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

TL;DR

This paper introduces a saturated pairwise interaction Gibbs point process model to analyze complex multi-species spatial patterns, capturing both attraction and repulsion, with proven stability and practical inference methods, demonstrated on ecological datasets.

Contribution

It presents a novel, easy-to-implement Gibbs point process model for multi-species interactions, including stability proof and inference techniques, applicable to ecological data analysis.

Findings

Model effectively captures attraction and repulsion in species distributions.

Proven local stability enables sampling via coupling from the past.

Demonstrated robustness on three ecological datasets.

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 datasets, demonstrating in each one that our model helps disentangle competing ecological effects on species' distribution.