The apportionment of quadratic entropy: A useful alternative for partitioning diversity in ecological data

Environmental and Ecological Statistics

Volumn 12, Issue 2, 2005, Pages 125-138

  Pavoine, Sandrine ^a   Dolédec, Sylvain ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Dissimilarity; Functional diversity; Macroinvertebrates; Rao's axiomatization; Taxonomy

Indexed keywords

TAXONOMY;

EID: 20344393108     PISSN: 13528505     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10651-005-1037-2     Document Type: Article

References (77)

1. J.D. Allan 1975 Components of diversity Oecologia 18 359-67 10.1007/ BF00345855
2. M.J. Anderson 2001 A new method for non-parametric multivariate analysis of variance Austral Ecology 26 32-46 10.1046/j.1442-9993.2001.01070.x
3. E. Bosch F. Calafell F.R. Santos A. Perez-Lezaun D. Comas N. Benchemsi C. Tyler-Smith and J. Bertranpetit 1999 Variation in short tandem repeats is deeply structured by genetic background on the human Y chromosome American Journal of Human Genetics 65 1623-38 10.1086/302676 1:CAS:528:DC%2BD3cXjvFemtQ%3D%3D 10577916
4. J.R. Bray and J.T. Curtis 1957 An ordination of the upland forest communities of Southern Wisconsin Ecological Monographs 27 325-49
5. F. Cailliez 1983 The analytical solution of the additive constant problem Psychometrika 48 305-10
6. S. Champely and D. Chessel 2002 Measuring biological diversity using Euclidean metrics Environmental and Ecological Statistics 9 167-77 10.1023/A:1015170104476 MR1898428
7. F. Chevenet S. Dolédec and D. Chessel 1994 A fuzzy coding approach for the analysis of long-term ecological data Freshwater Biology 31 295-309
8. L.D. Corkum and J.J.H. Ciborowski 1988 Use of alternative classifications in studying broad-scale distributional patterns of lotic invertebrates Journal of the North American Benthological Society 7 167-79
9. S.H. Cousins 1991 Species diversity measurement: Choosing the right index Trends in Ecology and Evolution 6 190-92 10.1016/ 0169-5347(91)90212-G
10. T.J. Crease M. Lynch and K. Spitze 1990 Hierarchical analysis of population genetic variation in mitochondrial and nuclear genes of Daphnia pulex Molecular Biology and Evolution 7 444-58 1:CAS:528:DyaK3cXmt1yhsrY%3D 2263195
11. K.W. Cummins 1974 Structure and function of stream ecosystems BioScience 24 631-41
12. L. Excoffier 2001 Analysis of population subdivision In D.J. Balding M. Bishop and C. Cannings (eds.), Handbook of Statistical Genetics John Wiley & Sons, Ltd New York 271-307
13. L. Excoffier P.E. Smouse and J.M. Quattro 1992 Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data Genetics 131 479-91 1:CAS:528:DyaK38XlsVCntro%3D 1644282
14. R. Finkeldey 1994 A simple derivation of the partitioning of genetic differentiation within subdivided populations Theoretical and Applied Genetics 89 198-200 10.1007/BF00225141
15. R.A. Fisher 1925 Statistical Methods for Research Workers Oliver & Boyd Edinburgh
16. C.A. Frissell W.J. Liss C.E. Warren and M.D. Hurley 1986 A hierarchical framework for stream habitat classification: Viewing streams in a watershed context Environmental Management 10 199-214
17. S. Gayraud B. Statzner P. Bady A. Haybach F. Schöll P. Usseglio-Polatera and M. Bachi 2003 Invertebrate traits for the biomonitoring of European large rivers: An initial assessment of alternative metrics Freshwater Biology 48 2045-64 10.1046/ j.1365-2427.2003.01139.x
18. J.C. Gower and P. Legendre 1986 Metric and Euclidean properties of dissimilarity coefficients Journal of Classification 3 5-48
19. J.A.J. Hendrickson and P.R. Ehrlich 1971 An expanded concept of "species diversity" Notulae Naturae 439 1-6
20. V.H. Heywood and R.T. Watson 1995 Global biodiversity assessment Cambridge University Press Cambridge
21. K.E. Holsinger and R.J. Mason-Gamer 1996 Hierarchical analysis of nucleotide diversity in geographically structured populations Genetics 142 629-39 1:CAS:528:DyaK28XhsFKjs7c%3D 8852859
22. R. Ihaka and R. Gentleman 1996 R: A language for data analysis and graphics Journal of Computational and Graphical Statistics 5 299-314
23. J.M. Ivol B. Guinand P. Richoux and H. Tachet 1997 Longitudinal changes in Trichoptera and Coleoptera assemblages and environmental conditions in the Loire River (France) Archiv für Hydrobiologie 138 525-57
24. J. Izsak and L. Papp 1995 Application of the quadratic entropy indices for diversity studies of drosophilid assemblages Environmental and Ecological Statistics 2 213-24 10.1007/BF00456668
25. J. Izsak and L. Papp 2000 A link between ecological diversity indices and measures of biodiversity Ecological Modelling 130 151-56 10.1016/ S0304-3800(00)00203-9
26. J. Izsak and L. Szeidl 2002 Quadratic diversity: Its maximization can reduce the richness of species Environmental and Ecological Statistics 9 423-30 10.1023/A:1020970824646 MR1951718
27. J. Kolasa 1989 Ecological systems in hierarchical perspective: Breaks in community structure and other consequences Ecology 70 36-47
28. R. Lande 1996 Statistics and partitioning of species diversity, and similarity among multiple communities Oikos 76 5-13
29. R. Lecis and K. Norris 2004 Population genetic diversity of the endemic Sardinian newt Euproctus platycephalus: Implications for conservation Biological Conservation 119 263-70 10.1016/j.biocon.2003.11.011
30. P. Legendre and M.J. Anderson 1999 Distance-based redundancy analysis: Testing multispecies responses in multifactorial ecological experiments Ecological Monographs 69 1-24
31. R. Levins 1968 Evolution in changing environments. Monographs in population biology Princeton University Press Princeton
32. S.A. Levins and R.T. Paine 1974 Disturbance, patch formation, and community structure Proceedings of the National Academy of Sciences of the USA 71 2744-47 4527752
33. R.C. Lewontin 1972 The apportionment of human diversity Evolutionary Biology 6 381-98
34. R.J. Light and B.H. Margolin 1971 An analysis of variance for categorical data Journal of the American Statistical Association 66 534-44
35. J.C. Lingoes 1971 Some boundary conditions for a monotone analysis of symmetric matrices Psychometrika 36 195-203
36. Z.J. Liu and C.R. Rao 1995 Asymptotic distribution of statistics based on quadratic entropy and bootstrapping Journal of Statistical Planning and Inference 43 1-18 10.1016/0378-3758(94)00005-G
37. M. Lynch and T.J. Crease 1990 The analysis of population survey data on DNA sequence variation Molecular Biology and Evolution 7 377-94 1:CAS:528:DyaK3cXkvFCgs7c%3D 1974693
38. B.F. Manly 1994 Multivariate Statistical Methods. A primer 2 Chapman & Hall London
39. B.H. McArdle and M.J. Anderson 2001 Fitting multivariate models to community data: Comment on distance-based redundancy analysis Ecology 82 290-97
40. T.K. Nayak 1986a An analysis of diversity using Rao's quadratic entropy Sankhya: The Indian Journal of Statistics 48B 315-30
41. T.K. Nayak 1986b Sampling distributions in analysis of diversity Sankhya: The Indian Journal of Statistics 48B 1-9
42. M. Nei 1973 Analysis of gene diversity in subdivised populations Proceedings of the National Academy of Sciences of the United States of America 70 3321-23 1:STN:280:CSuD2MrkvVM%3D 4519626
43. M. Nei and L. Jin 1989 Variances of the average numbers of nucleotide substitutions within and between populations Molecular Biology and Evolution 6 290-300 1:CAS:528:DyaL1MXktVeksL0%3D 2576093
44. M. Nei and W.-H. Li 1979 Mathematical model for studying genetic variation in terms of restriction endonucleases Proceedings of the National Academy of Sciences of the United States of America 76 5269-73 1:CAS:528:DyaL3cXitVWn 291943
45. M. Nei and J.C. Miller 1990 A simple method for estimating average number of nucleotide substitutions within and between populations from restriction data Genetics 125 873-9 1:CAS:528:DyaK3cXlvVKjsbo%3D 1975792
46. M. Nei and F. Tajima 1981 DNA polymorphism detectable by restriction endonucleases Genetics 97 145-63 1:CAS:528:DyaL3MXksFKmu7c%3D 6266912
47. J.B. Olsen S.J. Miller W.J. Spearman and J.K. Wenburg 2003 Patterns of intra- and inter-population genetic diversity in Alaska coho salmon: Implications for conservation Conservation Genetics 4 557-69 10.1023/ A:1025684104113 1:CAS:528:DC%2BD3sXntFGhs7Y%3D
48. M. Parsons M.C. Thoms and R.H. Norris 2003 Scales of macroinvertebrate distribution in relation to the hierarchical organization of river systems Journal of the North American Benthological Society 22 105-22
49. O.L. Petchey and K. Gaston 2002 Functional diversity (FD), species richness and community composition Ecology Letters 5 402-11 10.1046/ j.1461-0248.2002.00339.x
50. Pielou, E.C. (1967) The use of information theory in the study of the diversity of biological populations. In Proc. Fifth Berkeley Symposium on Math. Stat. and Prob. pp. 163-77.
51. E.C. Pielou 1975 Ecological diversity Wiley & Sons New York
52. Y.-X. Qiu D.-Y. Hong C.-X. Fu and K.M. Cameron 2004 Genetic variation in the endangered and endemic species Changium smyrnioides (Apiaceae) Biochemical Systematics and Ecology 32 583-96 10.1016/j.bse.2003.08.004 1:CAS:528:DC%2BD2cXjtV2hs7o%3D
53. C.R. Rao 1982a Diversity and dissimilarity coefficients: A unified approach Theoretical Population Biology 21 24-43 10.1016/ 0040-5809(82)90004-1
54. C.R. Rao 1982b Diversity: Its measurement, decomposition, apportionment and analysis Sankhya: The Indian Journal of Statistics A44 1-22
55. C.R. Rao 1984 Convexity properties of entropy functions and analysis of diversity Inequalities in statistics and probability 5 68-77
56. C.R. Rao 1986 Rao's axiomatization of diversity measures In S. Kotz and N.L. Johnson (eds.), Encyclopedia of Statistical Sciences Wiley & Sons New York 614-17
57. C.R. Rao and T.K. Nayak 1985 Cross entropy, dissimilarity measures, and characterizations of Quadratic Entropy IEEE Transactions on Information Theory IT-31 589-93 10.1109/TIT.1985.1057082
58. R.E. Ricklefs 1987 Community diversity: Relative roles of local and regional processes Science 235 167-71
59. C. Ricotta 2003 Additive partition of parametric information and its associated beta-diversity measure Acta Biotheoretica 51 91-100 10.1023/ A:1024539526618 12870771
60. S. Schneider D. Roessli and L. Excoffier 2000 Arlequin Ver 2.000: A Software for Population Genetics Data Analysis Genetics and Biometry Laboratory, Department of Anthropology, University of Geneva Switzerland
61. K. Shimatani 2001 On the measurement of species diversity incorporating species differences Oikos 93 135-47 10.1034/j.1600-0706.2001.930115.x
62. M. Slatkin 1995 A measure of population subdivision based on microsatellite allele frequencies Genetics 139 457-62 1:STN:280:ByqB38%2FmvVE%3D 7705646
63. B. Statzner 1987 Characteristics of lotic ecosystem and consequences for future research directions Ecological studies 61 365-90
64. B. Statzner B. Bis S. Dolédec and P. Usseglio-Polatera 2001 Perspectives for biomonitoring at large spatial scales: A unified measure for the functional composition of invertebrate communities in European running waters Basic and Applied Ecology 2 73-85
65. B. Statzner K. Hoppenhaus M.-F. Arens and P. Richoux 1997 Reproductive traits, habitat use and templet theory: A synthesis of world-wide data on aquatic insects Freshwater Biology 38 109-35 10.1046/ j.1365-2427.1997.00195.x
66. B.A. Sweeney and E. Cook 2001 A landscape-level assessment of understory diversity in upland forests of North-Central Wisconsin, USA Landscape Ecology 16 55-69 10.1023/A:1008157108667
67. P. Usseglio-Polatera M. Bournaud P. Richoux and H. Tachet 2000 Biological and ecological traits of benthic freshwater macroinvertabrates: Relationships and definition of groups with similar traits Freshwater Biology 43 175-205 10.1046/j.1365-2427.2000.00535.x
68. R.L. Vannote G.W. Minshall K.W. Cummins J.A. Sedell and C.E. Cushing 1980 The river continuum concept Canadian Journal of Fisheries and Aquatic Sciences 37 130-37
69. J.A. Veech K.S. Summerville T.O. Crist and J.C. Gering 2002 The additive partitioning of species diversity: Recent revival of an old idea Oikos 99 3-9 10.1034/j.1600-0706.2002.990101.x
70. M. Vences Y. Chiari L. Raharivololoniaina and A. Meyer 2004 High mitochondrial diversity within and among populations of Malagasy poison frogs Molecular Phylogenetics and Evolution 30 295-307 10.1016/ S1055-7903(03)00217-3 1:CAS:528:DC%2BD2cXjtVGjsA%3D%3D 14715222
71. M.R. Vinson and C.P. Hawkins 1998 Biodiversity of stream insects: variation at local, basin, and regional scales Annual Review of Entomology 43 271-93
72. H.H. Wagner O. Wildi and K.C. Ewald 2000 Additive partitioning of plant species diversity in an agricultural mosaic landscape Landscape Ecology 15 219-27 10.1023/A:1008114117913
73. R.M. Warwick and K.R. Clarke 1995 New 'biodiversity' measures reveal a decrease in taxonomic distinctness with increasing stress Marine Ecology Progress Series 129 301-5
74. M.G. Watve and R.M. Gangal 1996 Problems in measuring bacterial diversity and a possible solution Applied and Environmental Microbiology 62 4299-301 1:CAS:528:DyaK28Xms1Khsb4%3D
75. B.S. Weir and C.C. Cockerham 1984 Estimating F-statistics for the analysis of population structure Evolution 38 1358-70
76. R.H. Whittaker 1960 Vegetation of the Siskiyou Mountains, Oregon and California Ecological Monographs 30 279-338
77. R.H. Whittaker 1972 Evolution and measurement of species diversity TAXON 21 213-51