Global epistasis emerges from a generic model of a complex trait
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Evaluation Summary:
The authors consider Darwinian evolution for large systems, with a main focus on how adaptation changes over time. Frequently observed patterns of declining adaptability for a population in a new environment are discussed, i.e., that fitness tends to increase fast initially and then at a slower rate. Another topic is historical contingency in adaptation. A condition for minimal contingency is provided, and a new model (the connectedness model, or CN model) is introduced accordingly. The manuscript is innovative, conceptually interesting, and provides quantitative precision beyond most related studies in the field. However, the presentation currently does not work well for a general audience.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewers #1, #2, and #3 agreed to share their names with the authors.)
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Abstract
Epistasis between mutations can make adaptation contingent on evolutionary history. Yet despite widespread ‘microscopic’ epistasis between the mutations involved, microbial evolution experiments show consistent patterns of fitness increase between replicate lines. Recent work shows that this consistency is driven in part by global patterns of diminishing-returns and increasing-costs epistasis, which make mutations systematically less beneficial (or more deleterious) on fitter genetic backgrounds. However, the origin of this ‘global’ epistasis remains unknown. Here, we show that diminishing-returns and increasing-costs epistasis emerge generically as a consequence of pervasive microscopic epistasis. Our model predicts a specific quantitative relationship between the magnitude of global epistasis and the stochastic effects of microscopic epistasis, which we confirm by reanalyzing existing data. We further show that the distribution of fitness effects takes on a universal form when epistasis is widespread and introduce a novel fitness landscape model to show how phenotypic evolution can be repeatable despite sequence-level stochasticity.
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Author Response to Public Reviews
Reviewer #2 (Public Review):
[]... A somewhat puzzling point is that the authors emphasize that their proposed frame work explains diminishing-return and increased-costs epistasis. Diminishing return has been described as a "regression to the mean effect" of sorts in Draghi and Plotkin (2013) for the NK model, and it was argued that a similar regression effect applies to a broad category of fitness landscapes in Greene and Crona (2014). Moreover, "increased-costs epistasis" is likely to apply broadly as well with a similar argument also for landscapes that fall outside the category discussed by in the manuscript (an example is in the Recommendation section). On the other hand, a major strength of the manuscript is that it provides a superior quantitative precision, and some quantitative understanding …
Author Response to Public Reviews
Reviewer #2 (Public Review):
[]... A somewhat puzzling point is that the authors emphasize that their proposed frame work explains diminishing-return and increased-costs epistasis. Diminishing return has been described as a "regression to the mean effect" of sorts in Draghi and Plotkin (2013) for the NK model, and it was argued that a similar regression effect applies to a broad category of fitness landscapes in Greene and Crona (2014). Moreover, "increased-costs epistasis" is likely to apply broadly as well with a similar argument also for landscapes that fall outside the category discussed by in the manuscript (an example is in the Recommendation section). On the other hand, a major strength of the manuscript is that it provides a superior quantitative precision, and some quantitative understanding for when one can expect diminishing returns and increased costs epistasis (that should be emphasized more in my view).
We thank the reviewer for bringing the above two references to our attention. We have added the two refs and a statement in the Discussion (line 472-476 in RM) to emphasize the above.
[...] From a conceptual point of view, the locus specific framework, as well as the historical contingency discussion are valuable contributions. The fact that the author could construct a model (the CN model) that satisfy their minimal contingency condition is very interesting as well.
The weakness of the manuscript is the presentation of the work, especially for a general audience. More context and background, explanations of quantitative results and references would help. There are also a few cases of unclear claims and confusing notation (SSWM seems to be assumed without that being stated, the notation for Fourier coefficients is unclear in some cases) and the text has some other minor issues. Fortunately, a limited effort (in terms of time) would resolve the problem, and also improve the prospects for high impact.
We thank the reviewer for the detailed comments.
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Reviewer #3 (Public Review):
The proposed model is a variation on existing probabilistic fitness landscapes with a number of novel ingredients that are crucial for explaining the observed patterns. The model successfully accounts for the experimental results and makes new predictions, some of which are confirmed by the analysis of existing data. It also provides a coherent picture of the dynamics of adaptation that matches experimental observations. Overall, this is a conceptually deep and potentially highly influential study.
I see only one major issue that requires clarification. This concerns the distinction between the directed mutation scheme (leading to Eqs.(3,4) in the main text) and the symmetric version (Eqs.(5,6)).
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Reviewer #2 (Public Review):
The authors analyze diminishing-return (beneficial mutations likely having a small effects for genotypes of high fitness) and increasing-costs epistasis (deleterious mutations likely having large effects for genotypes of high fitness). A framework is proposed where the fitness of genotype after a mutation at a single locus can be estimated from (i) the additive effect at the locus and (ii) a component determined by the fitness of the original genotype at the locus, referred to as "global epistasis". The concept of locus-specific global epistasis is new, even if variants of global epistasis have been discussed in published work. The manuscript shows that the locus specific assumption is empirically justified and it provides applications to a study of yeast.
Regression effects (diminishing returns and …
Reviewer #2 (Public Review):
The authors analyze diminishing-return (beneficial mutations likely having a small effects for genotypes of high fitness) and increasing-costs epistasis (deleterious mutations likely having large effects for genotypes of high fitness). A framework is proposed where the fitness of genotype after a mutation at a single locus can be estimated from (i) the additive effect at the locus and (ii) a component determined by the fitness of the original genotype at the locus, referred to as "global epistasis". The concept of locus-specific global epistasis is new, even if variants of global epistasis have been discussed in published work. The manuscript shows that the locus specific assumption is empirically justified and it provides applications to a study of yeast.
Regression effects (diminishing returns and increasing costs epistasis) are quantified under the assumption that epistasis can be considered noise (idiosyncratic epistasis). The result is expressed in terms of Fourier representation for the fitness of a genotype, and the proof depends on a locus-specific analysis of correlations derived from the Fourier representation. In particular, the author clarify under what circumstances one can expect the regression effects. Several conclusions are very precise, and numerical results are provided as a complement to the analytical work.
The second part of the manuscript concerns historical contingency. Absence of contingency means that the expected fitness effect of new mutation for a genotype is independent of previous substitutions. A condition for minimal contingency in provided, and a new model (The Connected Network model, or CN-model) which satisfies is introduced.
A somewhat puzzling point is that the authors emphasize that their proposed frame workexplains diminishing-return and increased-costs epistasis. Diminishing return has been described as a "regression to the mean effect" of sorts in Draghi and Plotkin (2013) for the NK model, and it was argued that a similar regression effect applies to a broad category of fitness landscapes in Greene and Crona (2014). Moreover, "increased-costs epistasis" is likely to apply broadly as well with a similar argument also for landscapes that fall outside the category discussed by in the manuscript (an example is in the Recommendation section). On the other hand, a major strength of the manuscript is that it provides a superior quantitative precision, and some quantitative understanding for when one can expect diminishing returns and increased costs epistasis (that should be emphasized more in my view).
From a conceptual point of view, the locus specific framework, as well as the historical contingency discussion are valuable contributions. The fact that the author could construct a model (the CN model) that satisfy their minimal contingency condition is very interesting as well.
The weakness of the manuscript is the presentation of the work, especially for a general audience. More context and background, explanations of quantitative results and references would help. There are also a few cases of unclear claims and confusing notation (SSWM seems to be assumed without that being stated, the notation for Fourier coefficients is unclear in some cases) and the text has some other minor issues. Fortunately, a limited effort (in terms of time) would resolve the problem, and also improve the prospects for high impact.
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Reviewer #1 (Public Review):
One of the most consistent and thus surprising patterns revealed by experimental evolutionary studies is the observation of a very predictable pattern of increase in fitness of replicate populations. The fitness increase tends to be very rapid at the beginning and then slows down but continues to increase for tens of thousands of generations (e.g. the Lenski LTEE). The studies from the Desai group specifically two: one by Kryazhmisky et al and one by Jonnson et al further established that the pattern of decrease in the fitness gain is due to really counterintuitive patterns of global epistasis. In particular it is not due to the evolution running out of adaptive mutations but rather to the fact that the same adaptive mutations are less beneficial on fitter backgrounds (Kryazhmisky et al). Johnson et al …
Reviewer #1 (Public Review):
One of the most consistent and thus surprising patterns revealed by experimental evolutionary studies is the observation of a very predictable pattern of increase in fitness of replicate populations. The fitness increase tends to be very rapid at the beginning and then slows down but continues to increase for tens of thousands of generations (e.g. the Lenski LTEE). The studies from the Desai group specifically two: one by Kryazhmisky et al and one by Jonnson et al further established that the pattern of decrease in the fitness gain is due to really counterintuitive patterns of global epistasis. In particular it is not due to the evolution running out of adaptive mutations but rather to the fact that the same adaptive mutations are less beneficial on fitter backgrounds (Kryazhmisky et al). Johnson et al further found that the fitter backgrounds are more fragile with deleterious mutations being more deleterious on fitter backgrounds. All of this is rather bizarre at first glance as the microscopic epistasis is known to be highly idiosyncratic.
This paper, along with one by Lyons et al (Nat Ecol Evol 2020), resolves this paradox and shows that the observed pattern of global epistasis is in fact directly dependent on microscopic epistasis being widespread, involving multiple loci - with most parts of the organisms being connected in an "everything affecting everything" pattern, and being idiosyncratic. The Lyons et al paper focused on the data showing the epistasis is in fact idiosyncratic - their key observation - and provided an intuition for why such widespread idiosyncrasy would result in the observed pattern of global epistasis. Although neither set of authors seems to use this term, this should fit the notion of the Anna Karenina principle: "All happy families are alike; each unhappy family is unhappy in its own way." That is, in order for the right things to happen, most things need to go right, but in order for things to fail, anyone of many such things can go wrong. The more adapted systems are more fragile and more difficult to improve, because in both cases it is easier to disrupt what is already working.
The Reddy and Desai paper takes this notion and develops a very simple and transparent quantitative theory of this principle that generates specific quantitative predictions about the dynamics of adaptation that we, as a field, will spend considerable time now testing. The work has the potential to become a seminal paper in the field.
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Evaluation Summary:
The authors consider Darwinian evolution for large systems, with a main focus on how adaptation changes over time. Frequently observed patterns of declining adaptability for a population in a new environment are discussed, i.e., that fitness tends to increase fast initially and then at a slower rate. Another topic is historical contingency in adaptation. A condition for minimal contingency is provided, and a new model (the connectedness model, or CN model) is introduced accordingly. The manuscript is innovative, conceptually interesting, and provides quantitative precision beyond most related studies in the field. However, the presentation currently does not work well for a general audience.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive …
Evaluation Summary:
The authors consider Darwinian evolution for large systems, with a main focus on how adaptation changes over time. Frequently observed patterns of declining adaptability for a population in a new environment are discussed, i.e., that fitness tends to increase fast initially and then at a slower rate. Another topic is historical contingency in adaptation. A condition for minimal contingency is provided, and a new model (the connectedness model, or CN model) is introduced accordingly. The manuscript is innovative, conceptually interesting, and provides quantitative precision beyond most related studies in the field. However, the presentation currently does not work well for a general audience.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewers #1, #2, and #3 agreed to share their names with the authors.)
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