapping the free-swimming attack volume of a planktonic copepod, Euchaeta rimana. Mar. Biol. 140 (2002) 871-879
21. Dodson S.I. Optimal swimming behaviour of zooplankton. In: Lenz P.H., Hartline D.K., Purcell J.E., and Macmillan D.L. (Eds). Zooplankton: Sensory Ecology and Physiology (1996), Gordon and Breach, Amsterdam 365-374
22. Evans G.T. The encounter speed of moving predator and prey. J. Plankton Res. 11 2 (1989) 415-417
23. Gerritsen J. Adaptive responses to encounter problems. In: Kerfoot W.C. (Ed). Evolution and Ecology of Zooplankton Communities. Special Symposium III American Society of Limnology and Oceanography (1980), University Press of New England, Hanover 52-62
24. Gerritsen J., and Strickler J.R. Encounter probabilities and community structure in zooplankton: a mathematical model. J. Fish. Res. Board Can. 34 (1977) 73-82
25. Griffiths A.M., and Frost B.W. Chemical communication in the marine planktonic copepods Calanus pacificus and Pseudocalanus sp. Crustaceana 30 1 (1976) 1-8
26. GuruPrasad B.R., and Borges R.M. Searching on patch networks using correlated random walks: space usage and optimal foraging predictions using Markov chain models. J. Theor. Biol. 240 (2006) 149-241
27. Halley J.M., Hartley S., Kallimanis A.S., Kunin W.E., Lennon J.J., and Sgardelis S.P. Uses and abuses of fractal methodology in ecology. Ecol. Lett. 7 (2004) 254-271
28. Haury L., and Weihs D. Energetically efficient swimming behavior of negatively buoyant zooplankton. Limnol. Oceanogr. 21 6 (1976) 797-803
29. Heller J. Catch 22 (1961), Simon & Schuster, New York
30. Hill N.A., and Häder D.-P. A biased random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol. 186 4 (1997) 503-526
31. Holling C.S. The functional response of invertebrate predators to prey density. Mem. Entomol. Soc. Can. 48 (1966) 1-86
32. Jørgensen S.E. Integration of Ecosystem Theories: A Pattern. second ed (1997), Kluwer Academic Press, Dordecht
33. Jumars P.A. Concepts in Biological Oceanography: An Interdisciplinary Primer (1993), Oxford University Press, New York
34. Kareiva P.M., and Shigesada N. Analyzing insect movement as a correlated random walk. Oecologia 56 (1983) 234-238
35. Kenyon R. The asymptotic determinant of the discrete Laplacian. Acta Math. 185 2 (2000) 239-286
36. Kerfoot W.C. Combat between predatory copepods and their prey: Cyclops, Epischura, and Bosmina. Limnol. Oceanogr. 23 6 (1978) 1089-1102
37. Klyashtorin L.B., and Yarzhombek A.A. Energy consumption in active movements of planktonic organisms. Oceanology 13 (1973) 575-580
38. Kundu P.J. Fluid Mechanics (1990), Academic Press, San Diego
39. Landry M.R. Detection of prey by Calanus pacificus: implications of the first antennae. Limnol. Oceanogr. 25 3 (1980) 545-549
40. Laverack M.S. On the receptors of marine invertebrates. Oceanogr. Mar. Biol. Ann. Rev. 6 (1968) 249-324
41. Lewis D.M. Planktonic encounter rates in homogeneous isotropic turbulence: the case of predators with limited fields of sensory perception. J. Theor. Biol. 222 (2003) 73-97
42. Lewis D.M., and Pedley T.J. Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations. J. Theor. Biol. 205 (2000) 377-408
43. Lewis D.M., and Pedley T.J. The influence of turbulence on plankton predation strategies. J. Theor. Biol. 210 (2001) 347-365
44. Lewis D.M., and Bala S.I. Plankton predation rates in turbulence: a study of the limitations imposed on a predator with a non-spherical field of sensory perception. J. Theor. Biol. 242 1 (2006) 44-61
45. Mandelbrot B.B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156 (1967) 636-638
46. Mann J., Ott S., Pécseli H.L., and Trulsen J. Turbulent particle flux to a perfectly absorbing surface. J. Fluid Mech. 534 (2005) 1-21
47. Mann J., Ott S., Pécseli H.L., and Trulsen J. Laboratory studies of predator-prey encounters in turbulent environments: effects of changes in orientation and field of view. J. Plankton Res. 28 5 (2006) 509-522
48. McCulloch C.E., and Cain M.L. Analyzing discrete movement data as a correlated random walk. Ecology 70 2 (1989) 383-388
49. McKenzie D.S. Polymers and scaling. Phys. Rep. 27 2 (1976) 38-88
50. Nienhuis B. Exact critical point and critical exponents of O (n) models in two dimensions. Phys. Rev. Lett. 49 (1982) 1062-1065
51. Nienhuis B. Critical behaviour in two dimensions and charge symmetry of the Coulomb gas. J. Stat. Phys. 34 (1984) 731-761
52. Nogués J., Costa-Krämer J.L., and Rao K.V. Are random walks random?. Physica A 250 (1998) 327-334
53. O'Brien W.J., Evans B.I., and Brownman H.I. Flexible search tactics and efficient foraging in saltatory searching animals. Oecologia 80 (1989) 100-110
54. Okubo A. Diffusion and Ecological Problems: Mathematical Models (1980), Springer, Berlin
55. Orr W.J.C. Statistical treatment of polymer solutions at infinite dilution. Trans. Faraday Soc. 43 (1947) 12-27
56. Paffenhöfer G.-A., and Knowles S.C. Omnivorousness in marine planktonic copepods. J. Plankton Res. 2 4 (1980) 355-365
57. Pitchford J.W., James A., and Brindley J. Optimal foraging in patchy turbulent environments. Mar. Ecol. Prog. Ser. 256 (2003) 99-110
58. Pyke G.H. Optimal foraging theory: a critical review. Ann. Rev. Ecol. Syst. 15 (1984) 523-575
59. Rothschild B.J., and Osborn T.R. Small-scale turbulence and plankton contact rates. J. Plankton Res. 10 3 (1988) 465-474
60. Saucier A., and Soumis F. Fractal methods and the problem of estimating scaling exponents: a new approach based on upper and lower linear bounds. Chaos Solitons Fractals 28 (2006) 1337-1346
61. Seuront L., Brewer M.C., and Strickler J.R. Quantifying zooplankton swimming behavior: the question of scale. In: Seuront L., and Strutton P.G. (Eds). Handbook of Scaling Methods in Aquatic Ecology-Measurements, Analysis, Simulation (2004), CRC Press, Boca Raton, FL 333-359
62. Skellam J.G. Random dispersal in theoretical populations. Biometrika 38 (1951) 196-218
63. Sokal R.R., and Rohlf F.J. Biometry. third ed (1995), W. H. Freeman and Company, New York
64. Sreenivasan K.R., Prasad R.R., Menevau C., and Ramshauker R. The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows. In: Scholz C.H., and Mandelbrot B.B. (Eds). Fractals in Geophysics (1989), Birkäuser, Basel 43-60
65. Strickler J.R. Calanoid copepods, feeding currents, and the role of gravity. Science 218 (1982) 158-160
66. Strickler J.R., and Bal A.K. Setae of the first antennae of the copepod Cyclops scrutifer (Sars): their structure and importance. Proc. Natl. Acad. Sci. USA 70 9 (1973) 2656-2659
67. Tiselius P. Behavior of Acartia tonsa in patchy food environments. Limnol. Oceanogr. 37 8 (1992) 1640-1651
68. Tukey J.W. Exploratory Data Analysis (1977), Addison-Wesley, Reading, MA
69. Turchin P. Fractal analyses of animal movement: a critique. Ecology 77 7 (1996) 2086-2090
70. Uttieri, M., Nihongi, A., Mazzocchi, M.G., Strickler, J.R., Zambianchi, E., 2007. Pre-copulatory swimming behaviour of Leptodiaptomus ashlandi (Copepoda: Calanoida): a fractal approach. J. Plankton Res. 29 (Suppl. 1), i17-i26.
71. Uttieri M., Mazzocchi M.G., Nihongi A., Ribera d'Alcalà M., Strickler J.R., and Zambianchi E. Lagrangian description of zooplankton swimming trajectories. J. Plankton Res. 26 1 (2004) 99-105
72. Uttieri M., Zambianchi E., Strickler J.R., and Mazzocchi M.G. Fractal characterization of three-dimensional zooplankton swimming trajectories. Ecol. Model. 185 1 (2005) 51-63
73. Visser A.W., and Kiørboe T. Plankton motility patterns and encounter rates. Oecologia 148 3 (2006) 538-546
74. Viswanathan G.M., Buldyrev S.V., Havlin S., da Luz M.G.E., Raposo E.P., and Stanley H.E. Optimizing the success of random searches. Nature 401 (1999) 911-914
75. Vlymen W.J. Energy expenditure of swimming copepods. Limnol. Oceanogr. 15 (1970) 348-356
76. Weissburg M.J., Doall M.H., and Yen J. Following the invisible trail: kinematic analysis of mate-tracking in the copepod Temora longicornis. Phil. Trans. R. Soc. London B 353 (1998) 701-712
77. Wolfram S. A New Kind of Science (2002), Wolfram Media, Champaign, IL
78. Zambianchi E., and Griffa A. Effects of finite scales of turbulence on dispersion estimates. J. Mar. Res. 52 (1994) 129-148
79. Zar J.H. Biostatistical Analysis (1984), Prentice-Hall, Englewood Cliffs, NJ