A generalized stochastic approach to particle dispersal in soils and sediments

Geochimica et Cosmochimica Acta

Volumn 72, Issue 14, 2008, Pages 3460-3478

  Meysman, Filip J R ^a,b   Malyuga, Volodymyr S ^a   Boudreau, Bernard P ^c   Middelburg, Jack J ^a  

^a NETHERLANDS INSTITUTE OF ECOLOGY NIOO KNAW   (Netherlands)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^c DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ABUNDANCE; BIOTURBATION; BURROWING ORGANISM; DISPERSAL; FAUNA; MODELING; PARTICLE SETTLING; PROBABILITY; RANDOM WALK METHOD; SEDIMENT; SOIL; STOCHASTICITY;

EID: 45849149295     PISSN: 00167037     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gca.2008.04.023     Document Type: Article

References (77)

1. Aller R.C. Quantifying solute distributions in the bioturbated zone of marine-sediments by defining an average micro-environment. Geochim. Cosmochim. Acta 44 (1980) 1955-1965
2. Aller R.C. The effects of macrobenthos on chemical properties of marine sediment and overlying water. In: McCall P.L., and Tevesz M.J.S. (Eds). Animal-Sediment Relations (1982), Plenum 53-102
3. Aller R.C. Benthic fauna and biogeochemical processes in marine sediments: the role of burrow structures. In: Blackburn T.H., and Sorensen J. (Eds). Nitrogen Cycling in Coastal Marine Sediments (1988), John Wiley & Sons 301-338
4. Berg H.C. Random Walks in Biology (1993), Princeton University Press
5. Berg H.C., and Brown D.A. Chemotaxis in Escherichia coli analyzed by 3-dimensional tracking. Nature 239 (1972) 500
6. Berkowitz B., and Scher H. The role of probabilistic approaches to transport theory in heterogeneous media. Transp. Porous Media 42 (2001) 241-263
7. Berkowitz B., Cortis A., Dentz M. and Scher H. (2006) Modeling non-fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44, Art. No. RG2003.
8. Bock M.J., and Miller D.C. Particle selectivity, gut volume, and the response to a step change in diet for deposit-feeding polychaetes. Limnol. Oceanogr. 44 (1999) 1132-1138
9. Boudreau B.P. Mathematics of tracer mixing in sediments: I. Spatially-dependent, diffusive mixing. Am. J. Sci. 286 (1986) 161-198
10. Boudreau B.P. The diffusion and telegraph equations in diagenetic modeling. Geochim. Cosmochim. Acta 53 (1989) 1857-1866
11. Boudreau B.P. Mean mixed depth of sediments: the wherefore and the why. Limnol. Oceanogr. 43 (1998) 524-526
12. Boudreau B.P. The mathematics of early diagenesis: from worms to waves. Rev. Geophys. 38 (2000) 389-416
13. Boudreau B.P. Modelling mixing and diagenesis. In: Kristensen E., Kostka J.E., and Haese R.R. (Eds). Interactions Between Macro- and Microorganisms in Marine Sediments (2005), American Geophysical Union 323-340
14. Boudreau B.P., and Imboden D.M. Mathematics of tracer mixing in sediments: III. The theory of nonlocal mixing within sediments. Am. J. Sci. 287 (1987) 693-719
15. Boudreau B.P., Choi J., Meysman F., and Francois-Carcaillet F. Diffusion in a lattice-automaton model of bioturbation by small deposit feeders. J. Mar. Res. 59 (2001) 749-768
16. Brockmann D., Hufnagel L., and Geisel T. The scaling laws of human travel. Nature 439 (2006) 462-465
17. Bunzl K. Transport of fallout radiocesium in the soil by bioturbation: a random walk model and application to a forest soil with a high abundance of earthworms. Sci. Total Environ. 293 (2002) 191-200
18. Choi J., Francois-Carcaillet F., and Boudreau B.P. Lattice-automaton bioturbation simulator (Labs): implementation for small deposit feeders. Comput. Geosci. 28 (2002) 213-222
19. Codling E.A., and Hill N.A. Sampling rate effects on measurements of correlated and biased random walks. J. Theor. Biol. 233 (2005) 573-588
20. Crank J. The Mathematics of Diffusion (1975), Oxford University Press
21. Crusius J., and Kenna T.C. Ensuring confidence in radionuclide-based sediment chronologies and bioturbation rates. Estuar. Coast. Shelf Sci. 71 (2007) 537-544
22. Darwin C. The Formation of Vegetable Mould Through the Action of Worms with Observation of Their Habits (1881), John Murray
23. Delmotte S., Meysman F.J.R., Ciutat A., Boudou A., Sauvage S., and Gerino M. Cadmium transport in sediments by tubificid bioturbation: an assessment of model complexity. Geochim. Cosmochim. Acta 71 (2007) 844-862
24. Dorgan K.M., Jumars P.A., Johnson B., Boudreau B.P., and Landis E. Burrow extension by crack propagation. Nature 433 (2005) 475
25. Einstein A. Uber die von der molekularkinetischen Theorie der Warme geforderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen. Ann. d. Phys. 17 (1905) 549-560
26. Feller W. An Introduction to Probability Theory and its Applications (1968), John Wiley & Sons
27. Fernandes S., Meysman F.J.R., and Sobral P. The influence of cu contamination on nereis diversicolor bioturbation. Mar. Chem. 102 (2006) 148-158
28. Fornes W.L., Demaster D.J., and Smith C.R. A particle introduction experiment in santa catalina basin sediments: testing the age-dependent mixing hypothesis. J. Mar. Res. 59 (2001) 97-112
29. Foster D.W. BIOTURB: a Fortran program to simulate the effects of bioturbation on the vertical distribution of sediments. Comput. Geosci. 11 (1985) 39-45
30. Francois F., Poggiale J.C., Durbec J.P., and Stora G. A new approach for the modelling of sediment reworking induced by a macrobenthic community. Acta Biotheor. 45 (1997) 295-319
31. Gardiner C.W. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (2002), Springer-Verlag
32. Goldberg E.D., and Koide M. Geochronological studies of deep-sea sediments by the Io/Th method. Geochim. Cosmochim. Acta 26 (1962) 417-450
33. Guinasso N.L., and Schink D.R. Quantitative estimates of biological mixing rates in abyssal sediments. J. Geophys. Res. Ocean. Atmos. 80 (1975) 3032-3043
34. Herman P.M.J., Middelburg J.J., Van De Koppel J., and Heip C.H.R. Ecology of estuarine macrobenthos. Adv. Ecol. Res. 29 (1999) 195-240
35. Hughes B.D. Random Walks and Random Environments. vol. 1 (1995), Clarendon Press
36. Jumars P.A., Nowell A.R.M., and Self R.F.L. A simple-model of flow-sediment-organism interaction. Mar. Geol. 42 (1981) 155-172
37. Kittel C. Thermal Physics (1969), John Wiley & Sons
38. Klafter J., and Sokolov I.M. Anomalous diffusion spreads its wings. Phys. World 18 (2005) 29-32
39. Maire O., Duchene J.C., Gremare A., Malyuga V.S., and Meysman F.J.R. A comparison of sediment reworking rates by the surface deposit-feeding bivalve Abra ovata during summertime and wintertime with a comparison between two models of sediment reworking. J. Exp. Mar. Biol. Ecol. 343 (2007) 21-36
40. Matisoff G. Mathematical models of bioturbation. In: McCall R.L., and Tevesz M.J.S. (Eds). Animal-Sediment Relations (1982), Plenum Press 289-330
41. Meile C. and Van Cappellen P. (2005) Particle age distributions and O-2 exposure times: timescales in bioturbated sediments. Glob. Biogeochem. Cycle 19, Art. No. GB3013.
42. Metzler R., and Compte A. Generalized diffusion-advection schemes and dispersive sedimentation: a fractional approach. J. Phys. Chem. B 104 (2000) 3858-3865
43. Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep.-Rev. Sec. Phys. Lett. 339 (2000) 1-77
44. Meysman F.J.R., Boudreau B.P., and Middelburg J.J. Relations between local, nonlocal, discrete and continuous models of bioturbation. J. Mar. Res. 61 (2003) 391-410
45. Meysman F.J.R., Middelburg J.J., and Heip C.H.R. Bioturbation: a fresh look at Darwin's last idea. Trends Ecol. Evol. (2006) 688-695
46. Meysman F. J. R., Malyuga V. S., Boudreau B. P. and Middelburg J. J. (2008) Quantifying particle dispersal in aquatic sediments at short time scales: model selection. Aquat. Biol. (in press), doi:10.3354/ab00054.
47. Montroll E.W., and Weiss G.H. Random walks on lattices, II. J. Math. Phys. 6 (1965) 167-181
48. Murray J.D. Mathematical Biology (1998), Springer
49. Othmer H.G., Dunbar S.R., and Alt W. Models of dispersal in biological systems. J. Math. Biol. 26 (1988) 263-298
50. Pearson K. The problem of the random walk. Nature 72 (1905) 294
51. Rayleigh L. The problem of the random walk. Nature 72 (1905) 318
52. Reed D.C., Huang K., Boudreau B.P., and Meysman F.J.R. Steady-state tracer dynamics in a lattice-automaton model of bioturbation. Geochim. Cosmochim. Acta 70 (2006) 5855-5867
53. Reible D., and Mohanty S. A Levy flight-random walk model for bioturbation. Environ. Toxicol. Chem. 21 (2002) 875-881
54. Rhoads D.C. Organism-sediment relations on the muddy sea floor. Oceanogr. Mar. Biol. Ann. Rev. 12 (1974) 263-300
55. Rice D.L. Early diagenesis in bioadvective sediments-relationships between the diagenesis of beryllium-7, sediment reworking rates, and the abundance of conveyor-belt deposit-feeders. J. Mar. Res. 44 (1986) 149-184
56. Richardson L.F. Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. A 110 (1926) 709-737
57. Richter R. Fluidal-texture in sediment-Gesteinen und ober Sedifluktion uberhaupt. Notizbl. Hess. L.-Amt. Bodenforsch. 3 (1952) 67-81
58. Risken H. THe Fokker-Planck Equation: Methods of Solution and Application (1996), Springer
59. Robbins J.A., Krezoski J.R., and Mozley S.C. Radioactivity in sediments of Great Lakes-post-depositional redistribution by deposit-feeding organisms. Earth Planet. Sci. Lett. 36 (1977) 325-333
60. Ross S.M. Introduction to Probability Models (2003), Academic Press
61. Scher H., and Lax M. Stochastic transport in a disordered solid. 1 Theory. Phys. Rev. B 7 (1973) 4491-4502
62. Scher H., and Montroll E.W. Anomalous transit-time dispersion in amorphous solids. Phys. Rev. B 12 (1975) 2455-2477
63. Shull D.H. Transition-matrix model of bioturbation and radionuclide diagenesis. Limnol. Oceanogr. 46 (2001) 905-916
64. Smoluchowski M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. d. Phys. 21 (1906) 756-780
65. Soetaert K., Herman P.M.J., Middelburg J.J., Heip C., Destigter H.S., Vanweering T.C.E., Epping E., and Helder W. Modeling Pb-210-derived mixing activity in ocean margin sediments: diffusive versus nonlocal mixing. J. Mar. Res. 54 (1996) 1207-1227
66. Sokolov I.M., Klafter J., and Blumen A. Fractional kinetics. Phys. Today 55 (2002) 48-54
67. Solan M., and Wigham B.D. Biogenic particle reworking and bacterial-invertebrate interactions in marine sediments. In: Kristensen E., Kostka J.E., and Haese R.R. (Eds). Interactions Between Macro- and Microorganisms in Marine Sediments (2005), American Geophysical Union 105-124
68. Solan M., Wigham B.D., Hudson I.R., Kennedy R., Coulon C.H., Norling K., Nilsson H.C., and Rosenberg R. In situ quantification of bioturbation using time-lapse fluorescent sediment profile imaging (F-Spi), luminophore tracers and model simulation. Mar. Ecol.-Prog. Ser. 271 (2004) 1-12
69. Swift D.J.P., Stull J.K., Niedoroda A.W., Reed C.W., and Wong G.T.F. Contaminant dispersal on the palos verdes continental margin. 2. Estimates of the biodiffusion coefficient, D-B, from composition of the benthic infaunal community. Sci. Total Environ. 179 (1996) 91-107
70. Trauth M.H. Turbo: a dynamic-probabilistic simulation to study the effects of bioturbation on paleoceanographic time series. Comput. Geosci. 24 (1998) 433-441
71. 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
72. Weiss G.H. Aspects and Applications of the Random Walk (1994), North-Holland
73. Wheatcroft R.A. Conservative tracer study of horizontal sediment mixing rates in a Bathyal Basin, California Borderland. J. Mar. Res. 49 (1991) 565-588
74. Wheatcroft R.A. Time-series measurements of macrobenthos abundance and sediment bioturbation intensity on a flood-dominated shelf. Prog. Oceanogr. 71 (2006) 88-122
75. Wheatcroft R.A., Jumars P.A., Smith C.R., and Nowell A.R.M. A mechanistic view of the particulate biodiffusion coefficient-step lengths, rest periods and transport directions. J. Mar. Res. 48 (1990) 177-207
76. Yarmola E., Calabrese P.P., Chrambach A., and Weiss G.H. Interaction with the matrix: the dominant factor in macromolecular band spreading in gel electrophoresis. J. Phys. Chem. B 101 (1997) 2381-2387
77. Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys. Rep.-Rev. Sec. Phys. Lett. 371 (2002) 461-580