Environmental and Ecological Statistics

, Volume 19, Issue 4, pp 545–572 | Cite as

A family of spatial biodiversity measures based on graphs



While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two non-independent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neighbourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice of neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen.


Biodiversity Neighbourhood Spatial Point pattern Geometric graphs 


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  1. Aguirre O, Hui G, von Gadow K, Jiménez J (2003) An analysis of forest structure using neighbourhood-based variables. For Ecol Manag 183: 137–145CrossRefGoogle Scholar
  2. Baddeley A (1998) Spatial sampling and censoring. In: Barndorff-Nielsen O, Kendall W, van Lieshout M (eds) Stochastic geometry, likelihood and computation. Chapman & Hall, LondonGoogle Scholar
  3. Baddeley AJ, van Lieshout MNM (1995) Area-interaction point processes. Ann Inst Stat Math 47(4): 601–619CrossRefGoogle Scholar
  4. Bossdorf O, Schurr F, Schumacher J (2000) Spatial patterns of plant association in grazed and ungrazed shrublands in the semi-arid karoo, south africa. J Veg Sci 11(2): 253–258CrossRefGoogle Scholar
  5. Buckland S, Magurran A, Green R, Fewster R (2005) Monitoring change in biodiversity through composite indices. Philos Trans R Soc B-Biol Sci 28(360): 243–254CrossRefGoogle Scholar
  6. Cardinale B, Nelson K, Palmer M (2000) Linking species diversity to the functioning of ecosystems: on the importance of environmental context. Oikos 91: 175–183CrossRefGoogle Scholar
  7. Ceyhan E (2009) Overall and pairwise segregation tests based on nearest neighbor contingency tables. Comput Stat Data Anal 53: 2786–2808CrossRefGoogle Scholar
  8. Clark P, Evans F (1954) Distance to nearest neigbor as a measure of spatial relationships in populations. Ecology 35: 445–453CrossRefGoogle Scholar
  9. Condit R (1998) Tropical forest cencus plots. Springer, BerlinGoogle Scholar
  10. Condit R et al (2000) Spatial patterns in the distribution of tropical tree species. Science 288: 1414–1418PubMedCrossRefGoogle Scholar
  11. Dixon P (1994) Testing spatial segregation using a nearest-neighbor contingency table. Ecology 75(7): 1940–1948CrossRefGoogle Scholar
  12. Gore A, Paranjpe S (2001) A course in mathematical and statistical ecology. Kluwer, DordrechtGoogle Scholar
  13. Hill MO (1973) Diversity and evenness: a unifying notation and its consequences. Ecology 54(2): 427–432CrossRefGoogle Scholar
  14. Hubbell S, Foster R, O’Brien S, Harms K, Condit R, Wechsler B, Wright S, de Lao SL (1999) Light gap disturbances, recruitment limitation, and tree diversity in a neotropical forest. Science 283: 554–557PubMedCrossRefGoogle Scholar
  15. Hubbell S, Ahumada J, Condit R, Foster R (2001) Local neighborhood effects on long-term survival of individual trees in a neotropical forest. Ecol Res 16: 859–875CrossRefGoogle Scholar
  16. Hubbell S, Condit R, Foster R (2005) Barro Colorado forest census plot data. http://www.ctfs.si.edu/datasets
  17. Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Statistics in practice. Wiley, New YorkGoogle Scholar
  18. Law R, Dieckmann U (2000) A dynamical system for neighbourhoods in plant communities. Ecology 81: 2137–2148Google Scholar
  19. Law R, Illian J, Burslem D, Gratzer G, Gunatilleke CVS, Gunatilleke IAUN (2009) Ecological information from spatial patterns of plants: insights from point process theory. J Ecol 97: 616–628CrossRefGoogle Scholar
  20. Lewandowski A, Pommerening A (1997) Zur Beschreibung der Waldstruktur—Erwartete und beobachtete Arten-Durchmischung. Forstwiss Centralbl 116: 129–139CrossRefGoogle Scholar
  21. Loreau M, Naeem S, Inchausti P, Bengtsson J, Grime J, Hector A, Hooper DU, Huston MA, Raffaelli D, Schmid B, Tilman D, Wardle DA (2001) Biodiversity and ecosystem functioning: current knowledge and future challenges. Science 294: 804–808PubMedCrossRefGoogle Scholar
  22. Magurran A (1988) Ecological diversity and its measurement. Princeton University Press, PrincetonGoogle Scholar
  23. Magurran A (2004) Measuring biological diversity. Blackwell, OxfordGoogle Scholar
  24. Mahdi A, Law R (1987) On the spatial organization of plant species in a limestone grassland community. J Ecol 75: 259–476CrossRefGoogle Scholar
  25. Marchette DJ (2004) Random graphs for statistical pattern recognition. Wiley, New YorkCrossRefGoogle Scholar
  26. McGill BJ, Etienne RS, Gray JS et al (2007) Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecol Lett 10: 995–1015PubMedCrossRefGoogle Scholar
  27. Møller J, Waagepetersen RP (2003) Statistical inference and simulation for spatial point processes. Chapman & Hall/CRC, LondonCrossRefGoogle Scholar
  28. Møller J, Waagepetersen RP (2007) Modern statistics for spatial point processes. Scand J Stat 34(4): 643–684Google Scholar
  29. Morlon H, Chuyong G, Condit R, Hubbell S, Kenfack D, Duncan T, Valencia R, Green J (2008) A general framework for the distance-decay of similarity in ecological communities. Ecol Lett 11: 904–917PubMedCrossRefGoogle Scholar
  30. Motz K, Sterba H, Pommerening A (2010) Sampling measures of tree diversity. For Ecol Manag 260: 1985–1996CrossRefGoogle Scholar
  31. Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tessellations: concepts and applications of Voronoi diagrams. Wiley, New YorkGoogle Scholar
  32. Patil G, Taillie C (1982) Diversity as a concept and its measurement. JASA 77(379): 548–561Google Scholar
  33. Pielou EC (1961) Segregation and symmetry in two-species populations as studied by nearest neighbour relationships. J Ecol 49(2): 255–269CrossRefGoogle Scholar
  34. Pielou EC (1977) Mathematical ecology. Wiley, New YorkGoogle Scholar
  35. Podani J, Czaran T (1997) Individual-centered analysis of mapped point patterns representing multi-species assemblages. J Veg Sci 8(2): 259–270CrossRefGoogle Scholar
  36. Reardon S, O’Sullivan D (2004) Measures of spatial segregation. Sociol Methodol 34: 121–162CrossRefGoogle Scholar
  37. Ripley BD (1977) Modelling spatial patterns. J R Stat Soc Ser B-Stat Methodol 39: 172–212Google Scholar
  38. Scheiner S (2003) Six types of species-area curves. Glob Ecol Biogeogr 12(6): 441–447CrossRefGoogle Scholar
  39. Shimatani K (2001) Multivariate point processes and spatial variation of species diversity. For Ecol Manag 142: 215–229CrossRefGoogle Scholar
  40. Shimatani K, Kubota Y (2004) Quantitative assessment of multispecies spatial pattern with high species diversity. Ecol Res 19: 149–163CrossRefGoogle Scholar
  41. Stoyan D, Kendall WS, Mecke J (1995) Stochastic geometry and its applications. 2. Wiley, New YorkGoogle Scholar
  42. Tóthmérész B (1995) Comparison of different methods for diversity ordering. J Veg Sci 6: 283–290CrossRefGoogle Scholar
  43. Tscheschel A, Stoyan D (2006) Statistical reconstruction of random point patterns. Comput Stat Data Anal 51: 859–871CrossRefGoogle Scholar
  44. Vuorinen V, Peltomäki M, Rost M, Alava M (2004) Networks in metapopulation dynamics. Eur Phys J B 38: 261–268CrossRefGoogle Scholar
  45. Waagepetersen RP, Guan Y (2009) Two step estimation for inhomogeneous spatial point processes and a simulation study. J R Stat Soc Ser B-Stat Methodol 71: 685–702CrossRefGoogle Scholar
  46. Wiegand T, Gunatilleke CVS, Gunatilleke IAUN, Huth A (2007) How individual species structure diversity in tropical forests. PNAS 104: 19029–19033PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland
  2. 2.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsUK

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