Why are viral genomes so fragile? The bottleneck hypothesis.

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.

Luria-delbruck estimation of turnip mosaic virus mutation rate in vivo.

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.

Competition between high- and higher-mutating strains of Escherichia coli.

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.

Fitness effects of fixed beneficial mutations in microbial populations.

Beneficial mutations are intuitively relevant to understanding adaptation, yet not all beneficial mutations are of consequence to the long-term evolutionary outcome of adaptation. Many beneficial mutations-mostly those of small effect-are lost due either to (1) genetic drift or to (2) competition among clones carrying different beneficial mutations, a phenomenon called the "Hill-Robertson effect" for sexual populations and "clonal interference" for asexual populations. Competition among clones becomes more prevalent with increasing genetic linkage and increasing population size, and it is thus generally characteristic of microbial populations. Together, these two phenomena suggest that only those beneficial mutations of large fitness effect should achieve fixation, despite the fact that most beneficial mutations produced are predicted to have very small fitness effects. Here, we confirm this prediction-both empirically and theoretically-by showing that fitness effects of fixed beneficial mutations follow a distribution whose mode is positive.

Evaluating the impact of population bottlenecks in experimental evolution.

Experimental evolution involves severe, periodic reductions in population size when fresh media are inoculated during serial transfer. These bottlenecks affect the dynamics of evolution, reducing the probability that a beneficial mutation will reach fixation. We quantify the impact of these bottlenecks on the evolutionary dynamics, for populations that grow exponentially between transfers and for populations in which growth is curbed by a resource-limited environment. We find that in both cases, mutations that survive bottlenecks are equally likely to occur, per unit time, at all times during the growth phase. We estimate the total fraction of beneficial mutations that are lost due to bottlenecks during experimental evolution protocols and derive the "optimal" dilution ratio, the ratio that maximizes the number of surviving beneficial mutations. Although more severe dilution ratios are often used in the literature, we find that a ratio of 0.1-0.2 minimizes the chances that rare beneficial mutations are lost. Finally, we provide a number of useful approximate results and illustrate our approach with applications to experimental evolution protocols in the literature.

Mutation rate and the efficacy of antimicrobial drug treatment.

Despite rapid progress in drug development, microbial infections in general are becoming increasingly difficult to treat as a result of the emergence of drug-resistant strains. In some cases, such as HIV-1, the early goal of eradicating infections with antimicrobial drugs is, for now, being replaced with the more pragmatic goal of controlling infections over long periods of time through a succession of transiently effective treatments. Because treatment efficacy is often incomplete, studying the degree of treatment efficacy has great relevance to clinical disease management. We derived a model describing the association between the mutation rate of the pathogen and the degree of treatment efficacy. We found that drug treatment is most effective when the mutation rate of the pathogen is either very low or, perhaps counterintuitively, very high. We discuss this finding in the light of a promising new treatment strategy for RNA viruses that combines antiviral compounds with a mutagen.

Genomic mutation rates that neutralize adaptive evolution and natural selection.

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.

Real time forecasting of near-future evolution.

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 in light of experimental evolution.

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.

Beneficial mutations and the dynamics of adaptation in asexual populations.

We discuss the dynamics of adaptive evolution in asexual (clonal) populations. The classical 'periodic selection' model of clonal evolution assumed that beneficial mutations are very rare and therefore substitute unfettered into populations as occasional, isolated events. Newer models allow for the possibility that beneficial mutations are sufficiently common to coexist and compete for fixation within populations. Experimental evolution studies in microbes provide empirical support for stochastic models in which both selection and mutation are strong effects and clones compete for fixation; however, the relative importance of competition among clones bearing mutations of different selective effects versus competition among clones bearing multiple mutations remains unresolved. We provide some new theoretical results, moreover, suggesting that population dynamics consistent with the periodic selection model can arise even in a deterministic model that can accommodate a very high beneficial mutation rate.

Complete genetic linkage can subvert natural selection.

The intricate adjustment of organisms to their environment demonstrates the effectiveness of natural selection. But Darwin himself recognized that certain biological features could limit this effectiveness, features that generally reduce the efficiency of natural selection or yield suboptimal adaptation. Genetic linkage is known to be one such feature, and here we show theoretically that it can introduce a more sinister flaw: when there is complete linkage between loci affecting fitness and loci affecting mutation rate, positive natural selection and recurrent mutation can drive mutation rates in an adapting population to intolerable levels. We discuss potential implications of this finding for the early establishment of recombination, the evolutionary fate of asexual populations, and immunological clearance of clonal pathogens.

The fixation probability of a beneficial allele in a population dividing by binary fission.

We derive formulae for the fixation probability, P, of a rare benefical allele segregating in a population of fixed size which reproduces by binary fission, in terms of the selection coefficient for the beneficial allele, s. We find that an earlier result P approximately = 4s does not depend on the assumption of binary fission, but depends on an assumption about the ordering of events in the life cycle. We find that P approximately = 2s for mutations occurring during chromosome replication and P approximately = 2.8s for mutations occurring at random times between replication events.

An investigation of error sources and their impact in estimating the time to the most recent ancestor of spatially and temporally distributed HIV sequences.

This is an investigation of significant error sources and their impact in estimating the time to the most recent common ancestor (MRCA) of spatially and temporally distributed human immunodeficiency virus (HIV) sequences. We simulate an HIV epidemic under a range of assumptions with known time to the MRCA (tMRCA). We then apply a range of baseline (known) evolutionary models to generate sequence data. We next estimate or assume one of several misspecified models and use the chosen model to estimate the time to the MRCA. Random effects and the extent of model misspecification determine the magnitude of error sources that could include: neglected heterogeneity in substitution rates across lineages and DNA sites; uncertainty in HIV isolation times; uncertain magnitude and type of population subdivision; uncertain impacts of host/viral transmission dynamics, and unavoidable model estimation errors. Our results suggest that confidence intervals will rarely have the nominal coverage probability for tMRCA. Neglected effects lead to errors that are unaccounted for in most analyses, resulting in optimistically narrow confidence intervals (CI). Using real HIV sequences having approximately known isolation times and locations, we present possible confidence intervals for several sets of assumptions. In general, we cannot be certain how much to broaden a stated confidence interval for tMRCA. However, we describe the impact of candidate error sources on CI width. We also determine which error sources have the most impact on CI width and demonstrate that the standard bootstrap method will underestimate the CI width.