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Nonlinear Reaction–Diffusion Process Models Improve Inference For Population Dynamics, Xinyi Lu, Perry J. Williams, Mevin B. Hooten, James A. Powell, Jamie N. Womble, Michael R. Bower

United States National Park Service: Publications

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long-term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a …