Deleterious Mutation Rate Research Articles

167P - Clinicopathological characteristics and BRCA1/2 mutation rate in male breast cancer: a retrospective case series by the Hellenic Society of Medical Oncology

Due to its rarity, male breast cancer (MBC) remains an inadequately characterized disease. Germline mutations in the BRCA1/2 genes are considered the most significant risk factor for MBC development. We retrospectively analyzed the clinicopathological characteristics, treatment patterns, and the BRCA1/2 germline mutation rate of BC patients (pts) treated from 1995 to 2014. Pts who were still alive were identified and were invited for genetic counseling and testing. The study was coordinated by the University of Crete School of Medicine. A total of 166 pts were identified through their medical records. Median age at diagnosis was 64. Family history of either FBC or ovarian cancer was positive in 19,9% while 9% had a personal history of gynecomastia. Histology was of Ductal Invasive type in 84% of the pts. Node positive locally advanced disease was diagnosed at 30% of pts, while 18% were metastatic at presentation. ER and/or PR-positive, HER2-negative was the predominant subtype (78.4%), followed by triple-positive (18.1%) and only in few pts triple-negative subtype (3.4%). Histologic grade distribution was: gr. I in 5.4%, gr. II in 53.4% and gr III in 41%. All 99 patients who received genetic counselling consented to BRCA1/2 genetic testing. Overall BRCA1/2 deleterious mutation rate was 6 % (5% BRCA2 and 1% BRCA1), while 3 pts (3%) carried a VUS. Most pts (80%) underwent modified radical mastectomy, 41% of which received adjuvant radiotherapy. Adjuvant systemic therapy was administered to 71.6% (10% had chemotherapy only, 27% hormonotherapy only and 63% both). Metastatic disease was treated with at least 1 line of systemic therapy in 31.9% of pts (chemotherapy in 60% of them), 60% of which proceeded to subsequent lines. In one of the largest national cohorts of MBC pts reported yet, we confirmed similar biological patterns to post-menopausal FBC. BRCA1/2 germline mutation rate is comparable to other European populations. Male Breast Cancer Working Group of the Hellenic Society of Medical Oncology Koumarianou A., Bournakis E., Boutis A., Diamantopoulos N., Katsaounis P., Korantzis I., Lianos E., Tsoukalas N., Bakogeorgos M., Kalampaliki T.

The LORE1 insertion mutant resource.

Long terminal repeat (LTR) retrotransposons are closely related to retroviruses, and their activities shape eukaryotic genomes. Here, we present a complete Lotus japonicus insertion mutant collection generated by identification of 640653 new insertion events following de novo activation of the LTR element Lotus retrotransposon 1 (LORE1) (http://lotus.au.dk). Insertion preferences are critical for effective gene targeting, and we exploit our large dataset to analyse LTR element characteristics in this context. We infer the mechanism that generates the consensus palindromes typical of retroviral and LTR retrotransposon insertion sites, identify a short relaxed insertion site motif, and demonstrate selective integration into CHG-hypomethylated genes. These characteristics result in a steep increase in deleterious mutation rate following activation, and allow LORE1 active gene targeting to approach saturation within a population of 134682 L. japonicus lines. We suggest that saturation mutagenesis using endogenous LTR retrotransposons with germinal activity canbe used as a general and cost-efficient strategy for generation of non-transgenic mutant collections for unrestricted use in plant research.

Watching Populations Melt Down

One of the curious features ofDarwinian Evolution is that it requireserrors to be made during genome repli-cation.Otherwise,beneficialmutationscould not occur and adaptation wouldarrest. Not surprisingly, however,random DNA copy errors usually donot lead to improvement—most muta-tions are deleterious or have little ef-fect (1). Because, as far as we know,evolution has not found away to selec-tively boost beneficial mutations, onewonders how large replication errorrates could possibly be without over-whelming the population with delete-rious mutations (2). This question ofmaximal sustainable mutation rateshas fascinated theoretical evolutionarybiologists for decades (2,3), yetexperimental results are scarce. Now,Max Lavrentovich (a theorist), MaryWahl (an experimenter), and theircolleagues (4) describe an elegantway to watch microbial populationson the verge of succumbing to delete-rious mutants.The simplest model for the trade-off between natural selection anddeleterious mutations is illustrated ina two-state population model inFig. 1. One-way mutations occurringat rate m per generation supply acontinuous flux from the wild-type tothe mutant type. This flux is compen-sated by the wild-type growing 1 þ stimes faster than the mutant type. Asa consequence, both types reach ‘‘mu-tation-selection balance’’ when thefraction of the mutant type is m/s (5).Hence, if the rate of deleterious muta-tions is larger than their typical effect,the wild-type goes extinct and the mu-tants take over. If this process con-tinues due to further deleteriousmutations, the population is at risk ofcontinuously accumulating deleteriousmutations in a phenomenon called‘‘mutational meltdown’’ (3) or ‘‘errorcatastrophe’’ (2) (for a discussion ofthese two terms and their differences,see Wilke (6)). Obviously, then, natureneeds to ensure that mutation rates donot exceed the selective disadvantageof typical mutations to avoid thecomplete loss of the wild-type. Indeed,sophisticated error correction mecha-nisms are in place, which keep muta-tion rates below 10

Lower prevalence but similar fitness in a parasitic fungus at higher radiation levels near Chernobyl.

Nuclear disasters at Chernobyl and Fukushima provide examples of effects of acute ionizing radiation on mutations that can affect the fitness and distribution of species. Here, we investigated the prevalence of Microbotryum lychnidis-dioicae, a pollinator-transmitted fungal pathogen of plants causing anther-smut disease in Chernobyl, its viability, fertility and karyotype variation, and the accumulation of nonsynonymous mutations in its genome. We collected diseased flowers of Silene latifolia from locations ranging by more than two orders of magnitude in background radiation, from 0.05 to 21.03μGy/h. Disease prevalence decreased significantly with increasing radiation level, possibly due to lower pollinator abundance and altered pollinator behaviour. Viability and fertility, measured as the budding rate of haploid sporidia following meiosis from the diploid teliospores, did not vary with increasing radiation levels and neither did karyotype overall structure and level of chromosomal size heterozygosity. We sequenced the genomes of twelve samples from Chernobyl and of four samples collected from uncontaminated areas and analysed alignments of 6068 predicted genes, corresponding to 1.04×10(7) base pairs. We found no dose-dependent differences in substitution rates (neither dN, dS, nor dN/dS). Thus, we found no significant evidence of increased deleterious mutation rates at higher levels of background radiation in this plant pathogen. We even found lower levels of nonsynonymous substitution rates in contaminated areas compared to control regions, suggesting that purifying selection was stronger in contaminated than uncontaminated areas. We briefly discuss the possibilities for a mechanistic basis of radio resistance in this nonmelanized fungus.

An Evolving Genetic Architecture Interacts with Hill-Robertson Interference to Determine the Benefit of Sex.

Sex is ubiquitous in the natural world, but the nature of its benefits remains controversial. Previous studies have suggested that a major advantage of sex is its ability to eliminate interference between selection on linked mutations, a phenomenon known as Hill-Robertson interference. However, those studies may have missed both important advantages and important disadvantages of sexual reproduction because they did not allow the distributions of mutational effects and interactions (i.e., the genetic architecture) to evolve. Here we investigate how Hill-Robertson interference interacts with an evolving genetic architecture to affect the evolutionary origin and maintenance of sex by simulating evolution in populations of artificial gene networks. We observed a long-term advantage of sex-equilibrium mean fitness of sexual populations exceeded that of asexual populations-that did not depend on population size. We also observed a short-term advantage of sex-sexual modifier mutations readily invaded asexual populations-that increased with population size, as was observed in previous studies. We show that the long- and short-term advantages of sex were both determined by differences between sexual and asexual populations in the evolutionary dynamics of two properties of the genetic architecture: the deleterious mutation rate ([Formula: see text]) and recombination load ([Formula: see text]). These differences resulted from a combination of selection to minimize [Formula: see text] which is experienced only by sexuals, and Hill-Robertson interference experienced primarily by asexuals. In contrast to the previous studies, in which Hill-Robertson interference had only a direct impact on the fitness advantages of sex, the impact of Hill-Robertson interference in our simulations was mediated additionally by an indirect impact on the efficiency with which selection acted to reduce [Formula: see text].

Background Selection in Partially Selfing Populations.

Self-fertilizing species often present lower levels of neutral polymorphism than their outcrossing relatives. Indeed, selfing automatically increases the rate of coalescence per generation, but also enhances the effects of background selection and genetic hitchhiking by reducing the efficiency of recombination. Approximations for the effect of background selection in partially selfing populations have been derived previously, assuming tight linkage between deleterious alleles and neutral loci. However, loosely linked deleterious mutations may have important effects on neutral diversity in highly selfing populations. In this article, I use a general method based on multilocus population genetics theory to express the effect of a deleterious allele on diversity at a linked neutral locus in terms of moments of genetic associations between loci. Expressions for these genetic moments at equilibrium are then computed for arbitrary rates of selfing and recombination. An extrapolation of the results to the case where deleterious alleles segregate at multiple loci is checked using individual-based simulations. At high selfing rates, the tight linkage approximation underestimates the effect of background selection in genomes with moderate to high map length; however, another simple approximation can be obtained for this situation and provides accurate predictions as long as the deleterious mutation rate is not too high.

Fixation probability of rare nonmutator and evolution of mutation rates.

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation-selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift-barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.

Evolution of haploid selection in predominantly diploid organisms

Diploid organisms manipulate the extent to which their haploid gametes experience selection. Animals typically produce sperm with a diploid complement of most proteins and RNA, limiting selection on the haploid genotype. Plants, however, exhibit extensive expression in pollen, with actively transcribed haploid genomes. Here we analyze models that track the evolution of genes that modify the strength of haploid selection to predict when evolution intensifies and when it dampens the "selective arena" within which male gametes compete for fertilization. Considering deleterious mutations, evolution leads diploid mothers to strengthen selection among haploid sperm/pollen, because this reduces the mutation load inherited by their diploid offspring. If, however, selection acts in opposite directions in haploids and diploids ("ploidally antagonistic selection"), mothers evolve to reduce haploid selection to avoid selectively amplifying alleles harmful to their offspring. Consequently, with maternal control, selection in the haploid phase either is maximized or reaches an intermediate state, depending on the deleterious mutation rate relative to the extent of ploidally antagonistic selection. By contrast, evolution generally leads diploid fathers to mask mutations in their gametes to the maximum extent possible, whenever masking (e.g., through transcript sharing) increases the average fitness of a father's gametes. We discuss the implications of this maternal-paternal conflict over the extent of haploid selection and describe empirical studies needed to refine our understanding of haploid selection among seemingly diploid organisms.

Accelerating Mutational Load Is Not Due to Synergistic Epistasis or Mutator Alleles in Mutation Accumulation Lines of Yeast.

Much of our knowledge about the fitness effects of new mutations has been gained from mutation accumulation (MA) experiments. Yet the fitness effect of single mutations is rarely measured in MA experiments. This raises several issues, notably for inferring epistasis for fitness. The acceleration of fitness decline in MA lines has been taken as evidence for synergistic epistasis, but establishing the role of epistasis requires measuring the fitness of genotypes carrying known numbers of mutations. Otherwise, accelerating fitness loss could be explained by increased genetic mutation rates. Here we segregated mutations accumulated over 4800 generations in haploid and diploid MA lines of the yeast Saccharomyces cerevisiae. We found no correspondence between an accelerated fitness decline and synergistic epistasis among deleterious mutations in haploid lines. Pairs of mutations showed no overall epistasis. Furthermore, several lines of evidence indicate that genetic mutation rates did not increase in the MA lines. Crucially, segregant fitness analyses revealed that MA accelerated in both haploid and diploid lines, even though the fitness of diploid lines was nearly constant during the MA experiment. This suggests that the accelerated fitness decline in haploids was caused by cryptic environmental factors that increased mutation rates in all lines during the last third of the lines' transfers. In addition, we provide new estimates of deleterious mutation rates, including lethal mutations, and highlight that nearly all the mutational load we observed was due to one or two mutations having a large effect on fitness.

Effects of Interference Between Selected Loci on the Mutation Load, Inbreeding Depression, and Heterosis.

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.

Mutation load under additive fitness effects.

Under the traditional mutation load model based on multiplicative fitness effects, the load in a population is 1-e-U , where U is the genomic deleterious mutation rate. Because this load becomes high under large U, synergistic epistasis has been proposed as one possible means of reducing the load. However, experiments on model organisms attempting to detect synergistic epistasis have often focused on a quadratic fitness model, with the resulting general conclusion being that epistasis is neither common nor strong. Here, I present a model of additive fitness effects and show that, unlike multiplicative effects, the equilibrium frequency of an allele under additivity is dependent on the average absolute fitness of the population. The additive model then results in a load of U/(U+1), which is much lower than 1-e-U for large U. Numerical iterations demonstrate that this analytic derivation holds as a good approximation under biologically relevant values of selection coefficients and U. Additionally, regressions onto Drosophila mutation accumulation data suggest that the common method of inferring epistasis by detecting large quadratic terms from regressions is not always necessary, as the additive model fits the data well and results in synergistic epistasis. Furthermore, the additive model gives a much larger reduction in load than the quadratic model when predicted from the same data, indicating that it is important to consider this additive model in addition to the quadratic model when inferring epistasis from mutation accumulation data.

Clonal interference and Mullerʼs ratchet in spatial habitats

Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Mullerʼs ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using, again, an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation.

Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

Selfing, adaptation and background selection in finite populations

Classic deterministic genetic models of the evolution of selfing predict species should be either completely outcrossing or completely selfing. However, even species considered high selfers outcross to a small degree (e.g. Arabidopsisthaliana and Caenorhabditiselegans). This discrepancy between theory and data may exist because the classic models ignore the effects of drift interacting with selection, that is, Hill-Robertson effects. High selfing rates make the effective rate of recombination near zero, which is expected to cause the build-up of negative disequilibria in finite populations. Despite the transmission advantage associated with complete selfing, low levels of outcrossing may be favoured because of the benefits of increasing the effective rate of recombination to dissipate negative disequilibria. Using multilocus simulations, we confirm that selfing reduces effective population size through background selection and causes negative disequilibria between selected sites. Consequently, the rate of adaptation is substantially reduced in strong selfers. When selfing rate is allowed to evolve, populations evolve to be either strong outcrossers or strong selfers, depending on the parameter values. Amongst selfers, low, but nonzero, levels of outcrossing can be maintained by selection even when all mutations are deleterious; more outcrossing is maintained with higher rates of deleterious mutation. The addition of beneficial mutations can (i) lead to a quantitative increase in the degree of outcrossing amongst stronger selfers but (ii) may cause outcrossing species to evolve into stronger selfers.

Accumulation of spontaneous mutations in the ciliate Tetrahymena thermophila.

Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U=0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s=11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h=0.26; 95% CI: -0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.

Somatic deleterious mutation rate in a woody plant: estimation from phenotypic data

We conducted controlled crosses in populations of the long-lived clonal shrub, Vaccinium angustifolium (lowbush blueberry) to estimate inbreeding depression and mutation parameters associated with somatic deleterious mutation. Inbreeding depression level was high, with many plants failing to set fruit after self-pollination. We also compared fruit set from autogamous pollinations (pollen collected from within the same inflorescence) with fruit set from geitonogamous pollinations (pollen collected from the same plant but from inflorescences separated by several meters of branch growth). The difference between geitonogamous versus autogamous fitness within single plants is referred to as 'autogamy depression' (AD). AD can be caused by somatic deleterious mutation. AD was significantly different from zero for fruit set. We developed a maximum-likelihood procedure to estimate somatic mutation parameters from AD, and applied it to geitonogamous and autogamous fruit set data from this experiment. We infer that, on average, approximately three sublethal, partially dominant somatic mutations exist within the crowns of the plants studied. We conclude that somatic mutation in this woody plant results in an overall genomic deleterious mutation rate that exceeds the rate measured to date for annual plants. Some implications of this result for evolutionary biology and agriculture are discussed.

Genomic background and generation time influence deleterious mutation rates in Daphnia.

Understanding how genetic variation is generated and how selection shapes mutation rates over evolutionary time requires knowledge of the factors influencing mutation and its effects on quantitative traits. We explore the impact of two factors, genomic background and generation time, on deleterious mutation in Daphnia pulicaria, a cyclically parthenogenic aquatic microcrustacean, using parallel mutation-accumulation experiments. The deleterious mutational properties of life-history characters for individuals from two different populations, and for individuals maintained at two different generation times, were quantified and compared. Mutational properties varied between populations, especially for clutch size, suggesting that genomic background influences mutational properties for some characters. Generation time was found to have a greater effect on mutational properties, with higher per-generation deleterious mutation rates in lines with longer generation times. These results suggest that differences in genetic architecture among populations and species may be explained in part by demographic features that significantly influence generation time and therefore the rate of mutation.

Lineage dynamics and mutation–selection balance in non-adapting asexual populations

In classical population genetics, mutation–selection balance refers to the equilibrium frequency of a deleterious allele established and maintained under two opposing forces: recurrent mutation, which tends to increase the frequency of the allele; and selection, which tends to decrease its frequency. In a haploid population, if μ denotes the per capita rate of production of the deleterious allele by mutation and s denotes the selective disadvantage of carrying the allele, then the classical mutation–selection balance frequency of the allele is approximated by μ/s. This calculation assumes that lineages carrying the mutant allele in question—the ‘focal allele’—do not accumulate deleterious mutations linked to the focal allele. In principle, indirect selection against the focal allele caused by such additional mutations can decrease the frequency of the focal allele below the classical mutation–selection balance. This effect of indirect selection will be strongest in an asexual population, in which the entire genome is in linkage. Here, we use an approach based on a multitype branching process to investigate this effect, analyzing lineage dynamics under mutation, direct selection, and indirect selection in a non-adapting asexual population. We find that the equilibrium balance between recurrent mutation to the focal allele and the forces of direct and indirect selection against the focal allele is closely approximated by γμ/(s + U) (s = 0 if the focal allele is neutral), where γ ≈ eθθ−(ω+θ)(ω + θ)(Γ(ω + θ) − Γ(ω + θ,θ)), , and ; U denotes the genomic deleterious mutation rate and denotes the geometric mean selective disadvantage of deleterious mutations elsewhere on the genome. This mutation–selection balance for asexual populations can remain surprisingly invariant over wide ranges of the mutation rate.

Modelling the evolution of genetic instability during tumour progression.

The role of genetic instability in driving carcinogenesis remains controversial. Genetic instability should accelerate carcinogenesis by increasing the rate of advantageous driver mutations; however, genetic instability can also potentially retard tumour growth by increasing the rate of deleterious mutation. As such, it is unclear whether genetically unstable clones would tend to be more selectively advantageous than their genetically stable counterparts within a growing tumour. Here, we show the circumstances where genetic instability evolves during tumour progression towards cancer. We employ a Wright–Fisher type model that describes the evolution of tumour subclones. Clones can acquire both advantageous and deleterious mutations, and mutator mutations that increase a cell's intrinsic mutation rate. Within the model, cancers evolve with a mutator phenotype when driver mutations bestow only moderate increases in fitness: very strong or weak selection for driver mutations suppresses the evolution of a mutator phenotype. Genetic instability occurs secondarily to selectively advantageous driver mutations. Deleterious mutations have relatively little effect on the evolution of genetic instability unless selection for additional driver mutations is very weak or if deleterious mutations are very common. Our model provides a framework for studying the evolution of genetic instability in tumour progression. Our analysis highlights the central role of selection in shaping patterns of mutation in carcinogenesis.