Simpson diversity and the Shannon-Wiener index as special cases of a generalized entropy

Oikos

Volumn 109, Issue 1, 2005, Pages 203-207

  Keylock, C J ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; SPECIES DIVERSITY; STATISTICAL ANALYSIS;

EID: 17144428129     PISSN: 00301299     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0030-1299.2005.13735.x     Document Type: Review

References (34)

1. Aoki, I. 1995. Diversity and rank-abundance relationship concerning biotic compartments. - Ecol. Model. 82: 21-26.
2. Brown, J. H., Gupta, V. J., Li, B. et al. 2002. The fractal nature of nature: power-laws, ecological complexity and biodiversity. - Philos. Trans. R. Soc. B. 357: 619-626.
3. Condit, R., Pitman, N., Leigh Jr, E. G. et al. 2002. Beta diversity in tropical forest trees. - Science 295: 666-669.
4. Curado, E. M. F. and Tsallis, C. 1991. Generalized statistical mechanics-connection with thermodynamics. - J. Phys. A-Math. Gen. 24: L69-L72.
5. Denisov, S. 1997. Fractal binary sequences: Tsallis thermodynamics and the Zipf law. - Phys. Lett. A 235: 447-451.
6. Frontier, S. 1985. Diversity and structure in aquatic ecosystems. - Mar. Biol. Annu. Rev. 23: 253-312.
7. Harte, J., Kinzig, A. P. and Green, J. 1999. Self-similarity in the distribution and abundance of species. - Science 284: 334-336.
8. Hill, M. O. 1973. Diversity and evenness: a unifying notation and its consequences. - Ecology 54: 427-432.
9. Hubbell, S. P. 2001. The unified neutral theory of biodiversity and biogeography. - Princeton Univ. Press.
10. Lande, R. 1996. Statistics and partitioning of species diversity, and similarity among multiple communites. - Oikos 76: 5-13.
11. Lande, R., DeVries, P. J. and Walla, T. R. 2000. When species accumulation curves intersect: implications for ranking diversity using small samples. - Oikos 89: 601-605.
12. Lewontin, R. C. 1972. The apportionment of human diversity. - Evol. Biol. 6: 381-398.
13. Li, B.-L. 2000. Fractal geometry applications in description and analysis of patch patterns and patch dynamics. - Ecol. Model. 132: 33-50.
14. Ludwig, J. A. and Reynolds, J. F. 1988. Statistical ecology. A primer on methods and computing. - Wiley.
15. May, R. M. 1975. Patterns of species abundance and diversity. - In: Cody, M. L. and Diamond, J. M. (eds), Ecology and evolution of communities. Harvard Univ. Press, pp. 81-120.
16. McGill, B. J. 2003. A test of the unified neutral theory of biodiversity. - Nature 422: 881-885.
17. Montemurro, M. A. 2001. Beyond the Zipf-Mandelbrot law in quantitative linguistics. - Physica A 300: 567-578.
18. Mouillot, D. and Leprêtre, A. 1999. A comparison of species diversity estimators. - Res. Popul. Ecol. 41: 203-215.
19. Okland, R. H., Rydgren, K. and Okland, T. 2003. Plant species composition of boreal spruce swamp forests: closed doors and windows of opportunity. - Ecology 84: 1909-1919.
20. Papa, A. R. R. and Tsallis, C. 1998. Imitation games: power-law sensitivity to initial conditions and nonextensivity. - Phys. Rev. E 57: 3923-3927.
21. Pielou, E. C. 1966. Shannon's formula as a measure of specific diversity: its use and misuse. - Am. Nat. 100: 463-465.
22. Plastino, A. R. and Plastino, A. 1993. Tsallis entropy, ehrenfest theorem and information-theory. - Phys. Lett. A 177: 177-179.
23. Preston, F. W. 1948. The commonness and rarity of species. - Ecology 29: 254-283.
24. Routledge, R. D. 1979. Diversity indices: which ones are admissible? - J. Theor. Biol. 76: 503-515.
25. Scheuring, I. and Riedi, R. H. 1994. Application of multifractals to the analysis of vegetation pattern. - J. Veg. Sci. 5: 489-496.
26. Simpson, E. H. 1949. Measurement of species diversity. - Nature 163: 688.
27. Solé, R. V., Manrubia, S. C. and Luque, B. 1994. Multifractals in rainforest ecosystems: modelling and simulation. - In: Novak, M. M. (ed.), Fractals in the natural and applied sciences. North-Holland, pp. 397-407.
28. Spellerberg, I. F. and Fedor, P. J. 2003. A tribute to Claude Shannon (1916-2001) and a plea for more rigorous use of species richness, species diversity and the 'Shannon-Wiener' index. - Global Ecol. Biogeogr. 12: 177-179.
29. Tamarit, F. A., Cannas, S. A. and Tsallis, C. 1998. Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution. - Eur. Phys. J. B 1: 545-548.
30. Tsallis, C. 1988. Possible generalization of Boltzmann-Gibbs statistics. - J. Stat. Phys. 52: 479-487.
31. Tsallis, C., Mendes, R. S. and Plastino, A. R. 1998. The role of constraints within generalized nonextensive statistics. - Physica A 261: 534-554.
32. Volkov, I., Banavar, J. R., Hubbell, S. P. et al. 2003. Neutral theory and relative species abundance in ecology. - Nature 424: 1035-1037.
33. Whittaker, R. H. 1972. Evolution and measurement of species diversity. - Taxon 21: 213-251.
34. Wilson, J. B., Wells, T. C. E., Trueman, I. C. et al. 1996. Are there assembly rules for plant species abundance? An investigation in relation to soil resources and successional trends. - J. Ecol. 84: 527-538.