Cancer as a disease causes about 8.8 million deaths worldwide per year, a number that will largely increase in the next decades. Although the cellular processes involved in tumor emergence are more and more understood, the implications of specific changes at the cellular scale on tumor emergence at the tissue scale remain elusive. Main reasons for this lack of understanding are that the cellular processes are often hardly observable especially in the early phase of tumor development and that the interplay between cellular and tissue scale is difficult to deduce. Cell-based mathematical models provide a valuable tool to investigate in which way observable phenomena on the tissue scale develop by cellular processes. The implications of these models can elucidate underlying mechanisms and generate quantitative predictions that can be experimentally validated. In this thesis, we infer the role of genetic and phenotypic cell changes on tumor development with the help of cell-based Markov chain models which are calibrated by tissue-scale data. In the first part, we utilize data on the diagnosed fractions of benign and malignant tumor subtypes to unravel the consequences of genetic cell changes on tumor development. We introduce extensions of Moran models to investigate two specific biological questions. First, we evaluate the tumor regression behavior of pilocytic astrocytoma which represents the most common brain tumor in children and young adults. We formulate a Moran model with two absorbing states representing different subtypes of this tumor, derive the absorption probabilities in these states and calculate the tumor regression probability within the model. This analysis allows to predict the chance for tumor regression in dependency of the remaining tumor size and implies a different clinical resection strategy for pilocytic astrocytoma compared to other brain tumors. Second, we shed light on the hardly observable early cellular dynamics of tumor development and its consequences on the emergence of different tumor subtypes on the tissue scale. For this purpose, we utilize spatial and non-spatial Moran models with two absorbing states which describe both benign and malignant tumor subtypes and estimate lower and upper bounds for the range of cellular competition in different tissues. Our results suggest the existence of small and tissue-specific tumor-originating niches in which the fate of tumor development is decided long before a tumor manifests. These findings might help to identify the tumor-originating cell types for different cancer types. From a theoretical point of view, the novel analytical results regarding the absorption behavior of our extended Moran models contribute to a better understanding of this model class and have several applications also beyond the scope of this thesis. The second part is devoted to the investigation of the role of phenotypic plasticity of cancer cells in tumor development. In order to understand how phenotypic heterogeneity in tumors arises we describe cell state changes by a Markov chain model. This model allows to quantify the cell state transitions leading to the observed heterogeneity from experimental tissue-scale data on the evolution of cell state proportions. In order to bridge the gap between mathematical modeling and the analysis of such data, we developed an R package called CellTrans which is freely available. This package automatizes the whole process of mathematical modeling and can be utilized to (i) infer the transition probabilities between different cell states, (ii) predict cell line compositions at a certain time, (iii) predict equilibrium cell state compositions and (iv) estimate the time needed to reach this equilibrium. We utilize publicly available data on the evolution of cell compositions to demonstrate the applicability of CellTrans. Moreover, we apply CellTrans to investigate the observed cellular phenotypic heterogeneity in glioblastoma. For this purpose, we use data on the evolution of glioblastoma cell line compositions to infer to which extent the heterogeneity in these tumors can be explained by hierarchical phenotypic transitions. We also demonstrate in which way our newly developed R package can be utilized to analyze the influence of different micro-environmental conditions on cell state proportions. Summarized, this thesis contributes to gain a better understanding of the consequences of both genetic and phenotypic cell changes on tumor development with the help of Markov chain models which are motivated by the specific underlying biological questions. Moreover, the analysis of the novel Moran models provides new theoretical results, in particular regarding the absorption behavior of the underlying stochastic processes.

Die Intra-Tumor-Heterogenität spiegelt eine kontinuierliche Entwicklung zwischen den Zellen eines einzelnen Tumors wider. Sie ist eine der Hauptursachen für Arzneimittelresistenz bei der Krebsbehandlung. Um dieses Problem anzugehen, ist es daher wichtig, die Tumorevolution innerhalb eines einzelnen Patienten zu verstehen und erfolgreich zu modellieren. Bisherige Arbeiten haben sich nicht erfolgreich mit der Evolution von Tumoren befasst, deren Treiber strukturelle Veränderungen im Genom sind, wie z. B. somatische Kopienzahlveränderungen (SCNAs). Diese Arbeit befasst sich mit der Herausforderung, die Tumorevolution als Folge solcher Veränderungen zu charakterisieren. Wir verwenden einen phylogenetischen Ansatz zur Analyse von multiregionalen Datensätzen in einer großen Pan-Krebs-Kohorte. Wir untersuchen häufige SCNAs in verschiedenen Stadien der Tumorentwicklung und führen eine neue Methode, MEDICC2, ein, die die Tumorevolution innerhalb eines einzelnen Patienten rekonstruiert. In dieser Arbeit haben wir häufige SCNAs charakterisiert, die früh in der Tumorentwicklung auftreten. Aufgrund der Struktur der Kohorte ist die Charakterisierung der subklonalen SCNAs nicht eindeutig. Unsere neue Methode, MEDICC2, akzeptiert höhere Kopienzahlzustände und berücksichtigt die Verdopplung des gesamten Genoms, ein häufiges Ereignis in Tumoren, was eine genauere Modellierung der Tumorevolution ermöglicht. / Intra-tumor heterogeneity reflects an ongoing evolution among cells of a single tumor. It is one of the leading causes of drug resistance in cancer treatments. Therefore, to address this issue, it is important to understand and successfully model tumor evolution within a single patient. Previous work has failed to successfully address the evolution of tumors whose drivers are structural changes in the genome, such as somatic copy number alterations (SCNAs). This work addresses the challenge of characterizing tumor evolution as a result of such changes. We use a phylogenetic approach to analyze multi-region datasets in a large pan-cancer cohort. We investigate frequent SCNAs at different stages of tumor development, and introduce a new method, MEDICC2, which reconstructs tumor evolution within a single patient. In this work, we characterized frequent SCNAs that occur early in tumor development. Due to the structure of the cohort, the characterization of subclonal SCNAs remains inconclusive. Our new method, MEDICC2, accepts higher copy number states and takes into account whole-genome doubling, a frequent event in tumors, which allows for a more precise modeling of tumor evolution.