Document Type


Journal/Book Title/Conference



John Wiley & Sons Ltd.

Publication Date


First Page


Last Page



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 logistic reaction component instead of a Malthusian component when population growth demonstrates asymptotic behavior. As a case study, we demonstrated that our model improves spatiotemporal abundance forecasts of sea otters in Glacier Bay, Alaska. Furthermore, we predicted spatially varying local equilibrium abundances as a result of environmentally driven diffusion and density‐regulated growth. Integrating equilibrium abundances over the study area in our application enabled us to infer the overall carrying capacity of sea otters in Glacier Bay, Alaska.


This is the pre-peer reviewed version of the following article: Lu, X, Williams, PJ, Hooten, MB, Powell, JA, Womble, JN, Bower, MR. Nonlinear reaction–diffusion process models improve inference for population dynamics. Environmetrics. 2019;e2604., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

Included in

Mathematics Commons