A theoretical framework for abundance distributions in complex systems

Complexity International

Volumn 6, Issue , 1998, Pages

  Halloy, Stephan R P ^a  

^a THE NEW ZEALAND INSTITUTE FOR PLANT AND FOOD RESEARCH LIMITED   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

AGRICULTURE; BIODIVERSITY; COMPUTER SIMULATION; ECOSYSTEMS; HEALTH; MATHEMATICAL MODELS; PLANNING;

DIVERSIFICATION; LOGNORMAL FUNCTIONS; NATURAL SYSTEMS; POLO DISTRIBUTION;

LARGE SCALE SYSTEMS;

EID: 0141811292     PISSN: 13200682     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. W. B. Arthur. Increasing Returns and Path Dependence in the Economy. University of Michigan Press, Ann Arbor, 1994.
2. P. Bak. How Nature Works: The Science of Self-Organized Criticality. Oxford UP, Oxford, 1997.
3. P. Bak, C. Tang, and K. Wiesenfeld. Self-organized criticality. Phys. Rev. A, 38(1):364-374, 1988.
4. N.D. Barlow. Size distributions of butterfly species and the effect of latitude on species sizes. Oikos, 71:326-332, 1994.
5. E. R. Berlekamp, J. H. Conway, and R. K. Guy. What is life? In Winning Ways for Your Mathematical Plays, volume 2. Academic Press, London, 1982.
6. J.H. Brown and B.A. Maurer. Macroecology: the division of food and space among species on continents. Science, 243:1145-1150, 1989.
7. J.H. Brown and P.F. Nicoletto. Spatial scaling of species composition: Body masses of North American land mammals. Am. Nat., 138:1478-1512, 1991.
8. M. Chown. Anything goes. New Scientist, 158(2137):26-30, 1998.
9. S. Cuperman, A. Harten, and M. Lecar. A phase-space boundary integration of the Vlasov equation for collisionless one-dimensional stellar systems. Astrophys. and Space Sci., 13:411-424, 1971.
10. S. Douady and Y. Couder. Phyllotaxis as a physical self-organized growth process. Phys. Rev. Lett., 68:2098-2101, 1992.
11. S. Frontier. Diversity and structure in aquatic ecosystems. Oceanography and Marine Biology Annual Review, 23:253-312, 1985.
12. S. Halloy. Long term trends in the relative abundance of New Zealand agricultural plants. Otago Conference Series, 2:125-141, 1994.
13. S. Halloy. Indicadores de perturbación de ecosistemas: Especies claves y estructura de biodiversidad. In M. Liberman and C. Baied, editors, Desarrollo Sostenible de Ecosistemas de Montaña: Manejo de Areas Frágiles en los Andes, pages 73-81. UNU y PL-480, La Paz, Bolivia, 1997.
14. S. Halloy. The dynamic contribution of new crops to the agricultural economy - is it predictable? In Proceedings of the Fourth National New Crops Symposium, Phoenix, Arizona, 1998.
15. S. Halloy and A.F. Mark. Comparative leaf morphology spectra of plant communities in New Zealand, the Andes and the Alps. J. Royal Soc. NZ, 26(1):41-78, 1996.
16. G.E. Hutchinson and R. MacArthur. A theoretical ecological model of size distributions among species of animals. Am. Nat., 93:117-126, 1959.
17. S.A. Kauffman. The Origins of Order. Oxford UP, New York, 1993.
18. P.G. Kevan, C. F. Greco, and S. Belaousoff. Log-normality of biodiversity and abundance in diagnosis and measuring of ecosystemic health: Pesticide stress on pollinators on blueberry heaths. J. Applied Ecology, 34:1122-1136, 1997.
19. D.R. Lockwood and J.A. Lockwood. Evidence of self-organized criticality in insect populations. Complexity, 2(4):49-58, 1997.
20. R. H. MacArthur. On the relative abundance of bird species. Proc. Nat. Acad. Sci. USA, 43:293-295, 1957.
21. R.H. MacArthur. On the relative abundance of species. Am. Nat., 94:25-36, 1960.
22. A.E. Magurran. Ecological Diversity and its Measurement. Princeton UP, Princeton, New Jersey, 1988.
23. B.B. Mandelbrot. The Fractal Geometry of Nature. W.H. Freeman, N.Y., 1983.
24. R.M. May. The dynamics and diversity of insect faunas. In L.A. Mound and N. Waloff, editors, Diversity of Insect Faunas, pages 188-204. Blackwell, Oxford, 1978.
25. C. Pahl-Wostl. The Dynamic Nature of Ecosystems. Chaos and Order Entwined. John Wiley, Chichester, 1995.
26. F.W. Preston. The commonness, and rarity, of species. Ecology, 29:254-283, 1948.
27. F.W. Preston. The canonical distribution of commonness and rarity. Ecology, 43:185-215,410-432, 1962.
28. F.W. Preston. Noncanonical distributions of commonness and rarity. Ecology, 61:88-97, 1980.
29. C. Raunkiaer. The Life Form of Plants and Statistical Plant Geography. Clarendon, Oxford, 1934.
30. G. B. Rybicki. Exact statistical mechanics of a one-dimensional self-gravitating system. Astrophys. Space Sci., 14:56-72, 1971.
31. R.L. Schmoyer, J.J. Beauchamp, C.C. Brandt, and P.O. Hoffman, Jr. Difficulties with the lognormal model in mean estimation and testing. Environ. and Ecol. Stat., 3 (1):81-97, 1998.
32. J. Soderlund, L.B. Kiss, G.A. Niklasson, and C.G. Granqvist. Lognormal size distributions in particle growth processes without coagulation. Phys. Rev. Lett., 1998. in press.
33. R. V. Sole and D. Alonso. Random walks, fractals and the origins of rainforest diversity. Working Papers 98-07-060, Santa Fe Institute, 1998.
34. G. Sugihara. Minimal community structure: an explanation of species abundance patterns. Am. Nat., 116:770-787, 1980.
35. Max Tegmark. Is the "Theory of Everything" merely the ultimate ensemble theory? http://www.sns.ias.edu/~max/toe.html, 1997.
36. R. Tokeshi. Species abundance patterns and community structure. Adv. Ecol. Res., 24:111-195, 1993.
37. G.B. West, J.H. Brown, and B.J. Enquist. A general model for the origin of allometric scaling laws in biology. Science, 276:122-126, 1997.
38. A. Wuensche and M. Lesser. The Global Dynamics of Cellular Automata - An Atlas of Basin of Attraction Fields of One-Dimensional Cellular Automata. Addison-Wesley, Reading, Mass., 1992.
39. K. R. Yawn and B. N. Miller. Ergodic properties and equilibrium of one-dimensional self-gravitating systems. Phys. Rev. E, 56:2429-2436, 1997.
40. G.K. Zipf. Human Behavior and the Principle of Least Effort - An Introduction to Human Ecology. Addison-Wesley, Cambridge, Mass., 1949.