Mean-field stochastic theory for species-rich assembled communities

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 6 B, 2000, Pages 8466-8484

  McKane, Alan ^a   Alonso, David ^b,c   Solé, Ricard V ^b,d  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^c UNIVERSITY OF BARCELONA   (Spain)

^d SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; ECOLOGY; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

MEAN-FIELD STOCHASTIC THEORY; VAN KAMPEN APPROXIMATIONS;

ECOSYSTEMS;

BIOLOGICAL MODEL; BIOPHYSICS; ECOSYSTEM; STATISTICS; TIME;

BIOPHYSICAL PHENOMENA; BIOPHYSICS; ECOSYSTEM; MODELS, BIOLOGICAL; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 0034352136     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.8466     Document Type: Article

References (33)

1. E. C. Pielou, Mathematical Ecology, 2nd ed. (Wiley, New York, 1977), Sec. IV.
2. -γ with γ∈ (1,1.25), spanning three to four decades (S. Pueyo [17]).
3. -γ with γ∈ (1,1.25), spanning three to four decades (S. Pueyo [17]).
4. R. J. Putman, Community Ecology (Chapman and Hall, London, 1994), Chap. 3; S. L. Pimm, J. H. Lawton, and J. E. Cohen, Nature (London) 350, 699 (1991); K. Havens, Science 257, 1107 (1992); 260, 243 (1993); N. D. Martinez, ibid. 260, 242 (1993).
5. R. J. Putman, Community Ecology (Chapman and Hall, London, 1994), Chap. 3; S. L. Pimm, J. H. Lawton, and J. E. Cohen, Nature (London) 350, 699 (1991); K. Havens, Science 257, 1107 (1992); 260, 243 (1993); N. D. Martinez, ibid. 260, 242 (1993).
6. R. J. Putman, Community Ecology (Chapman and Hall, London, 1994), Chap. 3; S. L. Pimm, J. H. Lawton, and J. E. Cohen, Nature (London) 350, 699 (1991); K. Havens, Science 257, 1107 (1992); 260, 243 (1993); N. D. Martinez, ibid. 260, 242 (1993).
7. R. J. Putman, Community Ecology (Chapman and Hall, London, 1994), Chap. 3; S. L. Pimm, J. H. Lawton, and J. E. Cohen, Nature (London) 350, 699 (1991); K. Havens, Science 257, 1107 (1992); 260, 243 (1993); N. D. Martinez, ibid. 260, 242 (1993).
8. R. J. Putman, Community Ecology (Chapman and Hall, London, 1994), Chap. 3; S. L. Pimm, J. H. Lawton, and J. E. Cohen, Nature (London) 350, 699 (1991); K. Havens, Science 257, 1107 (1992); 260, 243 (1993); N. D. Martinez, ibid. 260, 242 (1993).
9. T. H. Keitt and P. A. Marquet, J. Theor. Biol. 182, 161 (1996); T. H. Keitt and H. E. Stanley, Nature (London) 393, 257 (1998).
10. T. H. Keitt and P. A. Marquet, J. Theor. Biol. 182, 161 (1996); T. H. Keitt and H. E. Stanley, Nature (London) 393, 257 (1998).
11. R. V. Solé, D. Alonso, and A. J. McKane, Physica A 286, 337 (2000).
12. E. P. Odum, Fundamentals of Ecology, 3rd ed. (Saunders, London, 1971).
13. R. M. May, Nature (London) 238, 413 (1972); T. Hogg, B. Huberman, and J. M. McGlade, Proc. R. Soc. London, Ser. B 237, 43 (1989).
14. R. M. May, Nature (London) 238, 413 (1972); T. Hogg, B. Huberman, and J. M. McGlade, Proc. R. Soc. London, Ser. B 237, 43 (1989).
15. S. L. Pimm, Food Webs (Chapman and Hall, London, 1982); D. O. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology (CRC Press, London, 1993); K. McCann and A. Hastings, Proc. R. Soc. London, Ser. B 264, 1249 (1997); A. R. Solow, C. Costello, and A. R. Beet, Am. Nat. 154, 587 (1999).
16. S. L. Pimm, Food Webs (Chapman and Hall, London, 1982); D. O. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology (CRC Press, London, 1993); K. McCann and A. Hastings, Proc. R. Soc. London, Ser. B 264, 1249 (1997); A. R. Solow, C. Costello, and A. R. Beet, Am. Nat. 154, 587 (1999).
17. S. L. Pimm, Food Webs (Chapman and Hall, London, 1982); D. O. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology (CRC Press, London, 1993); K. McCann and A. Hastings, Proc. R. Soc. London, Ser. B 264, 1249 (1997); A. R. Solow, C. Costello, and A. R. Beet, Am. Nat. 154, 587 (1999).
18. S. L. Pimm, Food Webs (Chapman and Hall, London, 1982); D. O. Logofet, Matrices and Graphs: Stability Problems in Mathematical Ecology (CRC Press, London, 1993); K. McCann and A. Hastings, Proc. R. Soc. London, Ser. B 264, 1249 (1997); A. R. Solow, C. Costello, and A. R. Beet, Am. Nat. 154, 587 (1999).
19. S. Jain and S. Krishna, Phys. Rev. Lett. 81, 5684 (1998).
20. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1981).
21. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, Berlin. 1985).
22. Handbook of Mathematical Functions, edited by M. Abramovitz and A. Stegun (Dover, New York, 1965).
23. R. H. MacArthur and E. O. Wilson, The Theory of Island Biogeography (Princeton University Press, Princeton, 1967).
24. R. M. May, Ecology and Evolution of Communities, edited by M. L. Cody and J. M. Diamond (Harvard University Press, Cambridge, MA, 1973), pp. 81-120.
25. R. A. Fisher, A. S. Corbet, and C. W. Williams, J. Anim. Ecol. 12, 42 (1943).
26. S. Engen and R. Lande, J. Theor. Biol. 178, 325 (1996).
27. S. Pueyo (unpublished).
28. F. W. Preston, Ecology 29, 254 (1948).
29. F. W. Preston, Ecology 43, 185, 410 (1962).
30. W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes. The Art of Scientific Computing, 1st ed. (Cambridge University Press, Cambridge, 1988).
31. P. J. DeVries, D. Murray, and R. Lande, Biol. J. Linnean Soc. 62, 343 (1997).
32. R. Margalef, Our Biosphere (Ecology Institute, Oldenforf/ Luhe, Germany, 1997), pp. 91-95.
33. E. Renshaw, Modelling Biological Populations in Space and Time (Cambridge University Press, Cambridge, England, 1991).