Analisi di un modello matematico per la simulazione della formazione di pattern nel Paspalum Vaginatum ​

Understanding the dynamics of plant communities in water-limited systems as drylands is crucial as these areas currently occupy the 41% of the Earth’s land surface, with climate models predicting that their extension will further increase in the future due to climate change. Field research in drylands revealed that in these biomes, vegetation dynamics includes mechanisms that can result either in long-range competition for the scarce resources or in short-range facilitation for the growth of new plants. The combination of these processes show how plants self-organize into patterns. By organizing spatially, vegetation can accumulate resources in limited areas, thus allowing the system to withstand arid conditions. However, the large spatio-temporal scales involved in the process do not allow for the observation of the pattern formation dynamics. To overcome this issue, it was proposed to couple manipulative experiments conducted on species that display pattern formation on a fine spatio-temporal scale to numerical models. Currently, the species employed in those experiments is the grass P.Vaginatum, which has been observed to form regular patterns in some contexts. Running simulations on a model coupled to the experiment allows, primarily, to verify that the observed mechanisms which are represented numerically can actually lead to pattern formation. Furthermore, they are also useful for simulating experiments that would require multiple manipulations to be conducted experimentally, such as studying the conditions for which patterns are stable or how vegetation reacts to a change in the environmental conditions. There are many examples of vegetation dynamics models in literature, however, the vast majority of those represent plant reproduction as a diffusive process: while this could be a good approximation for vegetation communities that expand by dispersing seeds, this can’t be said for clonal plants, species such as P.Vaginatum that colonize its surroundings by continuously growing new clones of themselves on their branches. Therefore, this work proposes a new mathematical model, developed for simulating the vegetation dynamics induced by clonal growth in an experimental setup. Adapting a well-known model (Gilad et al., 2004) to a lab conditions, the model was also modified by substituting the typical diffusion term with a ”clonal growth term”, conceived to represent clonal plants’ features during their expansion. Mathematical analyses focused on the stability of the non-spatial solutions against uniform and periodic perturbations. After that, the model was tested numerically to understand its behaviour under different initial biomass distribution or simulated drought stress conditions. Within some limits on the simulation conditions, such as wide enough spatial perturbations on the initial conditions or iterations performed over relatively short simulated-time scales, the proposed model reproduced the original model’s solutions. However, it was observed that outside those boundaries the model produced peculiar results, such as the production of amorphous patterns, which differentiate it from those already present in literature. While some numerical issues related to the particular mathematical form chosen for the clonal growth term were identified, the results shown in this work demonstrate how the proposed model can be considered as the prototype of new alternatives to the diffusive models currently employed.