Dataset for: Nonlinear reaction-diffusion process models improve inference for population dynamics

Partial differential equations (PDEs) are a useful tool for modeling spatio-temporal 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 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 spatio-temporal abundance forecasts of sea otters in Glacier Bay, Alaska. Further, we predicted spatially-varying local equilibrium abundances as a result of environmentally-driven diffusion and density-regulated growth, and 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.