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The saturated pairwise interaction Gibbs point process as a joint species distribution model

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  • Ian Flint
  • Nick Golding
  • Peter Vesk
  • Yan Wang
  • Aihua Xia

Abstract

In an effort to effectively model observed patterns in the spatial configuration of individuals of multiple species in nature, we introduce the saturated pairwise interaction Gibbs point process. Its main strength lies in its ability to model both attraction and repulsion within and between species, over different scales. As such, it is particularly well‐suited to the study of associations in complex ecosystems. Based on the existing literature, we provide an easy to implement fitting procedure as well as a technique to make inference for the model parameters. We also prove that under certain hypotheses the point process is locally stable, which allows us to use the well‐known ‘coupling from the past’ algorithm to draw samples from the model. Different numerical experiments show the robustness of the model. We study three different ecological data sets, demonstrating in each one that our model helps disentangle competing ecological effects on species' distribution.

Suggested Citation

  • Ian Flint & Nick Golding & Peter Vesk & Yan Wang & Aihua Xia, 2022. "The saturated pairwise interaction Gibbs point process as a joint species distribution model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1721-1752, November.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:5:p:1721-1752
    DOI: 10.1111/rssc.12596
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    References listed on IDEAS

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    1. Jean-François Coeurjolly & Ege Rubak, 2013. "Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 669-684, December.
    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. Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
    4. Adrian Baddeley & Jean-François Coeurjolly & Ege Rubak & Rasmus Waagepetersen, 2014. "Logistic regression for spatial Gibbs point processes," Biometrika, Biometrika Trust, vol. 101(2), pages 377-392.
    5. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
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