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

The balance between intrinsic and ecological fitness defines new regimes in eco-evolutionary population dynamics

Selection upon intrinsic fitness differences is one of the most basic mechanisms of evolution, fundamental to all biology. Equally, within macroscopic populations and microscopic environments, ecological interactions influence evolution. Direct experimental evidence of ecological selection between microscopic agents continues to grow. Whilst eco-evolutionary dynamics describes how interactions influence population fitness and composition, we build a model that allows ecological aspects of these interactions to fall on a spectrum independent of the intrinsic fitness of the population. With our mathematical framework, we show how ecological interactions between mutating populations modify the estimated evolutionary trajectories expected from monoculture fitnesses alone. We derive and validate analytical stationary solutions to our partial differential equations that depend on intrinsic and ecological terms, and mutation rates. We determine cases in which these interactions modify evolution in such ways as to, for example, maintain or invert existing monoculture fitness differences. This work discusses the importance of understanding ecological and intrinsic selection effects to avoid misleading conclusions from experiments and defines new ways to assess this balance from experimental results. Using published experimental data, we also show evidence that real microbiological systems can span intrinsic fitness dominant and ecological-effect dominant regimes and that ecological contributions can change with an environment to exaggerate or counteract the composite populations' intrinsic fitness differences.

Characterization of Cancer Evolution Landscape Based on Accurate Detection of Somatic Mutations in Single Tumor Cells

Accurate detection of somatic mutations in single tumor cells is greatly desired as it allows us to quantify the single-cell mutation burden and construct the mutation-based phylogenetic tree. Here we developed scNanoSeq chemistry and profiled 842 single cells from 21 human breast cancer samples. The majority of the mutation-based phylogenetic trees comprise a characteristic stem evolution followed by the clonal sweep. We observed the subtype-dependent lengths in the stem evolution. To explain this phenomenon, we propose that the differences are related to different reprogramming required for different subtypes of breast cancer. Furthermore, we reason that the time that the tumor-initiating cell took to acquire the critical clonal-sweep-initiating mutation by random chance set the time limit for the reprogramming process. We refer to this model as a reprogramming and critical mutation co-timing (RCMC) subtype model. Next, in the sweeping clone, we observed that tumor cells undergo a branched evolution with rapidly decreasing selection. In the most recent clades, effectively neutral evolution has been reached, resulting in a substantially large number of mutational heterogeneities. Integrative analysis with 522-713X ultra-deep bulk whole genome sequencing (WGS) further validated this evolution mode. Mutation-based phylogenetic trees also allow us to identify the early branched cells in a few samples, whose phylogenetic trees support the gradual evolution of copy number variations (CNVs). Overall, the development of scNanoSeq allows us to unveil novel insights into breast cancer evolution.

Single-cell phylogenies reveal changes in the evolutionary rate within cancer and healthy tissues

Cell lineages accumulate somatic mutations during organismal development, potentially leading to pathological states. The rate of somatic evolution within a cell population can vary due to multiple factors, including selection, a change in the mutation rate, or differences in the microenvironment. Here, we developed a statistical test called the Poisson Tree (PT) test to detect varying evolutionary rates among cell lineages, leveraging the phylogenetic signal of single-cell DNA sequencing (scDNA-seq) data. We applied the PT test to 24 healthy and cancer samples, rejecting a constant evolutionary rate in 11 out of 15 cancer and five out of nine healthy scDNA-seq datasets. In six cancer datasets, we identified subclonal mutations in known driver genes that could explain the rate accelerations of particular cancer lineages. Our findings demonstrate the efficacy of scDNA-seq for studying somatic evolution and suggest that cell lineages often evolve at different rates within cancer and healthy tissues.

Cancer genomes tolerate deleterious coding mutations through somatic copy number amplifications of wild-type regions

Cancers evolve under the accumulation of thousands of somatic mutations and chromosomal aberrations. While most coding mutations are deleterious, almost all protein-coding genes lack detectable signals of negative selection. This raises the question of how tumors tolerate such large amounts of deleterious mutations. Using 8,690 tumor samples from The Cancer Genome Atlas, we demonstrate that copy number amplifications frequently cover haploinsufficient genes in mutation-prone regions. This could increase tolerance towards the deleterious impact of mutations by creating safe copies of wild-type regions and, hence, protecting the genes therein. Our findings demonstrate that these potential buffering events are highly influenced by gene functions, essentiality, and mutation impact and that they occur early during tumor evolution. We show how cancer type-specific mutation landscapes drive copy number alteration patterns across cancer types. Ultimately, our work paves the way for the detection of novel cancer vulnerabilities by revealing genes that fall within amplifications likely selected during evolution to mitigate the effect of mutations.

Agent-based methods facilitate integrative science in cancer

In this opinion, we highlight agent-based modeling as a key tool for exploration of cell-cell and cell-environment interactions that drive cancer progression, therapeutic resistance, and metastasis. These biological phenomena are particularly suited to be captured at the cell-scale resolution possible only within agent-based or individual-based mathematical models. These modeling approaches complement experimental work (in vitro and in vivo systems) through parameterization and data extrapolation but also feed forward to drive new experiments that test model-generated predictions.

Natural Coevolution of Tumor and Immunoenvironment in Glioblastoma

Isocitrate dehydrogenase (IDH) wild-type glioblastoma (GBM) has a dismal prognosis. A better understanding of tumor evolution holds the key to developing more effective treatment. Here we study GBM's natural evolutionary trajectory by using rare multifocal samples. We sequenced 61,062 single cells from eight multifocal IDH wild-type primary GBMs and defined a natural evolution signature (NES) of the tumor. We show that the NES significantly associates with the activation of transcription factors that regulate brain development, including MYBL2 and FOSL2. Hypoxia is involved in inducing NES transition potentially via activation of the HIF1A-FOSL2 axis. High-NES tumor cells could recruit and polarize bone marrow-derived macrophages through activation of the FOSL2-ANXA1-FPR1/3 axis. These polarized macrophages can efficiently suppress T-cell activity and accelerate NES transition in tumor cells. Moreover, the polarized macrophages could upregulate CCL2 to induce tumor cell migration.

SIGNIFICANCE

GBM progression could be induced by hypoxia via the HIF1A-FOSL2 axis. Tumor-derived ANXA1 is associated with recruitment and polarization of bone marrow-derived macrophages to suppress the immunoenvironment. The polarized macrophages promote tumor cell NES transition and migration. This article is highlighted in the In This Issue feature, p. 2711.

Very large hidden genetic diversity in one single tumor: evidence for tumors-in-tumor

Despite the concern of within-tumor genetic diversity, this diversity is in fact limited by the kinship among cells in the tumor. Indeed, genomic studies have amply supported the 'Nowell dogma' whereby cells of the same tumor descend from a single progenitor cell. In parallel, genomic data also suggest that the diversity could be >10-fold larger if tumor cells are of multiple origins. We develop an evolutionary hypothesis that a single tumor may often harbor multiple cell clones of independent origins, but only one would be large enough to be detected. To test the hypothesis, we search for independent tumors within a larger one (or tumors-in-tumor). Very high density sampling was done on two cases of colon tumors. Case 1 indeed has 13 independent clones of disparate sizes, many having heavy mutation burdens and potentially highly tumorigenic. In Case 2, despite a very intensive search, only two small independent clones could be found. The two cases show very similar movements and metastasis of the dominant clone. Cells initially move actively in the expanding tumor but become nearly immobile in late stages. In conclusion, tumors-in-tumor are plausible but could be very demanding to find. Despite their small sizes, they can enhance the within-tumor diversity by orders of magnitude. Such increases may contribute to the missing genetic diversity associated with the resistance to cancer therapy.

Genomic Analysis of SARS-CoV-2 Alpha, Beta and Delta Variants of Concern Uncovers Signatures of Neutral and Non-Neutral Evolution

Due to the emergence of new variants of the SARS-CoV-2 coronavirus, the question of how the viral genomes evolved, leading to the formation of highly infectious strains, becomes particularly important. Three major emergent strains, Alpha, Beta and Delta, characterized by a significant number of missense mutations, provide a natural test field. We accumulated and aligned 4.7 million SARS-CoV-2 genomes from the GISAID database and carried out a comprehensive set of analyses. This collection covers the period until the end of October 2021, i.e., the beginnings of the Omicron variant. First, we explored combinatorial complexity of the genomic variants emerging and their timing, indicating very strong, albeit hidden, selection forces. Our analyses show that the mutations that define variants of concern did not arise gradually but rather co-evolved rapidly, leading to the emergence of the full variant strain. To explore in more detail the evolutionary forces at work, we developed time trajectories of mutations at all 29,903 sites of the SARS-CoV-2 genome, week by week, and stratified them into trends related to (i) point substitutions, (ii) deletions and (iii) non-sequenceable regions. We focused on classifying the genetic forces active at different ranges of the mutational spectrum. We observed the agreement of the lowest-frequency mutation spectrum with the Griffiths-Tavaré theory, under the Infinite Sites Model and neutrality. If we widen the frequency range, we observe the site frequency spectra much more consistently with the Tung-Durrett model assuming clone competition and selection. The coefficients of the fitting model indicate the possibility of selection acting to promote gradual growth slowdown, as observed in the history of the variants of concern. These results add up to a model of genomic evolution, which partly fits into the classical drift barrier ideas. Certain observations, such as mutation "bands" persistent over the epidemic history, suggest contribution of genetic forces different from mutation, drift and selection, including recombination or other genome transformations. In addition, we show that a "toy" mathematical model can qualitatively reproduce how new variants (clones) stem from rare advantageous driver mutations, and then acquire neutral or disadvantageous passenger mutations which gradually reduce their fitness so they can be then outcompeted by new variants due to other driver mutations.

Population genetics of clonally transmissible cancers

Populations of cancer cells are subject to the same core evolutionary processes as asexually reproducing, unicellular organisms. Transmissible cancers are particularly striking examples of these processes. These unusual cancers are clonal lineages that can spread through populations via physical transfer of living cancer cells from one host individual to another, and they have achieved long-term success in the colonization of at least eight different host species. Population genetic theory provides a useful framework for understanding the shift from a multicellular sexual animal into a unicellular asexual clone and its long-term effects on the genomes of these cancers. In this Review, we consider recent findings from transmissible cancer research with the goals of developing an evolutionarily informed perspective on transmissible cancers, examining possible implications for their long-term fate and identifying areas for future research on these exceptional lineages.

Modes of Selection in Tumors as Reflected by Two Mathematical Models and Site Frequency Spectra

The tug-of-war model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the tug-of-war model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian." We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness. We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. Our work is related to the past theoretical work in the field of evolutionary genetics, concerning the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra (SFS), to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution. To put our models in context, we carried out an exploratory study of how publicly accessible data from breast, prostate, skin and ovarian cancers fit a range of models found in the literature.

Quantification of neoantigen-mediated immunoediting in cancer evolution

Immunoediting includes three temporally distinct stages, termed elimination, equilibrium, and escape, and has been proposed to explain the interactions between cancer cells and the immune system during the evolution of cancer. However, the status of immunoediting in cancer remains unclear, and the existence of neoantigen depletion in untreated cancer has been debated. Here we developed a distribution pattern-based method for quantifying neoantigen-mediated negative selection in cancer evolution. The method can provide a robust and reliable quantification for immunoediting signal in individual cancer patients. Moreover, this method demonstrated the prevalence of immunoediting in immunotherapy-naive cancer genome. The elimination and escape stages of immunoediting can be quantified separately, where tumor types with strong immunoediting-elimination exhibit a weak immunoediting-escape signal, and vice versa. The quantified immunoediting-elimination signal was predictive of clinical response to cancer immunotherapy. Collectively, immunoediting quantification provides an evolutionary perspective for evaluating the antigenicity of neoantigens and reveals a potential biomarker for precision immunotherapy in cancer.

Gattaca: Base-Pair Resolution Mutation Tracking for Somatic Evolution Studies using Agent-based Models

Research over the past two decades has made substantial inroads into our understanding of somatic mutations. Recently, these studies have focused on understanding their presence in homeostatic tissue. In parallel, agent-based mechanistic models have emerged as an important tool for understanding somatic mutation in tissue; yet no common methodology currently exists to provide base-pair resolution data for these models. Here, we present Gattaca as the first method for introducing and tracking somatic mutations at the base-pair resolution within agent-based models that typically lack nuclei. With nuclei that incorporate human reference genomes, mutational context, and sequence coverage/error information, Gattaca is able to realistically evolve sequence data, facilitating comparisons between in silico cell tissue modeling with experimental human somatic mutation data. This user-friendly method, incorporated into each in silico cell, allows us to fully capture somatic mutation spectra and evolution.

Evolution under spatially heterogeneous selection in solid tumors

Spatial genetic and phenotypic diversity within solid tumors has been well documented. Nevertheless, how this heterogeneity affects temporal dynamics of tumorigenesis has not been rigorously examined because solid tumors do not evolve as the standard population genetic model due to the spatial constraint. We therefore, propose a neutral spatial (NS) model whereby the mutation accumulation increases toward the periphery; the genealogical relationship is spatially determined and the selection efficacy is blunted (due to kin competition). In this model, neutral mutations are accrued and spatially distributed in manners different from those of advantageous mutations. Importantly, the distinctions could be blurred in the conventional model. To test the NS model, we performed a three-dimensional multiple microsampling of two hepatocellular carcinomas. Whole-genome sequencing (WGS) revealed a 2-fold increase in mutations going from the center to the periphery. The operation of natural selection can then be tested by examining the spatially determined clonal relationships and the clonal sizes. Due to limited migration, only the expansion of highly advantageous clones can sweep through a large part of the tumor to reveal the selective advantages. Hence, even multiregional sampling can only reveal a fraction of fitness differences in solid tumors. Our results suggest that the NS patterns are crucial for testing the influence of natural selection during tumorigenesis, especially for small solid tumors.

Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability

The site frequency spectrum (SFS) is a popular summary statistic of genomic data. While the SFS of a constant-sized population undergoing neutral mutations has been extensively studied in population genetics, the rapidly growing amount of cancer genomic data has attracted interest in the spectrum of an exponentially growing population. Recent theoretical results have generally dealt with special or limiting cases, such as considering only cells with an infinite line of descent, assuming deterministic tumor growth, or taking large-time or large-population limits. In this work, we derive exact expressions for the expected SFS of a cell population that evolves according to a stochastic branching process, first for cells with an infinite line of descent and then for the total population, evaluated either at a fixed time (fixed-time spectrum) or at the stochastic time at which the population reaches a certain size (fixed-size spectrum). We find that while the rate of mutation scales the SFS of the total population linearly, the rates of cell birth and cell death change the shape of the spectrum at the small-frequency end, inducing a transition between a 1/j² power-law spectrum and a 1/j spectrum as cell viability decreases. We show that this insight can in principle be used to estimate the ratio between the rate of cell death and cell birth, as well as the mutation rate, using the site frequency spectrum alone. Although the discussion is framed in terms of tumor dynamics, our results apply to any exponentially growing population of individuals undergoing neutral mutations.

Clonal Evolution of Multiple Myeloma-Clinical and Diagnostic Implications

Plasma cell dyscrasias are a heterogeneous group of diseases characterized by the expansion of bone marrow plasma cells. Malignant transformation of plasma cells depends on the continuity of events resulting in a sequence of well-defined disease stages, from monoclonal gammopathy of undetermined significance (MGUS) through smoldering myeloma (SMM) to symptomatic multiple myeloma (MM). Evolution of a pre-malignant cell into a malignant cell, as well as further tumor progression, dissemination, and relapse, require development of multiple driver lesions conferring selective advantage of the dominant clone and allowing subsequent evolution under selective pressure of microenvironment and treatment. This process of natural selection facilitates tumor plasticity leading to the formation of genetically complex and heterogenous tumors that are notoriously difficult to treat. Better understanding of the mechanisms underlying tumor evolution in MM and identification of lesions driving the evolution from the premalignant clone is therefore a key to development of effective treatment and long-term disease control. Here, we review recent advances in clonal evolution patterns and genomic landscape dynamics of MM, focusing on their clinical implications.

Normal tissue architecture determines the evolutionary course of cancer

Cancer growth can be described as a caricature of the renewal process of the tissue of origin, where the tissue architecture has a strong influence on the evolutionary dynamics within the tumor. Using a classic, well-studied model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Time-varying competition leads to an emergent transition from Darwinian premalignant growth to subsequent invasive neutral tumor growth. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects. Driver acquisition during the Darwinian precancerous stage may be modulated en route to neutral evolution by the combination of two factors: spatial constraints and limited cellular mixing. These two factors occur naturally in ductal carcinomas, where the branching topology of the ductal network dictates spatial constraints and mixing rates.

Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective

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.

Phylodynamics for cell biologists

Multicellular organisms are composed of cells connected by ancestry and descent from progenitor cells. The dynamics of cell birth, death, and inheritance within an organism give rise to the fundamental processes of development, differentiation, and cancer. Technical advances in molecular biology now allow us to study cellular composition, ancestry, and evolution at the resolution of individual cells within an organism or tissue. Here, we take a phylogenetic and phylodynamic approach to single-cell biology. We explain how "tree thinking" is important to the interpretation of the growing body of cell-level data and how ecological null models can benefit statistical hypothesis testing. Experimental progress in cell biology should be accompanied by theoretical developments if we are to exploit fully the dynamical information in single-cell data.

An enhanced genetic model of relapsed IGH-translocated multiple myeloma evolutionary dynamics

Most patients with multiple myeloma (MM) die from progressive disease after relapse. To advance our understanding of MM evolution mechanisms, we performed whole-genome sequencing of 80 IGH-translocated tumour-normal newly diagnosed pairs and 24 matched relapsed tumours from the Myeloma XI trial. We identify multiple events as potentially important for survival and therapy-resistance at relapse including driver point mutations (e.g., TET2), translocations (MAP3K14), lengthened telomeres, and increased genomic instability (e.g., 17p deletions). Despite heterogeneous mutational processes contributing to relapsed mutations across MM subtypes, increased AID/APOBEC activity is particularly associated with shorter progression time to relapse, and contributes to higher mutational burden at relapse. In addition, we identify three enhanced major clonal evolution patterns of MM relapse, independent of treatment strategies and molecular karyotypes, questioning the viability of "evolutionary herding" approach in treating drug-resistant MM. Our data show that MM relapse is associated with acquisition of new mutations and clonal selection, and suggest APOBEC enzymes among potential targets for therapy-resistant MM.

Neutral syndrome

Neutral models of evolution assume the absence of natural selection. Formerly confined to ecology and evolutionary biology, neutral models are spreading. In recent years they've been applied to explaining the diversity of baby names, scientific citations, cryptocurrencies, pot decorations, literary lexica, tumour variants and much more besides. Here, we survey important neutral models and highlight their similarities. We investigate the most widely used tests of neutrality, show that they are weak and suggest more powerful methods. We conclude by discussing the role of neutral models in the explanation of diversity. We suggest that the ability of neutral models to fit low-information distributions should not be taken as evidence for the absence of selection. Nevertheless, many studies, in increasingly diverse fields, make just such claims. We call this tendency 'neutral syndrome'.

Tumour heterogeneity and the evolutionary trade-offs of cancer

Tumours vary in gene expression programmes and genetic alterations. Understanding this diversity and its biological meaning requires a theoretical framework, which could in turn guide the development of more accurate prognosis and therapy. Here, we review the theory of multi-task evolution of cancer, which is based upon the premise that tumours evolve in the host and face selection trade-offs between multiple biological functions. This theory can help identify the major biological tasks that cancer cells perform and the trade-offs between these tasks. It introduces the concept of specialist tumours, which focus on one task, and generalist tumours, which perform several tasks. Specialist tumours are suggested to be sensitive to therapy targeting their main task. Driver mutations tune gene expression towards specific tasks in a tissue-dependent manner and thus help to determine whether a tumour is specialist or generalist. We discuss potential applications of the theory of multi-task evolution to interpret the spatial organization of tumours and intratumour heterogeneity.

Minimal barriers to invasion during human colorectal tumor growth

Intra-tumoral heterogeneity (ITH) could represent clonal evolution where subclones with greater fitness confer more malignant phenotypes and invasion constitutes an evolutionary bottleneck. Alternatively, ITH could represent branching evolution with invasion of multiple subclones. The two models respectively predict a hierarchy of subclones arranged by phenotype, or multiple subclones with shared phenotypes. We delineate these modes of invasion by merging ancestral, topographic, and phenotypic information from 12 human colorectal tumors (11 carcinomas, 1 adenoma) obtained through saturation microdissection of 325 small tumor regions. The majority of subclones (29/46, 60%) share superficial and invasive phenotypes. Of 11 carcinomas, 9 show evidence of multiclonal invasion, and invasive and metastatic subclones arise early along the ancestral trees. Early multiclonal invasion in the majority of these tumors indicates the expansion of co-evolving subclones with similar malignant potential in absence of late bottlenecks and suggests that barriers to invasion are minimal during colorectal cancer growth.

Modeling genetic heterogeneity of drug response and resistance in cancer

Heterogeneity in tumors is recognized as a key contributor to drug resistance and spread of advanced disease, but deep characterization of genetic variation within tumors has only recently been quantifiable with the advancement of next generation sequencing and single cell technologies. These data have been essential in developing molecular models of how tumors develop, evolve, and respond to environmental changes, such as therapeutic intervention. A deeper understanding of tumor evolution has subsequently opened up new research efforts to develop mathematical models that account for evolutionary dynamics with the goal of predicting drug response and resistance in cancer. Here, we describe recent advances and limitations of how models of tumor evolution can impact treatment strategies for cancer patients.

On measuring selection in cancer from subclonal mutation frequencies

Recently available cancer sequencing data have revealed a complex view of the cancer genome containing a multitude of mutations, including drivers responsible for cancer progression and neutral passengers. Measuring selection in cancer and distinguishing drivers from passengers have important implications for development of novel treatment strategies. It has recently been argued that a third of cancers are evolving neutrally, as their mutational frequency spectrum follows a 1/f power law expected from neutral evolution in a particular intermediate frequency range. We study a stochastic model of cancer evolution and derive a formula for the probability distribution of the cancer cell frequency of a subclonal driver, demonstrating that driver frequency is biased towards 0 and 1. We show that it is difficult to capture a driver mutation at an intermediate frequency, and thus the calling of neutrality due to a lack of such driver will significantly overestimate the number of neutrally evolving tumors. Our approach provides quantification of the validity of the 1/f statistic across the entire range of relevant parameter values. We also show that our conclusions remain valid for non-exponential models: spatial 3d model and sigmoidal growth, relevant for early- and late stages of cancer growth.

Darwinian evolution in cancer is responsible for the emergence of malignant traits in initially benign tumors. As tumor cells divide, they accumulate new mutations and while most of them are “passengers” which do not confer any selective growth advantage, “driver” mutations endow cells with traits that contribute to cancer spread. Identifying driver mutations that are under selection in cancer can point to new targets for cancer therapeutics and open new avenues for personalized cancer treatment. It has recently been argued that the presence or absence of selection in cancer can be deduced from deviation of mutant allele frequencies from 1/f power law in an intermediate frequency range. Using a stochastic mathematical model of cancer evolution we derive a formula for the frequency of a subclonal driver and show that frequencies of cancer drivers are biased towards 0 and 1; thus most mutations will inevitably appear to be either neutral (frequency ≈ 0) or clonal (frequency ≈ 1) despite very different levels of selection. Consequently, the proposed 1/f statistic will significantly overestimate the number of cancers deemed to be evolving neutrally. Our work quantifies the validity of the proposed neutral evolution statistic across the entire range of relevant parameter values.