PDE models for vegetation biomass and autotoxicity

Numerical techniques are widely used to simulate population dynamics in space. In vegetation dynamics, these techniques are very useful to investigate how plants grow, compete for resources, and react to environmental factors within the ecosystem. Plant–soil feedback (PSF) refers to the process where plants or a community alter the biotic and abiotic characteristics of soil that affects the growth of plants or community subsequently growing in that soil. During the last three decades, PSF has been recognized as an important driver for the emergence of vegetation patterns. The importance of studying such vegetation patterns is that they provide an insight into potential ecological changes and illustrate the flexibility and resilience of an ecosystem. Despite the fact that water depletion was once thought to be a major factor in the development of vegetation patterns the existence of patterns in ecosystems without water limitations serves as evidence that this is not the case. In this study, we examine how negative plant–soil feedback contributes to the dynamics of plant biomass. We provide a comparison of different reaction–diffusion PDE models explaining the dynamics of plant biomass in the presence of autotoxicity produced by litter decomposition. We introduce different growth terms, including logistic and exponential, along with additional factors such as extra mortality and inhibitor terms, and develop six distinct models to investigate their individual and combined effects on biomass toxicity distribution. By applying appropriate numerical techniques, we solve the proposed reaction–diffusion PDE models in MATLAB to predict the impact of soil toxicity on plant biomass.