Measuring Cancer Evolution from the Genome

Bibliographic Reference

Graham, T. A., & Sottoriva, A. (2017). Measuring cancer evolution from the genome. The Journal of Pathology, 241(2), 183–191. https://doi.org/10.1002/path.4821

Core Argument

To detect selection in cancer genomes, we must first understand what the absence of selection looks like. The cancer genome records the temporal history of mutation and selection through the frequency distribution of mutations. Under neutral evolution, this distribution follows a 1/f pattern — a predictable null model against which selection can be detected. Applying this framework reveals that selection signatures are rarer than gradualist models predict, with ~30% of cancers across 14 types showing no evidence of subclonal selection.

Methods

This is a review synthesizing population genetics theory, mathematical modeling, and cancer genomics. It describes two primary approaches for detecting selection: (1) the 1/f test — testing whether the cumulative distribution of subclonal mutation frequencies follows the 1/f power law predicted under neutral exponential growth, and (2) the dN/dS ratio — testing whether non-synonymous mutations are enriched relative to synonymous ones at specific loci. The review integrates computational modeling of clone growth and spatial constraint, phylogenetic methods, and empirical data from multi-region sequencing studies.

Key Findings

• Neutral evolution provides a necessary null model. Under neutrality in a growing population, the cumulative number of mutations at frequency f follows a 1/f distribution: the number of mutations doubles each time the frequency halves. Deviations from 1/f indicate recent selection. Without this null model, selection cannot be reliably detected — one must distinguish a selected clonal outgrowth from a clone that reached high frequency by drift alone.
• Selection signatures appear rarer than expected. Applying the 1/f test across 14 solid cancer types, ~30% of cancers showed no evidence of subclonal selection — the null hypothesis of neutral evolution could not be rejected. This is lower than gradualist models would predict.
• Clone detectability is limited by timing and selective advantage. A selected clone is only detectable if “caught in the act” — after reaching minimal detectable size but before repopulating the entire tumor (after which neutrality resumes). Empirical measurements of selective advantage in tumors are lacking, but modeling suggests even sizable advantages produce only slight frequency changes in a growing population, especially when a clone arises in an already-large tumor.
• The 1/f test has important caveats. Limited sequencing depth can blur the signal. A specific combination of selected subclones could theoretically masquerade as a 1/f distribution. However, neutral evolution remains the more parsimonious explanation when a 1/f-like VAF distribution is observed. The test provides an objective indication of subclonal selection without requiring prior knowledge of subclonal driver identity.
• Punctuated phenotype evolution is compatible with both gradual and punctuated genome evolution. A saltatory genotype change (e.g., whole-genome doubling, chromothripsis) can produce punctuated phenotype evolution, but gradual accumulation of small-effect mutations can also produce apparent phenotypic leaps when a threshold is crossed.

Concepts Introduced or Used

• neutral-evolution — the null case against which selection must be detected; all cells grow at the same average rate
• 1/f distribution: the cumulative frequency distribution of subclonal mutations expected under neutral exponential growth
• clonal-evolution — the central paradigm; the review provides the analytical toolkit for measuring it
• driver-mutation — positively selected mutations; their detection requires distinguishing over-representation from drift
• passenger-mutation — more numerous than drivers and more informative for detecting clonal expansions because they provide the statistical signal
• variant-allele-fraction — the measurable proxy for clone frequency; subject to sequencing depth limitations
• cancer-cell-fraction — corrected VAF estimate used in the 1/f test
• punctuated-evolution — discussed as a competing theory to gradualism; distinction between genome-level and phenotype-level punctuation
• subclonal-architecture — revealed by the frequency distribution of mutations
• branching-evolution — detectable through phylogenetic analysis of shared and private mutations
• intratumor-heterogeneity — both the product of and the window into evolutionary dynamics
• dN/dS ratio: normalized ratio of non-synonymous to synonymous mutations; >1 indicates positive selection
• Molecular clock: constant-rate mutation accumulation enabling relative timing of clonal branching events
• Genetic drift: random frequency fluctuations in a neutrally evolving population; can produce clones indistinguishable from selected ones

Entities Referenced

• Genes: APC, KRAS (examples of drivers with context-dependent selective advantage)
• Methods: 1/f test, dN/dS ratio, phylogenetic reconstruction, multi-region sequencing
• Cancer types: 14 solid cancer types analyzed in the neutrality study
• Software tools referenced: bioinformatics tools for identifying mutation clusters (not named specifically)

Limitations (as stated by authors)

• The 1/f test must be applied with caution — limited sequencing depth can blur the evolutionary signal for both selection and neutrality. A specific combination of selected subclones could theoretically masquerade as a 1/f distribution.
• Empirical measurements of selective advantage of clones in growing human tumors are lacking; expectations about clone detectability are largely model-based.
• dN/dS applied to subclonal selection within a single tumor is extremely challenging because the signal from a single driver locus is drowned out by passenger mutations; it works better in cohort-level analyses.
• Clone detectability is limited by both timing (clones must be caught mid-expansion) and sequencing resolution (~5% VAF at 100x coverage). Low selective advantages that cause only slight frequency changes are largely indistinguishable from background neutral evolution.

Relevance to Clonal Evolution

This is the conceptual and methodological bridge between population genetics theory and cancer genomics practice. It formalizes why neutral evolution must be understood before selection can be claimed, and provides the 1/f test as an operational null model. The paper’s finding that selection is rarer than expected — and its discussion of how growth dynamics and clone detectability interact — directly informs how cancer-cell-fraction distributions should be interpreted in studies of subclonal-architecture and neutral-evolution. A key implicit assumption of the 1/f null is exponential growth; whether decelerating growth models (such as gompertzian-growth) alter the expected null distribution is not addressed in this paper but is a natural extension.