Measuring diversity from dissimilarities with Rao's quadratic entropy: Are any dissimilarities suitable?

Theoretical Population Biology

Volumn 67, Issue 4, 2005, Pages 231-239

  Pavoine, S ^a   Ollier, S ^a   Pontier, D ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Dissimilarity; Diversity; Quadratic entropy; Smallest enclosing hypersphere; Ultrametric

Indexed keywords

BIODIVERSITY; ENTROPY; MEASUREMENT METHOD;

ANIMAL; ARTICLE; BIODIVERSITY; BIOLOGICAL MODEL; BIRD; CARNIVORA; CATTLE; GENETICS; POPULATION GENETICS; STATISTICAL MODEL;

ANIMALS; BIODIVERSITY; BIRDS; CARNIVORA; CATTLE; GENETICS, POPULATION; MODELS, BIOLOGICAL; MODELS, STATISTICAL;

EID: 18844397307     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.01.004     Document Type: Article

References (34)

1. J. Blondel, F. Vuilleumier, L.F. Marcus, and E. Terouanne Is there ecomorphological convergence among mediterranean bird communities of Chile, California, and France M.K. Hecht B. Wallace R.J. MacIntyre Evolution Biology 1984 Plenum Press New York 141 213
2. S. Champely, and D. Chessel Measuring biological diversity using Euclidean metrics Environ. Ecol. Stat. 9 2002 167 177
3. W.S. Cleveland The Elements of Graphing Data 1994 AT&T Bell Laboratories Murray Hill, New Jersey
4. S.H. Cousins Species diversity measurement: choosing the right index Trend. Ecol. Evol. 6 1991 190 192
5. F. Critchley, and B. Fichet On (super-)spherical distance matrices and two results from Schoenberg Linear Algebra Appl. 251 1997 145 165
6. J.A.F. Diniz-Filho, and N.M. Tôrres Phylogenetic comparative methods and the geographic range size - body size relationship in New World terrestrial Carnivora Evol. Ecol. 16 2002 351 367
7. A.W.F. Edwards Distance between populations on the basis of gene frequencies Biometrics 27 1971 873 881
8. R.S. Etienne, and H. Olff How dispersal limitation shapes species - body size distributions in local communities Am. Naturalist 163 2004 69 83
9. K. Fisher, B. Gärtner, and M. Kutz Fast smallest-Enclosing-Ball computation in High dimensions G. Di Battista U. Zwick Proceedings of the 11th Annual European Symposium on Algorithms (ESA 2003) 2003 Springer Budapest 630 641
10. J.C. Gower Euclidean distance geometry Math. Scientist 7 1982 1 14
11. J.C. Gower Distance matrices and their Euclidean approximation E. Diday M. Jambu L. Lebart J. Pagès R. Tomassone Data Analysis and Informatics III 1984 Elsevier Amsterdam, North-Holland 3 21
12. J.C. Gower Some distance properties of latent root and vector methods used in multivariate analysis Biometrika 53 1966 325 338
13. J.C. Gower, and P. Legendre Metric and Euclidean properties of dissimilarity coefficients J. Classif. 3 1986 5 48
14. R. Ihaka, and R. Gentleman A language for data analysis and graphics J. Comp. Graph. Stat. 5 1996 299 314
15. J. Izsak, and L. Papp Application of the quadratic entropy indices for diversity studies of drosophilid assemblages Environ. Ecol. Stat. 2 1995 213 224
16. J. Izsak, and L. Szeidl Quadratic diversity: its maximization can reduce the richness of species Environ. Ecol. Stat. 9 2002 423 430
17. M. Kimura The Neutral Theory of Molecular Evolution 1983 Cambridge University Press Cambridge
18. A.E. Magurran Ecological Diversity and its Measurement 1988 Croom Helm Limited London
19. S. Martinez, G. Michon, and J. San Martin Inverse of strictly ultrametric matrices are of Stieltjes type SIAM J. Matrix Anal. A 15 1994 98 106
20. K. Moazami-Goudarzi, D. Laloë, J.P. Furet, and F. Grosclaude Analysis of genetic relationships between 10 cattle breeds with 17 microsatellites Anim. Genetics 28 1997 338 345
21. R. Nabben, and R.S. Varga A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix SIAM J. Matrix Anal. A 15 1994 107 113
22. M. Nei Genetic distance between populations Am. Naturalist 106 1972 283 292
23. M. Nei Estimation of average heterozygosity and genetic distance from a small number of individuals Genetics 89 1978 583 590
24. M. Nei, and W.-H. Li Mathematical model for studying genetic variation in terms of restriction endonucleases Proc. Natl. Acad. Sci. USA 76 1979 5269 5273
25. M. Nei, and F. Tajima DNA polymorphism detectable by restriction endonucleases Genetics 97 1981 145 163
26. E.C. Pielou Ecological Diversity 1975 Wiley New York
27. C.R. Rao Diversity and dissimilarity coefficients: a unified approach Theor. Popul. Biol. 21 1982 24 43
28. C.R. Rao Diversity: its measurement, decomposition, apportionment and analysis Sankhya: Ind. J. Stat. A 44 1982 1 22
29. C.R. Rao Rao's axiomatization of diversity measures S. Kotz N.L. Johnson Encyclopedia of Statistical Sciences 1986 Wiley New York 614 617
30. C.R. Rao, and T.K. Nayak Cross entropy, dissimilarity measures, and characterizations of Quadratic Entropy IEEE Trans. Inf. Theory IT-31 1985 589 593
31. K. Shimatani On the measurement of species diversity incorporating species differences Oikos 93 2001 135 147
32. Y. Van de Peer Phylogeny inference based on distance methods M. Salemi A.-M. Vandamme The Phylogenetic Handbook, a Practical Approach to DNA and Protein Phylogeny 2003 Cambridge University Press Cambridge 101 136
33. R.M. Warwick, and K.R. Clarke New 'biodiversity' measures reveal a decrease in taxonomic distinctness with increasing stress Mar. Ecol. Prog. Ser. 129 1995 301 305
34. M.G. Watve, and R.M. Gangal Problems in measuring bacterial diversity and a possible solution Appl. Environ. Microbiol. 62 1996 4299 4301