How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?

Ecological Research

Volumn 21, Issue 3, 2006, Pages 334-345

  Kawasaki, Kohkichi ^a   Takasu, Fugo ^b   Caswell, Hal ^c   Shigesada, Nanako ^a  

^a DOSHISHA UNIVERSITY   (Japan)

^b NARA WOMEN'S UNIVERSITY   (Japan)

^c WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

Biological invasion; Cellular automaton; Long distance dispersal; Stochastic colonization; Stratified diffusion

Indexed keywords

CELLULAR AUTOMATON; COLONIZATION; EMPIRICAL ANALYSIS; NUMERICAL MODEL; STOCHASTICITY;

EID: 33746434353     PISSN: 09123814     EISSN: 14401703     Source Type: Journal    
DOI: 10.1007/s11284-006-0166-x     Document Type: Review

References (56)

1. Andow D, Kareiva P, Levin S, Okubo A (1990) Spread of invading organisms. Landscape Ecol 4:177-188
2. Andow D, Kareiva P, Levin S, Okubo A (1993) Spread of invading organisms: patterns of spread. In: Kim KC (ed) Evolution of insect pests: the pattern of variations. Wiley, New York, pp 219-242
3. Broadbent SR, Kendall DG (1953) The random walk of Trichostrongylus retortaeformis. Biometrics 9:460-466
4. Buttel L, Durrett R, Levin S (2002) Competition and species packing in patchy environments. Theor Popul Biol 61:265-276
5. Cannas AS, Marco DE, Paez SA (2003) Modelling biological invasions: species traits, species interactions, and habitat heterogeneity. Math Biosci 183:93-110
6. Caswell H, Cohen JE (1991) Disturbance, interspecific interaction and diversity in metapopulations. Biol J Linn Soc 42:193-218
7. Caswell H, Etter RJ (1992) Ecological interactions in patchy environments: from patch-occupancy models to cellular automata. In: Levin SA, Powell TM, Steele JH (eds) Patch dynamics. Springer, Berlin Heidelberg New York, pp 93-109
8. Caswell H, Etter RJ (1999) Cellular automaton models for competition in patchy environments: facilitation, inhibition, and tolerance. Bull Math Biol 61:625-649
9. Chave J, Muller-Landau HC, Levin SA (2002) Comparing classical community models: theoretical consequences for patterns of diversity. Am Nat 159:1-23
10. Clark JS (1998) Why trees migrate so fast: confronting theory with dispersal biology and the paleorecord. Am Nat 152:204-224
11. Clark JS, Lewis M, Horvath L (2001) Invasion by extremes: population spread with variation in dispersal and reproduction. Am Nat 157:537-554
12. Durrett R (1988) Lectures on particle systems and percolation. Wadsworth & Brooks/Cole, Pacific Grove, CA
13. Durrett R, Levin S (1994a) Stochastic spatial models: a user's guide to ecological applications. Philos Trans R Soc Lond B 343:329-350
14. Durrett R, Levin SA (1994b) The importance of being discrete (and spatial). Theor Popul Biol 46:363-394
15. Durrett R, Levin S (1998) Spatial aspects of interspecific competition. Theor Popul Biol 53:30-43
16. Eden M (1961) A two dimensional growth process. In: Neyman J (ed) Proceedings of Fourth Berkeley Symposium on Math, Statistics and Probability. University of California Press, Berkeley, CA, pp 223-239
17. Ellner SP, Sasaki A, Haraguchi Y, Matsuda H (1998) Speed of invasion in lattice population models: pair-edge approximation. J Math Biol 36:469-484
18. Etter RJ, Caswell H (1994) The advantages of dispersal in a patchy environment: effects of disturbance in a cellular automaton model. In: Eckelbarger KJ, Young CM (eds) Reproduction, larval biology and recruitment in the deep-sea benthos. Columbia University Press, New York, pp 285-305
19. Filipe JAN, Maule MM (2004) Effects of dispersal mechanisms on spatio-temporal development of epidemics. J Theor Biol 226:125-141
20. Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugen (Lond) 7:255-369
21. Harada Y, Iwasa Y (1994) Lattice population dynamics for plants with dispersing seeds and vegetative propagation. Res Popul Ecol 36:237-249
22. Harada Y, Ezoe H, Iwasa Y, Matsuda H, Sato K (1995) Population persistence and spatially limited social interaction. Theor Popul Biol 48:65-91
23. Hassell MP, Comins HN, May RM (1991) Spatial structure and chaos in insect population dynamics. Nature 353:255-258
24. Hengeveld R (1989) Dynamics of biology invasions. Chapman & Hall, London
25. Higgins SI, Nathan R, Cain ML (2003) Are long-distance dispersal events in plants usually caused by nonstandard means of dispersal? Ecology 84:1945-1956
26. Kot M, Lewis MA, van den Driessche P (1996) Dispersal data and the spread of invading organisms. Ecology 77:2027-2042
27. Kot M, Medlock J, Reluga T, Walton DB (2004) Stochasticity, invasions, and branching random walks. Theor Popul Biol 66:175-184
28. Kubo T, Iwasa Y, Furumoto N (1996) Forest spatial dynamics with gap expansion: total gap area and gap size distribution. J Theor Biol 180:229-246
29. Levin S (1992) The problem of pattern and scale in ecology: the Robert H MacArthur Award Lecture. Ecology 73:1943-1967
30. Levin SA, Durrett R (1997) From individuals to epidemics. Philos Trans R Soc Lond B 351:1615-1621
31. Lewis MA (2000) Spread rate for a nonlinear stochastic invasion. J Math Biol 41:430-454
32. Lewis MA, Pacala S (2000) Modeling and analysis of stochastic invasion processes. J Math Biol 41:387-429
33. Metz JAJ, Mollison D, van den Bosch F (2000) The dynamics of invasion waves. In: Dieckmann U, Law R, Metz JAJ (eds) The geometry of ecological interactions simplifying spatial complexity. Cambridge University Press, Cambridge, pp 482-512
34. Mollison D (1977) Spatial contact model for ecological and epidemic spread. J R Stat Soc 39:283-326
35. Mollison D, Kuulasmaa K (1985) Spatial epidemic models: theory and simulations. In: Bacon PJ (ed) Population dynamics of rabies in wildlife. Academic, London, pp 291-309
36. Nakamaru M, Levin SA (2004) Spread of two linked social norms on complex interaction networks. J Theor Biol 230:57-62
37. Nakamaru M, Matsuda H, Iwasa Y (1996) The evolution of cooperation in a lattice-structured population. J Theor Biol 184:65-81
38. Neubert MG, Caswell H (2000) Demography and dispersal: calculation and sensitivity analysis of invasion speed for structured populations. Ecology 81:1613-1628
39. Nowak MA, May RM, Sigmund K (1995) The arithmetics of mutual help. Sci Am 272(6):76-81
40. Okubo A (1980) Diffusion and ecological problems: mathematical models. Springer, Berlin Heidelberg New York
41. Okubo A, Levin S (2001) Diffusion and ecological problems: new perspectives, 2nd edn. Springer, Berlin Heidelberg New York
42. Petrovskii SV, Malchow H, Hilker FM, Venturino E (2005) Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biol Invasions 7:771-793
43. Richardson D (1973) Random growth in a tessellation. Proc Camb Philos Soc 74:515-528
44. Satake A, Iwasa Y, Hakoyama H, Hubbell SP (2004) Estimating local interaction from spatiotemporal forest data, and Monte Carlo bias correction. J Theor Biol 226:225-235
45. Sato K, Matsuda H, Sasaki A (1994) Pathogen invasion and host extinction in lattice structured populations. J Math Biol 32:251-268
46. Shaw MW (1994) Modeling stochastic processes in plant pathology. Annu Rev Phytopathol 32:523-544
47. Shigesada N (1980) Spatial distribution of dispersing animals. J Math Biol 9:85-96
48. Shigesada N, Kawasaki K (1997) Biological invasions: theory and practice. Oxford University Press, Oxford
49. Shigesada N, Kawasaki K (2002) Invasion and species range expansion: effects of long-distance dispersal. In: Bullock J, Kenward R, Hails R (eds) Dispersal ecology. Blackwell, Oxford, pp 350-373
50. Shigesada N, Kawasaki K, Takeda Y (1995) Modeling stratified diffusion in biological invasions. Am Nat 146:229-251
51. Skellam JG (1951) Random dispersal in theoretical populations. Biometrika 38:196-218
52. Snyder RE (2003) How demographic stochasticity can slow biological invasions. Ecology 84:1333-1339
53. Tainaka K (1988) Lattice model for the Lotka-Volterra system. J Phys Soc Jpn 57:2588-2590
54. Tilman D, Lehman LL, Yin C (1997) Habitat destruction, dispersal, and deterministic extinction in competitive communities. Am Nat 149:407-435
55. Van den Bosch F, Hengeveld R, Metz JAJ (1992) Analyzing the velocity of animal range expansion. J Biogeogr 19:135-150
56. Williamson M (1996) Biological invasions. Chapman & Hall, London