GENERALIZED FISHER-TYPE MODEL FOR COASTAL GREEN INFRASTRUCTURE DYNAMICS

Speaker: Associate Professor Dr. Ikha Magdalena

Here, we present a generalized Fisher-type reaction–diffusion model to characterize the spatiotemporal dynamics of the density of coastal green infrastructures (particularly coastal vegetation, such as mangrove and seagrass) that accounts for interactions with hydrodynamic conditions. It means that the model has a nonlinear growth term, whose exponent can be modulated in order to describe some class of density dependent ecological processes that are defined in a more general form than the classic logistic one. These mechanisms enable the model to reproduce threshold-mediated growth behavior characteristic of coastal environments subject to diverse hydrodynamic and sedimentary regimes. We develop a high-order numerical scheme numerical scheme, which discretizes the governing equation in space using the fourth-order accurate finite difference method and time using an explicit solver. This method offers significantly better accuracy at narrower vegetation fronts than any other methods available, while maintaining computational efficiency. Homogeneous Neumann boundary conditions are used (at the open side) to simulate isolated coastal domains and no vegetation flux. The interaction between diffusion and nonlinear growth generates traveling-wave-like fronts, which is the natural inclination of plant life moving into unplanted territory according to numerical simulations. A systematic parametric study reveals that local density is highly sensitive to a nonlinear growth exponent, while the rate of spatial distribution is controlled by diffusion. These findings show a strong connectivity between model parameters and ecological interpretations, e.g. dispersal mechanisms and environmental gradients resistance. This generic framework provides a robust and tractable modelling tool for coastal systems vegetation dynamics. It also opens opportunities for future coupling to hydrodynamic models, such as the Shallow Water Equations (SWE), in order to explore wave–vegetation interactions, including wave attenuation induced by the vegetation, and provide further support towards designing nature-based solutions for coastal protection.