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Currently available bulk sequencing data do not necessarily support a model of neutral tumor evolution

Nature Genetics volume 50, pages 1620–1623 (2018)Cite this article

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To the Editor — Williams et al.1 analyzed next-generation sequencing data from bulk tumor samples, supporting the hypothesis that selection is limited to times before malignant transformation while tumor cell populations afterward evolve exclusively by neutral evolution. The authors arrived at their conclusions by showing that the expected number of mutations (M) in an exponentially increasing population undergoing only neutral evolution grows linearly with the inverse allele frequency (1/f) of mutant alleles. The allele frequency of a variant is defined as the proportion of cells containing that particular variant. Their reasoning was based on the fact that, in a neutrally evolving cell population, all subclones grow at the same rate, so the allele frequency is fixed as the inverse of the number of cells present at the time of appearance of a new variant. The authors then concluded that a tumor displaying a linear relationship between the number of mutations and the inverse allele frequency should imply that the population evolves without selection. They also performed simulations of a branching-process model with selection to show that selection cannot explain a linear relationship between M and 1/f. Furthermore, they observed a high correlation between M and 1/f in about one-third of the patient samples investigated as further indication of neutral tumor evolution. Their findings corroborate previous results2 based on the ‘Big Bang’ model that suggested a similar conclusion in colorectal cancer using single-time-point bulk sequencing data.

We believe that the authors arrived at an erroneous conclusion, which also stands in contrast to other recent findings in this field3,4,5, based on flawed logic known as the ‘fallacy of the converse’. The fact that a model of neutral evolution leads to a linear relationship between M and 1/f does not imply that a linear relationship proves the presence of neutral evolution. In more abstract terms, A implying B does not necessarily mean that B implies A. Here we demonstrate that models with selection can also lead to a linear relationship between M and 1/f and that, therefore, linearity is a test statistic that cannot be used to distinguish between populations evolving with and without selection. Our results indicate that the claims made by Williams et al.1 have little merit.

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Fig. 1: A simple branching-process model of tumor evolution.
Fig. 2: An infinite-allele branching-process model of tumor evolution, including sampling as in the original study.
Fig. 3: The model from the original study for multiple simulations.

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Acknowledgements

The authors would like to acknowledge discussions with members of the Michor laboratory and with N. Navin, D. Pellman and K. Polyak. This work was supported by the Dana-Farber Cancer Institute Physical Sciences Oncology Center (NCI U54CA193461).

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Author notes

  1. These authors contributed equally: Thomas O. McDonald, Shaon Chakrabarti.

Authors and Affiliations

  1. Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA, USA

    Thomas O. McDonald, Shaon Chakrabarti & Franziska Michor

  2. Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, USA

    Thomas O. McDonald, Shaon Chakrabarti & Franziska Michor

  3. Center for Cancer Evolution, Dana-Farber Cancer Institute, Boston, MA, USA

    Thomas O. McDonald & Franziska Michor

  4. Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, MA, USA

    Thomas O. McDonald, Shaon Chakrabarti & Franziska Michor

Authors
  1. Thomas O. McDonald
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  2. Shaon Chakrabarti
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  3. Franziska Michor
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Contributions

T.O.M. and S.C. developed the models, performed simulations and analyzed results. F.M. conceived the idea. All authors wrote the manuscript.

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Correspondence to Franziska Michor.

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McDonald, T.O., Chakrabarti, S. & Michor, F. Currently available bulk sequencing data do not necessarily support a model of neutral tumor evolution. Nat Genet 50, 1620–1623 (2018). https://doi.org/10.1038/s41588-018-0217-6

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