Mathematical models to study toxicity effects on vegetation

The last few decades have seen significant changes in many ecosystems, as well as noticeable climate shifts in several areas. The need to understand these changes and their causes, as well as methods to predict them and possible solutions to critical scenarios, are issues of the utmost importance that are being investigated across all scientific disciplines. In recent years it has become increasingly clear that one factor that can serve as an indicator to critical climate changes, and how resilient a given ecosystem is, is vegetation dynamics. This realisation has made the understanding of its underlying mechanisms extremely important to explore. Motivated by this, a new biological theory has recently emerged, which identifies the toxic compounds produced by the decomposition of organic material as an essential element in the behaviour of local vegetation. The impact of this theory was immediate and significant: the accumulation of these toxic compounds, known as toxicity, was shown to play an important role in several ecological phenomena: few examples include the formation of patterns on a larger scale, and the diversity of vegetation species. These phenomena can be crucial in certain contexts, such as arid environments. The aim of my research programme is to investigate how toxicity affects plants dynamics, from a mathematical modelling viewpoint. I will focus my attention on two mathematical models and delve deeper into the investigation of how toxicity influences the spatial organisation of vegetation and the biodiversity in a given area. The first model I will explore, one that I have helped create in 2014, is the first model to include effects from both toxicity and water (an important source of nutrients to the vegetation). This model predicted the emergence of asymmetric and dynamic patterns - new and notable ecological results that are in line with experimental data. However, these patterns were only observed numerically in this study. I plan to build a mathematically sound framework for this model which could be later extended to other relevant biological scenarios, such as cell dynamics and cancer invasion. The second model I will investigate, a new model that I will construct, will examine the effects of toxicity in the setting of several different species of plants. The way inter-species effects induced by toxicity affect vegetation dynamics is a question that has not been addressed before; moreover, additional spatial effects that I intend to include in this model may reveal the formation of patterns of coexisting species in this case too. The importance of the study of these models, and the approaches I will undertake, goes beyond the mathematical tools I will develop and the advances I will make. As the breadth of toxicity theory includes biology as well, my proposed research programme has the potential to help us model and understand paramount biological phenomena that include a similar mechanism, such as tumour growth.

The last few decades have seen significant changes in many ecosystems, as well as noticeable climate shifts in several areas. The need to understand these changes and their causes, as well as methods to predict them and possible solutions to critical scenarios, are issues of the utmost importance that are being investigated across all scientific disciplines. In recent years it has become increasingly clear that one factor that can serve as an indicator to critical climate changes, and how resilient a given ecosystem is, is vegetation dynamics. This realisation has made the understanding of its underlying mechanisms extremely important to explore. Motivated by this, a new biological theory has recently emerged, which identifies the toxic compounds produced by the decomposition of organic material as an essential element in the behaviour of local vegetation. The impact of this theory was immediate and significant: the accumulation of these toxic compounds, known as toxicity, was shown to play an important role in several ecological phenomena: few examples include the formation of patterns on a larger scale, and the diversity of vegetation species. These phenomena can be crucial in certain contexts, such as arid environments. During my fellowship, I have built and analysed feasible mathematical models to better explain the formation of vegetation patterns in various ecosystems, and in particular to better understand the role played by toxicity in the formation of such patterns - especially in environments where water is not a limited resource. Few examples include the so called "Janzen Connell distribution" in tropical forests and "tiger bushes" or "travelling arcs" on sloped terrains. In collaboration with experts from ecology and hydrology, we have identified the core mechanisms to include in the models and calibrated the parameter values used to carry out realistic predictions of the underlying dynamics. From the mathematical perspective, on the other hand, the complexity of the constructed models pushed us to extend the available theoretical methods in order to rigorously obtain the emerging patterns exploiting their multiscale structure. The results obtained during the fellowship definitely represent a significant step in the understanding of complex spatio-temporal vegetation dynamics and provide a crucial starting point for further advancements: a more detailed representation of biomass-toxicity dynamics on both flat and sloped terrains may include for instance competition and inertial effects, which in turn lead to so called cross-diffusion and hyperbolic models, respectively. All of this is possible thanks to the analytical techniques developed during the fellowship as well as the interdisciplinary network established in this fundamental period.