The Finite Element method to aid modelling of complex ecological systems

Klementyna A. Gawecka, James M. Bullock

Predicting how biodiversity responds to environmental change and management interventions remains a major challenge in ecology. Ecological systems are shaped by the interplay of demographic processes, species interactions, dispersal, and spatial heterogeneity across landscapes. Yet, many existing modelling approaches face a trade-off between spatial and ecological complexity, which limits their ability to realistic settings. Reaction-diffusion-advection (RDA) models – a class of partial differential equations (PDEs) – provide a flexible framework for describing community dynamics in continuous space and time. Despite their conceptual appeal, the application of RDAs to realistic ecological systems has been constrained by the computational difficulty of solving coupled nonlinear PDEs on heterogeneous landscapes. Here, we argue that the Finite Element (FE) method provides a practical and scalable solution to this challenge. Widely used in engineering and applied sciences, the FE method enables efficient numerical solutions of spatially explicit PDEs on irregular domains. We outline how combining RDA models with FE methods can expand the predictive capacity of ecological models by allowing realistic representation of landscape structure, dispersal, and species interactions. We also discuss key challenges, including parameterisation, software accessibility, and training, and provide a practical workflow for implementing FE-based ecological models. Broader adoption of FE approaches could substantially strengthen predictive ecology and help bridge the gap between ecological theory and applications.