ENHANCED FORECASTING OF BIOMASS-TOXICITY-WATER MODELS USING NUMERICAL SIMULATIONS

Numerical techniques are essential tools to solve reaction-diffusion models in ecology, addressing the intrinsic complexity arising from nonlinear and coupled systems. Advanced numerical methods provide efficient spatial and temporal resolution in order to predict the emergence of complex patterns, such as the ones arising in vegetation. The emergence of vegetation patterns is significantly influenced by plant-soil feedback, which alters soil properties, shapes nutrient availability, influences plant interactions, and develops mutualistic relationships with soil microbes. Understanding these feedback processes is essential to manage and conserve ecosystems, predict responses to environmental change, and implement appropriate land management strategies. The formation of vegetation patterns has been the focus of significant study and debate over the years and has been linked to two main mechanisms: the depletion of water in the center of vegetation patches and the production of toxicity by litter decomposition in soil. In this study, we investigate the role of water depletion and autotoxicity in the formation of spatial vegetation patterns. We propose and compare various reaction-diffusion PDE models that describe the dynamics of plant biomass under water scarcity and the presence of toxicity caused by litter decomposition. We incorporate logistic and exponential growth functions to capture different growth mechanisms, along with mortality and inhibition terms to simulate the components' individual death rates and inhibitory effects. This leads us to six alternative reaction-diffusion PDE models, which we solve using suitable numerical techniques.