# Mutation rate and Evolutionary rate?

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What is the difference between then?I have read some jobs that describes analysis about mutations rates and another ones with evolutionary rates.I want to know the diferrence between then.

Mutation rate

A mutation rate is a rate at which mutation occur. It is typically expressed as number of mutations per site (per nucleotide) per reproduction event. In humans, the average mutation rate per site per reproduction is of the order of $$10^{-8}$$.

When a mutation occurs, it will exist in only one copy in the population. This mutations might, over time, reach a higher frequency and even eventually reach a frequency of 1.0 (we talk about "fixation" then) but most mutations will never reach a high frequency and just disappear in the coming few generations whether or not the selection was deleterious.

Evolutionary rate

The term "evolution rate" has no commonly agreed upon definition. Depending upon your definition the mutation rate will be more or less correlated with the evolutionary rate.

Phenotypic evolutionary rate

Evolution rate might refer to phenotypic evolution. The Darwin (named after Charles Darwin, obviously) is a common unit to measure phenotypic evolution. Other unit of evolutionary rate could consist at measuring how much time it take for the mean phenotypic trait to change by one standard deviation of the original phenotypic distribution.

Genetic evolutionary rate

One can also consider genetic measure of evolutionary rate such as the number of neutral substitutions in a lineage per unit of time. With this definition, the difference between the mutation rate and the evolutionary rate become a little more blurry as the expected substitution rate at neutral site is equal to the mutation rate.

You say

I have read some jobs that describes analysis

Please, always include your source. There is no way to give any information about what they mean by these terms without having a look at the original paper.

Related post

The post Are we “more evolved” than present-day bacteria? is somewhat related.

## High mutation rates limit evolutionary adaptation in Escherichia coli

Mutation is fundamental to evolution, because it generates the genetic variation on which selection can act. In nature, genetic changes often increase the mutation rate in systems that range from viruses and bacteria to human tumors. Such an increase promotes the accumulation of frequent deleterious or neutral alleles, but it can also increase the chances that a population acquires rare beneficial alleles. Here, we study how up to 100-fold increases in Escherichia coli's genomic mutation rate affect adaptive evolution. To do so, we evolved multiple replicate populations of asexual E. coli strains engineered to have four different mutation rates for 3000 generations in the laboratory. We measured the ability of evolved populations to grow in their original environment and in more than 90 novel chemical environments. In addition, we subjected the populations to whole genome population sequencing. Although populations with higher mutation rates accumulated greater genetic diversity, this diversity conveyed benefits only for modestly increased mutation rates, where populations adapted faster and also thrived better than their ancestors in some novel environments. In contrast, some populations at the highest mutation rates showed reduced adaptation during evolution, and failed to thrive in all of the 90 alternative environments. In addition, they experienced a dramatic decrease in mutation rate. Our work demonstrates that the mutation rate changes the global balance between deleterious and beneficial mutational effects on fitness. In contrast to most theoretical models, our experiments suggest that this tipping point already occurs at the modest mutation rates that are found in the wild.

### Conflict of interest statement

The authors have declared that no competing interests exist.

### Figures

Fig 1. Experimental design.

Fig 1. Experimental design.

We evolved eight replicate populations for each of four E .…

Fitness of the evolving replicate…

Fitness of the evolving replicate populations relative to their ancestors (A) over time,…

Fig 3. Replicate populations with higher mutation…

Fig 3. Replicate populations with higher mutation rates have increased genetic diversity and more high…

Fig 4. Cell density after 24 hours…

Fig 4. Cell density after 24 hours of growth in stressful conditions increased with increasing…

## The effect of population bottlenecks on mutation rate evolution in asexual populations

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 modelling 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-affecting mutations.

Keywords: asexual populations beneficial mutations hitchhiking mutation rate population bottlenecks yeast.

© 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.

### Figures

Figure 1. The effect of population bottlenecks…

Figure 1. The effect of population bottlenecks on mutator dynamics at different supply rates of…

Figure 2. Selection strength of beneficial mutations…

Figure 2. Selection strength of beneficial mutations and mutator dynamics in bottlenecked populations

## Evolutionary rescue of a parasite population by mutation rate evolution

The risk of antibiotic resistance evolution in parasites is a major problem for public health. Identifying factors which promote antibiotic resistance evolution is thus a priority in evolutionary medicine. The rate at which new mutations enter the parasite population is one important predictor however, mutation rate is not necessarily a fixed quantity, as is often assumed, but can itself evolve. Here we explore the possible impacts of mutation rate evolution on the fate of a disease circulating in a host population, which is being treated with drugs, the use of which varies over time. Using an evolutionary rescue framework, we find that mutation rate evolution provides a dramatic increase in the probability that a parasite population survives treatment in only a limited region, while providing little or no advantage in other regions. Both epidemiological features, such as the virulence of infection, and population genetic parameters, such as recombination rate, play important roles in determining the probability of evolutionary rescue and whether mutation rate evolution enhances the probability of evolutionary rescue or not. While efforts to curtail mutation rate evolution in parasites may be worthwhile under some circumstances, our results suggest that this need not always be the case.

Keywords: Drug resistance Evolutionary rescue Modifier model Mutation rate Parasites.

## Introduction

Mutation is fundamental to evolution. Without it, evolution cannot occur, because mutation provides the genetic variation necessary for selection and genetic drift. Each new mutation in an individual can increase its fitness, decrease its fitness, or have no effect on its fitness. Unfortunately, most mutations with fitness effects are deleterious, and fitness-increasing beneficial mutations constitute only a small fraction of all possible mutations [1]. The mutation rate can itself evolve, because it is subject to genetic change in the "mutation rate genome", the part of a genome encoding DNA replication and repair systems [2,3]. Here, we characterize the long-term effects of a range of mutation rates on adaptation, as well as the evolution of the mutation rate itself, by evolving multiple replicate populations of asexual Escherichia coli in a minimal medium in the laboratory.

Evolutionary adaptation under increased mutation pressure in large non-recombining populations like ours has been explored in past work (all mutations that occur in our E. coli laboratory strain's genome are linked). The joint effects of mutation and linkage on selection (and the related topics of diversity and the evolution of sex) have been much studied since Fisher [4] and Muller [5] ([6–10], recently reviewed in [11–14]). Under increased mutation pressure, multiple clones within a population may acquire new mutations, and then compete with each other for fixation. While relevant studies show that the speed of adaptation can increase with the genomic mutation rate [10,15–18], they leave open the possibility that extremely high mutation rates could hinder adaptation. This possibility is raised by a variety of models that predict declining fitness in populations with extreme mutation rates. An early, influential, but simple model predicted that a population's fitness will decrease when the rate of mutation increases beyond a critical “error threshold” [19] whose value depends on model details. Other models of populations evolving at high mutation rates are more realistic and take into account phenomena like beneficial mutations and demography. However, they also predict that adaptation can be slowed and eventually reversed at sufficiently high mutation rates by the effects of deleterious mutations [20–24].

Many studies have documented the evolution of increased mutation rates [25–31], which can evolve in certain conditions. For example, after a recent environmental change that creates opportunities for novel adaptations and new beneficial mutations [32,33], a cell with a mutator allele is more likely to produce large-effect beneficial mutations than a cell with a wild-type mutation rate. Because of their improved fitness, cell lineages with newly acquired beneficial alleles (and their linked mutator alleles) can increase in frequency in the population. Thus, hypermutation can readily evolve when mutator alleles hitchhike to fixation with beneficial mutations [34–37].

In the long term, however, hypermutation can be detrimental, because most non-neutral mutations have deleterious consequences [1]. Thus, an individual with a higher mutation rate may accumulate more deleterious mutations overall, which can result in lower fitness. For this reason, selection has been predicted to reduce mutation rates [38]. However, there are several potential reasons why mutation rates may not decline all the way to zero. One of them is that the physiological mechanisms required to improve replication fidelity and DNA repair carry a fitness cost [39–42]. Another is that the power of selection to reduce the mutation rate is limited by population size via the so-called drift-barrier [43,44]. Experimental observations of evolved reductions in the mutation rate have been reported, but are relatively infrequent [27,31,45–50] (reviewed in [51]).

While some previous experiments explored the adaptive responses and mutation rate changes that can take place under increased mutational pressure [46–48,50], they focused on one or two mutation rates, and did not include genomic analyses (except [50]). Here, we sought to provide a uniquely comprehensive empirical data set across a range of mutation rates, including whole genome population sequencing data, mutation rate data, and fitness measurements in a number of environments. To do so, we engineered four isogenic E. coli K12 MG1655 derivative strains with increased mutation rates and evolved eight replicate populations of each strain for 3000 generations in a serial-transfer experiment. Genomic mutation rates differed more than a hundred-fold among these strains and ranged from U = 0.00034 to U = 0.036 point mutations per genome per generation by one method of estimation. During evolution, we periodically characterized the growth rate and stationary population density of each population. We also assayed the fitness of evolved populations in a variety of stressful environments. High-throughput population sequencing allowed us to characterize how far our populations spread through sequence space, and to study the mutations occurring in each population.

## Results

### Cumulative Number of Observed Mutations in Each Population Reveals Dynamics Caused by Both Hypermutator and Antimutator Alleles

We examined the number of observed mutations over time in each LTEE population ( figs. 1 and 2, supplementary figs. S1–S3, Supplementary Material online). These results show that mutation rates have evolved idiosyncratically over the LTEE. Figure 1A shows the number of point mutations over time in each population. The rate of observed point mutations decreased in three of the six hypermutator populations (Ara−2, Ara+3, and Ara+6). The decrease in the rate of molecular evolution in these populations was previously ascribed to the evolution of antimutator alleles ( Tenaillon et al. 2016 Good et al. 2017). Although antimutator alleles of mutY compensating for defects in mutT have been reported in Ara−1 ( Wielgoss et al. 2013), the change in slope observed at 40,000 generations in Ara−1 is subtle compared with the slope changes in Ara−2, Ara+3, and Ara+6.

Divergent evolution of mutation rates in the LTEE. Each panel shows the cumulative number of observed mutations, subdivided by mutation class, over time in each LTEE population. The top six panels show the nonmutator LTEE populations, and the bottom six panels show the hypermutator LTEE populations. (A) Point mutations are shown in red. (B) Indel mutations are shown in purple. (C) sv associated with transposons are shown in green, whereas those that are not associated with transposons are shown in gray.

Divergent evolution of mutation rates in the LTEE. Each panel shows the cumulative number of observed mutations, subdivided by mutation class, over time in each LTEE population. The top six panels show the nonmutator LTEE populations, and the bottom six panels show the hypermutator LTEE populations. (A) Point mutations are shown in red. (B) Indel mutations are shown in purple. (C) sv associated with transposons are shown in green, whereas those that are not associated with transposons are shown in gray.

The dynamics of hypermutator and antimutator alleles affect the spectrum of observed point mutations over time. (A) Spectrum of point mutations over time in the hypermutator LTEE populations. (B) Inset figure showing nondominant point mutation spectra over time in the hypermutator LTEE populations.

The dynamics of hypermutator and antimutator alleles affect the spectrum of observed point mutations over time. (A) Spectrum of point mutations over time in the hypermutator LTEE populations. (B) Inset figure showing nondominant point mutation spectra over time in the hypermutator LTEE populations.

Figure 1B shows the number of observed indel mutations over time in each population. Five of the six point-mutation hypermutator populations also show an indel hypermutator phenotype. These five populations all evolved defects in mismatch repair (MMR) ( table 1 and fig. 4). The exception is Ara−1, which evolved a frameshift mutT allele ( table 1 and fig. 3) that induces a high point mutation rate, absent a corresponding indel hypermutator phenotype.

Oxidative damage repair alleles in hypermutator LTEE populations. This visualization uses computer code from Good et al. (2017). Stars indicate the time (and allele frequency) at which mutations are reliably estimated to appear in the time series. The allele frequency trajectories for all observed mutations in the hypermutator populations are shown in gray. The allele frequency trajectories of de novo mutations (excepting synonymous mutations) in oxidative damage repair genes ( supplementary file 1 , Supplementary Material online) are colored and labeled in each population.

Oxidative damage repair alleles in hypermutator LTEE populations. This visualization uses computer code from Good et al. (2017). Stars indicate the time (and allele frequency) at which mutations are reliably estimated to appear in the time series. The allele frequency trajectories for all observed mutations in the hypermutator populations are shown in gray. The allele frequency trajectories of de novo mutations (excepting synonymous mutations) in oxidative damage repair genes ( supplementary file 1 , Supplementary Material online) are colored and labeled in each population.

Putative Hypermutator and Antimutator Alleles Described in the Text

Population . Gene . DNA Repair Pathway . Appearance Time (Generations) . Position (bp) . Mutation .
Ara−1 uvrCOxidative damage repair 26,250 1,972,086 Q183P
Ara−1 mutTOxidative damage repair 26,250 114,034 (C)6→7
Ara−1 mutYOxidative damage repair 28,750 2,988,792 L40W
Ara−1 mutYOxidative damage repair 32,250 2,989,164 L164*
Ara−2 mutLMMR 2,250 4,375,786 (TGGCGC)3→4
Ara−2 uvrAOxidative damage repair 12,250 4,251,585 A407T
Ara−2 mutTOxidative damage repair 13,750 114,113 R89H
Ara−2 mutLMMR *This in-frame reversion fixes at 42,250 generations 4,375,781 (TGGCGC)3→2
Ara−3 mutSMMR 34,750 2,753,768 Q606*
Ara−3 mutYOxidative damage repair 48,250 2,989,624 Δ1 bp
Ara−4 mutLMMR 7,250 4,375,781 (TGGCGC)3→2
Ara+3 mutSMMR 2,750 2,752,473 +G
Ara+6 mutSMMR 1,250 2,752,473 +G
Ara+6 uvrAOxidative damage repair 4,750 4,250,341 I821M
Ara+6 mutTOxidative damage repair 4,750 114,034 (C)6→5
Ara+6 mutYOxidative damage repair 31,750 2,988,917 Y82D
Ara+6 mutYOxidative damage repair 49,750 2,989,297 C208W
Population . Gene . DNA Repair Pathway . Appearance Time (Generations) . Position (bp) . Mutation .
Ara−1 uvrCOxidative damage repair 26,250 1,972,086 Q183P
Ara−1 mutTOxidative damage repair 26,250 114,034 (C)6→7
Ara−1 mutYOxidative damage repair 28,750 2,988,792 L40W
Ara−1 mutYOxidative damage repair 32,250 2,989,164 L164*
Ara−2 mutLMMR 2,250 4,375,786 (TGGCGC)3→4
Ara−2 uvrAOxidative damage repair 12,250 4,251,585 A407T
Ara−2 mutTOxidative damage repair 13,750 114,113 R89H
Ara−2 mutLMMR *This in-frame reversion fixes at 42,250 generations 4,375,781 (TGGCGC)3→2
Ara−3 mutSMMR 34,750 2,753,768 Q606*
Ara−3 mutYOxidative damage repair 48,250 2,989,624 Δ1 bp
Ara−4 mutLMMR 7,250 4,375,781 (TGGCGC)3→2
Ara+3 mutSMMR 2,750 2,752,473 +G
Ara+6 mutSMMR 1,250 2,752,473 +G
Ara+6 uvrAOxidative damage repair 4,750 4,250,341 I821M
Ara+6 mutTOxidative damage repair 4,750 114,034 (C)6→5
Ara+6 mutYOxidative damage repair 31,750 2,988,917 Y82D
Ara+6 mutYOxidative damage repair 49,750 2,989,297 C208W

Putative Hypermutator and Antimutator Alleles Described in the Text

Population . Gene . DNA Repair Pathway . Appearance Time (Generations) . Position (bp) . Mutation .
Ara−1 uvrCOxidative damage repair 26,250 1,972,086 Q183P
Ara−1 mutTOxidative damage repair 26,250 114,034 (C)6→7
Ara−1 mutYOxidative damage repair 28,750 2,988,792 L40W
Ara−1 mutYOxidative damage repair 32,250 2,989,164 L164*
Ara−2 mutLMMR 2,250 4,375,786 (TGGCGC)3→4
Ara−2 uvrAOxidative damage repair 12,250 4,251,585 A407T
Ara−2 mutTOxidative damage repair 13,750 114,113 R89H
Ara−2 mutLMMR *This in-frame reversion fixes at 42,250 generations 4,375,781 (TGGCGC)3→2
Ara−3 mutSMMR 34,750 2,753,768 Q606*
Ara−3 mutYOxidative damage repair 48,250 2,989,624 Δ1 bp
Ara−4 mutLMMR 7,250 4,375,781 (TGGCGC)3→2
Ara+3 mutSMMR 2,750 2,752,473 +G
Ara+6 mutSMMR 1,250 2,752,473 +G
Ara+6 uvrAOxidative damage repair 4,750 4,250,341 I821M
Ara+6 mutTOxidative damage repair 4,750 114,034 (C)6→5
Ara+6 mutYOxidative damage repair 31,750 2,988,917 Y82D
Ara+6 mutYOxidative damage repair 49,750 2,989,297 C208W
Population . Gene . DNA Repair Pathway . Appearance Time (Generations) . Position (bp) . Mutation .
Ara−1 uvrCOxidative damage repair 26,250 1,972,086 Q183P
Ara−1 mutTOxidative damage repair 26,250 114,034 (C)6→7
Ara−1 mutYOxidative damage repair 28,750 2,988,792 L40W
Ara−1 mutYOxidative damage repair 32,250 2,989,164 L164*
Ara−2 mutLMMR 2,250 4,375,786 (TGGCGC)3→4
Ara−2 uvrAOxidative damage repair 12,250 4,251,585 A407T
Ara−2 mutTOxidative damage repair 13,750 114,113 R89H
Ara−2 mutLMMR *This in-frame reversion fixes at 42,250 generations 4,375,781 (TGGCGC)3→2
Ara−3 mutSMMR 34,750 2,753,768 Q606*
Ara−3 mutYOxidative damage repair 48,250 2,989,624 Δ1 bp
Ara−4 mutLMMR 7,250 4,375,781 (TGGCGC)3→2
Ara+3 mutSMMR 2,750 2,752,473 +G
Ara+6 mutSMMR 1,250 2,752,473 +G
Ara+6 uvrAOxidative damage repair 4,750 4,250,341 I821M
Ara+6 mutTOxidative damage repair 4,750 114,034 (C)6→5
Ara+6 mutYOxidative damage repair 31,750 2,988,917 Y82D
Ara+6 mutYOxidative damage repair 49,750 2,989,297 C208W

The hypermutator dynamics in Ara−2 are particularly striking. An antimutator allele eventually fixes, and reverts both the point and indel hypermutator phenotype back to ancestral or near ancestral levels ( fig. 1A and B). The hypermutator phenotype is caused by phase variation of a (TGGCGC)3 repeat in mutL ( table 1). Reversions to the triplet state reverse the hypermutator phenotype. The number of new point and indel mutations in Ara−2 ( supplementary figs. S1 and S2 , Supplementary Material online) fluctuates with the allele frequency dynamics of this mutL repeat ( fig. 4). Although fixations are usually irreversible in large asexual populations, phase variation is an exception: polymerases often slip on repetitive sequences, causing those repeats to expand or contract at relatively high rates ( Moxon et al. 2006).

MMR alleles in the hypermutator LTEE populations. This visualization uses computer code from Good et al. (2017). Stars indicate the time (and allele frequency) at which mutations are reliably estimated to appear in the time series. The allele frequency trajectories for all observed mutations in the hypermutator populations are shown in gray. The allele frequency trajectories of de novo mutations (except synonymous mutations) in MMR genes ( supplementary file 1 , Supplementary Material online) are colored and labeled in each population.

MMR alleles in the hypermutator LTEE populations. This visualization uses computer code from Good et al. (2017). Stars indicate the time (and allele frequency) at which mutations are reliably estimated to appear in the time series. The allele frequency trajectories for all observed mutations in the hypermutator populations are shown in gray. The allele frequency trajectories of de novo mutations (except synonymous mutations) in MMR genes ( supplementary file 1 , Supplementary Material online) are colored and labeled in each population.

At first glance, figure 1B seems to show that Ara+6 fixed a mutation reverting the indel hypermutator phenotype. However, a close examination of the indel mutation rate and allele frequency dynamics in Ara+6 reveals that a super-hypermutator clade evolved within the first 1,000 generations ( supplementary fig. S2 , Supplementary Material online). Additional evidence for the super-hypermutator clade comes from the evolution and extinction of an A:T→G:C and G:C→A:T hypermutator phenotype ( fig. 2) that parallels the evolution of the indel hypermutator phenotype. This super-hypermutator clade carries a frameshift allele of the MMR gene mutS ( table 1 and fig. 4), is distinguished by marker alleles of the nucleotide excision repair genes uvrA and uvrB ( fig. 3), and persists at low frequency until going extinct by 20,000 generations ( figs. 3 and 4, supplementary fig. S2 , Supplementary Material online). The majority clade in Ara+6 evolved a mutation in mutT at 4,750 generations ( table 1 and fig. 3) that causes a point mutation hypermutator phenotype without causing an indel hypermutator phenotype. The coexistence of clades with different hypermutator phenotypes, and the eventual extinction of the super-hypermutator clade, most reasonably explains the loss of the indel hypermutator phenotype from Ara+6.

Figure 1C shows the number of observed structural mutations over time. As described in the original report for this data set ( Good et al. 2017), structural mutations (or structural variants, sv) are defined by junctions between two distinct locations in the reference genome. The vast majority of these structural mutations are caused by insertion sequence (IS) transpositions. Three of the canonical nonmutator populations (Ara−5, Ara−6, and Ara+1) show an IS hypermutator phenotype. The IS hypermutator phenotype in Ara+1 was reported previously ( Papadopoulos et al. 1999 Tenaillon et al. 2016). In contrast, only one of the canonical hypermutator populations, Ara−3, shows an IS hypermutator phenotype. The rate of observed structural mutations in Ara−3 shows three different slopes. Ara−3 evolved an IS hypermutator phenotype very early in the LTEE. Around 30,000 generations, the IS rate intensifies, either due to genetic evolution, or as a consequence of stress induced by the citrate metabolic innovation that evolved around that time ( Blount et al. 2012, 2020). Finally, the IS rate decreases around 45,000 generations. More than 100 mutations go to fixation in the selective sweep at 45,000 generations in Ara−3, including mutations in the DNA repair genes recR, recE, ligA, uvrA, and ybaZ. The distinct IS rates observed in Ara−3 may, in part, reflect clonal interference between deeply diverged, competing lineages in that population ( Blount et al. 2012 Leon et al. 2018), especially if those lineages have different IS transposition rates.

We also examined the spectrum of point mutations in each hypermutator population over time ( fig. 2). Ara–1 and Ara+6 show a high frequency of A:T→C:G transversion mutations, characteristic of defects in mutT ( Tajiri et al. 1995 Fowler et al. 2003 Wielgoss et al. 2013). Ara–2, Ara–3, Ara–4, and Ara+3, which all have defects in MMR ( table 1 and fig. 4), show a high frequency of A:T→G:C and G:C→A:T mutations. These findings are consistent with genomic analyses of LTEE hypermutators ( Couce et al. 2017). Furthermore, Ara−1, Ara−3, and Ara+6 all show late increases in the frequency of G:C→T:A transversion mutations, characteristic of defects in mutY ( Tajiri et al. 1995 Fowler et al. 2003 Wielgoss et al. 2013).

In examining mutT, we noticed that two of the three cases of mutT alleles arising to high frequency in the LTEE occur on an uvrA background (Ara−2 and Ara+6), whereas the third, in Ara−1, occurs on an uvrC background ( fig. 3). The mutT allele in Ara−2 does not cause the characteristic mutT A:T→C:G hypermutator phenotype found in Ara−1 and Ara+6 ( fig. 2), so its association with uvrA may be coincidental. However, the same uvrA substitution that goes to fixation with mutT in Ara+6 also occurs in a 40,000 generation isolate from the Ara−1 population called REL10939 ( Tenaillon et al. 2016), which suggests that this particular uvrA allele may be beneficial in those contexts. Furthermore, it has been reported that uvrA/mutT and uvrB/mutT double knockouts have a substantially lower mutation rate than mutT knockouts, in the presence of hydrogen peroxide ( Hori et al. 2007). Based on these observations, we hypothesize that the mutT alleles that successfully went to fixation in the LTEE may have evolved on an uvrABC genetic background that reduced the intensity of the mutT hypermutator phenotype.

### Gene-Orientation Mutation Bias Evolves in the LTEE

Several reports indicate that mutation rates differ between the leading and lagging strands of the DNA replication bubble ( Lee et al. 2012 Paul et al. 2013). Potential causes include asymmetry in nucleotide composition around the replication origin (GC skew) ( Marín and Xia 2008), context-dependent mutation rates that are asymmetric around the replication origin ( Sung et al. 2015), and head-on collisions between the replication and transcription molecular machinery ( Paul et al. 2013). Such reports motivated us to ask whether the LTEE metagenomics data showed evidence of gene-orientation mutation biases, such that genes oriented with (or against) the leading or lagging strand of DNA synthesis have different mutation rates.

Our null expectation is that the distribution of synonymous mutations on each strand of the chromosome should be related to the amount of coding sequence on each strand (i.e., the density of genes multiplied by their length). Furthermore, the spectrum of nucleotide substitutions on each strand should reflect local G:C content in the ancestral LTEE clone REL606: for example, G:C→A:T substitutions should be more common in G:C-rich regions. Figure 5A shows this null expectation. Both the amount of coding sequence and G:C content per strand are asymmetric about the replication origin of REL606. At the replication origin, one DNA strand switches from leading to lagging, while its complement switches from lagging to leading. This switch occurs because DNA replication is bidirectional, such that two replisomes move in opposite directions from the replication origin. Even in the absence of gene-orientation mutation bias, figure 5A shows that some asymmetry in the distribution of synonymous mutations over the replication origin is expected.

Gene-orientation mutation bias evolves in the LTEE. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. In each labeled subfigure, top and bottom panels show genes occurring on each of the two strands of the chromosome, with the arbitrary labels 1 and −1. (A) The nucleotide composition of genes on the two strands of the chromosome of the LTEE ancestral clone REL606. (B) The genomic distribution of mutations within genes, summed over MMR-deficient LTEE populations (left panel) and MutT-deficient LTEE populations (right panel).

Gene-orientation mutation bias evolves in the LTEE. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. In each labeled subfigure, top and bottom panels show genes occurring on each of the two strands of the chromosome, with the arbitrary labels 1 and −1. (A) The nucleotide composition of genes on the two strands of the chromosome of the LTEE ancestral clone REL606. (B) The genomic distribution of mutations within genes, summed over MMR-deficient LTEE populations (left panel) and MutT-deficient LTEE populations (right panel).

The observed distributions of synonymous mutations on each strand of the chromosome are shown in figure 5B. We separately analyzed MMR- and MutT-deficient hypermutator populations. In both cases, the number of observed mutations significantly differs between genes oriented with or against the movement of the replisome, based on comparing the expected ratio of mutations to the observed ratio of mutations. The MMR-deficient hypermutator populations show significantly more gene-orientation mutation bias than expected (two-tailed binomial test: observed ratio of 2,066:2,664 mutations vs. expected ratio of 1,730,238:2,066,587 nucleotides P = 0.0090), whereas the MutT-deficient hypermutator populations show significantly less gene-orientation bias than expected (two-tailed binomial test: observed ratio of 947:1,033 mutations vs. expected ratio of 1,730,238:2,066,587 nucleotides P = 0.0446). Note that these calculations do not account for the characteristic mutation spectra of MMR- and MutT-deficient hypermutators ( fig. 5B). For example, the extreme rate of A:T→C:G mutations seen in MutT-deficient hypermutators ( Foster et al. 2015) should cause A:T rich genes to mutate faster than A:T poor genes.

### The Genomic Distribution of Observed Mutations in Ara+3 Shows a Strong, Symmetric Wave Pattern over the Origin of Replication

Multiple studies ( Sharp et al. 1989 Lang and Murray 2011 Foster et al. 2013 Dillon et al. 2018 Niccum et al. 2019) have reported correlations between local mutation rates and distance from the origin of replication. One hypermutator LTEE population, called Ara+3, shows a symmetric wave pattern reflected over oriC ( fig. 6). Indeed, the genomic distribution of observed mutations in Ara+3 is significantly different from the genomic distribution of observed mutations summed over all hypermutator populations (two-sample Kolmogorov–Smirnov test: D = 0.0567, P < 10 −14 ). The wave in Ara+3 has a trough-to-peak ratio of ∼25:75 ( fig. 6). Excluding Ara+3, the genomic distribution of observed mutations summed over the remaining MMR-deficient LTEE populations shows a weak wave pattern, whereas the populations with defects in mutT shows no evidence of the wave pattern ( fig. 7). The genomic distribution of observed mutations in the MMR-deficient populations (excluding Ara+3) is significantly different from the genomic distribution of observed mutations in the MutT-deficient populations (two-sample Kolmogorov–Smirnov test: D = 0.040916, P < 10 −9 ).

One hypermutator LTEE population, Ara+3, shows a strong wave pattern of mutation rate variation centered on the replication origin. Each panel shows the genomic distribution of mutations observed in each hypermutator LTEE population in the metagenomics data. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. Indels are in purple, missense mutations are in dark blue, noncoding mutations are blue green, nonsense mutations are sea green, sv are green, and synonymous mutations are yellow.

One hypermutator LTEE population, Ara+3, shows a strong wave pattern of mutation rate variation centered on the replication origin. Each panel shows the genomic distribution of mutations observed in each hypermutator LTEE population in the metagenomics data. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. Indels are in purple, missense mutations are in dark blue, noncoding mutations are blue green, nonsense mutations are sea green, sv are green, and synonymous mutations are yellow.

MMR-deficient LTEE populations (excluding Ara+3) show a weak wave pattern, whereas MutT-deficient LTEE populations show no wave pattern. The left panel shows the genomic distribution of mutations observed in Ara−2, Ara−3, and Ara−4. The right panel shows the genomic distribution of mutations observed in Ara−1 and Ara+6. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. Indels are in purple, missense mutations are in dark blue, noncoding mutations are blue green, nonsense mutations are sea green, sv are green, and synonymous mutations are yellow.

MMR-deficient LTEE populations (excluding Ara+3) show a weak wave pattern, whereas MutT-deficient LTEE populations show no wave pattern. The left panel shows the genomic distribution of mutations observed in Ara−2, Ara−3, and Ara−4. The right panel shows the genomic distribution of mutations observed in Ara−1 and Ara+6. The x axis is the reference genome, centered on the replication origin, partitioned into 46 equally sized bins of ∼100 kb. Indels are in purple, missense mutations are in dark blue, noncoding mutations are blue green, nonsense mutations are sea green, sv are green, and synonymous mutations are yellow.

### Evidence for Epistasis and Historical Contingency in the Evolution of DNA Topology

Why does a strong wave pattern only appear in Ara+3? Others have hypothesized that local chromatin structure affects local mutation rates ( Foster et al. 2013 Niccum et al. 2019). Furthermore, DNA topology has evolved in parallel in the LTEE, and artificially increasing DNA supercoiling is beneficial under LTEE conditions ( Crozat et al. 2005, 2010). Therefore, we hypothesized that mutations in genes that affect DNA topology might affect the wave pattern. To test this hypothesis, we examined the timing and distribution of mutations in topA, fis, and dusB (yhdG). We focused on these genes for several reasons. First, these loci show strong parallel evolution in the LTEE ( Crozat et al. 2010). Second, introducing evolved alleles of topA and fis into the ancestral genome are sufficient to confer a fitness benefit as well as additive changes to DNA topology ( Crozat et al. 2005). Finally, statistical analysis of the pattern of evolution for dusB and fis in the LTEE led to the discovery that dusB regulates fis expression ( Crozat et al. 2005, 2010). We excluded synonymous mutations from this analysis. We counted both fixations and mutations destined for extinction, because many beneficial mutations go extinct in large asexual populations due to clonal interference ( Gerrish and Lenski 1998 Lang et al. 2013 Levy et al. 2015 Maddamsetti, Lenski, et al. 2015 Ba et al. 2019).

All LTEE populations evolved missense, indel, or structural mutations in topA, fis, and dusB within the first 10,000 generations, except two: Ara+2 and Ara+3 ( fig. 8). The timing and distribution of mutations in these genes across populations suggests epistasis and historical contingency ( Good et al. 2017). The early arrival times for mutations in these genes suggests that there is an early, limited window of opportunity for those mutations to go to fixation. Quantitative evidence comes from Ara+3, which has no missense, nonsense, indel, or structural mutations in topA, fis, and dusB whatsoever, despite its strong hypermutator phenotype. The probability of this event is P = (1−(t/g)) n , where t is the effective mutational target size, g is the length of the chromosome (g = 4,629,812), and n is the number of observed missense, indel, and structural mutations in Ara+3 (n = 4,368). Given the wave pattern in Ara+3, the effective mutational target size of topA, fis, and dusB could be smaller than their combined physical target size (3,861 bp), say if they occurred in the trough of the wave. To take this into account, we partitioned the chromosome into bins, counted mutations per bin, and calculated the effective mutational target size by multiplying the physical target size (length) of topA, fis, and dusB by the number of mutations per base pair in their respective bins. These genes are significantly depleted of mutations in Ara+3, for bin sizes ranging from 100 kb to the entire chromosome (one-tailed randomization tests with 10,000 bootstraps: P < 0.05 in all cases).

The strong wave pattern in Ara+3 anticorrelates with mutations (excluding synonymous changes) in the DNA topology genes topA, fis, and dusB. This visualization uses computer code written by Good et al. (2017). The allele frequency trajectories for all observed mutations in the 12 LTEE populations are shown in gray. The allele frequency trajectories of de novo mutations in topA, fis, and dusB (excepting synonymous mutations) are colored and labeled in each population.

The strong wave pattern in Ara+3 anticorrelates with mutations (excluding synonymous changes) in the DNA topology genes topA, fis, and dusB. This visualization uses computer code written by Good et al. (2017). The allele frequency trajectories for all observed mutations in the 12 LTEE populations are shown in gray. The allele frequency trajectories of de novo mutations in topA, fis, and dusB (excepting synonymous mutations) are colored and labeled in each population.

The distribution of synonymous mutations in topA, fis, and dusB across the LTEE populations is interesting ( supplementary fig. S4 and Supplementary Material online). A single, synonymous A312A substitution in dusB went to fixation at ∼4,000 generations in Ara+3, simultaneously with alleles in the MMR genes mutS and mutH that apparently caused the early hypermutator phenotype in this population. No other synonymous mutations in dusB are observed in Ara+3. Furthermore, there is evidence of parallel evolution at this particular position in dusB. The same synonymous mutation occurs in Ara+6, and another synonymous mutation, one base pair downstream in the next codon, is the only synonymous mutation in topA, fis, or dusB observed in Ara−2 ( supplementary fig. S4 , Supplementary Material online). This parallelism suggests that positive selection may be acting on these synonymous variants. Overall, it is striking how few synonymous mutations in topA, fis, and dusB occur in the hypermutator LTEE populations, which implies that synonymous variants in these genes may not be evolving neutrally. Indeed, STIMS ( Maddamsetti and Grant 2020) finds a significant signal of purifying selection on synonymous mutations in topA, fis, and dusB in Ara−1 and Ara−3 (one-tailed randomization test with 10,000 bootstraps: P < 0.0001).

We also examined the genes that encode the nucleoid-binding protein HU and the terminus-organizing protein MatP, as deletions of these loci were shown to affect the wave pattern ( Niccum et al. 2019). Notwithstanding the relevance of HU and MatP in Niccum et al. (2019), these genes show limited evidence of parallel evolution in the LTEE ( supplementary fig. S5 , Supplementary Material online).

### Synonymous Nucleotide Diversity in Natural E. coli Populations Does Not Predict Mutation Rate Variation in the LTEE

Finally, we used the LTEE metagenomic data to revisit previous work, which found that the distribution of synonymous mutations in the LTEE does not reflect patterns of synonymous variation among natural E. coli isolates ( Maddamsetti et al. 2015). During our reanalysis, we found a potential coding error affecting the results of the Kolmogorov–Smirnov test reported in that paper. Therefore, we used Poisson regression to ask whether the estimates of synonymous nucleotide diversity θs published in Martincorena et al. (2012), when treated as gene-specific estimates of the point-mutation rate per base pair, predict the distribution of synonymous mutations observed in the LTEE. A null model in which mutations occur uniformly over the chromosome (Akaike’s Information Criterion, AIC = 8,529.6) fits the data far better than the θs model (AIC = 9,171.3). When we fit both models to Ara+3, we again find that the null model is better than the θs model at predicting the observed distribution of synonymous mutations (AIC = 2,168.2 for null model vs. AIC = 2,190.8 for θs model). This finding validates the conclusions reported in Maddamsetti et al. (2015), despite the potential problems in that analysis.

## Faster rates of evolution are linked to tiny genomes

Inside every cell lies a genome -- a full set of DNA that contains the instructions for building an organism. Across the biological world, genomes show a staggering diversity in size. For example, the genome of the Japanese white flower, Paris japonica, is over 150 billion base pairs, meaning that almost 100 meters of DNA is squeezed into each cell. In comparison, single-celled prokaryotes, like bacteria, have tiny genomes, averaging less than 5 million base pairs. Some prokaryotes have even smaller genomes that are fewer than 500,000 base pairs. But scientists still don't fully understand the driving forces responsible for reducing the size of genomes.

Now, in an international collaboration, led by the Okinawa Institute of Science and Technology Graduate University (OIST) and the University of Sydney, and including researchers from the University of the Ryukyus, the Tokyo Institute of Technology, and RIKEN, scientists have found a link between mutation rate -- how quickly the DNA sequence changes -- and genome size. Writing in Current Biology, the researchers reported that prokaryotes with higher mutation rates lose genes at a faster pace, and therefore have smaller genomes.

"This was a really surprising result," said Professor Tom Bourguignon, co-first author of the study and head of the Evolutionary Genomics Unit at OIST. "Currently, the most accepted idea is that population size is the main factor that determines genome size in prokaryotes, particularly in endosymbionts, but our research challenges this view."

Endosymbionts are organisms that live inside the bodies or cells of other organisms, and typically have much smaller genomes than their free-living counterparts. The Evolutionary Genomics Unit researches an endosymbiont called Blattabacterium, a bacterial species that lives inside cockroaches and termites and provides their hosts with vital nitrogen-containing nutrients. But only a small number of these bacteria are passed on from a mother insect host to a daughter insect host, which keeps their effective population size very low.

"At small population sizes, natural selection is much less effective, and evolution is driven more strongly by chance," said Dr. Yukihiro Kinjo, co-first author and a postdoctoral scholar from the Evolutionary Genomics Unit. "Without enough selection pressure to maintain specific genes, mutations can arise that inactive and erode these genes, eventually leading to their total loss from the genome."

While population size as a driving force for genome reduction may be an attractive idea, many free-living prokaryotes that live in larger populations have also evolved smaller genomes, suggesting that it's only part of the story. Additional explanations have also been proposed but, until now, the mutation rate -- or the speed at which evolution occurs -- has been overlooked.

In the study, the scientists collected genome data from a diverse range of prokaryotes, including strains from two endosymbiotic lineages and seven free-living lineages.

For each lineage, the team constructed an evolutionary tree that showed how the strains had diverged from each other. With the help of the OIST Biological Complexity Unit, led by Professor Simone Pigolotti, the scientists then created models that reconstructed how gene loss had occurred in each strain. They then estimated the mutation rate, population size and selection pressure for each strain and compared it to the amount of gene loss.

Surprisingly, the scientists did not find a clear link between estimated population size and rate of gene loss. Instead, they found a relationship between mutation rate and gene loss for seven out of the nine lineages studied, with higher mutation rates associated with faster rates of gene loss, resulting in smaller genomes.

"Although we haven't established a cause, there is a theoretical prediction that explains this observation if the rate of mutation outweighs a selection pressure to maintain a gene, the gene will be lost from the genome," said Dr. Kinjo.

The scientists also found clues as to how the gene loss occurred, as strains with smaller genomes had lost genes involved in repairing DNA.

"DNA repair genes fix damaged DNA, so when they are lost the mutation rate of a strain can quickly increase. Most mutations are harmful, so this can quickly inactivate other genes and drive their loss from the genome. If some of these inactivated genes are also involved in DNA repair, this can further accelerate mutation rate and gene loss," explained Professor Gaku Tokuda, from the University of the Ryukyus.

Although the answers to how gene loss occurs are becoming clearer, whether there are evolutionary reasons behind why prokaryotes increase their rate of mutation to shrink their genome, and if so, what these reasons are, remains an open question.

"Figuring out the evolutionary explanation for what we see is really complicated. It could be that an increased rate of mutation occurs to provide an adaptive advantage, such as the removal of unwanted or unnecessary genes. But we still can't rule out the possibility that the increased rate of mutation is non-adaptive and due to chance," said Dr. Kinjo.

Overall, their findings shed new light on the evolution of small genomes, prompting a re-think of the current dominant idea of genome reduction being driven by small population sizes.

"Unlike with population size, our results suggest that mutation rate could drive genome reduction in both free-living and endosymbiotic prokaryotes. This could be the first step in comprehensively understanding what drives changes in genome size across all prokaryotes," said Prof. Bourguignon.

## Analysis

1. Describe how the simulation models natural selection (and evolution), include a definition of both of these terms.

2. Explain HOW the mutation rate affects the evolution of your populations, use the prediction statements above to help you make a concise statement about the efffect of mutation rate on evolution.

Explain WHY the mutation rate affects the evolution of your populations.

3. Explain HOW altering the selection rate affects the evolution of your populations, use the prediction statement again.

Explain WHY altering the selection rate affects the evolution of your populations and include a definition of what selection strength is for your population.

HS- LS4-2 Construct an explanation based on evidence that the process of evolution primarily results from four factors: (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment

Credits: Special thanks to Leif Saul, author of Biology in Motion and the creator of the Evolution Lab.

## Population Genetics

### 12.3.2.2 Mutation

When mutations occur in the germ cells, they may be passed on to the next generation. The change in the DNA may be a single nucleotide substitution or it may involve many nucleotides, such as in the case of an insertion or deletion. Many hemoglobinopathies are due to point mutations that cause the replacement of an amino acid (missense) and consequently an abnormal protein product. The most common mutation causing Tay–Sachs disease is a 4-base-pair (bp) insertion (frameshift), while the F508del mutation in the cystic fibrosis gene is a 3-bp deletion.

The source of genetic variation in a population is mutation. Mutation rates in humans have been estimated to be on the order of 10− 4 to 10− 6 per gene per generation. The rate of nucleotide substitutions is estimated to be 1 in 10 8 per generation, implying that 30 nucleotide mutations would be expected in each human gamete.

Most new mutations are lost due to chance. However, new mutations arise in each generation, and some become established in the population. Suppose μ is the mutation rate from A1 to A2 per generation. If the frequencies of A1 and A2 are pt and qt, respectively, in generation t, then in the (t + 1)th generation the frequency of A2 is

assuming no back mutation.

Because μ is very small, (1 − μ) t is approximately equal to et μ. Thus, the number of generations required to change the frequency of A2 from q0 to qt is inversely proportional to the mutation rate. Also note that as t gets larger and larger, qt gets closer and closer to 1. In other words, if mutation from A1 to A2 is the only force acting to change the allele frequencies, then A2 will eventually become fixed in the population. The change in allele frequency from one generation to the next is qt+1qt = μ(1 − qt), meaning that the change in allele frequency is greater for smaller frequencies of A2.

So far we have considered mutation in only one direction. Now suppose the mutation rate from A1 to A2 is μ and the reverse rate from A2 to A1 is ν. Then the change in the frequency of A2 per generation is μpνq, and equilibrium is reached when this change is equal to zero. Thus, the equilibrium frequencies are p = ν/(μ + ν) and q = μ/(μ + ν). This equilibrium is stable, meaning that if the frequencies are disturbed, they will eventually return to their equilibrium values as long as no other forces are affecting them.

Mutation rates have been estimated for a number of autosomal dominant disorders, such as neurofibromatosis type I, which has the high rate of 10 −4 , and tuberous sclerosis, with a rate of about 10 −5 . Some of these disorders (e.g., achondroplasia, for which the mutation rate is estimated to be 10 −5 ) have reduced fitness, which is discussed in the next section.

#### Examples

How many generations will be required to change the frequency of A2 (1) from 0.1 to 0.2, (2) from 0.8 to 0.9, if the mutation rate from A1 to A2 is 10 −4 ?

The number of generations is

Therefore, for a mutation rate of 10 −4 , 1178 generations are required, whereas for a mutation rate of 10 −5 , 11,780 generations are required to change the frequency of A2 from 0.1 to 0.2. On the other hand, to change the frequency from 0.8 to 0.9 requires 6932 generations if the mutation rate is 10 −4 and 69,315 generations if the mutation rate is 10 −5 .

Suppose the mutation rate from A1 to A2 is 10 −4 and the reverse rate is 10 −5 . What is the equilibrium frequency of A1?

The equilibrium frequency of A1 is 10 −5 /(10 −4 + 10 −5 ) = 0.091. However, to reach this equilibrium frequency may take tens of thousands of generations, depending on the initial allele frequencies.

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