Cancer progression is driven by mutation and selection in an asexually reproducing population of tumor cells. We present mathematical models for the genetic progression of cancer. A statistical model is introduced to describe the ordered accumulation of mutations in cancer genomes and shown to improve genetics-based survival predictions for patients with renal cell carcinoma. We analyze the evolutionary dynamics of tumor progression using a population genetics approach and derive an approximate closed-form expression for the waiting time to cancer. Finally, we discuss statistical methods for inferring the genetic diversity of tumors from ultra-deep sequencing experiments and compare experimental results to model predictions.
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