Cartenì, Fabrizio (2014) Self-organization in the development of plant spatial patterns. [Tesi di dottorato]

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The study of self-organization is a relatively new field that received great attention in the last decades related to the study of complex systems. In particular, self-organizing properties of some systems are particularly important in the development of spatial patterns, and their analysis could lead to interesting insights into their functioning. Self-organization is a process in which pattern at the global level of a system emerges solely from the interactions among the lower-level components of the system and the best tool to study such interactions is the use of mathematical models to simulate the emergent behaviour of the system. This thesis addresses two specific problems related to pattern formation in plants at different scales. The first topic is the emergence of vegetation patterns at landscape level. Different putative mechanisms have been proposed as drivers of vegetation pattern formation in different environments. The most studied mechanism is related to short range positive feedbacks and long range negative feedbacks between plants and the available water. Such explanation provides important insights on the dynamics of arid and semiarid environments where water is a limiting factor, but fails to explain the emergence of similar patterns in humid environments. For this reason we formulated a mathematical model to test the effects of the release of autotoxic compounds during litter decomposition, i.e. plant-soil negative feedback, on the emergence of vegetation patterns, in particular the formation of ring structures by clonal plants. Model simulations show that the formation of rings can be explained by autotoxicity and that resource scarcity is not a necessary condition. Moreover, we further developed the model to consider both water and toxic compounds influences on plant biomass growth in order to assess the relative importance of the two mechanisms. Numerical simulations show that water/biomass feedbacks lead to stable spatial patterns, while autotoxicity has a destabilizing effect on the system, leading to unstable patterns that continuously evolve in time. The second topic is the differentiation of primary vascular patterns at cellular/tissue level. Most of the attention has focused on the genetic regulation and the hormonal control of specific aspects of the development of vascular tissues. In this study, we formulated a model defining a set of logical and functional rules to simulate the differentiation of procambium, phloem and xylem and their emerging spatial patterns, starting from an homogeneous group of undifferentiated cells. Specific attention has been given to the factors responsible for the intra- and inter-specific variability of the arrangements observed in plants. Simulation results show that the model is capable of reproducing most vascular patterns observed in plants, from primitive and simple structures constituted of a single strand of vascular bundles (protostele), to more complex and evolved ones, with separated vascular bundles arranged in an ordered pattern within the plant section (e.g. eustele). Presented results demonstrate, as a proof of concept, that a common genetic-molecular machinery can be at the base of different spatial patterns of plant vascular tissues.

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