Ruiz-Reynés, Daniel (Supervisor: Gomila, Damià)
PhD Thesis (2019)
In this thesis we study the dynamics of vegetation patterns in Posidonia oceanica meadows. The first introductory chapter presents a review of vegetation patterns in different ecosystems, the methodologies used in the literature to study each case, and the previous works of Posidonia oceanica with implications in the description of the meadows growth. In the second chapter of the thesis, based on previous knowledge of clonal-growth plants, we develop a coarse grained model that describes the evolution of the meadows. We show that long-range competition is the mechanism responsible for the formation of patterns and we are able to infer the interaction distance. The model allows to reproduce the spatial features of vegetation approaching to the coast, where mortality increases. Additionally, we study the relevance of the dependence on the angle of the model in the spatiotemporal dynamics. We conclude that the density of apices in different directions of growth homogenizes with time, only being enhanced those particular directions growing at the front facing outwards the meadow. The third chapter presents a systematic derivation of a simplified equation from the original model, reducing substantially the difficulty of the problem. We discuss the different approximations made and the validity of the equations derived. The fourth chapter focuses on an intermediate equation obtained from the derivation, that provides quantitative agreement with the original model. We study in detail its bifurcation diagram characterizing different patterns and localized structures. In the last part of this chapter we study the dynamics of vegetation fronts in the simplest one dimensional case. The last chapter tries to determine if the presence of hydrogen sulfide in the sediment, result of the spreading of organic matter due to water movement that later decomposes, is a valid long-range competition mechanism able to explain the formation of patterns. We conclude that patterns form as a result of this interaction. Furthermore, the model predicts an oscillatory instability of the homogeneous solution which creates a very rich phase diagram with different dynamical behaviors still to explore.