Neutral tumor evolution?

Tumor growth is an evolutionary process governed by somatic mutation, clonal selection and random genetic drift, constrained by the co-evolution of the microenvironment^1,2. Tumor subclones are subpopulations of tumor cells with a common set of mutations resulting from the expansion of a single cell during tumor development, and have been observed in a significant fraction of cancers and across multiple cancer types³. Peter Nowell proposed that tumors evolve through sequential genetic events⁴, whereby one cell acquires a selective advantage so that its lineage becomes predominant. According to this traditional model, the selective advantage is conferred by a small set of driver mutations, but, as the subclones that bear them expand successively, they accumulate passenger mutations as well, which can be detected in sequencing experiments¹. Genomes of individual tumors contain hundreds to many thousands of these genetic variants, at a wide range of frequencies^5,6. Given that genetic drift alone can drive novel variants to high frequencies, it is of great interest to discern the relative importance of selection and drift in shaping the frequency distribution of variants in any given tumor.

Williams et al.⁷ recently proposed a way to do so. They found that a simple model of tumor growth in which all novel variants are selectively neutral, that is, whose dynamics are governed entirely by drift, predicts a linear relationship between the number of mutations M(f) present in a fraction f of cells and the reciprocal of that fraction: $M\left(f\right)\propto \frac{1}{f}.$ They argued that deviation from this null model, i.e. the R-squared of the linear fit is below the minimum observed in neutral simulations (R² < 0.98), indicates the presence of selection and that this can be tested by means of variant allele frequencies (VAFs) from which f can be derived. Applying this rationale to real cancer data from The Cancer Genome Atlas (TCGA), the test proposed by Williams et al. did not reject the null model, that is neutrality, in about one third of the cases and the authors concluded that these tumors are neutrally evolving. More recently, multiple myelomas with evidence for the proposed linear relationship were associated with poorer prognosis⁸.

While providing an interesting approach to infer selection in human cancers, unfortunately four major simplifying assumptions underlie the analysis by Williams et al. that might render the conclusions questionable.

First, inferring f of variants from their VAF requires accurate estimates of local copy number, overall tumor purity and ploidy. Williams et al. attempted to account for some of these factors by restricting their analyses to variants with VAF between 0.12 and 0.24 and located in copy-neutral regions of the genome. However, even in that limited VAF window, the VAF of a mutation does not reflect its true f in many cases. For example, in tumors with whole genome duplications, i.e. 37% of tumors in the analyzed dataset⁹, the peak of clonal mutations acquired after the whole genome doubling event is at or below VAF = 0.25 (one out of four copies in a 100% pure tumor sample), which would lead to artificial deviation from the linear fit within that VAF window.

Second, the interpretation of the analyses is inconsistent with the use of neutrality as a null model. Failure to reject the null hypothesis is not the same as proving it true, i.e. that all neutral simulations have R² > 0.98 does not prove that non-neutral simulations would never yield R² > 0.98. One would need to demonstrate that this condition is sufficient to infer neutrality but also, no equally suited models of non-neutral tumor growth should yield R² > 0.98.

To assess this, we simulated simple tumor growth in which we explicitly model one subclonal expansion with a selective advantage, i.e. increasing its division rate λ and/or the mutation rate µ of the subclone (Supplementary Methods). Using the original method described by Williams et al., neutrality is rejected only within a narrow range of λ and µ values tested that would lead to detectable subclones (true rejection of neutrality in ~11% of simulations; Fig. 1a). We conclude that a linear fit with R² > 0.98 is not sufficient to call neutrality and that improper use of this model could result in substantial over-calling of neutrality.

Figure 1.

(a) Neutrality calls in simulations of tumor growth with subclonal expansion underlying selective sweeps. The tree topology being modelled is represented on the right together with the parameters of the neutral evolution equations for the two subpopulations of cells (Supplementary Methods). The subclone’s fraction (subclone %) increases with its selective advantage adv_subclone. We vary the λ = 1 + adv_subclone and µ parameters of the subclone along a grid. Simulations are defined as true non-neutral (light blue) or false neutral (dark blue) when the growing subclone has expanded sufficiently to be detectable and the sweep is not complete, i.e. 10% ≤ subclone % ≤ 90%, otherwise the subclone is considered beyond detection (light green). Non-neutral call: R² < 0.98; neutral call: R² ≥ 0.98. (b) As (a), using the Gillespie algorithm to simulate branching processes¹⁰. Simulations leading to subclones beyond detection are either called neutral (light green) or non-neutral (dark green). Because of the stochastic nature of branching processes, different subclone % values are obtained across simulations from the same adv_subclone values. For five increasing adv_subclone values, we report median ± mad of the subclone % across the simulations. (c) Summary ROC curve for the neutral vs. non-neutral classification based on the R² values in 1,919 non-neutral simulations from (b), and 1,919 simulations of neutral tumors. The false positive rate and the true positive rate are highlighted for R² = 0.98 used by Williams et al. (d) dN/dS analysis. Maximum likelihood estimates of the dN/dS ratios and associated 95% confidence intervals for (sub)clonal mutations in TCGA tumors categorized into neutral and non-neutral groups. Ratios for missense and truncating mutations are given. dN/dS > 1 indicates positive selection.

Third, the deterministic model of tumor growth described by Williams et al. relies on strong biological assumptions, among which are synchronous cell divisions, constant cell death and constant mutation and division rates. Stochastic models of tumor growth are biologically more realistic, as they allow for asynchronous divisions and probabilistic mutation acquisition, cell death and division rates. Using simple branching processes to simulate neutral and non-neutral growth¹⁰ (Supplementary Methods), we show that R² > 0.98 for $M\left(f\right)\propto \frac{1}{f}$ is neither a necessary nor a sufficient property of neutrally evolving tumors (Fig. 1b). Although it can be shown that the expected cumulative number of mutations – i.e. the average over many independent samples – $\overline{M}\left(f\right)\propto \frac{1}{f},$¹⁰ due to the biological noise modeled in branching processes, a typical realization of the neutral process in a single sample deviates substantially from the expected linear fit, rendering an R-squared threshold inaccurate to infer neutrality. As a result, discrimination of neutral and non-neutral simulated tumors using a linear fit is almost arbitrary, with 53.5% false positive neutral calls in non-neutral tumors (Fig. 1b) and an area under the ROC curve of 0.42 for the classification of 1,919 neutral and 1,919 non-neutral tumors (Fig. 1c).

Fourth, we reason that in tumors called neutral, no subclonal selection should be detected. To evaluate this, we use an orthogonal method to identify selection, based on the observed variants themselves rather than on their allele frequencies. dN/dS analysis derives the fraction of mutated non-synonymous positions to the fraction of mutated synonymous positions in the coding regions. It has been widely used to detect the presence of negative or positive selection of non-synonymous variants in coding regions^11,12. We applied a dN/dS model optimized for the detection of selection in somatic cancer variants¹³ to TCGA exome data using a published list of 192 cancer genes¹⁴ (Supplementary Methods). The analysis was performed separately using variants called as clonal or subclonal (Supplementary Methods), in tumors called neutral and non-neutral based on the rationale outlined by Williams and colleagues⁷. dN/dS ratio analysis revealed significant positive selection in subclonal mutations of tumors classified as neutral (Fig. 1d), further suggesting that the approach described by Williams et al. is under-equipped to detect the presence or absence of selection.

In summary, Williams et al. proposed that about one third of tumors are neutrally evolving. However, we highlight four simplifying assumptions – to our knowledge not previously highlighted – and find that the proposed approach will often identify individual tumors as neutral when they are non-neutral and non-neutral when they are neutral. A new paper by the same group¹⁵ introduces a Bayesian test for detecting selection from VAFs. The test estimates selection coefficients and, as such, is an important advance over Williams et al.’s frequentist test, which does not. The authors acknowledge that the test can only detect large fitness differences, but nevertheless call tumors that fail it “neutral” when they are merely those in which a weak test has failed to detect selection. We note that neutral theory has been developed in population genetics, ecology and cultural evolution and that similar tests have been proposed in all of these fields and, in all, eventually been found wanting for the same reason: variant abundance distributions do not contain enough information to exclude selection^16–18. It is of clinical importance to identify and better understand the drivers of the potentially more aggressive (sub)clones expanding under selective biological or therapeutic pressure, as these are good candidates for predicting resistance and exploring combination therapy. Williams et al. are to be commended for having introduced explicit neutral tumor growth models into tumor genomics. However, quantifying the relative importance of drift and selection in shaping the allele frequencies of single tumors clearly remains an open challenge. Studies relying on their proposed test (e.g. ⁸) might, then, need reevaluation.