Reversions mask the contribution of adaptive evolution in microbiomes
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eLife assessment
This valuable study addresses the interpretation of patterns of synonymous and nonsynonymous diversity in microbial genomes. The authors present solid theoretical and computational evidence that adaptive mutations that revert the amino acids to an earlier state can significantly impact the observed ratios of synonymous and nonsynonymous mutations in human commensal bacteria. This paper will be of interest to microbiologists with a background in evolution.
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Abstract
When examining bacterial genomes for evidence of past selection, the results depend heavily on the mutational distance between chosen genomes. Even within a bacterial species, genomes separated by larger mutational distances exhibit stronger evidence of purifying selection as assessed by d N /d S , the normalized ratio of nonsynonymous to synonymous mutations. Here, we show that the classical interpretation of this scale dependence, weak purifying selection, leads to problematic mutation accumulation when applied to available gut microbiome data. We propose an alternative, adaptive reversion model with opposite implications for dynamical intuition and applications of d N /d S . Reversions that occur and sweep within-host populations are nearly guaranteed in microbiomes due to large population sizes, short generation times, and variable environments. Using analytical and simulation approaches, we show that adaptive reversion can explain the d N /d S decay given only dozens of locally fluctuating selective pressures, which is realistic in the context of Bacteroides genomes. The success of the adaptive reversion model argues for interpreting low values of d N /d S obtained from long timescales with caution as they may emerge even when adaptive sweeps are frequent. Our work thus inverts the interpretation of an old observation in bacterial evolution, illustrates the potential of mutational reversions to shape genomic landscapes over time, and highlights the importance of studying bacterial genomic evolution on short timescales.
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Author response:
Reviewer #1 (Public Review):
This study makes a substantial contribution to our understanding of the molecular evolutionary dynamics of microbial genomes by proposing a model that incorporates relatively frequent adaptive reversion mutations. In many ways, this makes sense from my own experience with evolutionary genomic data of microbes, where reversions are surprisingly familiar as evidence of the immense power of selection in large populations.
One criticism is the reliance on one major data set of B. fragilis to test fits of these models, but this is relatively minor in my opinion and can be caveated by discussion of other relevant datasets for parallel investigation.
We analyze data from 10 species of the Bacteroidales family, and we compare it to a dataset of Bacteroides fragilis. We have now …
Author response:
Reviewer #1 (Public Review):
This study makes a substantial contribution to our understanding of the molecular evolutionary dynamics of microbial genomes by proposing a model that incorporates relatively frequent adaptive reversion mutations. In many ways, this makes sense from my own experience with evolutionary genomic data of microbes, where reversions are surprisingly familiar as evidence of the immense power of selection in large populations.
One criticism is the reliance on one major data set of B. fragilis to test fits of these models, but this is relatively minor in my opinion and can be caveated by discussion of other relevant datasets for parallel investigation.
We analyze data from 10 species of the Bacteroidales family, and we compare it to a dataset of Bacteroides fragilis. We have now added a reference to a recent manuscript from our group showing phenotypic alteration by reversion of a stop codon and further breaking of the same pathway through stop codons in other genes in Burkholderia dolosa on page 9, and have added a new analysis of codon usage in support of the reversion model on page 14.
We have chosen not to analyze other species as there are no large data sets with rigorous and evenly-applied quality control across scales. We anticipate the reversion model would be able to fit the data in these cases. We now note that this work remains to be done in the discussion.
Another point is that this problem isn't as new as the manuscript indicates, see for example https://journals.asm.org/doi/10.1128/aem.02002-20 .
Loo et al puts forward an explanation similar to the purifying model proposed by Rocha et al, which we refute here. Quoting from Loo et al: “Our results confirm the observation that nonsynonymous SNPs are relatively elevated under shorter time periods and that purifying selection is more apparent over longer periods or during transmission.” While there is some linguistic similarity between the weak purifying model and our model of strong local adaptation model and strong adaptive reversion, we believe that the dynamical and predictive implications suggested by the reversion model are an important conceptual leap and correction to the literature. We now cite Loo et al and additional works cited therein. We have updated the abstract, introduction, and discussion to further emphasize the distinction of the reversion model from previous models: namely the implication of the reversion model that long-time scale dN/dS hides dynamics.
Nonetheless, the paper succeeds by both developing theory and offering concrete parameters to illustrate the magnitudes of the problems that distinguish competing ideas, for example, the risk of mutational load posed in the absence of frequent back mutation.
Reviewer #2 (Public Review):
This manuscript asks how different forms of selection affect the patterns of genetic diversity in microbial populations. One popular metric used to infer signatures of selection is dN/dS, the ratio of nonsynonymous to synonymous distances between two genomes. Previous observations across many bacterial species have found dN/dS decreases with dS, which is a proxy for the divergence time. The most common interpretation of this pattern was proposed by Rocha et al. (2006), who suggested the excess in nonsynonymous mutations on short divergence times represent transient deleterious mutations that have not yet been purged by selection.
In this study, the authors propose an alternative model based on the population structure of human gut bacteria, in which dN is dominated by selective sweeps of SNPs that revert previous mutations within local populations. The authors argue that contrary to standard population genetics models, which are based on the population dynamics of large eukaryotes, the large populations in the human gut mean that reversions may be quite common and may have a large impact on evolutionary dynamics. They show that such a model can fit the decrease of dN/dS in time at least as well as the purifying selection model.
Strengths
The main strength of the manuscript is to show that adaptive sweeps in gut microbial populations can lead to small dN/dS. While previous work has shown that using dN/dS to infer the strength of selection within a population is problematic (see Kryazhimskiy and Plotkin, 2008, cited in the paper) the particular mechanism proposed by the authors is new to my knowledge. In addition, despite the known caveats, dN/dS values are still routinely reported in studies of microbial evolution, and so their interpretation should be of considerable interest to the community.
The authors provide compelling justification for the importance of adaptive reversions and make a good case that these need to be carefully considered by future studies of microbial evolution. The authors show that their model can fit the data as well as the standard model based on purifying selection and the parameters they infer appear to be plausible given known data. More generally, I found the discussion on the implications of traditional population genetics models in the context of human gut bacteria to be a valuable contribution of the paper.
Thank you for the kind words and appreciation of the manuscript.
Weaknesses
The authors argue that the purifying selection model would predict a gradual loss in fitness via Muller's ratchet. This is true if recombination is ignored, but this assumption is inconsistent with the data from Garud, et al. (2019) cited in the manuscript, who showed a significant linkage decrease in the bacteria also used in this study.
We now investigate the effect of recombination on the purifying selection model on page 8 and in Supplementary Figure S6. In short, we show that reasonable levels of recombination (obtained from literature r/m values) cannot rescue the purifying selection model from Muller’s ratchet when s is so low and the influx of new deleterious mutations is so high. We thank the reviewers for prompting this improvement.
I also found that the data analysis part of the paper added little new to what was previously known. Most of the data comes directly from the Garud et al. study and the analysis is very similar as well. Even if other appropriate data may not currently be available, I feel that more could be done to test specific predictions of the model with more careful analysis.
In addition to new analyses regarding recombination and compensatory mutations using the Garud et al data set, we have now added two new analyses, both using Bacteroides fragilis . First, we show that de novo mutations in Zhao & Lieberman et al dataset include an enrichment of premature stop codons (page 9). Second we show that genes expected to be under fluctuating selection in B. fragilis displays a significant closeness to stop codons, consistent with recent stop codons and reversions. We thank the reviewer for prompting the improvement.
Finally, I found the description of the underlying assumptions of the model and the theoretical results difficult to understand. I could not, for example, relate the fitting parameters nloci and Tadapt to the simulations after reading the main text and the supplement. In addition, it was not clear to me if simulations involved actual hosts or how the changes in selection coefficients for different sites was implemented. Note that these are not simply issues of exposition since the specific implementation of the model could conceivably lead to different results. For example, if the environmental change is due to the colonization of a different host, it would presumably affect the selection coefficients at many sites at once and lead to clonal interference. Related to this point, it was also not clear that the weak mutation strong selection assumption is consistent with the microscopic parameters of the model. The authors also mention that "superspreading" may somehow make a difference to the probability of maintaining the least loaded class in the purifying selection model, but what they mean by this was not adequately explained.
We apologize for leaving the specifics of the implementation from the paper and only accessible through the Github page and have corrected this. We have added a new section in the methods further detailing the reversion model and the specifics of how nloci and Tadapt (now tau_switch as of the edits) are implemented in the code.
The possibility for clonal interference is indeed included in the simulation. Switching is not correlated with transmissions in our main figure simulations (Figure 4a). When we run simulations in which transmission and selection are correlated, the results remain essentially the same, barring higher variance at lower divergences (new Figure S10). We have now clarified these points in the results, and have also better clarified the selection only at transmission model in the main results.
Reviewer #3 (Public Review):
The diversity of bacterial species in the human gut microbiome is widely known, but the extensive diversity within each species is far less appreciated. Strains found in individuals on opposite sides of the globe can differ by as little as handfuls of mutations, while strains found in an individual's gut, or in the same household, might have a common ancestor tens of thousands of years ago. What are the evolutionary, ecological, and transmission dynamics that established and maintain this diversity?
The time, T, since the common ancestor of two strains, can be directly inferred by comparing their core genomes and finding the fraction of synonymous (non-amino acid changing) sites at which they differ: dS. With the per-site per-generation mutation rate, μ, and the mean generation times roughly known, this directly yields T (albeit with substantial uncertainty of the generation time.) A traditional way to probe the extent to which selection plays a role is to study pairs of strains and compare the fraction of non-synonymous (amino acid or stop-codon changing) sites, dN, at which the strains differ with their dS. Small dN/dS, as found between distantly related strains, is attributed to purifying selection against deleterious mutations dominating over mutations that have driven adaptive evolution. Large dN/dS as found in laboratory evolution experiments, is caused by beneficial mutations that quickly arise in large bacterial populations, and, with substantial selective advantages, per generation, can rise to high abundance fast enough that very few synonymous mutations arise in the lineages that take over the population.
A number of studies (including by Lieberman's group) have analyzed large numbers of strains of various dominant human gut species and studied how dN/dS varies. Although between closely related strains the variations are large -- often much larger than attributable to just statistical variations -- a systematic trend from dN/dS around unity or larger for close relatives to dN/dS ~ 0.1 for more distant relatives has been found in enough species that it is natural to conjecture a general explanation.
The conventional explanation is that, for close relatives, the effects of selection over the time since they diverged has not yet purged weakly deleterious mutations that arose by chance -- roughly mutations with sT<1 -- while since the common ancestor of more distantly related strains, there is plenty of time for most of those that arose to have been purged.
Torrillo and Lieberman have carried out an in-depth -- sophisticated and quantitative -- analysis of models of some of the evolutionary processes that shape the dependence of dN/dS on dS -- and hence on their divergence time, T. They first review the purifying selection model and show that -- even ignoring its inability to explain dN/dS > 1 for many closely related pairs -- the model has major problems explaining the crossover from dN/dS somewhat less than unity to much smaller values as dS goes through -- on a logarithmic scale -- the 10^-4 range. The first problem, already seen in the infinite-population-size deterministic model, is that a very large fraction of non-synonymous mutations would have to have deleterious s's in the 10^-5 per generation range to fit the data (and a small fraction effectively neutral). As the s's are naturally expected (at least in the absence of quantitative analysis to the contrary) to be spread out over a wide range on a logarithmic scale of s, this seems implausible. But the authors go further and analyze the effects of fluctuations that occur even in the very large populations: ~ >10^12 bacteria per species in one gut, and 10^10 human guts globally. They show that Muller's ratchet -- the gradual accumulation of weakly deleterious mutations that are not purged by selection - leads to a mutational meltdown with the parameters needed to fit the purifying selection model. In particular, with N_e the "effective population size" that roughly parametrizes the magnitude of stochastic birth-death and transition fluctuations, and U the total mutation rate to such deleterious mutations this occurs for U/s > log(sN_e) which they show would obtain with the fitted parameters.
Torrillo and Lieberman promise an alternate model: that there are a modest number of "loci" at which conditionally beneficial mutations can occur that are beneficial in some individual guts (or other environmental conditions) at some times, but deleterious in other (or the same) gut at other times. With the ancestors of a pair of strains having passed through one too many individuals and transmissions, it is possible for a beneficial mutation to occur and rise in the population, only later to be reverted by the beneficial inverse mutation. With tens of loci at which this can occur, they show that this process could explain the drop of dN/dS from short times -- in which very few such mutations have occurred -- to very long times by which most have flipped back and forth so that a random pair of strains will have the same nucleotide at such sites with 50% probability. Their qualitative analysis of a minimally simple model of this process shows that the bacterial populations are plenty big enough for such specific mutations to occur many times in each individual's gut, and with modest beneficials, to takeover. With a few of these conditionally beneficial mutations or reversions occurring during an individuals lifetime, they get a reasonably quantitative agreement with the dN/dS vs dS data with very few parameters. A key assumption of their model is that genetically exact reversion mutations are far more likely to takeover a gut population -- and spread -- than compensatory mutations which have a similar phenotypic-reversion effect: a mutation that is reverted does not show up in dN, while one that is compensated by another shows up as a two-mutation difference after the environment has changed twice.
Strengths:
The quantitative arguments made against the conventional purifying selection model are highly compelling, especially the consideration of multiple aspects that are usually ignored, including -- crucially -- how Muller's ratchet arises and depends on the realistic and needed-to-fit parameters; the effects of bottlenecks in transmission and the possibility that purifying selection mainly occurs then; and complications of the model of a single deleterious s, to include a distribution of selective disadvantages. Generally, the author's approach of focusing on the simplest models with as few as possible parameters (some roughly known), and then adding in various effects one-by-one, is outstanding and, in being used to analyze environmental microbial data, exceptional.
The reversion model the authors propose and study is a simple general one and they again explore carefully various aspects of it -- including dynamics within and between hosts -- and the consequent qualitative and quantitative effects. Again, the quantitive analysis of almost all aspects is exemplary. Although it is hard to make a compelling guess of the number of loci that are subject to alternating selection on the needed time-scales (years to centuries) they make a reasonable argument for a lower bound in terms of the number of known invertible promoters (that can genetically switch gene expression on and off).
We are very grateful for the reviewer’s kind words and careful reading.
Weaknesses:
The primary weakness of this paper is one that the author's are completely open about: the assumption that, collectively, any of possibly-many compensatory mutations that could phenotypically revert an earlier mutation, are less likely to arise and takeover local populations than the exact specific reversion mutation. While detailed analysis of this is, reasonably enough, beyond the scope of the present paper, more discussion of this issue would add substantially to this work. Quantitatively, the problem is that even a modest number of compensatory mutations occurring as the environmental pressures change could lead to enough accumulation of non-synonymous mutations that they could cause dN/dS to stay large -- easily >1 -- to much larger dS than is observed. If, say, the appropriate locus is a gene, the number of combinations of mutations that are better in each environment would play a role in how large dN would saturate to in the steady state (1/2 of n_loci in the author's model). It is possible that clonal interference between compensatory and reversion mutations would result in the mutations with the largest s -- eg, as mentioned, reversion of a stop codon -- being much more likely to take over, and this could limit the typical number of differences between quite well-diverged strains. However, the reversion and subsequent re-reversion would have to both beat out other possible compensatory mutations -- naively less likely. I recommend that a few sentences in the Discussion be added on this important issue along with comments on the more general puzzle -- at least to this reader! -- as to why there appear to be so little adaptive genetic changes in core genomes on time scales of human lifetimes and civilization.
We now directly consider compensatory mutations (page 14, SI text 3.2, and Supplementary Figure 12). We show that as long as true reversions are more likely than compensatory mutations overall, (adaptive) nonsynonymous mutations will still tend to revert towards their initial state and not contribute to asymptotic dN/dS, and show that true reversions are expected in a large swath of parameter space. Thank you for motivating this improvement!
We note in the discussion that directional selection could be incorporated into the parameter alpha (assuming even more of the genome is deleterious) on page 16.
An important feature of gut bacterial evolution that is now being intensely studied is only mentioned in passing at the end of this paper: horizontal transfer and recombination of core genetic material. As this tends to bring in many more mutations overall than occur in regions of a pair of genomes with asexual ancestry, the effects cannot be neglected. To what extent can this give rise to a similar dependence of dN/dS on dS as seen in the data? Of course, such a picture begs the question as to what sets the low dN/dS of segments that are recombined --- often from genetic distances comparable to the diameter of the species.
We now discuss the effect of recombination on the purifying selection model on page 8 and in Supplementary Figure S6. In short, we now show that reasonable levels of recombination cannot rescue the purifying selection model from Muller’s ratchet when s is so low and the influx of new deleterious mutations is so high. We thank the reviewers for prompting this improvement
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eLife assessment
This valuable study addresses the interpretation of patterns of synonymous and nonsynonymous diversity in microbial genomes. The authors present solid theoretical and computational evidence that adaptive mutations that revert the amino acids to an earlier state can significantly impact the observed ratios of synonymous and nonsynonymous mutations in human commensal bacteria. This paper will be of interest to microbiologists with a background in evolution.
-
Reviewer #1 (Public Review):
This study makes a substantial contribution to our understanding of the molecular evolutionary dynamics of microbial genomes by proposing a model that incorporates relatively frequent adaptive reversion mutations. In many ways, this makes sense from my own experience with evolutionary genomic data of microbes, where reversions are surprisingly familiar as evidence of the immense power of selection in large populations.
One criticism is the reliance on one major data set of B. fragilis to test fits of these models, but this is relatively minor in my opinion and can be caveated by discussion of other relevant datasets for parallel investigation.
Another point is that this problem isn't as new as the manuscript indicates, see for example https://journals.asm.org/doi/10.1128/aem.02002-20.
Nonetheless, the paper …
Reviewer #1 (Public Review):
This study makes a substantial contribution to our understanding of the molecular evolutionary dynamics of microbial genomes by proposing a model that incorporates relatively frequent adaptive reversion mutations. In many ways, this makes sense from my own experience with evolutionary genomic data of microbes, where reversions are surprisingly familiar as evidence of the immense power of selection in large populations.
One criticism is the reliance on one major data set of B. fragilis to test fits of these models, but this is relatively minor in my opinion and can be caveated by discussion of other relevant datasets for parallel investigation.
Another point is that this problem isn't as new as the manuscript indicates, see for example https://journals.asm.org/doi/10.1128/aem.02002-20.
Nonetheless, the paper succeeds by both developing theory and offering concrete parameters to illustrate the magnitudes of the problems that distinguish competing ideas, for example, the risk of mutational load posed in the absence of frequent back mutation.
-
Reviewer #2 (Public Review):
This manuscript asks how different forms of selection affect the patterns of genetic diversity in microbial populations. One popular metric used to infer signatures of selection is dN/dS, the ratio of nonsynonymous to synonymous distances between two genomes. Previous observations across many bacterial species have found dN/dS decreases with dS, which is a proxy for the divergence time. The most common interpretation of this pattern was proposed by Rocha et al. (2006), who suggested the excess in nonsynonymous mutations on short divergence times represent transient deleterious mutations that have not yet been purged by selection.
In this study, the authors propose an alternative model based on the population structure of human gut bacteria, in which dN is dominated by selective sweeps of SNPs that revert …
Reviewer #2 (Public Review):
This manuscript asks how different forms of selection affect the patterns of genetic diversity in microbial populations. One popular metric used to infer signatures of selection is dN/dS, the ratio of nonsynonymous to synonymous distances between two genomes. Previous observations across many bacterial species have found dN/dS decreases with dS, which is a proxy for the divergence time. The most common interpretation of this pattern was proposed by Rocha et al. (2006), who suggested the excess in nonsynonymous mutations on short divergence times represent transient deleterious mutations that have not yet been purged by selection.
In this study, the authors propose an alternative model based on the population structure of human gut bacteria, in which dN is dominated by selective sweeps of SNPs that revert previous mutations within local populations. The authors argue that contrary to standard population genetics models, which are based on the population dynamics of large eukaryotes, the large populations in the human gut mean that reversions may be quite common and may have a large impact on evolutionary dynamics. They show that such a model can fit the decrease of dN/dS in time at least as well as the purifying selection model.
Strengths
The main strength of the manuscript is to show that adaptive sweeps in gut microbial populations can lead to small dN/dS. While previous work has shown that using dN/dS to infer the strength of selection within a population is problematic (see Kryazhimskiy and Plotkin, 2008, cited in the paper) the particular mechanism proposed by the authors is new to my knowledge. In addition, despite the known caveats, dN/dS values are still routinely reported in studies of microbial evolution, and so their interpretation should be of considerable interest to the community.
The authors provide compelling justification for the importance of adaptive reversions and make a good case that these need to be carefully considered by future studies of microbial evolution. The authors show that their model can fit the data as well as the standard model based on purifying selection and the parameters they infer appear to be plausible given known data. More generally, I found the discussion on the implications of traditional population genetics models in the context of human gut bacteria to be a valuable contribution of the paper.
Weaknesses
The authors argue that the purifying selection model would predict a gradual loss in fitness via Muller's ratchet. This is true if recombination is ignored, but this assumption is inconsistent with the data from Garud, et al. (2019) cited in the manuscript, who showed a significant linkage decrease in the bacteria also used in this study.
I also found that the data analysis part of the paper added little new to what was previously known. Most of the data comes directly from the Garud et al. study and the analysis is very similar as well. Even if other appropriate data may not currently be available, I feel that more could be done to test specific predictions of the model with more careful analysis.
Finally, I found the description of the underlying assumptions of the model and the theoretical results difficult to understand. I could not, for example, relate the fitting parameters nloci and Tadapt to the simulations after reading the main text and the supplement. In addition, it was not clear to me if simulations involved actual hosts or how the changes in selection coefficients for different sites was implemented. Note that these are not simply issues of exposition since the specific implementation of the model could conceivably lead to different results. For example, if the environmental change is due to the colonization of a different host, it would presumably affect the selection coefficients at many sites at once and lead to clonal interference. Related to this point, it was also not clear that the weak mutation strong selection assumption is consistent with the microscopic parameters of the model. The authors also mention that "superspreading" may somehow make a difference to the probability of maintaining the least loaded class in the purifying selection model, but what they mean by this was not adequately explained.
-
Reviewer #3 (Public Review):
The diversity of bacterial species in the human gut microbiome is widely known, but the extensive diversity within each species is far less appreciated. Strains found in individuals on opposite sides of the globe can differ by as little as handfuls of mutations, while strains found in an individual's gut, or in the same household, might have a common ancestor tens of thousands of years ago. What are the evolutionary, ecological, and transmission dynamics that established and maintain this diversity?
The time, T, since the common ancestor of two strains, can be directly inferred by comparing their core genomes and finding the fraction of synonymous (non-amino acid changing) sites at which they differ: dS. With the per-site per-generation mutation rate, μ, and the mean generation times roughly known, this …
Reviewer #3 (Public Review):
The diversity of bacterial species in the human gut microbiome is widely known, but the extensive diversity within each species is far less appreciated. Strains found in individuals on opposite sides of the globe can differ by as little as handfuls of mutations, while strains found in an individual's gut, or in the same household, might have a common ancestor tens of thousands of years ago. What are the evolutionary, ecological, and transmission dynamics that established and maintain this diversity?
The time, T, since the common ancestor of two strains, can be directly inferred by comparing their core genomes and finding the fraction of synonymous (non-amino acid changing) sites at which they differ: dS. With the per-site per-generation mutation rate, μ, and the mean generation times roughly known, this directly yields T (albeit with substantial uncertainty of the generation time.) A traditional way to probe the extent to which selection plays a role is to study pairs of strains and compare the fraction of non-synonymous (amino acid or stop-codon changing) sites, dN, at which the strains differ with their dS. Small dN/dS, as found between distantly related strains, is attributed to purifying selection against deleterious mutations dominating over mutations that have driven adaptive evolution. Large dN/dS as found in laboratory evolution experiments, is caused by beneficial mutations that quickly arise in large bacterial populations, and, with substantial selective advantages, per generation, can rise to high abundance fast enough that very few synonymous mutations arise in the lineages that take over the population.
A number of studies (including by Lieberman's group) have analyzed large numbers of strains of various dominant human gut species and studied how dN/dS varies. Although between closely related strains the variations are large -- often much larger than attributable to just statistical variations -- a systematic trend from dN/dS around unity or larger for close relatives to dN/dS ~ 0.1 for more distant relatives has been found in enough species that it is natural to conjecture a general explanation.
The conventional explanation is that, for close relatives, the effects of selection over the time since they diverged has not yet purged weakly deleterious mutations that arose by chance -- roughly mutations with sT<1 -- while since the common ancestor of more distantly related strains, there is plenty of time for most of those that arose to have been purged.Torrillo and Lieberman have carried out an in-depth -- sophisticated and quantitative -- analysis of models of some of the evolutionary processes that shape the dependence of dN/dS on dS -- and hence on their divergence time, T. They first review the purifying selection model and show that -- even ignoring its inability to explain dN/dS > 1 for many closely related pairs -- the model has major problems explaining the crossover from dN/dS somewhat less than unity to much smaller values as dS goes through -- on a logarithmic scale -- the 10^-4 range. The first problem, already seen in the infinite-population-size deterministic model, is that a very large fraction of non-synonymous mutations would have to have deleterious s's in the 10^-5 per generation range to fit the data (and a small fraction effectively neutral). As the s's are naturally expected (at least in the absence of quantitative analysis to the contrary) to be spread out over a wide range on a logarithmic scale of s, this seems implausible. But the authors go further and analyze the effects of fluctuations that occur even in the very large populations: ~ >10^12 bacteria per species in one gut, and 10^10 human guts globally. They show that Muller's ratchet -- the gradual accumulation of weakly deleterious mutations that are not purged by selection - leads to a mutational meltdown with the parameters needed to fit the purifying selection model. In particular, with N_e the "effective population size" that roughly parametrizes the magnitude of stochastic birth-death and transition fluctuations, and U the total mutation rate to such deleterious mutations this occurs for U/s > log(sN_e) which they show would obtain with the fitted parameters.
Torrillo and Lieberman promise an alternate model: that there are a modest number of "loci" at which conditionally beneficial mutations can occur that are beneficial in some individual guts (or other environmental conditions) at some times, but deleterious in other (or the same) gut at other times. With the ancestors of a pair of strains having passed through one too many individuals and transmissions, it is possible for a beneficial mutation to occur and rise in the population, only later to be reverted by the beneficial inverse mutation. With tens of loci at which this can occur, they show that this process could explain the drop of dN/dS from short times -- in which very few such mutations have occurred -- to very long times by which most have flipped back and forth so that a random pair of strains will have the same nucleotide at such sites with 50% probability. Their qualitative analysis of a minimally simple model of this process shows that the bacterial populations are plenty big enough for such specific mutations to occur many times in each individual's gut, and with modest beneficials, to takeover. With a few of these conditionally beneficial mutations or reversions occurring during an individuals lifetime, they get a reasonably quantitative agreement with the dN/dS vs dS data with very few parameters. A key assumption of their model is that genetically exact reversion mutations are far more likely to takeover a gut population -- and spread -- than compensatory mutations which have a similar phenotypic-reversion effect: a mutation that is reverted does not show up in dN, while one that is compensated by another shows up as a two-mutation difference after the environment has changed twice.
Strengths:
The quantitative arguments made against the conventional purifying selection model are highly compelling, especially the consideration of multiple aspects that are usually ignored, including -- crucially -- how Muller's ratchet arises and depends on the realistic and needed-to-fit parameters; the effects of bottlenecks in transmission and the possibility that purifying selection mainly occurs then; and complications of the model of a single deleterious s, to include a distribution of selective disadvantages. Generally, the author's approach of focusing on the simplest models with as few as possible parameters (some roughly known), and then adding in various effects one-by-one, is outstanding and, in being used to analyze environmental microbial data, exceptional.
The reversion model the authors propose and study is a simple general one and they again explore carefully various aspects of it -- including dynamics within and between hosts -- and the consequent qualitative and quantitative effects. Again, the quantitive analysis of almost all aspects is exemplary. Although it is hard to make a compelling guess of the number of loci that are subject to alternating selection on the needed time-scales (years to centuries) they make a reasonable argument for a lower bound in terms of the number of known invertible promoters (that can genetically switch gene expression on and off).
Weaknesses:
The primary weakness of this paper is one that the author's are completely open about: the assumption that, collectively, any of possibly-many compensatory mutations that could phenotypically revert an earlier mutation, are less likely to arise and takeover local populations than the exact specific reversion mutation. While detailed analysis of this is, reasonably enough, beyond the scope of the present paper, more discussion of this issue would add substantially to this work. Quantitatively, the problem is that even a modest number of compensatory mutations occurring as the environmental pressures change could lead to enough accumulation of non-synonymous mutations that they could cause dN/dS to stay large -- easily >1 -- to much larger dS than is observed. If, say, the appropriate locus is a gene, the number of combinations of mutations that are better in each environment would play a role in how large dN would saturate to in the steady state (1/2 of n_loci in the author's model). It is possible that clonal interference between compensatory and reversion mutations would result in the mutations with the largest s -- eg, as mentioned, reversion of a stop codon -- being much more likely to take over, and this could limit the typical number of differences between quite well-diverged strains. However, the reversion and subsequent re-reversion would have to both beat out other possible compensatory mutations -- naively less likely. I recommend that a few sentences in the Discussion be added on this important issue along with comments on the more general puzzle -- at least to this reader! -- as to why there appear to be so little adaptive genetic changes in core genomes on time scales of human lifetimes and civilization.
An important feature of gut bacterial evolution that is now being intensely studied is only mentioned in passing at the end of this paper: horizontal transfer and recombination of core genetic material. As this tends to bring in many more mutations overall than occur in regions of a pair of genomes with asexual ancestry, the effects cannot be neglected. To what extent can this give rise to a similar dependence of dN/dS on dS as seen in the data? Of course, such a picture begs the question as to what sets the low dN/dS of segments that are recombined --- often from genetic distances comparable to the diameter of the species.
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