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A family of spatial biodiversity measures based on graphs

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graphs_exposure_EES_FINAL_tr.pdf (197.1Kb)
Date
12/2012
Author
Rajala, T
Illian, Janine Baerbel
Keywords
Biodiversity
Exposure
Neighbourhood
Spatial
Point pattern
QA Mathematics
Metadata
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Abstract
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 neigh-bourhood 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 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.
Citation
Rajala , T & Illian , J B 2012 , ' A family of spatial biodiversity measures based on graphs ' Environmental and Ecological Statistics , vol 19 , no. 4 , pp. 545-572 . DOI: 10.1007/s10651-012-0200-9
Publication
Environmental and Ecological Statistics
Status
Peer reviewed
DOI
http://dx.doi.org/10.1007/s10651-012-0200-9
ISSN
1352-8505
Type
Journal article
Rights
© Springer Science+Business Media, LLC 2012. This is the author's accepted manuscript. The original publication is available at www.springerlink.com
Collections
  • University of St Andrews Research
  • Mathematics & Statistics Research
  • Centre for Research into Ecological & Environmental Modelling (CREEM) Research
  • Scottish Oceans Institute Research
URI
http://hdl.handle.net/10023/3350

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