Nonlinear reaction–diffusion process models improve inference for population dynamics

• Main Authors: Lu, Xinyi, Williams, Perry J., Hooten, Mevin B., Powell, James A., Womble, Jamie N., Bower, Michael R.
• Format: Text
• Language: unknown
• Published: DigitalCommons@University of Nebraska - Lincoln 2019
• Subjects: Fokker–Planck equation; homogenization; spatiotemporal process; state-space model; Environmental Education; Environmental Policy; Environmental Sciences; Environmental Studies; Fire Science and Firefighting; Leisure Studies; Natural Resource Economics; Natural Resources Management and Policy; Nature and Society Relations; Other Environmental Sciences; Physical and Environmental Geography; Public Administration; Public Affairs; Public Policy and Public Administration; Recreation; Parks and Tourism Administration; Glacier Bay; glacier; Alaska
• Online Access: https://digitalcommons.unl.edu/natlpark/209; https://digitalcommons.unl.edu/context/natlpark/article/1205/viewcontent/Lu_ENVIRONOMETRICS_2020_Nonlinear_reaction.pdf

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.