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Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

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  • Grabarnik, Pavel
  • Särkkä, Aila

Abstract

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.

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  • Grabarnik, Pavel & Särkkä, Aila, 2009. "Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions," Ecological Modelling, Elsevier, vol. 220(9), pages 1232-1240.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:9:p:1232-1240
    DOI: 10.1016/j.ecolmodel.2009.02.021
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    References listed on IDEAS

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    1. Tscheschel, A. & Stoyan, D., 2006. "Statistical reconstruction of random point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 859-871, November.
    2. A. Baddeley & M. Lieshout, 1995. "Area-interaction point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 601-619, December.
    3. Sarkka, Aila & Renshaw, Eric, 2006. "The analysis of marked point patterns evolving through space and time," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1698-1718, December.
    4. 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. Cronie, Ottmar & Särkkä, Aila, 2011. "Some edge correction methods for marked spatio-temporal point process models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2209-2220, July.
    2. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    3. Genet, Astrid & Grabarnik, Pavel & Sekretenko, Olga & Pothier, David, 2014. "Incorporating the mechanisms underlying inter-tree competition into a random point process model to improve spatial tree pattern analysis in forestry," Ecological Modelling, Elsevier, vol. 288(C), pages 143-154.
    4. Lister, Andrew J. & Leites, Laura P., 2018. "Modeling and simulation of tree spatial patterns in an oak-hickory forest with a modular, hierarchical spatial point process framework," Ecological Modelling, Elsevier, vol. 378(C), pages 37-45.
    5. Nakagawa, Yoshiaki & Yokozawa, Masayuki & Hara, Toshihiko, 2015. "Competition among plants can lead to an increase in aggregation of smaller plants around larger ones," Ecological Modelling, Elsevier, vol. 301(C), pages 41-53.
    6. Ivan N. Kutyavin & Alexei V. Manov, 2022. "Spatial relationships of trees in middle taiga post-pyrogenic pine forest stands in the European North-East of Russia," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 68(6), pages 228-240.
    7. Shanin, Vladimir & Komarov, Alexander & Khoraskina, Yulia & Bykhovets, Sergey & Linkosalo, Tapio & Mäkipää, Raisa, 2013. "Carbon turnover in mixed stands: Modelling possible shifts under climate change," Ecological Modelling, Elsevier, vol. 251(C), pages 232-245.

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