Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem

Bulletin of Mathematical Biology

Volumn 71, Issue 4, 2009, Pages 863-887

  Morozov, Andrew ^a   Petrovskii, Sergei ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Biological control; Excitability; Excitable system; Holling type III; Pattern formation; Predator prey system

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL PEST CONTROL; COMPUTER SIMULATION; ECOSYSTEM; METHODOLOGY; POPULATION DYNAMICS; PREDATION;

ANIMALS; COMPUTER SIMULATION; ECOSYSTEM; MODELS, BIOLOGICAL; PEST CONTROL, BIOLOGICAL; POPULATION DYNAMICS; PREDATORY BEHAVIOR;

EID: 64449084527     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9385-3     Document Type: Article

References (58)

1. D. Alonso F. Bartumeus J. Catalan 2002 Mutual interference between predators can give rise to Turing spatial patterns Ecology 83 28 34
2. A.J. Belsky 1986 Population and community processes in a mosaic grassland in the Serengeti, Tanzania J. Ecol. 74 841 856
3. C.J. Briggs M.F. Hoopes 2004 Stabilizing effects in spatial parasitoid-host and predator-prey models: a review Theor. Popul. Biol. 65 299 315
4. P.A. Brodmann C.V. Wilcox S. Harrison 1997 Mobile parasitoids may restrict the spatial spread of an insect outbreak J. Anim. Ecol. 66 65 72
5. Cosper, E.M., Bricelj, V.M., Carpenter, E.J., 1989. Novel Phytoplankton Blooms. Coastal and Estuarine Studies, vol. 35. Springer, Berlin.
6. P. Couteron O. Lejeune 2001 Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model J. Ecol. 89 616 628
7. Crawley, M.J., 1997. Plant-herbivore dynamics. In: Crawley, M.J. (Ed.), Plant Ecology, pp. 463-465. Blackwell, Oxford.
8. A.M. Edwards J. Brindley 1999 Zooplankton mortality and the dynamical behavior of plankton population models Bull. Math. Biol. 61 202 239
9. B. Ermentrout X. Chen Z. Chen 1997 Transition fronts and localized structures in bistable reaction-diffusion equations Physica D 108 147 167
10. W.F. Fagan M.A. Lewis M.G. Neubert P. van den Driessche 2002 Invasion theory and biological control Ecol. Lett. 5 148 157
11. A. Ferran L. Guige R. Tourniaire J. Gambier D. Fournier 1998 An artificial non-flying mutation to improve the efficiency of the ladybird Harmonia axyridis in the biological control of aphids Biocontrol 43 53 64
12. P.C. Fife 1976 Pattern formation in reacting and diffusing systems J. Chem. Phys. 64 554 564
13. P. Franks 2001 Phytoplankton blooms in a fluctuating environment: the roles of plankton response time scales and grazing J. Plankt. Res. 23 1433 1441
14. W.S.C. Gurney A.R. Veitch I. Cruickshank G. McGeachin 1998 Circles and spirals: population persistence in a spatially explicit predator-prey model Ecology 79 2516 2530
15. S. Harrison 1997 Persistent localized outbreaks in the western tussock moth (Orgyia vetusta): the roles of resource quality, predation and poor dispersal Ecol. Entomol. 22 158 166
16. Hajek, A., 2004. Natural Enemies: An Introduction to Biological Control. Cambridge University Press, Cambridge.
17. A. Hastings S. Harisson K. McCann 1997 Unexpected spatial patterns in an insect outbreak match a predator diffusion model Proc. R. Soc. Lond. B 264 1837 1840
18. P.R. Hosseini 2006 Pattern formation and individual-based models: the importance of understanding individual-based movement Ecol. Model. 194 357 371
19. A.F. Hunter G. Dwyer 1998 Outbreaks and interacting factors: insect population explosions synthesized and dissected Integr. Biol. 1 166 177
20. K. Krischer A. Mikhailov 1994 Bifurcation to travelling spots in reaction-diffusion systems Phys. Rev. Lett. 73 3165 3168
21. B. Lindner J. García-Ojalvo A. Neiman L. Schimansky-Geier 2004 Effects of noise in excitable systems Phys. Rep. 392 321 424
22. Lotka, A.J., 1925. Elements of Physical Biology. Williams and Wilkins, Baltimore.
23. D. Ludwig D.D. Jones C.S. Holling 1978 Qualitative analysis of insect outbreak systems: the spruce budworm and forest J. Anim. Ecol. 47 315 332
24. Malchow, H., Petrovskii, S.V., Venturino, E., 2008. Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulations. Chapman & Hall/CRC Press, London.
25. May, R.M., 1974. Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton.
26. P. McEvoy C. Cox E. Coombs 1991 Successful biological control of Ragwort, Senecio Jacobaea, by introduced insects in Oregon Ecol. Appl. 1 430 442
27. Z. Mendel F. Assael S. Zeidan A. Zehavi 1998 Classical biological control of Palaeococcus fuscipennis (Burmeister) (Homoptera: Margarodidae) in Israel Biol. Control 12 151 157
28. M. Mimura M. Tabata Y. Hosono 1980 Multiple solutions of two-point boundary value problem of Neumann type with a small parameter SIAM J. Math. Anal. 11 613 631
29. A.Y. Morozov S.V. Petrovskii B.-L. Li 2006 Spatiotemporal complexity of the patchy invasion in a predator-prey system with the Allee effect J. Theor. Biol. 238 18 35
30. A.Y. Morozov S. Ruan B.L. Li 2008 Patterns of patchy spread in multi-species reaction-diffusion models Ecol. Complex. 5 313 328
31. C.B. Muratov 1996 Self-replication and splitting of domain patterns in reaction-diffusion systems with the fast inhibitor Phys. Rev. E 54 3369 3376
32. C.B. Muratov V.V. Osipov 1996 General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems Phys. Rev. E 53 3101 3116
33. C.B. Muratov V.V. Osipov 1996 Scenarios of domain pattern formation in a reaction-diffusion system Phys. Rev. E 54 4860 4879
34. Murray, J.D., 1989. Mathematical Biology. Springer, Berlin.
35. Nisbet, R.M., Gurney, W.S.C., 1982. Modelling Fluctuating Populations. Wiley, Chichester.
36. M. Pascual 1993 Diffusion-induced chaos in a spatial predator-prey system Proc. R. Soc. Lond. B 251 1 7
37. M. Pascual H. Caswell 1997 Environmental heterogeneity and biological pattern in a chaotic predator-prey system J. Theor. Biol. 185 1 13
38. J.E. Pearson 1993 Complex patterns in a simple system Science 261 189 192
39. S.V. Petrovskii B.-L. Li 2001 Increased coupling between sub-populations in a spatially structured environment can lead to population outbreaks J. Theor. Biol. 212 549 562
40. Petrovskii, S.V., Li, B.-L., 2006. Exactly Solvable Models of Biological Invasion. Chapman & Hall/CRC Press, London.
41. S.V. Petrovskii H. Malchow 1999 A minimal model of pattern formation in a prey-predator system Math. Comput. Model. 29 49 63
42. S.V. Petrovskii H. Malchow 2001 Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics Theor. Popul. Biol. 59 157 174
43. S.V. Petrovskii A.Y. Morozov E. Venturino 2002 Allee effect makes possible patchy invasion in a predator-prey system Ecol. Lett. 5 345 352
44. S.V. Petrovskii H. Malchow F. Hilker E. Venturino 2005 Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control Biol. Invasions 7 771 793
45. P.M. Room K.L.S. Harley I.W. Forno D.P.A. Sands 1981 Successful biological control of the floating weed salvinia Nature 294 78 80
46. N. Sapoukhina Y. Tyutyunov R. Arditi 2003 The role of prey-taxis in biological control: a spatial theoretical model Am. Nat. 162 61 76
47. M. Scheffer 1991 Fish and nutrients interplay determines algal biomass: a minimal model Oikos 62 271 282
48. Scheffer, M., 1998. Ecology of Shallow Lakes. Chapman & Hall, London.
49. L.A. Segel J.L. Jackson 1972 Dissipative structure: an explanation and an ecological example J. Theor. Biol. 37 545 559
50. J.A. Sherratt M.A. Lewis A.C. Fowler 1995 Ecological chaos in the wake of invasion Proc. Natl. Acad. Sci. USA 92 2524 2528
51. J.A. Sherratt M.J. Smith 2008 Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models Interface 5 483 505
52. Shigesada, N., Kawasaki, K., 1997. Biological Invasions: Theory and Practice. Oxford University Press, Oxford.
53. Smayda, T.J., Shimuza, Y. (Eds.), 1993. Toxic Phytoplankton Blooms in the Sea. Elsevier, Amsterdam.
54. Thomas, J., 1995. Numerical Partial Differential Equations: Finite Difference Methods. Texts in Applied Mathematics, vol. 22. Springer, New York.
55. J.E. Truscott J. Brindley 1994 Ocean plankton populations as excitable media Bull. Math. Biol. 56 981 998
56. J.E. Truscott J. Brindley 1994 Equilibria, stability and excitability in a general class of plankton population models Philos. Trans. R. Soc. Lond. A 347 703 718
57. V. Volterra 1926 Fluctuations in the abundance of a species considered mathematically Nature 118 558 560
58. L.P. White 1970 Brousse tigrée patterns in Southern Niger J. Ecol. 58 549 553