Integro-difference equations for spatiotemporal ecological forecasting in Stan.
Forecasting ecological dynamics in heterogeneous landscapes requires explicitly accounting for concurrent spatial and temporal changes in the system. Ecological theory can inform modeling decisions, including the mechanism for non-separable spatiotemporal evolution of the ecological process. Reaction-diffusion models represent an example that integrates knowledge of ecological theory for both intrinsic and spatial dynamics of the system but these models can be challenging to implement due to large computational demands. In this case study, we demonstrate how to fit models for population dynamics using spatiotemporal integro-difference equations in Stan. Specifically, we implement discrete semilinear PDE, combining ecological diffusion and logistic growth, in a hierarchical Bayesian framework to model the spatial dynamics of plant populations. The model, including the spatially-varying diffusion parameter, converged under uninformed prior specification using a medium-sized dataset. Spatial reaction-diffusion models are a promising tool to integrate intrinsic population processes, spatial dynamics, and forcing functions to increase the capacity for spatiotemporal ecological forecasting.
I’m a graduate student at Boise State University studying ecological restoration of plants. In my research, I strive to apply quantitative tools to help integrate ecological theory, management support, and different kinds of knowledge about the natural systems.