A mutator is a variant in a population of organisms whose mutation rate is higher than the average mutation rate in the population. For genetic and population dynamics reasons, mutators are produced and survive with much greater frequency than anti-mutators (variants with a lower-than-average mutation rate). This strong asymmetry is a consequence of both fundamental genetics and natural selection; it can lead to a ratchet-like increase in the mutation rate. The rate at which mutators appear is, therefore, a parameter that should be of great interest to evolutionary biologists generally; for example, it can influence: (1) the survival duration of a species, especially asexual species (which are known to be short-lived), (2) the evolution of recombination, a process that can ameliorate the deleterious effects of mutator abundance, (3) the rate at which cancer appears, (4) the ability of pathogens to escape immune surveillance in their hosts, (5) the long-term fate of mitochondria, etc. In spite of its great relevance to basic and applied science, the rate of mutation to a mutator phenotype continues to be essentially unknown. The reasons for this gap in our knowledge are largely methodological; in general, a mutator phenotype cannot be observed directly, but must instead be inferred from the numbers of some neutral “marker” mutation that can be observed directly: different mutation-rate variants will produce this marker mutation at different rates. Here, we derive the expected distribution of the numbers of the marker mutants observed, accounting for the fact that some of the mutants will have been produced by a mutator phenotype that itself arose by mutation during the growth of the culture. These developments, together with previous enhancements of the Luria–Delbrück assay (by one of us, dubbed the “Jones protocol”), make possible a novel experimental protocol for estimating the rate of mutation to a mutator phenotype. Simulated experiments using biologically reasonable parameters that employ this protocol show that such experiments in the lab can give us fairly accurate estimates of the rate of mutation to a mutator phenotype. Although our ability to estimate mutation-to-mutator rates from simulated experiments is promising, we view this study as a proof-of-concept study and an important first step towards practical empirical estimation.

Shuffling one’s genetic material with another individual seems a risky endeavor more likely to decrease than to increase offspring fitness. This intuitive argument is commonly employed to explain why the ubiquity of sex and recombination in nature is enigmatic. It is predicated on the notion that natural selection assembles selectively well-matched combinations of genes that recombination would break up resulting in low-fitness offspring – a notion often stated in the literature as a self-evident premise. We show however that, upon closer examination, this premise is flawed: we find to the contrary that natural selection in fact has an encompassing tendency to assemble selectively mismatched gene combinations; recombination breaks up these selectively mismatched combinations (on average), assembles selectively matched combinations, and should thus be favored. The new perspective our findings offer suggests that sex and recombination are not so enigmatic but are instead unavoidable byproducts of natural selection.

If they undergo new mutations at each replication cycle, why are RNA viral genomes so fragile, with most mutations being either strongly deleterious or lethal? Here we provide theoretical and numerical evidence for the hypothesis that genetic fragility is partly an evolutionary response to the multiple population bottlenecks experienced by viral populations at various stages of their life cycles. Modelling within-host viral populations as multi-type branching processes, we show that mutational fragility lowers the rate at which Muller's ratchet clicks and increases the survival probability through multiple bottlenecks. In the context of a susceptible-exposed-infectious-recovered epidemiological model, we find that the attack rate of fragile viral strains can exceed that of more robust strains, particularly at low infectivities and high mutation rates. Our findings highlight the importance of demographic events such as transmission bottlenecks in shaping the genetic architecture of viral pathogens.

The ubiquity of sex and recombination in nature has eluded unified explanation since the time of Darwin. Conditions that promote the evolution of recombination, broadly defined as any form of genetic mixing, are fairly well understood: it is favored when genomes tend to contain more selectively mismatched combinations of alleles than can be explained by chance alone. Yet, while a variety of theoretical approaches have been put forth to explain why such conditions would prevail in natural populations, each has turned out to be of limited scope and applicability. Here, we show, simply and surprisingly, that natural selection acting on standing heritable variation always creates conditions favoring the evolution of recombination, in expectation. Specifically, we find that, in expectation: 1) the mean selective advantage of recombinants is non-negative, 2) the mean selective advantage of a recombination-competent modifier is non-negative, and 3) the asymptotic frequency of a recombination-competent modifier is close to one and is independent of the strength of selection. Remarkably, these findings are independent of the distribution of genic fitnesses in the standing heritable variation upon which natural selection acts, implying that the source of this variation is immaterial. Taken together, our findings indicate that: 1) the evolution of recombination should be promoted in expectation wherever natural selection is operating, and 2) sex and recombination may have evolved more as a byproduct than as a catalyst of natural selection.

AbstractHealth officials warn that SARS-CoV-2 vaccines must be uniformly distributed within and among countries if we are to quell the ongoing pandemic. Yet there has been little critical assessment of the underlying reasons for this warning. Here, we explicitly show why vaccine equity is necessary. Perhaps counter-intuitively, we find that vaccine escape mutants are less likely to come from highly vaccinated regions where there is strong selection pressure favoring vaccine escape and more likely to come from neighboring unvaccinated regions where there is no selection favoring escape. Unvaccinated geographic regions thus provide evolutionary reservoirs from which new strains can arise and cause new epidemics within neighboring vaccinated regions and beyond. Our findings have timely implications for vaccine rollout strategies and public health policy.

The ubiquity of sex and recombination in nature is widely viewed as enigmatic, despite an abundance of limited-scope explanations. Natural selection, it seems, should amplify well-matched combinations of genes. Recombination would break up these well-matched combinations and should thus be suppressed. We show, to the contrary, that on average: 1) natural selection amplifies poorly-matched gene combinations and 2) creates time-averaged negative associations in the process. Recombination breaks up these poorly-matched combinations, neutralizes the negative associations, and should thus be passively and universally favored.

AbstractThe evolutionary trend toward increasing complexity and social function is ultimately the result of natural selection's paradoxical tendency to foster cooperation through competition. Cooperating populations ranging from complex societies to somatic tissue are constantly under attack, however, by non-cooperating mutants or transformants, called ‘cheaters’. Structure in these populations promotes the formation of cooperating clusters whose competitive superiority can alone be sufficient to thwart outgrowths of cheaters and thereby maintain cooperation. But we find that when cheaters appear too frequently – exceeding a threshold mutation or transformation rate – their scattered outgrowths infiltrate and break up cooperating clusters, resulting in a cascading loss of social cohesiveness, a switch to net positive selection for cheaters and ultimately in the loss of cooperation. Our findings imply that a critically low mutation rate had to be achieved (perhaps through the advent of proofreading and repair mechanisms) before complex cooperative functions, such as those required for multicellularity and social behaviour, could have evolved and persisted. When mutation rate in our model is also allowed to evolve, the threshold is crossed spontaneously after thousands of generations, at which point cheaters rapidly invade. Probing extrapolations of these findings suggest: (1) in somatic tissue, it is neither social retro-evolution alone nor mutation rate evolution alone but the interplay between these two that ultimately leads to oncogenic transitions; the rate of this coevolution might thereby provide an indicator of lifespan of species, terrestrial or not; (2) the likelihood that extraterrestrial life can be expected to be multicellular and social should be affected by ultraviolet and other mutagenic factors.

The Honduran incumbent president and his administration recently declared victory in an election riddled with irregularities and indicators of fraud. Perhaps most curious, however, was a numerical anomaly: the primary challenger carried a very significant lead of five percentage points more than half way through the election but was ultimately defeated by the incumbent. The incumbent (Hernandez) offered a plausible explanation for the surprising turnaround in the ballots: his popularity is greater in remote areas of the country but votes from remote areas were not counted until later in the election. Here, we mathematically formalize this argument, which we will call the Hernandez conjecture, and employ the resulting formulae together with geodemographic data from Honduras to quantitatively assess the conjectures veracity. When the departamentos were analyzed individually, three sparsely-populated departamentos (of 18 total) showed small but non-negligible probability of the conjectures veracity; however, when the country was analyzed as a whole, the overall probability of the conjectures veracity was calculated to be less than 0.0001 under a wide range of different assumptions. Results of our three-pronged analysis, taken together, indicate a negligible probability of a fair win by the incumbent.

Beneficial mutations drive adaptive evolution, yet their selective advantage does not ensure their fixation. Haldane’s application of single-type branching process theory showed that genetic drift alone could cause the extinction of newly arising beneficial mutations with high probability. With linkage, deleterious mutations will affect the dynamics of beneficial mutations and might further increase their extinction probability. Here, we model the lineage dynamics of a newly arising beneficial mutation as a multitype branching process. Our approach accounts for the combined effects of drift and the stochastic accumulation of linked deleterious mutations, which we call lineage contamination. We first study the lineage-contamination phenomenon in isolation, deriving dynamics and survival probabilities (the complement of extinction probabilities) of beneficial lineages. We find that survival probability is zero when U≳sb, where U is deleterious mutation rate and sb is the selective advantage of the beneficial mutation in question, and is otherwise depressed below classical predictions by a factor bounded from below by ∼1−U/sb. We then put the lineage contamination phenomenon into the context of an evolving population by incorporating the effects of background selection. We find that, under the combined effects of lineage contamination and background selection, ensemble survival probability is never zero but is depressed below classical predictions by a factor bounded from below by e−εU/s¯b, where s¯b is mean selective advantage of beneficial mutations, and ε=1−e−1≈0.63. This factor, and other bounds derived from it, are independent of the fitness effects of deleterious mutations. At high enough mutation rates, lineage contamination can depress fixation probabilities to values that approach zero. This fact suggests that high mutation rates can, perhaps paradoxically, (1) alleviate competition among beneficial mutations, or (2) potentially even shut down the adaptive process. We derive critical mutation rates above which these two events become likely.

The DFE characterizes the mutational "input" to evolution, while natural selection largely determines how this input gets sorted into an evolutionary "output". The output cannot contain novel genetic material that is not present in the input and, as such, understanding the DFE and its dynamics is crucial to understanding evolution generally. Despite this centrality to evolution, however, the DFE has remained elusive primarily due to methodological difficulties. Here, we propose and assess a novel framework for estimating the DFE which removes the biasing effects of selection statistically. We propose a statistic for characterizing the difference between two inferred DFEs, taken from two different populations or from the same population at different time points. This allows us to study the evolution of the DFE and monitor for structural changes in the DFE.

In contrast to expensive adaptive landscape approaches to predicting evolution, we explore an “adaptive process” approach. Instead of focusing on the fitness mountain to be climbed, adaptive process approaches focus on the mountaineer, i.e., the population, and how she climbs the mountain. The mountaineer’s gait and pace reveal something about the terrain on which she walks; similarly, a population’s composition carries information about the underlying adaptive landscape, about trends in that landscape, and even about what lies a few paces ahead. The adaptive process approach that we explore builds on classical theory, but where classical theory can predict the course of evolution over the course of a single generation, our approach in preliminary studies successfully predicts evolution tens of generations into the future based only on measurements taken from populations in real time.

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 mu 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 mu/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 gamma mu/(s + U) (s = 0 if the focal allele is neutral), where gamma approximate to c(theta)theta-((omega+theta))(omega + theta)(Gamma(omega + theta) - Gamma(omega + theta, theta)), theta = U/(s) over tilde, and w = s/(s) over tilde; U denotes the genomic deleterious mutation rate and (s) over tilde 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.

When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a detrimental effect because of the overwhelming presence of deleterious mutations. Indeed, if mutation rates are high enough: (i) adaptive evolution may be neutralized, resulting in a zero (or negative) adaptation rate despite the continued availability of adaptive and/or compensatory mutations, or (ii) natural selection may be neutralized, because the fitness of lineages bearing adaptive and/or compensatory mutations-whether established or newly arising-is eroded by excessive mutation, causing such lineages to decline in frequency. We apply these two criteria to a standard model of asexual adaptive evolution and derive mathematical expressions-some new, some old in new guise-delineating the mutation rates under which either adaptive evolution or natural selection is neutralized. The expressions are simple and require no a priori knowledge of organism- and/or environment-specific parameters. Our discussion connects these results to each other and to previous theory, showing convergence or equivalence of the different results in most cases.

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A metaphor for adaptation that informs much evolutionary thinking today is that of mountain climbing, where horizontal displacement represents change in genotype, and vertical displacement represents change in fitness. If it were known a priori what the ‘fitness landscape’ looked like, that is, how the myriad possible genotypes mapped onto fitness, then the possible paths up the fitness mountain could each be assigned a probability, thus providing a dynamical theory with long-term predictive power. Such detailed genotype–fitness data, however, are rarely available and are subject to change with each change in the organism or in the environment. Here, we take a very different approach that depends only on fitness or phenotype–fitness data obtained in real time and requires no a priori information about the fitness landscape. Our general statistical model of adaptive evolution builds on classical theory and gives reasonable predictions of fitness and phenotype evolution many generations into the future.

Cancer initiation, progression, and the emergence of therapeutic resistance are evolutionary phenomena of clonal somatic cell populations. Studies in microbial experimental evolution and the theoretical work inspired by such studies are yielding deep insights into the evolutionary dynamics of clonal populations, yet there has been little explicit consideration of the relevance of this rapidly growing field to cancer biology. Here, we examine how the understanding of mutation, selection, and spatial structure in clonal populations that is emerging from experimental evolution may be applicable to cancer. Along the way, we discuss some significant ways in which cancer differs from the model systems used in experimental evolution. Despite these differences, we argue that enhanced prediction and control of cancer may be possible using ideas developed in the context of experimental evolution, and we point out some prospects for future research at the interface between these traditionally separate areas.

ABSTRACT A potential drawback of recent antiviral therapies based on the transgenic expression of artificial microRNAs is the ease with which viruses may generate escape mutations. Using a variation of the classic Luria-Delbrück fluctuation assay, we estimated that the spontaneous mutation rate in the artificial microRNA (amiR) target of a plant virus was ca. 6 × 10 −5 per replication event.

Experimental studies have shown that a mutator allele can readily hitchhike to fixation with beneficial mutations in an asexual population having a low, wild-type mutation rate. Here, we show that a genotype bearing two mutator alleles can supplant a population already fixed for one mutator allele. Our results provide experimental support for recent theory predicting that mutator alleles will tend to accumulate in asexual populations by hitchhiking with beneficial mutations, causing an ever-higher genomic mutation rate.

Fisher's "fundamental theorem of natural selection" is famously robust and versatile but, frustratingly, it is dynamically insufficient: it can only predict how fitness will evolve over the course of a single generation. Consequently, his theorem has not been used for predicting the course of evolution but instead for detecting natural selection. His theorem employs only one facet of the fitness distribution, namely, the variance, and thus does not take advantage of all the available information. The theory we have developed shares some common ground with Fisher's theorem, but takes full advantage of the available information by employing the higher moments of the fitness distribution in addition to the variance. The theory developed here suggests: 1) a way to non-parametrically infer the distribution of mutational effects that feeds ongoing evolution, and 2) a framework for predicting fitness (and fitness-related) evolution.