Analytical evidence for scale-invariance in the shape of species abundance distributions

Mathematical Biosciences

Volumn 223, Issue 2, 2010, Pages 151-159

  Kůrka, Petr ^a   Šizling, Arnošt L ^a   Rosindell, James ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Area invariance; Correlated convolution; Macro ecology; Partition of unity; Splicing; Taxon invariance

Indexed keywords

AREA-INVARIANCE; CORRELATED CONVOLUTION; PARTITION OF UNITY; SPLICING; TAXON-INVARIANCE;

BIOLOGY; CONSERVATION; CONVOLUTION; ECOSYSTEMS;

FORESTRY;

ABUNDANCE; ANALYTICAL METHOD; CORRELATION; DATA INTERPRETATION; GEOGRAPHICAL DISTRIBUTION; MACROECOLOGY; MAXIMUM ENTROPY ANALYSIS; MODELING; TAXONOMY;

ARTICLE; CONSERVATION BIOLOGY; CONVERGENT EVOLUTION; ECOSYSTEM; ENERGY CONSERVATION; ENTROPY; MATHEMATICAL COMPUTING; POPULATION ABUNDANCE; SPECIES DISTRIBUTION; TAXON;

ANIMALS; BIODIVERSITY; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DYNAMICS;

EID: 74249106999     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2009.12.001     Document Type: Article

References (34)

1. McGill B.G., Etienne R.S., Gray J.S., et al. Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecol. Lett. 10 (2007) 995
2. Bibby C.J., Burgess N.D., and Hill D.A. Bird Census Techniques (1992), Academic Press, London
3. Reif J., Storch D., and Šímovà I. Scale-dependent habitat gradients structure bird assemblages: a case study from the Czech Republic. Acta Ornithol. 43 (2008) 197
4. Engen S., and Lande R. Population dynamic models generating the lognormal species abundance distribution. Math. Biosci. 132 (1996) 169
5. Hubbell S.P. The Unified Theory of Biodiversity and Biogeography (2001), Princeton University, Princeton, NJ
6. Motomura I. A statistical treatment of associations. Zool. Mag. Tokyo 44 (1932) 379 (in Japanese)
7. MacArthur R. On the relative abundance of bird species. Proc. Natl. Acad. Sci. USA 43 (1957) 293
8. Gray J.S. Pollution-induced changes in populations. Philos. Trans. Roy. Soc. Lond. Ser. B 286 (1979) 545
9. Šizling A.L., Storch D., Reif J., and Gaston K.J. Invariance in species-abundance distributions. Theor. Ecol. 2 (2008) 89
10. Šizling A.L., Storch D., Šizlingová E., Reif J., and Gaston K.J. Species-abundance distribution results from a spatial analogy of central limit theorem. Proc. Natl. Acad. Sci. USA 106 (2009) 6691
11. Harte J., Zillio T., Colinsk E., and Smith A.B. Maximum entropy and the state-variable approach to macroecology. Ecology 89 (2008) 2700
12. Pueyo S., He F., and Zillio T. The maximum entropy formalism and the idiosyncratic theory of biodiversity. Ecol. Lett. 10 (2008) 1017 10.1111/j.1461-0248.2007.01096.x
13. Dewara R.C., and Porté A. Statistical mechanics unifies different ecological patterns. J. Theor. Biol. 251 (2008) 389
14. Pueyo S. Diversity: between neutrality and structure. OIKOS 112 (2006) 392
15. Virkkala R. Ranges of northern forest passerines: a fractal analysis. OIKOS 67 (1993) 218
16. Kunin W.E. Extrapolating species abundances across spatial scales. Science 281 (1998) 1513
17. Harte J., Kinzig A., and Green J.L. Self-similarity in the distribution and abundance of species. Science 284 (1999) 334
18. Borda-de-Agua L., Hubbell S.P., and McAllister M. Species-area curves, diversity indices, and species abundance distributions: a multifractal analysis. Am. Nat. 159 (2002) 138
19. Martin H.G., and Goldenfeld N. Linearity and scaling of a statistical model for the species abundance distribution. Phys. Rev. E (2002) 10.1103/PhysRevE.65.032901
20. Williamson M., and Gaston K.J. The lognormal distribution is not an appropriate null hypothesis for the species-abundance distribution. J. Anim. Ecol. 74 (2005) 409
21. Zhang Y.X., Ma K.M., Anand M., and Fu B.J. Do generalized scaling laws exist for species abundance distribution in mountains?. OIKOS 115 (2006) 81
22. Hui C., and McGeoch M.A. Does the self-similar species distribution model lead to unrealistic predictions?. Ecology 89 (2008) 2946
23. Tjørve E., and Tjørve K.M.C. The species-area relationship, self-similarity, and the true meaning of the z-value. Ecology 89 (2008) 3528
24. Rényi A. Wahrscheinlichkeitsrechnung mit einem Anhang über Informationstheorie (1962), VEB Deutschen Verlag der Wissenschaften, Berlin
25. Ahlfors L.V. Complex Analysis (1966), McGraw-Hill, New York
26. Nekola J.C., Šizling A.L., Boyer A.G., and Storch D. Artifactions in the log-transformation of species abundance distributions. Folia Geobot. 43 (2008) 259
27. Storch D., Šizling A.L., Reif J., Polechová J., Šizlingová E., and Gaston K.J. The quest for a null model for macroecological patterns: geometry of species distributions at multiple spatial scales. Ecol. Lett. 11 (2008) 771
28. Storch D., and Šizling A.L. The concept of taxon invariance in ecology: do diversity patterns vary with changes in taxonomic resolution?. Folia Geobot. 43 (2008) 329
29. Visser S. Ectomycorrhizal fungal succession in jack pine stands following wildfire. New Phytol. 129 (1995) 389
30. Death R.G. The effect of habitat stability on benthic invertebrate communities: the utility of species abundance distributions. Hydrobiologia 317 (1996) 97
31. Kammesheidt L. The role of tree sprouts in the restorations of stand structure and species diversity in tropical moist forest after slash-and-burn agriculture in Eastern Paraguay. Plant Ecol. 139 (1998) 155
32. Salvador-Van-Eysendore D., Bogaert J., Zak-Mnacek V., et al. Sampling diversity in canopy gaps in an Equadorian rain forest. Forensic Sci. 49 (2003) 909
33. Caruso T.A., and Migliorini M. A new formulation of the geometric series with applications to oribatid (Acari, Oribatida) species assemblages from human-disturbed Mediterranean areas. Ecol. Model. 195 (2006) 402
34. Green J.L., and Plotkin J.B. A statistical theory for sampling species abundances. Ecol. Lett. 10 (2007) 1037