Emergent Functional Patterns in Microbial Communities: Data Analysis and Modelling

Recent advancements in sequencing technologies and bioinformatics pipelines have enabled in-depth studies of the taxonomic and functional compositions of microbial communities. A prominent application has been the investigation of the human microbiome, particularly its relationships with health and disease. However, the general properties of microbial compositional profiles and their associations with dysbiosis remain unclear. In this thesis, we analyze the composition of the human gut microbiome in relation to the onset of inflammatory pathologies linked to dysbiosis. Using the notion of a component system as a unifying framework, we examine both taxonomic and functional compositions through macroecological and data-geometry perspectives. Our goal is twofold: to understand the general structural organization of gut microbial communities and to identify specific compositional features that may serve as indicators of dysbiosis. Both perspectives are applied synergistically to provide a comprehensive view of microbial community dynamics and their relationship to health and disease. Our study reveals that the functional representation exhibits a rich correlation structure, particularly among the most abundant functions, which has no parallel in the taxonomic representation. Furthermore, this correlation structure weakens significantly in patients with inflammatory conditions, which may significantly contribute to the understanding of dysbiosis. Geometric analysis further highlights that both taxonomic and functional datasets can be characterized as "star-shaped centers" in a high-dimensional simplex, indicating that much of the observed variability may be represented in terms of a core region stretching along a few distinct directions. For taxonomic data, these directions appear mutually exclusive, while functional data reveal coordinated stretches across multiple directions. Notably, specific stretching directions appear to be preferentially associated with dysbiosis, providing insights into the compositional specificity of disease.