Spatial organization is a fundamental feature of tumor architecture that profoundly shapes cellular evolution and selection. This lecture examines how spatial structure influences evolutionary dynamics, with implications for driver mutation selection, tumor progression, and therapeutic resistance. I will begin by surveying spatially explicit computational modeling approaches for cellular dynamics and evolution, emphasizing the relationship between continuous-space agent-based models and coarse-grained deme models that enable analytical tractability. Through selected studies, I will explore mutant evolution in spatially structured populations, first examining expanding populations across different dimensions, then investigating mutant invasion at steady state, which is relevant for both non-neoplastic tissue and tumors in growth plateau phases during multi-step carcinogenesis. I will close by discussing our recent finding that spatial structure can reverse conventional selection: mutants with increased reproductive output may experience negative selection when multiple kinetic parameters change simultaneously, for instance, concurrent increases in both division and death rates. This challenges the assumption that higher reproductive output confers advantage. Overall, the lecture highlights how spatial population structure can fundamentally alter evolutionary principles in unexpected ways, deepening our understanding of tumor cell emergence during progression and therapy.
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