Characteristic length scales of spatial models in ecology via fluctuation analysis

Philosophical Transactions of the Royal Society B: Biological Sciences

Volumn 352, Issue 1361, 1997, Pages 1589-1601

  Keeling, M J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FLUCTUATION ANALYSIS; SCALE; SPATIAL MODEL;

EID: 0031448941     PISSN: 09628436     EISSN: None     Source Type: Journal    
DOI: 10.1098/rstb.1997.0143     Document Type: Article

References (31)

1. Casdagli, M. 1989 Nonlinear prediction of chaotic time series. Physica D35, 335-356.
2. Crawley, M. J. & May, R. M. 1987 Population dynamics and plant community structure: competition between annuals and perennials. J. Theor. Biol. 125, 475-489.
3. Czárán, T. & Bartha, S. 1992 Spatio-temporal dynamic models of plant populations and communities. Trends Ecol Evol. 7, 38-42.
4. DeRoos, A. M., McCauley, E. & Wilson, W. G. 1991 Mobility versus density-limited predator-prey dynamics on different spatial scales. Proc. R. Soc. Lond. B246, 117-122.
5. De Masi, A. & Presutti, E. Mathematical methods for hydrodynamic limits, Springer Lecture Notes in Mathematics 1501. New York: Springer.
6. Durrett, R. & Levin, S. A. 1994a Stochastic spatial models - a user's guide to ecological applications. Phil. Trans. R. Soc. Lond. B343, 329-350.
7. Durrett, R. & Levin, S. A. 19946 The importance of being discrete and spatial. Theor. Popul. Biol. 46, 363-394.
8. Hassell, M. P., Comins, H. N. & May, R. M. 1991 Spatial structure and chaos in insect population dynamics. Nature 353, 255-258.
9. Hendry, R. J. & McGlade, J. M. 1995 The role of memory in ecological systems. Proc. R. Soc. Lond. B259, 153-159.
10. Hendry, R. J., McGlade, J. M. & Weiner, J. 1996 A coupled map lattice model of the growth of plant monocultures. Ecol. Model. 84, 81-90.
11. Ibragimov, I. A. & Linnik, Y. V. 1971 Independent and stationary sequences of random variables. Groningen: Wblters-Noordhoff.
12. Keeling, M. J. & Rand, D. A. 1997 Space and fluctuations in the dynamics of infection. In From finite to infinite dimensional dynamical systems (ed. P. Glendinning). Amsterdam: Kluwer.
13. Keeling, M. J. 1997 Spatial models of interacting populations. In Theoretical ecology. Advances in principles and applications (ed. J. McGlade). London: Blackwell.
14. Levin, S. A. 1992 The problem of pattern and scale in ecology. Ecology 73, 1943-1967.
15. Levin, S. A. & Durrett, R. 1996 From individuals to epidemics. Phil. Trans. R. Soc. Lond. B351, 1615-1621.
16. Liggett 1985 Interacting particle systems. Berlin: Springer.
17. McGlade, J. 1995 Dynamics of complex ecologies. In Modelling the dynamics of biological systems (ed. E. Mosekilde & O. G. Mouritsen), Springer series in Synergetics 65. Berlin: Springer.
18. Mezić, I. 1997 FKG inequalities in cellular automata and coupled map lattices. Physica D (In the press.)
19. Mueller, C. & Tribe, R. 1994 A phase-transition for a stochastic PDE related to the contact process. Prob. Theory Related Fields 100, 131-156.
20. Mueller, C. & Tribe, R. 1995 Stochastic PDEs arising from the long-range contact and long-range voter processes. Prob. Theory Related Fields 102, 519-545.
21. Newman, C. M. 1980 Normal fluctuations and the FKG inequalities. Comm. Math. Phys. 74, 119-128.
22. Rand, D. A. 1994 Measuring and characterising spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies. Phil. Trans. R. Soc. Lond. A348, 497-514.
23. Rand, D. A., Keeling, M. J. & Wilson, H. B. 1995 Invasion, stability and evolution to criticality in spatially extended artificial host-pathogen systems. Proc. R. Soc. Lond. B259, 55-63.
24. Rand, D. A. & Wilson H. B. 1995 Using spatio-temporal chaos and intermediate scale determinism in artificial ecologies to quantify spatially extended systems. Proc. R. Soc. Lond. B259, 111-117.
25. Sinai, Y. G. 1976 Self-similar probability distributions. Theory Prob. Applic. 21, 64-80.
26. Solé, R. V. & Valls, J. 1991 Order and chaos in a 2D Lotka-Volterra coupled map lattice. Phys. Lett. 153A, 330-336.
27. Spohn, H. 1991 Large scale dynamics of interacting particles. Berlin: Springer.
28. Tribe, R. 1995 Large time behaviour of interface solutions to the heat-equation with Fisher-Wright white noise. Prob. Theory Related Fields 102, 289-311.
29. Weiner, J. & Conte, P. T. 1981 Dispersal and neighbourhood effects in an annual plant competition model. Ecol. Model 13, 131-147.
30. Wiens, J. A. 1989 Spatial scaling in ecology. Funct. Ecol. 3, 385-397.
31. Wissel, C. 1991 A model for the mosaic-cycle concept. In The mosaic-cycle concept of ecosystems, Springer Ecological Studies 85 (ed. H. Remmert), pp. 22-45. Berlin: Springer.