Modelling nematode movement using time-fractional dynamics

Journal of Theoretical Biology

Volumn 248, Issue 1, 2007, Pages 212-224

  Hapca, Simona ^a   Crawford, John W ^a   MacMillan, Keith ^b   Wilson, Mike J ^b   Young, Iain M ^a  

^a UNIVERSITY OF ABERTAY DUNDEE   (United Kingdom)

^b UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

Conditional probability; Correlated random walk; Mean square displacement; Stochastic process with memory

Indexed keywords

MODELING; MOVEMENT; NEMATODE; RANDOM WALK METHOD;

ANIMAL EXPERIMENT; ARTICLE; BODY MOVEMENT; CONTROLLED STUDY; CORRELATION ANALYSIS; DENSITY FUNCTIONAL THEORY; DYNAMICS; ENVIRONMENTAL FACTOR; LOCOMOTION; MEMORY; NEMATODE; NONHUMAN; PRIORITY JOURNAL; PROBABILITY; STATISTICAL ANALYSIS; STATISTICAL DISTRIBUTION; VELOCITY;

ANIMALS; COMPUTER SIMULATION; MODELS, BIOLOGICAL; MOVEMENT; RHABDITOIDEA; STOCHASTIC PROCESSES;

PHASMARHABDITIS HERMAPHRODITA;

EID: 34547689501     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.05.002     Document Type: Article

References (33)

1. Anderson A.R.A., Sleeman B.A., Young I.M., and Griffiths B.S. Nematode movement along a chemical gradient in a structurally heterogeneous environment. 1. Experiment. Fundam. Appl. Nematol. 20 (1997) 157-163
2. Anderson A.R.A., Sleeman B.A., Young I.M., and Griffiths B.S. Nematode movement along a chemical gradient in a structurally heterogeneous environment. 1. Theory. Fundam. Appl. Nematol. 20 (1997) 165-172
3. Atkinson R.P.D., Rhodes C.J., Macdonald D.W., and Anderson R.M. Scale-free dynamics in the movement patterns of jackals. OIKOS 98 (2002) 134-140
4. Barkai E. CTRW pathways to the fractional diffusion equation. Chem. Phys. (2002) 13-27 10.1016/S0301-0104(02)00533-5
5. Baudoin F., and Coutin L. Operators associated with a stochastic differential equation driven by fractional Brownian motions. Stochastic Process. Appl. 117 5 (2007) 550-574
6. Bell W.J. Searching Behaviour: The Behavioural Ecology of Finding Resources (1991), Chapman & Hall, London 358pp
7. Bengtsson G., Nilsson E., Ryden T., and Wiktorsson M. Irregular walks and loops combines in small-scale movement of a soil insect: implications for dispersal biology. J. Theor. Biol. 231 2 (2004) 299-306 10.1016/j.jtbi.2004.06.025
8. Banks H.T., Kareiva P.M., and Murphy K. Parameter-estimation techniques for interaction and redistribution models, a predator-prey example. Oecologica 74 (1987) 356-362
9. Blanche S., Casas J., Bigler F., and Janssen-van Bergeijk K.E. An individual-based model of Trichogramma foraging behaviour: parameter estimation for single female. J. Appl. Ecol. 33 (1996) 425-434
10. Bovet P., and Benhamou S. Spatial analysis of animal movement using a correlated random walk model. J. Theor. Biol. 131 (1988) 419-433 10.1016/S0022-5193(88)80038-9
11. Conradt L., Bodsworth E.J., Roper T.J., and Thomas C.D. Non-random dispersal in the butterfly Maniola jurtina: implications for metapopulation models. Proc. R. Soc. London, Ser. B-Biol. Sci. 267 (2000) 1505-1510
12. Croll N.A., and Sukhdeo M.V.K. Hierarchies in nematode behaviour. In: Zuckermann B.M., and Rohne R.A. (Eds). Plant Parasitic Nematodes vol. 3 (1981), Academic Press, New York 227-251
13. Enriquez N. A simple construction of the fractional Brownian motion. Stochastic Process. Appl. 109 (2004) 203-223 10.1016/j.spa.2003.10.008
14. Kareiva P.M., and Shigesada N. Analyzing insect movement as a correlated random walk. Oecologia 56 (1983) 234-238
15. Levandowsky M., White B.S., and Schuster F.L. Random movements of soil amebas. Acta Protozool. 36 (1997) 237-248
16. Levin S.A. Ecological and evolutionary aspects of dispersal. In: Hallam T., and Levin S.A. (Eds). Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics vol. 71 (1987), Springer, Berlin 80-87
17. Mandelbrot B.B. The Fractal Geometry of Nature (1982), W.H. Freeman et Co., New York 468pp
18. Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339 (2000) 1-77 10.1016/S0370-1573(00)00070-3
19. Metzler R., and Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A: Math. Gen. 37 (2004) 161-208
20. Metzler R., and Nonnenmacher T.F. Space- and time-fractional diffusion and wave equations, fractional Fokker-Plank equations, and physical motivation. Chem. Phys. 284 (2002) 67-90
21. Preisler H.K., Ager A.A., Johnson B.K., and Kie J.G. Modelling animal movement using stochastic differential equations. Environmetrics 15 (2004) 643-657
22. Ramos-Fernandez G., Mateos J.L., Miramontes O., Cocho G., Larralde H., and Ayala-Orozco B. Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behav. Ecol. Sociobiol. 55 (2004) 223-230 10.1007/s00265-003-0700-6
23. In: Rangarajan G., and Ding M. (Eds). Processes with Long Range Correlations: Theory and Applications. Springer Lecture Notes in Physics 621 (2003), Springer, New York 392pp
24. Raviart P.A., and Thomas J.M. Introduction a l'analyse numérique des équations aux dérivées partielles (1983), Masson, Paris 224pp
25. Revuz D., and Yor M. Continuous martingales and Brownian motion. third ed (1999), Springer, Berlin 602pp
26. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integral and Derivatives. Theory and Applications (1993), Gordon and Breach, New York 976pp
27. Shapiro D.I., and Glazer I. Comparison of entomopathogenic nematode dispersal from infected hosts versus aqueous suspension. Environ. Entomol. 25 (1996) 1455-1461
28. Stamps J.A., Buechner M., and Krishnan V.V. The effects of edge permeability and habitat geometry on immigration from patches of habitat. Am. Nat. 129 (1987) 533-552
29. Viswanathan G.M., Afanasyev V., Buldyrev S.V., Murphy E.J., Prince P.A., and Stanley H.E. Levy flight search patterns of wandering albatrosses. Nature 381 (1996) 413-415
30. Wiktorsson M., Ryden T., Nilsson E., and Bengtsson G. Modelling the movement of a soil insect. J. Theor. Biol. 231 (2004) 497-513 10.1016/j.jtbi.2004.06.024
31. Wilson M.J., Glen D.M., and George S.K. The Rhabditid nematode Phasmarhabditis hermaphrodita as a potential biological control agent for slugs. Biocontrol Sci. Technol. 3 (1993) 513-521
32. Wu H., Li B.-L., Springer T.A., and Neill W.H. Modelling animal movement as a persistent random walk in two dimensions: expected magnitude of net displacement. Ecol. Modelling 132 (2000) 115-124 10.1016/S0304-3800(00)00309-4
33. Zhang X., Johnson S.N., Crawford J.W., Gregory P.J., and Young I.M. A general random walk model for leptokurtic distribution of organisms movement: theory and application. Ecol. Modelling 200 (2007) 79-88 10.1016/j.ecolmodel.2006.07.016