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The Multi-scale Marked Area-interaction Point Process: A Model for the Spatial Pattern of Trees

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  • NICOLAS PICARD
  • AVNER BAR-HEN
  • FRÉDÉRIC MORTIER
  • JOËL CHADŒUF

Abstract

The spatial pattern of trees in forests often combines different types of structure (regularity, clustering or randomness) at different scales. Taking species or size into account leads to marked patterns. The question addressed is to model such multi-scale marked patterns using a single process. Within the category of Markov processes, the area-interaction process has the advantage of being locally stable, whether it is attractive or repulsive. This process was originally defined as a one-scale non-marked process. We propose an extension as a multi-scale marked process. Three examples are presented to show the adequacy of this process to model tree patterns: 1. A pine pattern showing anisotropic regularity and clustering at different scales. 2. A bivariate (adult/juvenile) kimboto pattern in French Guiana, showing regularity for one type, clustering for the other and repulsion between the two. 3. A marked pattern in Gabon where the mark is tree diameter. Copyright (c) 2008 Board of the Foundation of the Scandinavian Journal of Statistics.

Suggested Citation

  • Nicolas Picard & Avner Bar-Hen & Frédéric Mortier & Joël Chadœuf, 2009. "The Multi-scale Marked Area-interaction Point Process: A Model for the Spatial Pattern of Trees," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 23-41.
  • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:23-41
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    1. repec:eee:ecomod:v:288:y:2014:i:c:p:143-154 is not listed on IDEAS
    2. Baddeley, Adrian & Turner, Rolf & Mateu, Jorge & Bevan, Andrew, 2013. "Hybrids of Gibbs Point Process Models and Their Implementation," Journal of Statistical Software, Foundation for Open Access Statistics.

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