The Impact of Autotoxicity on Vegetation Dynamics: a Mathematical and Ecological Overview

Abstract

Understanding vegetation dynamics, particularly the mechanisms leading to the emergence of several types of vegetation patterns in different environments, is a crucial goal of our time. Such structures, in fact, are not simply interesting from the theoretical viewpoint, but also play a major role in preserving ecosystems’ resilience by being important ecological indicators of their “fitness”. In recent years, increasing attention has been devoted to the influence of so-called autotoxicity on the dynamics of living organisms - including vegetation. This has opened the door for new, biologically feasible explanations of experimental observations known to theoretical and applied ecologists which were hard to justify by means of “standard” models focusing only on the interplay between biomass and water dynamics. Together with several researchers both from the mathematical and the ecological field, we have explored how autotoxicity affects the formation of several types of patterns, including fairy circles and Janzen-Connell distribution. To this aim, we have constructed and analysed mathematical models based on partial differential equations including reaction, diffusion, and advection mechanisms (the latter to account for the case of sloped terrains). In this lecture, I will introduce the concept of autotoxicity from the biological viewpoint and then provide an overview of several models we constructed in recent years including this factor. The aim of my talk is to show the impact of autotoxicity on vegetation and its ability to lead to novel features in the emerging patterns, both in mathematical and ecological terms. From an analytical perspective, in fact, autotoxicity leads to more complicated stationary/travelling patterns, which can be investigated by extending tools in the area of Geometric Singular Perturbation Theory. Ecologically, the inclusion of autotoxicity provides a potential justification of observed patterns also in environments where water is not a limited resource.