Dataset for: Nonlinear reaction-diffusion process models improve inference for population dynamics
datasetposted on 04.11.2019 by Xinyi Lu, Perry J Williams, Mevin Hooten, James A Powell, Jamie N Womble, Michael R Bower
Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.
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.