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Life on Earth is characterised by an amazing variety of living forms which are in continuous evolution to better adapt to the surrounding environment and highly connected one to the other. A deep investigation of different living systems has recently been favoured by the huge quantity of data nowadays available. The present thesis is the final result of a journey through complex patterns in theoretical ecology. We study both models and issues in data analysis as well as the connections between them within a mathematical framework. In particular, we explore the different aspects of the biodiversity of an ecosystem, referring with this term to the variety of its species. Our interest is to investigate how these species interact with each other and with the surrounding environment and how these connections can structure recurrent macro-ecological patterns. Indeed, despite their diversity and complexity, it is straightforward that ecological systems share similar behaviours. This fact suggests that such systems are driven by a common mechanism, which is insensitive to the details of the systems on which it acts. A theoretical understanding is therefore possible through the development of mathematical models rich enough to reproduce the investigated patterns, but containing only the essential ingredients able to originate them. In the first part of the present thesis, we explore the fundamentals of spatial point process theory, a powerful mathematical tool to model data in the form of sets of spatial locations of points. In particular, since our datasets usually consist of information on trees belonging to different species, we focus on the so-called superposed process and its first and second-order statistics. We then study an algorithm to infer the intensity function of a point process which is capable to reduce sampling fluctuations and to capture relevant spatial characteristics of a spatial pattern, as space anisotropy and clustering. Finally, we explore in details the notions of ecological diversity and similarity and some of the most popular indexes used to measure them. In particular, we study how to insert them in the context of point processes’ theory. Our aim is at finding an analytical relation for the decay of similarity between two regions of a landscape as a function of the distance between them, by extending the classic notion of Sørensen’s index to incorporate spatial information. In the second part of the thesis, we tackle the problem of inferring the total bio- diversity of an ecosystem when only scattered samples are observed. In particular, we propose a novel upscaling method which, by exploiting the scaling invariance property of the negative binomial distribution, generates accurate and robust pre- dictions. We test it on both computer-generated and real forests and we show that it outperforms other methods previously proposed in literature.

The population of adults with congenital heart disease is increasing due to advancements in cardiology and cardiac surgery. Many patients face medical complications and psychosocial difficulties; however, it is not yet clear whether there is a direct relationship between medical status and the psychological functioning of these patients. This systematic review of the relevant literature is an attempt to: provide a comparison between the population of adults with congenital heart disease, the healthy reference population and similar cardiac populations when it comes to psychological functioning; explore the relationship between medical status/cardiac condition and psychological functioning; and identify the predictors of psychological distress in this population.