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The multipoint Morisita index for the analysis of spatial patterns

Author

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  • Golay, Jean
  • Kanevski, Mikhail
  • Vega Orozco, Carmen D.
  • Leuenberger, Michael

Abstract

In many fields, the spatial clustering of sampled data points has significant consequences. Therefore, several indices have been proposed to assess the degree of clustering affecting datasets (e.g. the Morisita index, Ripley’s K-function and Rényi’s information). The classical Morisita index measures how many times it is more likely to randomly select two sampled points from the same quadrat (the dataset is covered by a regular grid of changing size) than it would be in the case of a random distribution generated from a Poisson process. The multipoint version takes into account m points with m≥2. The present research deals with a new development of the multipoint Morisita index (m-Morisita) which is directly related to multifractality. This relationship to multifractality is first demonstrated and highlighted on a mathematical multifractal set. Then, the new version of the m-Morisita index is adapted to the characterization of environmental monitoring network clustering. And, finally, an additional extension, the functional m-Morisita index, is presented for the detection of structures in monitored phenomena.

Suggested Citation

  • Golay, Jean & Kanevski, Mikhail & Vega Orozco, Carmen D. & Leuenberger, Michael, 2014. "The multipoint Morisita index for the analysis of spatial patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 191-202.
    • Handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:191-202
    DOI: 10.1016/j.physa.2014.03.063
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    References listed on IDEAS

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    1. Julian Besag & Peter J. Diggle, 1977. "Simple Monte Carlo Tests for Spatial Pattern," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 327-333, November.
    2. Tél, Tamás & Fülöp, Ágnes & Vicsek, Tamás, 1989. "Determination of fractal dimensions for geometrical multifractals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(2), pages 155-166.
    3. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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    Cited by:

    1. Telesca, Luciano & Golay, Jean & Kanevski, Mikhail, 2015. "Morisita-based space-clustering analysis of Swiss seismicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 40-47.
    2. Kanevski, Mikhail & Pereira, Mário G., 2017. "Local fractality: The case of forest fires in Portugal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 400-410.

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