Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.
In large asexual populations, beneficial mutations have to compete with each other for fixation. Here, I derive explicit analytic expressions for the rate of substitution and the mean beneficial effect of fixed mutations, under the assumptions that the population size N is large, that the mean effect of new beneficial mutations is smaller than the mean effect of new deleterious mutations, and that new beneficial mutations are exponentially distributed. As N increases, the rate of substitution approaches a constant, which is equal to the mean effect of new beneficial mutations. The mean effect of fixed mutations continues to grow logarithmically with N. The speed of adaptation, measured as the change of log fitness over time, also grows logarithmically with N for moderately large N, and it grows double-logarithmically for extremely large N. Moreover, I derive a simple formula that determines whether at given N beneficial mutations are expected to compete with each other or go to fixation independently. Finally, I verify all results with numerical simulations.
Two important problems affect the ability of asexual populations to accumulate beneficial mutations and hence to adapt. First, clonal interference causes some beneficial mutations to be outcompeted by more-fit mutations that occur in the same genetic background. Second, multiple mutations occur in some individuals, so even mutations of large effect can be outcompeted unless they occur in a good genetic background that contains other beneficial mutations. In this article, we use a Monte Carlo simulation to study how these two factors influence the adaptation of asexual populations. We find that the results depend qualitatively on the shape of the distribution of the fitness effects of possible beneficial mutations. When this distribution falls off slower than exponentially, clonal interference alone reasonably describes which mutations dominate the adaptation, although it gives a misleading picture of the evolutionary dynamics. When the distribution falls off faster than exponentially, an analysis based on multiple mutations is more appropriate. Using our simulations, we are able to explore the limits of validity of both of these approaches, and we explore the complex dynamics in the regimes where neither one is fully applicable.
We study the dynamics of adaptation in asexual populations that undergo both beneficial and deleterious mutations. In particular, how the deleterious mutations affect the fixation of beneficial mutations was investigated. Using extensive Monte Carlo simulations, we find that in the “strong-selection weak mutation (SSWM)” regime or in the “clonal interference (CI)” regime, deleterious mutations rarely influence the distribution of “selection coefficients of the fixed mutations (SCFM)”; while in the “multiple mutations” regime, the accumulation of deleterious mutations would lead to a decrease in fitness significantly. We conclude that the effects of deleterious mutations on adaptation depend largely on the supply of beneficial mutations. And interestingly, the lowest adaptation rate occurs for a moderate value of selection coefficient of deleterious mutations.
When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects...
Mutators have been shown to hitchhike in asexual populations when the anticipated beneficial mutation supply rate of the mutator subpopulation, NUb (for subpopulation of size N and beneficial mutation rate Ub) exceeds that of the wild-type subpopulation. Here, we examine the effect of total population size on mutator dynamics in asexual experimental populations of Saccharomyces cerevisiae. Although mutators quickly hitchhike to fixation in smaller populations, mutator fixation requires more and more time as population size increases; this observed delay in mutator hitchhiking is consistent with the expected effect of clonal interference. Interestingly, despite their higher beneficial mutation supply rate, mutators are supplanted by the wild type in very large populations. We postulate that this striking reversal in mutator dynamics is caused by an interaction between clonal interference, the fitness cost of the mutator allele, and infrequent large-effect beneficial mutations in our experimental populations. Our work thus identifies a potential set of circumstances under which mutator hitchhiking can be inhibited in natural asexual populations, despite recent theoretical predictions that such populations should have a net tendency to evolve ever-higher genomic mutation rates.
In the absence of recombination, a mutator allele can spread through a population by hitchhiking with beneficial mutations that appear in its genetic background. Theoretical studies over the past decade have shown that the survival and fixation probability of beneficial mutations can be severely reduced by population size bottlenecks. Here we use computational modeling and evolution experiments with the yeast S. cerevisiae to examine whether population bottlenecks can affect mutator dynamics in adapting asexual populations. In simulation, we show that population bottlenecks can inhibit mutator hitchhiking with beneficial mutations and are most effective at lower beneficial mutation supply rates. We then subjected experimental populations of yeast propagated at the same effective population size to three different bottleneck regimes and observed that the speed of mutator hitchhiking was significantly slower at smaller bottlenecks, consistent with our theoretical expectations. Our results, thus, suggest that bottlenecks can be an important factor in mutation rate evolution and can in certain circumstances act to stabilize or, at least, delay the progressive elevation of mutation rates in asexual populations. Additionally, our findings provide the first experimental support for the theoretically postulated effect of population bottlenecks on beneficial mutations and demonstrate the usefulness of studying mutator frequency dynamics for understanding the underlying dynamics of fitness-effecting mutations.
Mutator alleles, which elevate an individual’s mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and ex- perimental populations. Mutators are continually produced from nonmu- tators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. How- ever, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleteri- ous mutation rates are high in mutators, there will often be many “young”, recently produced mutators in the population, and the fact that deleteri- ous mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations, and analyze the circumstances under which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.; Organismic and Evolutionary Biology
The fate of a newly arising beneficial mutation depends on many factors, such as the population size and the availability and fitness effects of other mutations that accumulate in the population. It has proven difficult to understand how these factors influence the trajectories of particular mutations, since experiments have primarily focused on characterizing successful clones emerging from a small number of evolving populations. Here, we present the results of a massively parallel experimental designed to measure the full spectrum of possible fates of new beneficial mutations in hundreds of experimental yeast populations, whether these mutations are ultimately successful or not. Using strains in which a particular class of beneficial mutation is detectable by fluorescence, we followed the trajectories of these beneficial mutations across 592 independent populations for 1,000 generations. We find that the fitness advantage provided by individual mutations plays a surprisingly small role. Rather, underlying “background” genetic variation is quickly generated in our initially clonal populations and plays a crucial role in determining the fate of each individual beneficial mutation in the evolving population.; Organismic and Evolutionary Biology
We investigate the dynamics of loss of favorable mutations in an asexual haploid population. In the current work, we consider homogeneous as well as spatially structured population models. We focus our analysis on statistical measurements of the probability distribution of the maximum population size N(sb) achieved by those mutations that have not reached fixation. Our results show a crossover behavior which demonstrates the occurrence of two evolutionary regimes. In the first regime, which takes place for small N(sb) , the probability distribution is described by a power law with characteristic exponent theta(d) =1.8 +/- 0.01. This power law is not influenced by the rate of beneficial mutations. The second regime, which occurs for intermediate to large values of N(sb), has a characteristic exponent theta(c) which increases as the rate of beneficial mutations grows. These results establish where genetic drift and clonal interference become the main underlying mechanism in the extinction of advantageous mutations.
We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find
that the accumulation of deleterious mutations, due to the operation of Muller’s ratchet, can considerably reduce the
rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the
effective population size. In the absence of Muller’s ratchet, a beneficial mutation can only become fixed if it creates
the best possible genotype; if Muller’s ratchet operates, however, mutations initially arising in a nonoptimal genotype
can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal
background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced,
the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations
as long as the rate of their occurrence is low and the deleterious effects of mutations (sd) are higher than the beneficial
effects (sa). When sa . sd, the advantage of a beneficial mutation can outweigh the deleterious effects of associated
mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated
with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the
rates of accumulation of deleterious and beneficial mutations. Furthermore...
Sexual reproduction and recombination are important for maintaining a stable copy number of transposable elements (TEs). In sexual populations, elements can be contained by purifying selection against host carriers with higher element copy numbers; however, in the absence of sex and recombination, asexual populations could be driven to extinction by an unchecked proliferation of TEs. Here we provide a theoretical framework for analyzing TE dynamics under asexual reproduction. Analytic results show that, in an infinite asexual population, an equilibrium in copy number is achieved if no element excision is possible, but that all TEs are eliminated if there is some excision. In a finite population, computer simulations demonstrate that small populations are driven to extinction by a Muller's ratchet-like process of element accumulation, but that large populations can be cured of vertically transmitted TEs, even with excision rates well below transposition rates. These results may have important consequences for newly arisen asexual lineages and may account for the lack of deleterious retrotransposons in the putatively ancient asexual bdelloid rotifers.
In large asexual populations, multiple beneficial mutations arise in the
population, compete, interfere with each other, and accumulate on the same
genome, before any of them fix. The resulting dynamics, although studied by
many authors, is still not fully understood, fundamentally because the effects
of fluctuations due to the small numbers of the fittest individuals are large
even in enormous populations. In this paper, branching processes and various
asymptotic methods for analyzing the stochastic dynamics are further developed
and used to obtain information on fluctuations, time dependence, and the
distributions of sizes of subpopulations, jumps in the mean fitness, and other
properties. The focus is on the behavior of a broad class of models: those with
a distribution of selective advantages of available beneficial mutations that
falls off more rapidly than exponentially. For such distributions, many aspects
of the dynamics are universal - quantitatively so for extremely large
populations. On the most important time scale that controls coalescent
properties and fluctuations of the speed, the dynamics is reduced to a simple
stochastic model that couples the peak and the high-fitness "nose" of the
fitness distribution. Extensions to other models and distributions of available
mutations are discussed briefly.; Comment: 3 figures
The importance of mutator clones in the adaptive evolution of asexual
populations is not fully understood. Here we address this problem by using an
ab initio microscopic model of living cells, whose fitness is derived directly
from their genomes using a biophysically realistic model of protein folding and
interactions in the cytoplasm. The model organisms contain replication
controlling genes (DCGs) and genes modeling the mismatch repair (MMR)
complexes. We find that adaptation occurs through the transient fixation of a
mutator phenotype, regardless of particular perturbations in the fitness
landscape. The microscopic pathway of adaptation follows a well-defined set of
events: stochastic switching to the mutator phenotype first, then mutation in
the MMR complex that hitchhikes with a beneficial mutation in the DCGs, and
finally a compensating mutation in the MMR complex returning the population to
a non-mutator phenotype. Similarity of these results to reported adaptation
events points out to robust universal physical principles of evolutionary
The adaptive evolution of large asexual populations is generally
characterized by competition between clones carrying different beneficial
mutations. This interference phenomenon slows down the adaptation speed and
makes the theoretical description of the dynamics more complex with respect to
the successional occurrence and fixation of beneficial mutations typical of
small populations. A simplified modeling framework considering multiple
beneficial mutations with equal and constant fitness advantage captures some of
the essential features of the actual complex dynamics, and some key predictions
from this model are verified in laboratory evolution experiments. However, in
these experiments the relative advantage of a beneficial mutation is generally
dependent on the genetic background. In particular, the general pattern is
that, as mutations in different loci accumulate, the relative advantage of new
mutations decreases, trend often referred to as "diminishing return" epistasis.
In this paper, we propose a phenomenological model that generalizes the
fixed-advantage framework to include in a simple way this feature. To evaluate
the quantitative consequences of diminishing returns on the evolutionary
dynamics, we approach the model analytically as well as with direct
Genome sizes have evolved to vary widely, from 250 bases in viroids to 670
billion bases in amoeba. This remarkable variation in genome size is the
outcome of complex interactions between various evolutionary factors such as
point mutation rate, population size, insertions and deletions, and genome
editing mechanisms that may be specific to certain taxonomic lineages. While
comparative genomics analyses have uncovered some of the relationships between
these diverse evolutionary factors, we still do not understand what drives
genome size evolution. Specifically, it is not clear how primordial mutational
processes of base substitutions, insertions, and deletions influence genome
size evolution in asexual organisms. Here, we use digital evolution to
investigate genome size evolution by tracking genome edits and their fitness
effects in real time. In agreement with empirical data, we find that mutation
rate is inversely correlated with genome size in asexual populations. We show
that at low point mutation rate, insertions are significantly more beneficial
than deletions, driving genome expansion and acquisition of phenotypic
complexity. Conversely, high mutational load experienced at high mutation rates
inhibits genome growth, forcing the genomes to compress genetic information.
Our analyses suggest that the inverse relationship between mutation rate and
genome size is a result of the tradeoff between evolving phenotypic innovation
and limiting the mutational load.
Two important problems affect the ability of asexual populations to
accumulate beneficial mutations, and hence to adapt. First, clonal interference
causes some beneficial mutations to be outcompeted by more-fit mutations which
occur in the same genetic background. Second, multiple mutations occur in some
individuals, so even mutations of large effect can be outcompeted unless they
occur in a good genetic background which contains other beneficial mutations.
In this paper, we use a Monte Carlo simulation to study how these two factors
influence the adaptation of asexual populations. We find that the results
depend qualitatively on the shape of the distribution of the effects of
possible beneficial mutations. When this distribution falls off slower than
exponentially, clonal interference alone reasonably describes which mutations
dominate the adaptation, although it gives a misleading picture of the
evolutionary dynamics. When the distribution falls off faster than
exponentially, an analysis based on multiple mutations is more appropriate.
Using our simulations, we are able to explore the limits of validity of both of
these approaches, and we explore the complex dynamics in the regimes where
neither are fully applicable.; Comment: 24 pages...
How self-incompatibility systems are maintained in plant populations is still
a debated issue. Theoretical models predict that self-incompatibility systems
break down according to the intensity of inbreeding depression and number of
S-alleles. Other studies have explored the function of asexual reproduction in
the maintenance of self-incompatibility. However, the population genetics of
partially asexual, self-incompatible populations are poorly understood and
previous studies have failed to consider all possible effects of asexual
reproduction or could only speculate on those effects. In this study, we
investigated how partial asexuality may affect genetic diversity at the S-locus
and fitness in small self-incompatible populations. A genetic model including
an S-locus and a viability locus was developed to perform forward simulations
of the evolution of populations of various sizes. Drift combined with partial
asexuality produced a decrease in the number of alleles at the S-locus. In
addition, an excess of heterozygotes was present in the population, causing an
increase in mutation load. This heterozygote excess was enhanced by the
self-incompatibility system in small populations. In addition, in highly
asexual populations, individuals produced asexually had some fitness advantages
over individuals produced sexually...
In large populations, multiple beneficial mutations may be simultaneously
spreading. In asexual populations, these mutations must either arise on the
same background or compete against each other. In sexual populations,
recombination can bring together beneficial alleles from different backgrounds,
but tightly linked alleles may still greatly interfere with each other. We show
for well-mixed populations that when this interference is strong, the genome
can be seen as consisting of many effectively asexual stretches linked
together. The rate at which beneficial alleles fix is thus roughly proportional
to the rate of recombination, and depends only logarithmically on the mutation
supply and the strength of selection. Our scaling arguments also allow to
predict, with reasonable accuracy, the distribution of effects of fixed
mutations when new mutations have broadly-distributed effects. We focus on the
regime in which crossovers occur more frequently than beneficial mutations, as
is likely to be the case for many natural populations.
In large asexual populations, beneficial mutations have to compete with each
other for fixation. Here, I derive explicit analytic expressions for the rate
of substitution and the mean beneficial effect of fixed mutations, under the
assumptions that the population size N is large, that the mean effect of new
beneficial mutations is smaller than the mean effect of new deleterious
mutations, and that new beneficial mutations are exponentially distributed. As
N increases, the rate of substitution approaches a constant, which is equal to
the mean effect of new beneficial mutations. The mean effect of fixed mutations
continues to grow logarithmically with N. The speed of adaptation, measured as
the change of log fitness over time, also grows logarithmically with N for
moderately large N, and it grows double-logarithmically for extremely large N.
Moreover, I derive a simple formula that determines whether at given N
beneficial mutations are expected to compete with each other or go to fixation
independently. Finally, I verify all results with numerical simulations.; Comment: 33 pages, 6 figures. Minor changes in discussion. To appear in