Abstract
Recent work of Sottoriva, Graham, and collaborators have led to the controversial claim that exponentially growing tumors have a site frequency spectrum that follows the 1/f law consistent with neutral evolution. This conclusion has been criticized based on data quality issues, statistical considerations, and simulation results. Here, we use rigorous mathematical arguments to investigate the site frequency spectrum in the two-type model of clonal evolution. If the fitnesses of the two types are λ0 < λ1, then the site frequency spectrum is c/fα where α = λ0/λ1. This is due to the advantageous mutations that produce the founders of the type 1 population. Mutations within the growing type 0 and type 1 populations follow the 1/f law. Our results show that, in contrast to published criticisms, neutral evolution in an exponentially growing tumor can be distinguished from the two-type model using the site frequency spectrum.
Highlights
Sottoriva et al introduced the Big Bang model of cancer initiation, which postulated that all the mutations needed were present when the tumor started growing
We use mathematical analysis to show that with enough sequence data the site frequency spectrum can be used to distinguish neutral evolution from the two-phase model of clonal evolution. This conclusion differs from previously published simulation results
Before we describe the math, we want to make it clear that that this work only discusses the theoretical aspects of cancer genomics and is not concerned with practical problems in making inferences on cancer genomic data, which could hide some of the theoretical effects due to errors, bias, sampling, and other issues discussed in the criticisms listed above
Summary
Following up on the introduction of the Big Bang model by Sottoriva et al [1], Sottoriva and Graham [2] described what they called “a pan-cancer signature of neutral tumor evolution:”. Neutral tumor evolution: a theoretical perspective the number of mutations with frequency f will have the form c/f. The derivation of this result is remarkably simple and is given in Methods. In 2016, Williams et al [3] found that 323 of 904 samples from 14 cancer types showed excellent straight line fits when the cumulative number of mutations of frequency f is plotted versus 1/f. This paper has been cited 200 times, but among these works, there are a number of papers criticizing the result.
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