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December 2021 Markov random field models for vector-based representations of landscapes
Patrizia Zamberletti, Julien Papaïx, Edith Gabriel, Thomas Opitz
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Ann. Appl. Stat. 15(4): 1628-1651 (December 2021). DOI: 10.1214/21-AOAS1447

Abstract

In agricultural landscapes the spatial distribution of cultivated and seminatural elements strongly impacts habitat connectivity and species dynamics. To allow for landscape structural analysis and scenario generation, we here develop statistical tools for real landscapes composed of geometric elements, including 2D patches but also 1D linear elements (e.g., hedges). Utilizing the framework of discrete Markov random fields, we design generative stochastic models that combine a multiplex network representation, based on spatial adjacency, with Gibbs energy terms to capture the distribution of landscape descriptors for land-use categories. We implement simulation of agricultural scenarios with parameter-controlled spatial and temporal patterns (e.g., geometry, connectivity, crop rotation), and we demonstrate through simulation that pseudo-likelihood estimation of parameters works well. To study statistical relevance of model components in real landscapes, we discuss model selection and validation, including cross-validated prediction scores. Model validation with a view toward ecologically relevant landscape summaries is achieved by comparing observed and simulated summaries (network metrics but also metrics and appropriately defined variograms using a raster discretization). Models fitted to subregions of the Lower Durance Valley (France) indicate strong deviation from random allocation and realistically capture landscape patterns. In summary, our approach improves the understanding of agroecosystems and enables simulation-based theoretical analysis of how landscape patterns shape biological and ecological processes.

Acknowledgments

We are thankful to Claire Lavigne and Katarzyna Adamczyk for help and their wise suggestions for landscape data processing and for the discussion part. We are grateful for the comments and suggestions of two anomymous reviewers and the Associate Editor that helped to significantly improve the quality of the manuscript.

Citation

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Patrizia Zamberletti. Julien Papaïx. Edith Gabriel. Thomas Opitz. "Markov random field models for vector-based representations of landscapes." Ann. Appl. Stat. 15 (4) 1628 - 1651, December 2021. https://doi.org/10.1214/21-AOAS1447

Information

Received: 1 July 2020; Revised: 1 January 2021; Published: December 2021
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.1214/21-AOAS1447

Keywords: Graphical model , Markov chain Monte Carlo simulation , multiplex-network , pseudo-likelihood , statistical landscape modeling , Stochastic geometry

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December 2021
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