  Cancer results from genetic alterations that disturb the normal cooperative
behavior of cells. Recent high-throughput genomic studies of cancer cells have
shown that the mutational landscape of cancer is complex and that individual
cancers may evolve through mutations in as many as 20 different
cancer-associated genes. We use data published by Sjoblom et al. (2006) to
develop a new mathematical model for the somatic evolution of colorectal
cancers. We employ the Wright-Fisher process for exploring the basic parameters
of this evolutionary process and derive an analytical approximation for the
expected waiting time to the cancer phenotype. Our results highlight the
relative importance of selection over both the size of the cell population at
risk and the mutation rate. The model predicts that the observed genetic
diversity of cancer genomes can arise under a normal mutation rate if the
average selective advantage per mutation is on the order of 1%. Increased
mutation rates due to genetic instability would allow even smaller selective
advantages during tumorigenesis. The complexity of cancer progression thus can
be understood as the result of multiple sequential mutations, each of which has
a relatively small but positive effect on net cell growth.
