Resolving discrepancies between deterministic population models and individual-based simulations

American Naturalist

Volumn 151, Issue 2, 1998, Pages 116-134

  Wilson, William G ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Individual based models; Long range dispersal; Predator prey theory; Spatial dynamics; Stochasticity

Indexed keywords

DETERMINISTIC MODEL; INDIVIDUAL-BASED MODEL; POPULATION DYNAMICS; POPULATION MODEL; PREDATOR-PREY SYSTEM;

EID: 0031889278     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/286106     Document Type: Article

References (52)

1. Balding, D. J., and N. J. B. Green. 1989. Diffusioncontrolled reactions in one dimension: exact solutions and deterministic approximations. Physical Review A 40:4585-4592.
2. Bascompte, J., and R. V. Sole. 1995. Rethinking complexity: modelling spatiotemporal dynamics in ecology. Trends in Ecology & Evolution 10:361-366.
3. Botsford, L. W., C. L. Moloney, A. Hastings, J. L. Largier, T. M. Powell, K. Higgins, and J. F. Quinn. 1994. The influence of spatially and temporally varying oceanographic conditions on meroplanktonic metapopulations. Deep-Sea Research II, Topical Studies in Oceanography 41:107-145.
4. Brown, D. B., and R. I. C. Hansell. 1987. Convergence to an evolutionarily stable strategy in the two-policy game. American Naturalist 130:929-940.
5. Chesson, P. 1978. Predator-prey theory and variability. Annual Reviews of Systematics 9:323-347.
6. _. 1981. Models for spatially distributed populations: the effect of within-patch variability. Theoretical Population Biology 19:288-325.
7. Chesson, P. L, and R. R. Warner. 1981. Environmental variability promotes coexistence in lottery competitive systems. American Naturalist 117:923-943.
8. Comins, H. N., and M. P. Hassell. 1987. The dynamics of predation and competition in patchy environments. Theoretical Population Biology 31:393-421.
9. Crowley, P. H. 1981. Dispersal and the stability of predator-prey interactions. American Naturalist 118: 673-701.
10. de Roos, A. M., E. McCauley, and W. G. Wilson. 1991. Mobility versus density-limited predator-prey dynamics on different spatial scales. Proceedings of the Royal Society of London B, Biological Sciences 246:117-122.
11. _. In press. Pattern formation and the spatial scale of interaction between predators and their prey. Theoretical Population Biology.
12. Doi, M. 1976. Stochastic theory of diffusion-controlled reaction. Journal of Physics A 9:1479-1495.
13. Durrett, R., and S. Levin. 1994. The importance of being discrete. Theoretical Population Biology 46:363-394.
14. Garcia, O. 1983. A stochastic differential equation model for the height growth of forest stands. Biometrics 39: 1059-1072.
15. Gourley, S. A., and N. F. Britton. 1996. A predator-prey reaction-diffusion system with nonlocal effects. Journal of Mathematical Biology 34:297-333.
16. Gourley, S. A., N. F. Britton, M. A. J. Chaplain, and H. M. Byrne. 1996. Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations. Journal of Mathematical Biology 34:857-877.
17. Harada, Y., H. Ezoe, Y. Iwasa, H. Matsuda, and K. Sato. 1995. Population persistence and spatially limited social interaction. Theoretical Population Biology 48: 65-91.
18. Hastings, A. 1992. Age dependent dispersal is not a simple process: density dependence, stability, and chaos. Theoretical Population Biology 41:388-400.
19. _. 1993. Complex interactions between dispersal and dynamics: lessons from coupled logistic equations. Ecology 74:1362-1372.
20. Huston, M., D. DeAngelis, and W. Post. 1988. New computer models unify ecological theory. BioScience 38: 682-691.
21. Jansen, V. A. A. 1995. Regulation of predator-prey systems through spatial interactions: a possible solution to the paradox of enrichment. Oikos 74:384-390.
22. Kang, K., and S. Redner. 1985. Fluctuation-dominated kinetics in diffusion-controlled reactions. Physical Review A 32:435-447.
23. Kareiva, P. M. 1983. Local movement in herbivorous insects: applying a passive diffusion model to markrecapture field experiments. Oecologia (Berlin) 57: 322-327.
24. Kot, M., and W. M. Schaffer. 1986. Discrete-time growth-dispersal models. Mathematical Biosciences 80: 109-136.
25. Leslie, P. H. 1958. A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika 45:16-31.
26. Leslie, P. H., and J. C. Gower. 1960. The properties of a stochastic model for the predator-prey type of interaction between two species. Biometrika 47:219-234.
27. Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943-1967.
28. Levin, S. A., and L. A. Segel. 1985. Pattern generation in space and aspect. SIAM Review 27:45-67.
29. Lewis, M. A. 1994. Spatial coupling of plant and herbivore dynamics: the contribution of herbivore dispersal to transient and persistent "waves" of damage. Theoretical Population Biology 45:277-312.
30. Matsuda, H., N. Ogita, A. Sasaki, and K. Sato. 1992. Statistical mechanics of population: the lattice LotkaVolterra model. Progress of Theoretical Physics 88: 1035-1049.
31. May, R. M. 1973. Stability in randomly fluctuating versus deterministic environments. American Naturalist 107: 621-650.
32. _. 1974. Stability and complexity in model ecosystems. 2d ed. Princeton University Press, Princeton, N.J.
33. McCauley, E., W. G. Wilson, and A. M. de Roos. 1993. Dynamics of age-structured and spatially structured predator-prey interactions: individual-based models and population-level formulations. American Naturalist 142:412-442.
34. _. 1996. Dynamics of age-structured predator-prey populations in space: asymmetrical effects of mobility in juvenile and adult predators. Oikos 76:485-497.
35. McLaughlin, J. F., and J. Roughgarden. 1992. Predation across spatial scales in heterogeneneous environments. Theoretical Population Biology 31:277-299.
36. Metz, J. A. J., and A. M. de Roos. 1992. The role of physiologiclly structured population models within a general individual-based modeling perspective. Pages 88-111 in D. L. DeAngelis and L. J. Gross, eds. Individual-based models and approaches in ecology. Chapman & Hall, New York.
37. Murray, J. D. 1989. Mathematical biology. Biomathematics, vol. 19. Springer, Berlin.
38. Nisbet, R. M., and W. S. C. Gurney. 1982. Modelling fluctuating populations. Wiley, New York.
39. Nisbet, R. M., S. Diehl, W. G. Wilson, S. D. Cooper, D. D. Donalson, and K. Kratz. In press. Primary productivity gradients and short-term population dynamics in open systems. Ecological Monographs.
40. Okubo, A. 1980. Diffusion and ecological problems: mathematical models. Biomathematics, vol. 10. Springer, Berlin.
41. Poole, R. W. 1974. A discrete time stochastic model of a two prey, one predator species interaction. Theoretical Population Biology 5:208-228.
42. Roff, D. A. 1974a. Spatial heterogeneity and the persistence of populations. Oecologia (Berlin) 15:245-258.
43. _. 1974b The analysis of a population model demonstrating the importance of dispersal in a heterogeneous environment. Oecologia (Berlin) 15:259-275.
44. Ruxton, G. D., and P. Rohani. 1996. The consequences of stochasticity for self-organized spatial dynamics, persistence and coexistence in spatially extended host-parasitoid communities. Proceedings of the Royal Society of London B, Biological Sciences 263:625-631.
45. Skellam, J. G. 1951. Random dispersal in theoretical populations. Biometrika 38:196-218.
46. Turchin, P. 1989. Population consequences of aggregative movement. Journal of Animal Ecology 58:75-100.
47. Turing, A. M. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London B, Biological Sciences 237:37-72.
48. Weinberger, H. F. 1978. Asymptotic behavior of a model in population genetics. Lecture Notes in Mathematics 648:47-95.
49. Wilson, W. G. 1996. Lotka's game in predator-prey theory: linking populations to individuals. Theoretical Population Biology 50:368-393.
50. Wilson, W. G., and R. M. Nisbet. 1997. Cooperation and competition along smooth environmental gradients. Ecology 78:2004-2017.
51. Wilson, W. G., A. M. de Roos, and E. M. McCauley. 1993. Spatial instabilities within the diffusive LotkaVolterra system: individual-based simulation results. Theoretical Population Biology 43:91-127.
52. Wilson, W. G., E. McCauley, and A. M. de Roos. 1995. Effect of dimensionality on Lotka-Volterra predatorprey dynamics: individual-based simulation results. Bulletin of Mathematical Biology 57:507-526.