Population genetics meets cancer genomics.

T here is a broad consensus that genetic alterations of normal body cells are the basis of cancer progression. Throughout the lifetime of an individual, her or his cells have to divide often, which is associated with occasional genetic changes. Some of the changes lead to uncontrolled cell proliferation and, at later stages of cancer progression, to blood vessel formation in the tumor tissue and distribution of tumor tissue across the body. The molecular genetics of cancer is a very advanced field: Many genetic alterations that predispose an individual to a certain cancer have been identified, and specific genetic pathways of cancer development have been elucidated (1). More recently, studies have been conducted on the scale of the entire genome to identify cancer-associated mutations (2–5). However, our understanding of the population genetic aspects of cancer development, that is, those aspects that relate to the dynamics of cancer cell replication, survival, and evolution, have not yet caught up with the advances in molecular genetics. A study by Bozic et al. (6) in PNAS brings the understanding of the population genetics of cancer cells closer to the edge defined by recent studies of the molecular genetics and genomics of various cancers. Mathematical studies of cancer development date back to the 1950s (7). The studies in this tradition (8–12) focus on the age-specific incidence of cancers. It is remarkable how much can be learned about molecular genetics from the analysis of incidence patterns. For example, in a seminal paper, Knudson (8) anticipated the discovery of tumor suppressor genes by comparing the incidence of retinoblastoma in groups with and without a family history of this cancer. Despite these successes, the analysis of incidence patterns has clear limitations. The mathematical models used to explain the relationship between age and cancer incidence conceptualize cancer progression as a series of component failures of a complex system [e.g., monograph by Frank (11)] and remain quite vague on the dynamics and genetics of tumor cells. With more and more data becoming available on the accumulation of mutations in tumor cell lineages (2–5), mathematical approaches need to be developed to infer the parameters characterizing the population genetics of cancer development. Bozic et al. (6) develop a mathematical model for tumorigenesis based on the multitype branching process—a stochastic process often used in population genetics. The model assumes that cells divide and accumulate mutations (Fig. 1). Some of these mutations, referred to as drivers, increase the fitness of the tumor cell, whereas others, called passengers, are neutral. The model can be used to predict the expected number of passenger mutations in a tumor cell with a certain number of driver mutations. This relationship between passenger and driver mutations depends on the selective advantage that a single driver mutation confers to the tumor cell lineage on average. Bozic et al. (6) then extract the number of driver and passenger mutations carried by tumor cells from previously published genomic data obtained from glioblastoma multiforme (the most common type of brain tumor) (4) and pancreatic adenocarcinoma (the most common type of pancreatic cancer) (5). To this end, they use the computational method called “cancer-specific highthroughput annotation of somatic mutations” (13). By fitting their model to the extracted numbers of driver and passenger mutations, Bozic et al. (6) estimate the average selective advantage of a driver mutation as 0.4% for both glioblastoma multiforme and pancreatic adenocarcinoma. Interestingly, the estimated selective advantage of drivers is almost the same for both cancer types and may therefore constitute a universal quantity not specific to the particular cancer type. Bozic et al. (6) further find that, with this estimate of the selective advantage, predictions of their mathematical model agree with the mean number of tumors and the tumor size observed in the clinical studies on familial adenomatous polyposis (14, 15). Why should we care about the fitness changes of tumor cell lineages during the progression to cancer? Fitness is at the Fig. 1. Sketch of the multitype branching process developed by Bozic et al. (6). A tumor start with one cell carrying a single driver mutation (D). This cell may either die or divide, and it can further mutate. The probabilities of these events are indicated. They depend on the number of driver mutations the cell carries and the selection coefficient s. Driver mutations arise in one of the daughter cells at division with a probability of u = 3.4 × 10. The model assumes discrete generations with a length of 4 d. Passenger mutations (not shown in this sketch) are accumulated at a rate of v = 0.016 from generation to generation.