Mutational robustness changes during long-term adaptation in laboratory budding yeast populations

Abstract

As an adapting population traverses the fitness landscape, its local neighborhood (i.e., the collection of fitness effects of single-step mutations) can change shape because of interactions with mutations acquired during evolution. These changes to the distribution of fitness effects can affect both the rate of adaptation and the accumulation of deleterious mutations. However, while numerous models of fitness landscapes have been proposed in the literature, empirical data on how this distribution changes during evolution remains limited. In this study, we directly measure how the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode-based mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in genetic backgrounds spanning 8,000-10,000 generations of evolution in two constant environments. We find that the mean of the distribution of fitness effects decreases in one environment, indicating a reduction in mutational robustness, but does not change in the other. We show that these distribution-level patterns result from differences in the relative frequency of certain patterns of epistasis at the level of individual mutations, including fitness-correlated and idiosyncratic epistasis.

Full text

Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 1 of 24
Mutational robustness changes during
long- term adaptation in laboratory
budding yeastpopulations
Milo S Johnson1,2,3*, Michael M Desai1,2,3,4*
1Department of Organismic and Evolutionary Biology, Harvard University, Cambridge,
United States; 2Quantitative Biology Initiative, Harvard University, Cambridge, United
States; 3NSF- Simons Center for Mathematical and Statistical Analysis of Biology,
Harvard University, Cambridge, United States; 4Department of Physics, Harvard
University, Cambridge, United States
Abstract As an adapting population traverses the fitness landscape, its local neighborhood (i.e.,
the collection of fitness effects of single- step mutations) can change shape because of interactions
with mutations acquired during evolution. These changes to the distribution of fitness effects can
affect both the rate of adaptation and the accumulation of deleterious mutations. However, while
numerous models of fitness landscapes have been proposed in the literature, empirical data on how
this distribution changes during evolution remains limited. In this study, we directly measure how
the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode- based
mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in
genetic backgrounds spanning 8000–10,000 generations of evolution in two constant environments.
We find that the mean of the distribution of fitness effects decreases in one environment, indi-
cating a reduction in mutational robustness, but does not change in the other. We show that these
distribution- level patterns result from differences in the relative frequency of certain patterns of epis-
tasis at the level of individual mutations, including fitness- correlated and idiosyncratic epistasis.
Editor's evaluation
Johnson and Desai developed an innovative yeast experimental- evolution system where they can
insert barcoded disruptive mutations into the genome and measure their individual effect on fitness.
They use this system to test whether these mutations have different effects on evolving lineages as
they adapt over time. As expected, the mean fitness effect does decline in most (but not all) popula-
tions as lineages adapt, but in another condition, mean fitness effects of mutations do not change as
the populations adapt. The authors suggest an intriguing interpretation that the ‘control coefficient’
of selection on growth can shift between different genetic modules over time, resulting in differing
magnitudes of epistasis.
Introduction
Evolutionary adaptation relies on recombination and spontaneous mutagenesis to constantly intro-
duce variation into populations, upon which natural selection can act. The fate of a single mutation
– and its impacts on the dynamics of adaptation – depends on how it affects organismal fitness, which
we know depends in complex ways on the rest of the genetic background (reviewed in de Visser
etal., 2011; Domingo etal., 2019; Lehner, 2011). Understanding this genotype dependence, or
RESEARCH ARTICLE
*For correspondence:
milo.s.johnson.13@gmail.com
(MSJ);
mdesai@oeb.harvard.edu (MMD)
Competing interest: The authors
declare that no competing
interests exist.
Funding: See page 20
Received: 17 December 2021
Preprinted: 20 December 2021
Accepted: 25 July 2022
Published: 26 July 2022
Reviewing Editor: Vaughn S
Cooper, University of Pittsburgh,
United States
Copyright Johnson and
Desai. This article is distributed
under the terms of the Creative
Commons Attribution License,
which permits unrestricted use
and redistribution provided that
the original author and source
are credited.

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epistasis, involves analyzing key features of the fitness landscape, the high- dimensional map between
genotype and fitness (Wright, 1932).
To investigate these questions, numerous studies have surveyed epistatic interactions among a
variety of different types of mutations. These studies have found that beneficial mutations isolated
from laboratory evolution experiments tend to exhibit negative epistasis. That is, they are less benefi-
cial in combination than would be expected from the combination of their effects in isolation (Karkare
etal., 2021; MacLean etal., 2010; Ono etal., 2017; Rokyta et al., 2011; Schenk et al., 2013;
Schoustra etal., 2016; Zee and Velicer, 2017). However, some examples of positive epistasis among
beneficial mutations have also been observed (Chou et al., 2009; Fumasoni and Murray, 2020;
Hsieh etal., 2020; Khan etal., 2011; Levin- Reisman etal., 2019). Surveys of interactions between
deleterious mutations have produced numerous examples of both positive and negative epistasis
(Costanzo et al., 2016; Elena and Lenski, 1997; Hall and MacLean, 2011; Jasnos and Korona,
2007; Lalić and Elena, 2012; Sanjuán etal., 2004; Van Leuven etal., 2021).
While this earlier work has identified a wide range of epistatic interactions among specific combi-
nations of mutations, several recent studies of epistasis in laboratory microbial systems have found
that general patterns of fitness- correlated epistasis often emerge. These fitness- correlated patterns
typically favor less- fit genotypes: for both beneficial and deleterious mutations, we usually find that
the fitness effect of a mutation is negatively (rather than positively) correlated with the fitness of the
genetic background on which it occurs (Chou etal., 2011; Johnson etal., 2019; Khan etal., 2011;
Kryazhimskiy et al., 2014). These patterns have been termed diminishing returns and increasing
costs for beneficial and deleterious mutations, respectively. These trends are particularly intriguing
to those interested in modeling the dynamics of adaptation for two reasons. The first is the analytical
promise of a simple, monotonic relationship between fitness and the fitness effects of mutations. The
second is the potential for these patterns of epistasis to explain declining adaptability, a commonly
observed phenomenon in laboratory evolution experiments in which the rate of fitness increase slows
as evolution proceeds (reviewed in Couce and Tenaillon, 2015; see Wünsche etal., 2017 for an anal-
ysis of the link between diminishing returns and declining adaptability).
The initial studies that identified patterns of fitness- mediated epistasis did so in the context of a
relatively small number of beneficial mutations, finding that these mutations became systematically
less beneficial in more- fit genetic backgrounds. More recent work has shown that as populations
evolve the average fitness effect of a spontaneous beneficial mutation decreases (Aggeli etal., 2021;
Wünsche etal., 2017). Much less work has been done to characterize how the effects of deleterious
mutations interact with the beneficial mutations that fix during evolution (Remold and Lenski, 2004).
We recently showed that the fitness effects of larger panels of~100–1000 random insertion muta-
tions (both beneficial and deleterious) tend to be systematically less beneficial or more deleterious in
more- fit backgrounds (Johnson etal., 2019). However, the genetic backgrounds in that study were
derived from a cross between two diverged yeast strains. It remains unclear whether similar patterns
would hold across genetic backgrounds that are the result of long- term laboratory evolution because
the mutations that drive evolutionary adaptation are selected along a line of descent, which in prin-
ciple could affect their epistatic interactions.
Here, we directly address this question by measuring the fitness effects of a panel of insertion
mutations during the course of a long- term laboratory evolution experiment in budding yeast. Specif-
ically, we isolated clones from six timepoints spanning 8000–10,000 generations of adaptation to each
of two constant laboratory environments from the ongoing evolution experiment we have recently
described (Johnson etal., 2021). While the yeast strains used in our prior experiment differed at tens
of thousands of segregating loci, the strains in this experiment differ by only tens or hundreds of muta-
tions that fixed successively during evolution. By looking at the effects of insertion mutations in these
strains, we are measuring a panel of hidden phenotypes (the fitness effects of the mutations) that may
change predictably or stochastically during evolution. The widespread presence of epistasis observed
in biological systems suggests that these hidden phenotypes may be important to long- term evolu-
tionary outcomes as the fitness effects of mutations effectively open and close doors to unique path-
ways for evolution (Johnson etal., 2021; Karkare etal., 2021; Kvitek and Sherlock, 2011).
Robustness can be broadly defined as invariance in the face of perturbation (Masel and Siegal,
2009). Here, we are concerned specifically with mutational robustness, a measure of how invariant
phenotypes are to mutations (Lauring et al., 2013). Our approach complements several recent

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studies that have analyzed changes in mutational robustness during evolution by conducting muta-
genesis followed by phenotypic measurements. For example, Novella etal., 2013 found that vesic-
ular stomatitis virus strains evolved in the lab gained robustness, measured based on survival after
mutagenesis. In contrast, Butković etal., 2020 found that a strain of turnip mosaic potyvirus evolved
in Arabidopsis thaliana lost robustness over time, measured as the change in the ability of the virus to
retain its level of plant infectivity after mutagenesis. Our barcode- based mutagenesis system makes it
possible to dissect these overall changes in robustness by measuring how they emerge as a result of
changes in the effects of individual mutations.
In this study, we aim to leverage this mutation- level data to better understand the structure of
epistasis in evolving populations. First, we analyze the overall distribution of fitness effects to measure
how mutational robustness changes during adaptation in each environment. Next, we ask whether
the distribution- level changes we observe can be explained by patterns of fitness- correlated epistasis
among individual mutations. Finally, we examine how the effects of these mutations change in each
of the evolving populations, asking whether epistasis is more often driven by predictable adaptations
common across populations or by specific mutations fixed in a single population.
Results
Changes in the distribution of fitness effects during evolution
We isolated two clones from each of six timepoints from six haploid populations evolved in rich media
at a permissive temperature (YPD 30°C) and from six haploid populations evolved in a defined media
environment at a high temperature (SC 37°C), a total of 144 clones. We measured the fitness of
each of these clones in the environment to which they adapted, finding that fitness increases steadily
through time in both the YPD 30°C and SC 37°C environments, and displays a general pattern of
declining adaptability (Figure1A).
We next created a library containing each of 91 insertion mutations in each of our 144 clones.
This set of mutations was identified previously as a subset of random insertion mutations that have
measurable effects in the strains from Johnson etal., 2019. These mutations have a similar spectrum
of effects in the clones isolated for this study (Figure1—figure supplement 8), suggesting that they
are also a broad sample of insertion mutations with measurable fitness effects in these strains. We
measured the fitness effect of each mutation in each clone using barcode- based competition assays
as described in Johnson etal., 2019. Because the molecular dynamics of evolution in these haploid
populations are characterized by successive selective sweeps, we expect the two clones isolated from
each population at each timepoint to have very similar genetic backgrounds. When we compare the
average fitness effect measurement for each insertion mutation between these clones, we generally
see strong agreement, with a few exceptions (Figure1—figure supplements 1–3). These exceptions
likely represent rare but important genetic differences between clones from the same population-
timepoint. Given this, we chose to analyze our data in two ways. First, we improve the reliability of our
fitness effect measurements for each population- timepoint by using measurements from combined
barcodes (cBCs) from both clones, treating them as we treated biological replicates in Johnson etal.,
2019. Second, we treat each clone independently. Figure1—figure supplement 7, Figure2—figure
supplement 5, Figure3—figure supplement 5, and Figure4—figure supplement 1 show that our
qualitative conclusions are unchanged when using this second approach.
We find that the distribution of fitness effects (DFE) of our 91 insertion mutations changes over the
course of the evolution experiment. In the YPD 30°C environment, the mean of the DFE decreases
over time as fitness increases during evolution (Figure1B), consistent with a general pattern of both
diminishing returns and increasing costs. The negative relationship between generations evolved and
the mean of the DFE is significant in the entire set of population- timepoints (p=2.0 × 10–6, Wald test)
and in four of our six individual populations (p<0.05, Wald test). In contrast, although the DFE does
shift in individual populations evolved in our SC 37°C environment, we do not see any consistent
patterns (Figure1B).
In both environments, we find that the changes in the mean of the DFE are modest compared to our
previous experiment (Figure1—figure supplement 6 shows that the slope of the regression between
the DFE mean and background fitness in YPD 30°C is less than half the magnitude of the corre-
sponding slope in Johnson etal., 2019). The reasons for this are unclear, but may reflect the fact that

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Figure 1. The distribution of tness effects (DFE) mean declines in one of two environments during evolution.
(A) Changes in tness during the evolution experiment, measured as the average tness of two clones isolated
from six timepoints in each population. In each graph, zero is the tness of a uorescent reference used in that
environment. Error bars represent the standard deviation of the tnesses measured for the two clones (points
without error bars have errors smaller than the point size). (B) The mean tness effect of the insertion mutations
measured in the clones isolated from each timepoint. Asterisks represent a signicant correlation (p<0.05, Wald
test) between generation and DFE mean in that population alone. In both (A)and (B),the six populations are
indicated by color. Error bars represent the standard error of the DFE mean, calculated from the standard errors
of individual mutations (see ‘Materials and methods’). Additional DFE statistics are shown in Figure1—figure
supplement 4.
The online version of this article includes the following gure supplement(s) for gure 1:
Figure supplement 1. Fitness effect measurement correlations in YPD 30°C.
Figure supplement 2. Fitness effect measurement correlations in SC 37°C.
Figure supplement 3. Fitness effect measurement correlations in clones evolved in YPD 30°C, assayed in SC 37°C.
Figure 1 continued on next page

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fitness differences between the strains we study here are caused by a smaller number of mutations.
We note that because of the modest differences in the DFE between clones, the noise in our measure-
ments contributes significantly to the variation. One potentially biased source of this noise is missing
measurements: not all mutations have fitness effects measured in each population- timepoint due to
differences in transformation efficiency or, most commonly, mutations that had too few read counts
in the first two timepoints of the fitness assay. As in Johnson etal., 2019, missing measurements of
strongly deleterious mutations are more common in more- fit strains (clones from later timepoints) in
YPD 30°C, suggesting that the negative correlation between generations evolved and the mean of
the DFE would be stronger if more of these deleterious mutations had been successfully measured
in clones from later timepoints. Indeed, if we look at a limited set of mutations with measurements in
every population- timepoint or if we ‘fill in’ missing measurements using their average fitness effect
across population- timepoints, we see similar or stronger patterns of change (p<5 × 10–7, Wald test)
in the DFE mean in YPD 30°C (Figure1—figure supplement 5). This relationship between the DFE
mean and generations evolved also holds (p<5 × 10–8, Wald test) in our analysis where clones are
treated independently (Figure1—figure supplement 7).
Epistasis at the level of individual mutations
We next turn to the components of these distribution- level patterns: epistatic patterns for individual
mutations. To look at these patterns, we focus on mutations that have fitness measurements in at
least 20 population- timepoints in each environment (77 mutations in YPD 30°C, 74 in SC 37°C, 70
in both). We start by looking for patterns of fitness- correlated epistasis. We classify each mutation in
each environment as correlated negatively or positively with background fitness if the correlation is
significant at the p<0.05 level (Wald test) and the absolute value of the slope is greater than 0.05, and
classify them as not significantly correlated if they do not meet these criteria. The cutoff of 0.05 for
the slope was chosen to filter for mutations with an effect size across the range of background fitness
that is larger than the typical standard error for our fitness effect measurements (see ‘Materials and
methods’). For both environments, we find numerous examples of both negative and positive correla-
tions, corresponding to increasing costs or decreasing costs, respectively, for deleterious mutations
(and to diminishing returns or increasing returns, respectively for beneficial mutations).
In Figure2, we show examples illustrating how the fitness effect of specific mutations vary across
clones isolated from each environment, plotted as a function of the fitness of each clone in that envi-
ronment (i.e., the background fitness). We find numerous examples of mutations that exhibit negative,
positive, and nonsignificant correlations with background fitness in both environments (panels along
the diagonal). We also find examples where a specific mutation exhibits a nonsignificant correlation
in one environment and either a positive or negative correlation in the other (off- diagonal panels).
Overall, consistent with our previous results, we observe about twice as many negative correla-
tions as positive correlations. As we would expect from the DFE- level results, this imbalance is more
pronounced in the YPD 30°C environment: 33/77 (~43%) mutations have fitness effects that decline
significantly as background fitness increases in YPC 30°C compared to 17/74 (~23%) in SC 37°C.
We also find that only 9/77 (~12%) mutations display the opposite pattern (fitness effects increase
significantly as background fitness increases) in YPD 30°C, while 13/74 (~18%) display this pattern in
SC 37°C. Because we are primarily focused on comparing the frequency of each pattern across envi-
ronments, we report these values before multiple- hypothesis- testing correction here and in Figure2;
Figure supplement 4. Additional distribution of tness effects (DFE) statistics.
Figure supplement 5. Accounting for missing tness effect measurements.
Figure supplement 6. Comparison of our distribution of tness effects (DFE) mean vs. background tness data
with the data from Johnson etal., 2019.
Figure supplement 7. Distribution of tness effects (DFE) statistics and missing tness effect measurements for
analysis considering clones separately.
Figure supplement 8. Distributions of all tness effects measured in Johnson etal., 2019 and this experiment.
Figure supplement 9. Excluding barcodes that experience sequencing cross- contamination.
Figure 1 continued

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Figure 2. Patterns of tness- correlated epistasis. Each panel shows an example of a specic mutation with a particular combination of relationships
(negative, positive, or nonsignicant correlation between tness effect of the mutation, s, and background tness) in the two environments; numbers
indicate the total number of mutations displaying each pair of relationships. Each point depicts the tness effect (y- axis) of one insertion mutation
measured in one population- timepoint, with the measured tness of that population- timepoint represented on the x- axis. Error bars show the standard
error of both measurements (see ‘Materials and methods’). Axes are colored to identify the environment: in each panel, the blue axes on the left are
data from YPD 30°C and the black axes on the right are data from SC 37°C. Points are colored by population, as in Figure1. Each set of example plots
is labeled by where the mutation is in the genome (i.e., which gene it disrupts). Additional comparisons of patterns of epistasis in these experiments and
those from Johnson etal., 2019 are shown in Figure2—figure supplements 1–4.
The online version of this article includes the following gure supplement(s) for gure 2:
Figure supplement 1. Comparison of patterns of tness- correlated epistasis between YPD 30°C and a previous study.
Figure supplement 2. Comparison of patterns of tness- correlated epistasis between SC 37°C and a previous study.
Figure supplement 3. Comparison of patterns of tness- correlated epistasis YPD 30°C and SC 37°C, in both cases using the set of clones isolated from
evolution in YPD 30°C.
Figure supplement 4. Comparison of patterns of tness- correlated epistasis in the SC 37°C environment for clones isolated from evolution in either
YPD 30°C or SC 37°C.
Figure supplement 5. Patterns of tness- correlated epistasis with clones treated separately.

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after a Benjamini–Hochberg multiple- hypothesis correction, these values fall to 24/77 (~31%), 15/74
(~20%), 9/77 (~12%), and 11/74 (~15%), respectively.
Modeling the determinants of fitness effects
The examples in Figure 2 demonstrate that correlations between fitness effects and fitness are
common but often do not explain the bulk of epistasis. By definition, the fitness- correlated patterns
we observe are the result of interactions between our insertion mutations and mutations that fix
during the evolution experiment. If these interactions are all strictly ‘fitness- mediated,’ the fitness
effects of mutations will be fully explained by a background fitness effect. Alternately, correlations
between fitness effects and fitness could arise based on the average effect of a number of idiosyn-
cratic effects that are more likely to be negative versus positive. To understand the relative contribu-
tion of these determinants of epistasis, we compare three linear models used to explain the fitness
effects of a single mutation in each of our two environments:
1. The fitness model (XM): the fitness effect of the mutation is a linear function of background
fitness.
2. The idiosyncratic model (IM): the fitness effect of the mutation can change in any population at
any timepoint (and all subsequent timepoints) when an interacting mutation fixes in that popu-
lation (see below for our constraints on fitting these parameters).
3. The full model (FM): the fitness effect of the mutation is affected by both a linear effect of
background fitness and the idiosyncratic interactions of fixed mutations, as in the idiosyncratic
model.
We fit each model by ordinary least squares (OLS). We define the fitness effect of each mutation in
the ancestral strain as the mean fitness effect measured among clones from the first timepoint, and fix
the intercept of each of our models accordingly. For the idiosyncratic and full models, we add idiosyn-
cratic parameters iteratively, choosing the parameter that improves the Bayesian information criteria
(BIC) the most at each step. These coefficients represent epistasis between the insertion mutation in
question and one or more unknown mutations that fix during evolution in one population. Because
mutations generally fix between every pair of timepoints during evolution, there could in principle be
one idiosyncratic parameter for each timepoint in each population, but allowing all of these param-
eters would constitute overfitting. To combat this possibility, we do not allow parameters that fit a
single point (e.g., a parameter for an effect at the final timepoint), and we only allow one parameter
per population. We stop this iterative process of adding parameters if the BIC improves by less than
2 during a step (or when there is one parameter per population). Note that because of this iterative
parameter adding procedure, the full model may have a different set of idiosyncratic parameters and
will sometimes have less explanatory power than the idiosyncratic model (i.e., IM is not nested in FM).
Figure3A shows how well each model explains the fitness effect data for each mutation in each
environment. We find that the fitness model often explains a modest amount of variance (mean R2:
18% in YPD 30°C, 19% in SC 37°C), but the idiosyncratic model (mean R2: 54% in YPD 30°C, 41% in SC
37°C) and the full model (mean R2: 53% in YPD 30°C, 44% in SC 37°C) usually offer more explanatory
power. The examples in Figure3B also demonstrate that epistasis is not strictly fitness- mediated; we
commonly observe a stepwise change in the fitness effect of an insertion mutation in one evolving
population, likely indicating epistasis between the insertion mutation and one or more mutations that
fix in that population at a particular timepoint.
We can also ask which model best explains the data using the BIC, which penalizes models based
on the number of parameters. The small squares below the bars in Figure3A indicate which model
has the lowest BIC for each mutation. In YPD 30°C, the full model has the lowest BIC for 40/77 (~52%)
mutations and the idiosyncratic model has the lowest BIC for 37/77 (~48%). In SC 37°C, the full model
has the lowest BIC for 49/73 (~67%) mutations and the idiosyncratic model has the lowest BIC for
24/73 (~33%). When we assess how well each model fits the entire dataset in each environment, the
full model has a lower BIC than the idiosyncratic model in both environments.
Positive and negative coefficients in the idiosyncratic model represent positive and negative epis-
tasis between mutations that fix during evolution and our insertion mutations. While these coefficients
can arise in our modeling procedure due to noise alone, we find far more coefficients in our empirical
dataset than in a simulated or shuffled dataset (see ‘Materials and methods,’ Figure3—figure supple-
ment 4). The bulk of the coefficients we find in YPD 30°C are negative (214/291, ~74%), while both

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Figure 3. Determinants of tness effects. (A) For each environment, we plot the standard deviation of the tness effect across all population- timepoints
and the square root of the variance explained by each of our three models. The colored squares below each bar represent which model has the lowest
Bayesian information criteria (BIC) for each mutation. Mutations shown in red or black are insertions in or near the corresponding gene, respectively;
stars indicate the mutations shown in panel (B). Only mutations with tness- effect measurements in at least 20 population- timepoints are shown.
The insets show the distribution of all coefcients in the idiosyncratic model (IM) and full model (FM), pooled across all mutations. (B) Examples of
idiosyncratic (left half) and full (right half) model ts. Model predictions are shown by dashed lines, and lines with contributions from indicator variables
associated with a particular population are the same color as the points from that population (colors are the same as in Figure1).
The online version of this article includes the following gure supplement(s) for gure 3:
Figure 3 continued on next page

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positive (131/245, ~53%) and negative (114/245, ~47%) coefficients are common in our idiosyncratic
model in SC 37°C (Figure3A insets). Note that many of the positive epistatic terms in our idiosyn-
cratic model in SC 37°C are the result of a consistent reduction in the fitness costs of some deleterious
mutations in the first 2000 generations of evolution in all populations (e.g., see the mutation in VAM6
in Figure3B and others in Figure3—figure supplements 6–37, and see Figure3—figure supple-
ment 3 for a breakdown of coefficients by individual mutations).
The differences we observe in epistatic patterns between environments could be caused by inter-
actions between epistasis and the environment (‘G×G×E’ effects), differences in the adaptive targets
(i.e., the functional modules subject to selection) in each environment, or a combination of the two. To
tease apart these possibilities, we measured the fitness effects of mutations in clones evolved in YPD
Figure supplement 1. Epistasis in mutations that are benecial on average at the rst timepoint in at least one environment.
Figure supplement 2. Idiosyncratic model coefcients, broken down by population and timepoint in each condition.
Figure supplement 3. Model coefcients plotted by mutation.
Figure supplement 4. Model coefcient distributions for empirical, shufed, and simulated datasets.
Figure supplement 5. Analogous to Figure3 but with clones treated separately.
Figure supplement 6. Determinants of tness effects under the idiosyncratic model.
Figure supplement 7. Determinants of tness effects under the idiosyncratic model.
Figure supplement 8. Determinants of tness effects under the idiosyncratic model.
Figure supplement 9. Determinants of tness effects under the idiosyncratic model.
Figure supplement 10. Determinants of tness effects under the idiosyncratic model.
Figure supplement 11. Determinants of tness effects under the idiosyncratic model.
Figure supplement 12. Determinants of tness effects under the idiosyncratic model.
Figure supplement 13. Determinants of tness effects under the idiosyncratic model.
Figure supplement 14. Determinants of tness effects under the idiosyncratic model.
Figure supplement 15. Determinants of tness effects under the idiosyncratic model.
Figure supplement 16. Determinants of tness effects under the idiosyncratic model.
Figure supplement 17. Determinants of tness effects under the idiosyncratic model.
Figure supplement 18. Determinants of tness effects under the idiosyncratic model.
Figure supplement 19. Determinants of tness effects under the idiosyncratic model.
Figure supplement 20. Determinants of tness effects under the idiosyncratic model.
Figure supplement 21. Determinants of tness effects under the idiosyncratic model.
Figure supplement 22. Determinants of tness effects under the full model.
Figure supplement 23. Determinants of tness effects under the full model.
Figure supplement 24. Determinants of tness effects under the full model.
Figure supplement 25. Determinants of tness effects under the full model.
Figure supplement 26. Determinants of tness effects under the full model.
Figure supplement 27. Determinants of tness effects under the full model.
Figure supplement 28. Determinants of tness effects under the full model.
Figure supplement 29. Determinants of tness effects under the full model.
Figure supplement 30. Determinants of tness effects under the full model.
Figure supplement 31. Determinants of tness effects under the full model.
Figure supplement 32. Determinants of tness effects under the full model.
Figure supplement 33. Determinants of tness effects under the full model.
Figure supplement 34. Determinants of tness effects under the full model.
Figure supplement 35. Determinants of tness effects under the full model.
Figure supplement 36. Determinants of tness effects under the full model.
Figure supplement 37. Determinants of tness effects under the full model.
Figure 3 continued

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30°C in the SC 37°C environment. We assayed the background fitness of each of these clones in SC
37°C and found that populations evolved in YPD 30°C sometimes experience large fitness declines
in the SC 37°C environment (Figure4C). We also observe widespread epistasis in this alternate envi-
ronment, but do not observe any overall trends in the mean of the DFE in SC 37°C over the course of
evolution in YPD 30°C (Figure4A and B). Instead, the variance in our data is dominated by one partic-
ularly low fitness clone (from population P1C05, generation 7550) in which several insertion mutations
were strongly beneficial (Figure4C).
When we apply the same set of models to this dataset, we again find that both background
fitness and idiosyncratic effects can explain how many mutations’ fitness effects vary, with the latter
again outperforming the former (Figure4A). Notably, we observe relatively more positive epistatic
Figure 4. Patterns of epistasis in a nonevolution environment. (A) Same as Figure3A, but for clones from YPD 30°C assayed in SC 37°C. We plot the
standard deviation of the tness effect across all population- timepoints and the square root of the variance explained by each of our three models. The
colored squares below each bar represent which model has the lowest Bayesian information criteria (BIC) for each mutation. Mutations shown in red or
black are insertions in or near the corresponding gene, respectively; stars indicate the mutations shown in panel (B). Only mutations with tness- effect
measurements in at least 20 population- timepoints are shown. The inset shows the distribution of all coefcients in the idiosyncratic model (IM) and full
model (FM), pooled across all mutations. (B) Example IM model t, as in Figure3B. The model predictions are shown by bold dashed lines, and lines
with contributions from indicator variables associated with a particular population are the same color as the points from that population (colors are
the same as in Figure1 and panel C). (C) The tness and distribution of tness effects (DFE) mean over time in YPD 30°C populations assayed in SC
37°C. The asterisk indicates a signicant correlation (p<0.05). Error bars on tness represent the standard deviation of the tnesses measured for the
two clones, but note that we were only able to measure the tness of one clone at several population- timepoints due to low tnesses relative to our
reference; the corresponding points here have no error bars. Error bars on the DFE mean represent the standard error of the DFE mean, calculated from
the standard errors of individual mutations (see ‘Materials and methods’).
The online version of this article includes the following gure supplement(s) for gure 4:
Figure supplement 1. Analogous to Figure4 but with clones treated separately.

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coefficients (109/241, ~45%) than in YPD 30°C (77/291, ~26%), though we also observe a heavy tail
of strongly negative coefficients. These patterns of idiosyncratic epistasis are not due to outsized
contributions from a few populations; the distributions of IM coefficients for YPD 30°C populations are
different in the two assay environments across populations (Figure3—figure supplement 2). Overall,
these results support the hypothesis that G×G×E effects underlie the differences we observe between
environments (see also Hall etal., 2019), though they do not rule out the possibility that differences
in adaptive targets between environments may also contribute.
Discussion
Shifting distributions of fitness effects
By using our barcode- based mutagenesis system to assay the fitness effects of 91 specific gene
disruption mutations across numerous genetic backgrounds spanning 8000–10,000 generations of
laboratory evolution, we have described how overall mutational robustness (defined in terms of the
average effect of this type of insertion mutation) changes during evolution. We then dissected these
overall effects in terms of how the fitness effects of individual mutations change during evolution.
We find that populations adapting to our YPD 30°C environment become less robust to deleterious
mutations over time. This shift in the mean of the DFE in YPD 30°C is not caused by strictly fitness-
mediated shifts in the fitness effects of mutations, but is instead the result of an excess of negative
idiosyncratic epistatic effects (Figure3). In contrast, in clones isolated from populations evolved in SC
37°C, epistatic interactions are more evenly divided between negative and positive effects.
The fact that populations evolved in YPD 30°C lost robustness as they increased in fitness over time
is broadly consistent with our earlier work showing that the DFE becomes more strongly deleterious
in more- fit genetic backgrounds (Johnson etal., 2019). However, the loss of robustness we observe
here was not as strong as in this previous work (see Figure1—figure supplement 6 for a comparison
to the effect size in Johnson etal., 2019), and we did not observe any predictable change in the DFE
mean in SC 37°C. One potential explanation for the weaker patterns we observe at the DFE level in
this experiment is that there are simply less mutations involved compared to the genetic backgrounds
from our earlier work: the genotypes in our previous experiment were derived from a cross between
two yeast strains that differed at tens of thousands of loci, so the pool of mutations was both larger
and more balanced (each mutation present in~50% of clones) than in this study. If the overall patterns
of fitness- correlated epistasis arise due to the collective effect of numerous idiosyncratic interactions,
rather than a genuine fitness- mediated effect, we would therefore expect weaker trends here (Lyons
etal., 2020; Reddy and Desai, 2021).
Our results also illustrate a form of hidden evolutionary unpredictability, despite the fact that our
populations increased in fitness over time along a predictable trajectory (Johnson etal., 2021). As
these populations adapted, they accumulated mutations that carry with them epistatic interactions
with potential future mutations across the rest of the genome. The patterns of epistasis we observe
among the insertion mutations in our study demonstrate that the predictability of these second- order
effects varies widely: some potential future mutations show strong fitness- correlated effects in every
population, while others are affected by a small number of idiosyncratic interactions with mutations
that fix during evolution. These kinds of unpredictable patterns of epistasis could lead to fundamen-
tally unpredictable evolutionary outcomes, with changes in the fitness effects of mutations dynami-
cally closing off or opening up evolutionary pathways during adaptation.
Patterns of epistasis among individual mutations
Most of the insertion mutations we analyze in this experiment are deleterious across most or all genetic
backgrounds. We find that these deleterious mutations tend to become more strongly deleterious
over time in populations evolved in the YPD 30°C environment. This pattern results from an over-
abundance of negative epistatic interactions, which could involve either the beneficial mutations that
drive fixation events or the neutral or weakly deleterious mutations that hitchhike to fixation during
selective sweeps (McDonald etal., 2016). The strong predictive power of background fitness for the
fitness effects of some mutations suggests that interactions with beneficial mutations are driving these
patterns of epistasis, but idiosyncratic effects that deviate from these relationships hint at a role for
interactions with hitchhiker mutations as well (Figure3). Systematic backcrossing and mutagenesis

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experiments would be required to disentangle these patterns (along with any cases of higher- order
epistasis involving multiple mutations that fix during evolution), but we suspect both types of interac-
tions contribute to the epistasis we observe.
Among the relatively small number of beneficial insertion mutations we analyze, we find that the
beneficial effects tend to decline over time, and almost universally shift to neutral or deleterious effects
later in the experiment (Figure 3—figure supplement 1). These results provide additional exam-
ples of diminishing- returns epistasis among beneficial mutations, which can at least partially explain
the pattern of declining adaptability often observed in microbial evolution experiments (Chou etal.,
2011; Khan etal., 2011; Kryazhimskiy etal., 2014; Wünsche etal., 2017). One of these mutations
has a clear functional story behind it: the beneficial effect of an insertion mutation in ADE5,7 is the
result of breaking the adenine synthesis pathway upstream of a toxic intermediate, so when popula-
tions in SC 37°C fix other loss- of- function mutations that also break the pathway between the first two
sampled timepoints in the evolution experiment, this mutation becomes neutral (we do not see this
effect in YPD 30°C because most populations have fixed a mutation in the adenine pathway by the
first sampled timepoint; for a more in- depth discussion of this case of epistasis and contingency, see
Johnson etal., 2021).
The picture that emerges from our data is one in which idiosyncratic epistatic effects are largely
unpredictable but also unbalanced (have a nonzero mean), which leads to correlations with back-
ground fitness. In both our own work and other studies of microbial evolution, the mean epistatic
effect is negative: beneficial mutations tend to have negative epistatic interactions with both delete-
rious (Johnson etal., 2019, this study) and beneficial mutations (Chou etal., 2011; Hall etal., 2019;
Karkare etal., 2021; Khan etal., 2011; Kryazhimskiy etal., 2014; Ono etal., 2017; Pearson etal.,
2012; Perfeito etal., 2014; Rokyta etal., 2011; Wünsche etal., 2017).
At the broadest level, we can distinguish two potential sources of these unbalanced patterns of
epistasis: the structure of biological systems and the set of mutations that fix during evolution. Both
theoretical and experimental work has shown that genes within functional modules tend to have
similar interaction profiles with other genes (Costanzo etal., 2016; Segrè etal., 2005). Given this
kind of ‘monochromatic’ epistasis, all that is necessary for fitness- correlated epistasis to appear during
evolution is for beneficial mutations to be clustered in a few modules. The strength and direction of
fitness- correlated epistasis will then depend on the particular modules targeted by selection and how
those modules interact with the rest of the cell. For example, the targets of adaptation in SC 37°C
may be more related to heat stress than general components of growth (e.g., mutations in LCB3,
which have been shown to reduce killing in certain heat stress conditions, are enriched in populations
in SC 37°C) (Ferguson- Yankey etal., 2002; Johnson etal., 2021). If the strongly deleterious effects
of some of our insertion mutations are exacerbated by heat stress, but a beneficial mutation reduces
heat stress, we can expect a positive interaction between the two mutations. In contrast, we hypothe-
size that the deleterious effects of some insertion mutations become more pronounced when growth
rate is increased by mutations in YPD 30°C (Johnson etal., 2019). In order to understand or predict
these differences in epistasis specific to the evolution environment, we will need to better understand
the functional structure of biological systems.
Higher-order epistasis and the evolution of robustness
Each mutation that fixes during evolution has an immediate first- order effect on fitness, but also
carries with it a second- order set of pairwise interactions whose strength and direction is determined
by the structure of functional relationships between genes and biological modules. Through higher-
order interactions, a mutation can also change the structure of these functional relationships, altering
the complexity, redundancy, robustness, and evolvability of biological systems (reviewed in de Visser
etal., 2003; Masel and Siegal, 2009; Masel and Trotter, 2010; Payne and Wagner, 2019). Our work
here suggests that mutational robustness tends to decrease during evolution in some environments,
but our data is limited to interactions with the set of~200 mutations that fixed during 10,000 gener-
ations of laboratory adaptation. We expect the effects we observe here to dominate during rapid
adaptation, but over longer evolutionary timescales, robustness may be more dependent on changes
in the higher- order structure of biological systems.

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Ideas and speculation
We find that in one evolution environment a tendency towards negative epistasis leads to a shift in the
DFE towards more deleterious mutations over time, while in another evolution environment no such
shift occurs. Clearly, the details matter, and it is difficult to draw general conclusions. In this section,
we speculate on how work in metabolic control theory (MCT) may help explain the functional under-
pinnings of our results and fitness- correlated epistasis more generally.
MCT describes how mutations in idealized metabolic pathways change the control coefficients of
other mutations (Szathmáry, 1993). In a strictly serial pathway, a mutation reducing the activity of one
enzyme will decrease the control other enzymes have over flux through the pathway, but a mutation
increasing the activity of one of the enzymes will increase the control of others. If two enzymes act
instead in parallel, these patterns are reversed: a mutation that increases activity of one will decrease
the control of the other on flux, and vice versa (for a thorough treatment of how epistasis arises and
propagates in metabolic networks, see Kryazhimskiy, 2021).
If flux through the pathway is correlated with fitness, these patterns of interactions predict epistasis
between mutations in different enzymes in the pathway. For example, if flux is negatively correlated
with fitness in a strictly serial pathway, beneficial mutations will be those that reduce flux, so they will
reduce the control of other enzymes in the pathway, such that these beneficial mutations exhibit nega-
tive epistasis. This is the case for beneficial loss- of- function mutations in the broken adenine- synthesis
pathway present in the ancestors of our evolution experiment (Johnson etal., 2021): one beneficial
loss- of- function mutation in this pathway (e.g., in ADE4) lowers the control coefficients of the rest
of the enzymes in that pathway, such that loss- of- function mutations in these enzymes become less
beneficial (e.g., our insertion mutation in ADE5,7 in this experiment, Figure3—figure supplement 1).
MCT is a mathematical framework for describing these interactions, but the general qualitative
principles can be applied beyond enzymes in metabolic pathways to understand patterns of fitness-
correlated epistasis (MacLean, 2010). One hypothesis for the functional underpinnings of increasing-
costs epistasis can be framed in this way. First, we assert that the large- scale components of growth in
the yeast cell functionally act in serial. While these components of growth (e.g., cell wall production,
ribosome production, and DNA replication) do not belong to an actual serial pathway, they clearly
do not act in parallel: these components generally cannot ‘fill in’ for each other. That is, they are
nonredundant. We therefore propose that an increase in the function of one of these components (in
terms of growth rate) will increase the control coefficients of the rest of the components. Similarly, a
decrease in the function of one component will decrease the control coefficients of the rest. We can
intuitively understand this based on the idea of limitation: if DNA replication slows to a halt, growth
rate will become less sensitive to changes in the speed of cell wall production. In contrast, if a popu-
lation in which growth is limited by DNA replication fixes a mutation that improves DNA replication,
we expect the control coefficient of cell wall production to increase, meaning deleterious mutations
that slow cell well production will become more deleterious. We believe this effect can explain much
of the increasing- costs epistasis we have observed.
Consider the following metaphor for this effect. You work for a car manufacturer, and your factory’s
goal is to produce cars as quickly as possible. You work with a small team that builds the wheels. Your
team is efficient, but the engine team is much slower. Because the engine team is limiting produc-
tion, you don’t feel under pressure from the boss at all – in fact, one of your team members slacks off
sometimes, but the company hardly suffers (read: their control coefficient is low, deleterious mutations
have small effects). One day the engine team purchases a new robot and dramatically speeds up their
process. Suddenly cars are waiting for wheels, and the pressure on your team increases dramatically
– now when your teammate is slacking, it slows the entire production line down (read: their control
coefficient is high, deleterious mutations have larger effects, costs have increased).
In our discussion, we speculate that we see increasing costs more frequently in YPD 30°C because
adaptation in that environment is more focused on improving core components of growth compared
to adaptation in SC 37°C where selection for improvement in heat tolerance or survival may be more
common. The phenotype of survival does not fit as neatly into our car manufacturing metaphor: we
have no strong hypotheses for how control coefficients should change as populations increase heat
tolerance or for how large- scale phenotypes such as growth and survival integrate in terms of compet-
itive fitness. However, we speculate that in SC 37°C adaptive mutations are less likely to be affecting
the core components of growth, and therefore cause increasing costs less often than mutations

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selected in YPD 30°C (i.e., adaptive mutations in SC 37°C are less likely to increase the control coeffi-
cients of random mutations). To move closer to predictive models of epistasis, we will need to better
understand the functional relationships between these large- scale cellular phenotypes.
We end our discussion by noting that changes in robustness over longer evolutionary timescales
may depend not on the type of changes we observe in our evolution experiment, but on changes to
the higher- order structure of biological systems. Within our metaphor, this is the difference between
changes to each team’s effectiveness and changes to the structure of the assembly line (or even to
the ultimate product of the system). Defining what constitutes a change to the structure of the system
itself is a difficult problem, analogous to defining ‘novelty’ in evolution (Murray, 2020), but most
would agree that there are fundamental differences in the complexity and redundancy of the genetic
systems of viruses and humans, for example.
Both experimental and theoretical work have suggested that higher genome complexity and
redundancy is associated with more negative epistasis between deleterious mutations (Macía etal.,
2012; Sanjuán and Elena, 2006; Sanjuán and Nebot, 2008; though see Agrawal and Whitlock,
2010). Negative epistasis between deleterious mutations implies that deleterious mutations increase
the control coefficients of other mutations and that beneficial mutations will decrease control coeffi-
cients. We can understand this pattern as a broad extension of MCT: the case of strictly parallel path-
ways and fitness correlated with flux, in which two deleterious mutations exhibit negative epistasis, is
one example of a functionally redundant relationship. Therefore, in organisms with higher functional
redundancy, we expect to observe more positive interactions between beneficial and deleterious
mutations and less increasing- costs epistasis. In other words, the second- order loss of mutational
robustness we observe during adaptation should be stronger in organisms with low redundancy. While
there may be more unseen factors affecting the types of interactions beneficial mutations participate
in, present data suggests that increasing- costs epistasis may be specific to organisms or environments
where the functional redundancy of genes or biological modules is low.
Epistasis between beneficial mutations
An apparent contradiction emerges from our explanation for increasing- costs epistasis: if adaptation
increases the control coefficients of core components of growth, why do we not see more positive epis-
tasis between beneficial mutations in evolution experiments? Why do we instead usually see negative,
diminishing- returns epistasis and declining adaptability? We propose that this discrepancy arises due
to differences in the availability and form of beneficial and deleterious mutations. Based on previous
work, we expect beneficial mutations in laboratory evolution experiments to be primarily loss- of-
function mutations (Murray, 2020). In contrast to deleterious mutations, which can be spread across
the genome, these types of beneficial mutations will rarely exist in well- adapted core components of
growth, and will instead be clustered in a few adaptive targets. Within these targets, we believe loss-
of- function beneficial mutations are often functionally redundant, meaning that they tend to decrease
each other’s control coefficients for fitness. Beneficial mutations can be redundant by inactivating the
same deleterious pathway (e.g., ADE pathway mutations discussed above), solving the same general
problem (e.g., mutations shortening lag in Karkare etal., 2021), or changing a phenotype with a
nonlinear fitness function (Chiu etal., 2012; Chou et al., 2014; Keren etal., 2016; Lunzer etal.,
2005; Otwinowski et al., 2018). Nonmonotonic fitness functions can arise from phenotypes with
both potential benefits and costs (Dekel and Alon, 2005), such that negative interactions between
beneficial mutations and the benefit can lead to fitness- correlated epistasis that crosses neutrality,
exhibiting diminishing returns, increasing costs, and sign epistasis (Figure3—figure supplement 1).
This explanation provides a prediction: we will be more likely to see synergistic epistasis during
evolution experiments when we observe beneficial gain- of- function mutations. Chou et al., 2009
provides a particularly strong example of a beneficial gain- of- function (promoter capture) mutation
that is more beneficial in more- fit genetic backgrounds. In the long- term Escherichia coli evolution
experiment, potentiating mutations acquired during adaptation in one population interacted posi-
tively with a beneficial gain- of- function mutation (also a promoter capture), enabling aerobic citrate
utilization (Blount etal., 2012). Studies of evolutionary repair also provide examples of synergistic
interactions between apparently nonredundant beneficial mutations (Fumasoni and Murray, 2020;
Hsieh et al., 2020). These counterexamples underscore the fact that diminishing- returns epistasis
is not a rule; it is a pattern that is overrepresented in evolution experiments due to a tendency for

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beneficial mutations to be loss- of- function mutations and to be clustered in a few adaptive targets.
These tendencies may be weaker later in evolution experiments when mutations are spread more
evenly across cellular modules, such that a period of declining adaptability caused by diminishing-
returns epistasis early in an experiment gives way to a period of relatively constant fitness gains (Good
and Desai, 2015).
A final note on terminology for epistasis
Very few papers discuss epistasis between beneficial and deleterious mutations – most theoretical
and experimental work has focused on epistasis between two beneficial mutations or two deleterious
mutations. With these same- signed pairs of mutations, the terms negative and positive epistasis are
consistent. Two beneficial mutations that interact negatively imply two deleterious reversions that
also interact negatively. However, when we consider one of these beneficial mutations and the dele-
terious reversion of the other, they interact positively. We provide this note to clarify that increasing-
costs epistasis, in which deleterious mutations exhibit negative epistasis with beneficial mutations,
should not be considered the same as previous results demonstrating negative epistasis between two
deleterious or two beneficial mutations. Instead, we should expect it in systems where more positive
epistasis is observed between same- signed mutations. While epistasis is already a concept overladen
with terminology, we submit that in some cases it may be more useful to classify interactions between
mutations or cellular components as being functionally redundant or nonredundant in terms of fitness.
Materials and methods
Strains
All strains used for this study were isolated from the evolution experiment described in Johnson
etal., 2021. We isolated two clones from each of our focal populations at each sequencing time-
point. For this experiment, we used clones from 12 MATa populations, 6 from the YPD 30°C environ-
ment and 6 from the SC 37°C environment. We decided to include population P1B04, which exhibits
a cell- clumping phenotype in preliminary imaging data, and to exclude population P1B03, which
diploidized during evolution, and populations P3C04, P3F05, P3D05, and P3E02, which lost G- 418
resistance during evolution (not being able to select on G- 418 during transformation could allow
the HygMX cassette to replace the KanMX cassette, leading to leakage during the selection step).
Otherwise, we chose populations randomly. The ancestor of these populations is MJM361 (MATa,
YCR043C:KanMX, STE5pr- URA3, ade2- 1, his3Δ::3xHA, leu2Δ::3xHA, trp1- 1, can1::STE2pr- HIS3
STE3pr- LEU2, HML::NATMX, rad5- 535).
Barcoded Tn7 libraries
We used a previously created set of Tn7- based plasmid libraries to introduce the same set of~100
mutations into each of our strains (Johnson etal., 2019). These plasmids contain a section of the yeast
genome corresponding to one of these~100 locations, interrupted by a Tn7 insertion containing a
random DNA barcode and a HygMX cassette. Each barcode uniquely identifies the mutation and the
plasmid library via a mapping established in earlier work (Johnson etal., 2019).
Transformation
Our yeast transformation protocol is a scaled- up version of that used in Johnson etal., 2019, based
on the method described in Gietz and Schiestl, 2007. We grew strains from freezer stocks overnight,
diluted 750μL into 15 mL YPD+ ampicillin (100g/mL), grew for 4hr, pelleted the cells, and resus-
pended in 900μL transformation mix and 100μL plasmid DNA cut with NotI- HF (corresponds to 2 μg
of plasmid; cut at 37°C for 3hr, then heat- inactivated at 65°C for 10min). We then heat- shocked this
mixture at 42°C for 1hr, recovered in 3mL YPD+ ampicillin for 2 hr, plated 25μL on antibiotic selec-
tion plates to check efficiency, and then combined the rest with 40mL YPD supplemented with antibi-
otics. For both agar and liquid- selective media, we included hygromycin (300μg/mL), clonNat (20μg/
mL), and G- 418 (200μg/mL). We made frozen glycerol stocks of each transformation after~48hr of
growth. All growth was conducted at 30°C either in a test tube on a roller drum (recovery) or in a
baffled flask on an orbital shaker (all other steps).

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We transformed 2 clones from 12 populations at 6 timepoints for a total of 144 transformations.
We organized these transformations into three ‘VTn assays,’ each associated with 48 transformations
using our 48 unique barcoded libraries.
Fitness assays
Again, we followed the protocols established in Johnson etal., 2019 for our fitness assays. We used
two types of media: rich YPD media (1% Bacto yeast extract [VWR #90000- 726], 2% Bacto peptone
[VWR #90000- 368], 2% dextrose [VWR #90000- 904]) and synthetic complete (SC) media (0.671% YNB
with nitrogen [Sunrise Science #1501- 250], 0.2% SC [Sunrise Science # 1300- 030], 2% dextrose). We
assayed our transformed libraries of clones from the YPD 30°C environment in both their evolution
environment (YPD 30°C) and the SC 37°C environment, and clones from the SC 37°C environment in
their evolution environment (SC 37°C). We first arrayed our transformation glycerol stocks into two
96- well plates corresponding to the two evolution environments, and then inoculated 8μL from each
well of these plates into four (for SC 37°C assays) or eight (for YPD 30°C assays) flat- bottom polypro-
pylene 96- well plates containing 126μL of media, supplemented with the same antibiotics as during
the initial selection. To ensure efficacy of the antibiotics in the SC 37°C environment, we used media
with MSG instead of ammonium sulfate (1.71g/L YNB without amino acids or ammonium sulfate,
2g/L SC, 1g/L MSG). After this period of growth, we used YPD and SC supplemented with ampicillin
(100μg/mL) and tetracycline (25μg/mL), matching the conditions of the evolution experiment. After
40hr of growth in these plates, we started daily transfers.
At each daily transfer, we diluted YPD 30°C cultures 1/210 and SC 37°C cultures 1/28. During these
transfers, we combined and mixed cultures from each well corresponding to the same clone/transfor-
mation to increase population size and reduce bottleneck noise. In the first (T0) transfer, we combined
cultures from the eight plates that were initially inoculated from the freezer stock and diluted them
into 20 96- well plates. In all subsequent transfers (T1–4), we combined cultures from all 20 plates and
diluted them into 20 new plates. Specifically, for YPD 30°C, we diluted 3μL from each well of 20 plates
into 60μL YPD (60μL total, 1/2 dilution), mixed, then diluted 16μL into 112μL YPD (1/23 dilution),
mixed, and distributed 2μL into 126μL YPD in 20 plates (1/26 dilution). For SC 37°C, we diluted 3μL
from each well of 20 plates into 60μL SC (60μL total, 1/2 dilution), mixed, then diluted 60μL into
60μL SC (1/2 dilution), mixed, and distributed 2μL into 126μL SC in 20 plates (1/26 dilution).
Barcode sequencing
Our fitness assays in YPD 30°C were originally performed alongside assays in SC 37°C that were later
abandoned due to an issue with expired reagents (and repeated with appropriate reagents in our
second round of assays). During these assays, we combined equal volumes of culture at the end of
each transfer from every well corresponding to each of the three VTn assays in each environment.
We can pool the cultures corresponding to each VTn assay because we know which barcodes corre-
spond to which plasmid library/clone, so we can divide our barcode count data appropriately during
sequencing analysis. We performed DNA extractions from two 1.5mL pellets for each assay- timepoint
from our YPD 30°C fitness assays and from four 1.5mL pellets from our SC 37°C fitness assays using
Protocol I from the Yeastar Genomic DNA Kit (Zymo Research), as described previously (Johnson
etal., 2019). We then amplified barcodes using a two- step PCR protocol. We performed four first-
round PCRs with 19µL gDNA, 25L 2X Kapa Hotstart Hifi MM, 3µL 10M TnRS1 primer, and 3µL 10M
TnFX primer, and ran the PCR protocol: (1) 95°C 3:00, (2) 98°C 0:20, (3) 60°C 0:30, (4) 72°C 0:30,
GO TO step 2 three times, and (5) 72°C 1:00. We purified these PCRs with PCRClean DX Magnetic
Beads (Aline) using a 0.85× ratio. We then set up two second- round PCRs per sample by combining
25µL purified PCR µ1 product, 1.5µL ddH2O, 10µL Kapa Hifi Buffer, 1µL KAPA HiFi HotStart DNA
Polymerase, 5µL 5M N7XX primer (Nextera), and 5µL 5M S5XX primer (Nextera), and ran the PCR
protocol: (1) 95°C 3:00, (2) 98°C 0:20, (3) 61°C 0:30, (4) 72°C 0:30, GO TO step 2 19 times, and (5)
72°C 2:00. We purified the resulting libraries with Aline beads, using a 0.7× ratio, then repeated the
purification with a 0.65× ratio, and finally sequenced our pooled libraries on a NextSeq 550 (Illumina).
From reads to barcode counts
We process our sequencing data as described previously (Johnson etal., 2019). We first filter reads
based on inline indices and quality scores, use regular expressions to extract barcode sequences, and

Research article Evolutionary Biology
Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 17 of 24
combine barcode counts across timepoints for each VTn assay. Next, we use a single- bp- deletion-
neighborhood method to correct errors in raw barcodes, assigning them to the set of known barcodes
from each of our plasmid libraries. By associating barcodes with plasmid libraries, we associate them
both with a fitness assay for a particular clone and with a particular insertion mutation, and we divide
our barcode count data accordingly.
Estimating fitness effects from barcode counts
Again, we follow Johnson etal., 2019, with minor differences. First, we convert barcode counts to
log- frequencies at each timepoint. After this preliminary step, we noticed a large number of log-
frequency spikes, restricted largely to one timepoint in one of our VTn assays in SC 37C. These spikes
in frequency very likely represent low- level sequencing library contamination from another timepoint
due to primer cross- contamination. In Figure1—figure supplement 9, we show that this is confined
to this single timepoint and demonstrate how we can use a simple heuristic (excluding lineages whose
log- frequency at timepoint 2 is 0.5 greater than both timepoint 1 and timepoint 3) to remove the
barcoded lineages affected by this sequencing library contamination. This step excludes, on average,
less than 1% of the reads from timepoint 2 in these assays. Next, we calculate fitness effects for each
barcode, as described in Johnson etal., 2019. After excluding timepoints with less than 5000 total
barcode counts, we measure the log- frequency slope for each barcode at each consecutive pair of
timepoints, excluding timepoints in which the barcode has less than 10 counts. We scale each of these
log- frequency slopes by the median log- frequency slope of barcodes associated with five neutral
reference mutations, and then average these scaled values to get one fitness measurement for each
barcode. As in Johnson etal., 2019, we observe a small fraction of outlier barcodes, which follow
starkly different log- frequency trajectories than the other barcodes associated with the same inser-
tion mutation, presumably due either to pre- existing mutations in the transformed culture or trans-
formation artifacts (including two mutations being transformed together). We use a log- likelihood
ratio test to identify barcodes whose read counts are inconsistent with barcodes near the median
fitness measured for one insertion mutation. Based on iterative exclusion and exploration of frequency
trajectories for this experiment, we chose a heuristic cutoff of 40 for the log- likelihood ratio required
to exclude barcodes (for a detailed description of this method, see Johnson etal., 2019). Finally, to
decrease noise from low- frequency barcode lineages while retaining the independent measurements
unique barcodes provide, we randomly combine counts from individual barcodes into a maximum of
five combined barcodes (‘cBCs’) per insertion mutation. Next, we repeat the fitness measurement
process described above to get final fitness measurements for each cBC (scbc).
Again following Johnson etal., 2019, we calculate the mean and standard error of all cBCs fitness
measurements for each insertion mutation (m) in each clone (c):
S
m,c=Σcbcsscbc
num_cbcs ,σm,c,cbc =
√∑
cbcs
(
scbc−sm,c
)
2
(
num
_
cbcs
−1)∗
num
_
cbcs
,
For each clone, we also calculate the standard error of our fitness measurements of our set of
neutral barcodes (σneut,c). Since sm,c is the difference between the measured cBC fitness for mutation m
and the measurement of neutrality, we calculate the standard error for sm,c as the square root of the
sum of squares of these two errors:
σ
m,c=
√
σ
2
m
,
c
,
cbc +σ
2
neut,c
To obtain the fitness effect of a mutation for a population- timepoint (sm,p,t), we calculate an inverse-
variance weighted average on the fitness effect measurements from each clone:
sm,p,t=
∑
clones
sm,c
σ2
m,c
∑
clones
1
σ2
m,c
We only calculate sm,p,t if there are at least three cBCs between the two clones. If one of the two
clones has only one cBC, we use
σm,c
from the other replicate as an estimate of the standard error
to be used in inverse- variance weighted averaging. Note that because we only consider data with at

Research article Evolutionary Biology
Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 18 of 24
least three cBCs during our analysis in which we treat clones independently, this estimate of the stan-
dard error is only used for the inverse- variance weighted averaging.
We calculate the standard error on this sm,pt measurement as described above for individual clones
using the s values for all cBCs associated with mutation m in both clones:
σ
m,pt,cbc =
√∑
cbcs
(
scbc−sm,p,t
)2
(
num
_
cbcs
−1)∗
num
_
cbcs
As described in Johnson etal., 2019, we use this conservative measure of standard error instead
of the one given by inverse- variance weighting in order to better capture unspecified biological error
between the two replicates. Again, we combine this standard error with the standard error of all
neutral cBCs in both clones (σneut,pt):
σ
m,p,t=
√
σ
2
m
,
p
,
t
,
cbc +σ
2
neut,p,t
To test whether mutations have effects significantly different from zero for each population-
timepoint, we fit all cBC s values for a single mutation by OLS as described in Johnson etal., 2019.
The OLS model includes a fitted term for the fitness effect of the mutation (
smut
), a fitted term (
βmut
) for
differences in the effect between clones (indicated by r), and a normally distributed noise term (
emut
).
scbc =smut +βmutr+emut
We use the t- statistic for the intercept to calculate p- values for whether
smut =0
for each mutation.
We perform a Benjamini–Hochberg correction at the 0.05 level on the entire set of p- values we find.
Measuring changes in the DFE and accounting for missing
measurements
For each population- timepoint or clone, in each condition, we calculate the mean of the fitness effects
of all mutations with at least three cBCs, excluding distributions with less than 60 mutations with
fitness effect measurements. We calculate the standard error of the mean of the distribution of fitness
effects by combining variances from two sources: error in our measurement of mutation fitness effects
and errors in our measurement of mean fitness. Since this second component of variance is shared
across mutations, it is not scaled by the number of mutations:
σ
DFEmean
,
p
,
t=
√∑
mutations
σ
2
m,p,t,cbc
n
2+σ2
neut,p,t
where n is the number of mutations with measurements in the distribution (we use an analogous
formula in our analysis on individual clones). Importantly, note that this measure of error for the DFE
mean describes only noise from measured mutations and does not address the fact that some muta-
tions do not have measurements in some clones or population- timepoints.
We examined the effect of these missing fitness effect measurements in several ways. First, we
examined the mean of the DFE in sets of mutations shared across the set of population- timepoints we
had assayed successfully in each condition. For the analysis of individual clone DFEs in each condition,
we try to find the largest set of clones with at least 40 mutations with measurements in every clone.
We do this by iterating through the list of clones, sorted by the number of measured mutations, and
adding them to a set of clones until the number of mutations with measurements in every clone drops
below 40. Next, we create ‘filled- in’ DFEs for each population- timepoint and each clone in which
missing measurements are replaced with the mean fitness effect measured across all strains in a given
condition. The pattern observed in YPD 30°C, in which the mean fitness effect decreases as popula-
tions evolve and gain fitness, is stronger (in terms of the p- value and R2 of the regression) in both the
set of shared mutations and the filled- in DFE than in our original analysis.
Finally, we examined the number of strongly deleterious mutations (defined as having a mean
fitness effect<–0.05 across all population- timepoints in a given condition) that were not measured
in each population- timepoint. In YPD 30°C, these strongly deleterious mutations are less likely to be
measured in more fit strains, again suggesting that the relationship we observe would be stronger
with complete data. The results of these analyses are plotted in Figure1—figure supplement 5.

Research article Evolutionary Biology
Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 19 of 24
Modeling the determinants of epistasis
Because our modeling approach can be strongly influenced by outliers, we only consider fitness effect
measurements for mutations with at least five cBCs across the two clones for these analyses (or three
cBCs for the corresponding analysis in which clones are treated separately). First, we perform least-
squares regression between background fitness and fitness effect for each mutation in each environ-
ment. As described in the main text, we classify mutations as being negatively or positively correlated
with fitness based on both a statistical test (p<0.05, Wald test) and the effect size (|slope|>0.05). This
heuristic slope cutoff is meant to filter for cases in which the range of fitness effects under consider-
ation is larger than the typical noise for a single fitness effect measurement. In the YPD 30°C environ-
ment, a slope of 0.05 across an~0.15 range of fitnesses will mean fitness effects should vary~0.007,
which is also the mean standard error of our fitness effect measurements in that environment (an
analogous calculation in SC 37°C would yield a lower threshold, but we keep 0.05 for consistency).
Next, we fit our data with the three linear models described in the main text. To fix the intercepts
of our models correctly, we first transform the fitness effect of each mutation by subtracting the mean
fitness effect measured across all populations at the first timepoint of the evolution experiment (we
denote each transformed fitness effect for mutation m in population p, timepoint t, measured in
condition e as
∼
sm,p,t,e
below). We similarly transform our background fitness variable by subtracting
the average fitness measurement across all populations at the first timepoint (we denote each trans-
formed background fitness in population p, timepoint t, measured in environment e as
∼
xp,t,e
below).
Then we fix the intercept at (0, 0) in the modeling described below. Note that our plots showing these
model fits use the natural scales for fitness and fitness effects, not these transformed scales. The
fitness model (XM) can be written as
∼
sm,p,t,e=βm,e
∼
xp,t,e+em,e
where
em,e
is a normally distributed noise term, and
βm,e
is a fitted parameter representing the
slope between background fitness and the fitness effect of the mutation.
The idiosyncratic model (IM) can then be written as
∼
s
m,p,t,e
=∑
p,t
αm,p,t,e
i
p,t,e
+e
m,
e
ip,t,e
is an indicator variable that is 1 at timepoints >= t in population p and zero in all other cases,
and
αm,p,t,e
is a fitted parameter associated with that indicator variable.
The full model (FM) can then be written as
∼
s
m,p,t,e
=
βm,e
∼
x
p,t,e
+∑
p,t
αm,p,t,e
i
p,t,e
+e
m,
e
In both idiosyncratic model and full model, the idiosyncratic epistasis terms (
αm,p,t,eip,t,e
) are added
iteratively. At each step, we add the parameter that decreases the BIC the most if that decrease is
more than 2. We do not allow parameters that fit only a single point, and we do not allow more than
one parameter per population (i.e., the maximum number of idiosyncratic parameters for a given
mutation in a given environment is the number of populations, six). Importantly, the idiosyncratic
terms in the idiosyncratic model and the full model for a given mutation in a given environment may
be different, so IM is not nested within FM and IM may explain more variance than FM in some cases.
Because we consider the fixed intercept term to be part of our models, we compute R2 for each model
as 1 – (the sum of squared residuals/the centered sum of squares). This R2 value can be negative if the
model explains less variance than a model with only a free intercept term, in which case we set R2 to
zero and do not plot the model in Figure3 or Figure4. All model fitting was performed by OLS using
the Python package statsmodels (Seabold and Perktold, 2010).
To test how much noise affects our model fitting procedure, we ran our analysis on a simulated
dataset and a shuffled dataset. In both cases, we focus on the sets of up to 36 fitness effect measure-
ments associated with a mutation and a condition (with measurements in six populations and six
timepoints). For the simulated dataset, we drew fitness effects for each set of mutations from a normal
distribution with a mean of zero and a standard deviation equal to the mean empirical standard error
for the fitness effects within the set of mutations (i.e., we drew all sm,p,t,e values for a given m and e

Research article Evolutionary Biology
Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 20 of 24
from a normal distribution with a standard deviation of
mean (
σ
m,p,t,e)
). For the shuffled dataset, we
randomly shuffled within each set (i.e., we randomly shuffled all sm,p,t,e values for a given m and e).
The distributions of the coefficients obtained from our modeling procedure for the empirical, shuf-
fled, and simulated datasets are plotted in Figure3—figure supplement 4. In YPD 30°C, we found
291, 91, and 87 IM coefficients in our empirical data, shuffled data, and simulated data, respectively. In
SC 37°C, we found 245, 78, and 81 IM coefficients in our empirical data, shuffled data, and simulated
data, respectively. In clones isolated from evolution in YPD 30°C and assayed in SC 37°C, we found
241, 60, and 60 IM coefficients in our empirical data, shuffled data, and simulated data, respectively.
In YPD 30°C, we found 140, 45, and 36 FM coefficients in our empirical data, shuffled data, and simu-
lated data, respectively. In SC 37°C, we found 88, 38, and 46 FM coefficients in our empirical data,
shuffled data, and simulated data, respectively. In clones isolated from evolution in YPD 30°C and
assayed in SC 37°C, we found 199, 63, and 57 FM coefficients in our empirical data, shuffled data, and
simulated data, respectively.
Measuring background fitness
We measured the background fitness of clones with fluorescence- based competitive fitness assays
in duplicate for each clone in each environment using the reference strains strain 2490A- GFP1 and
11470A- GFP1 for the YPD 30°C and SC 37°C clones, respectively. We used the 2490A- GFP1 refer-
ence when we assayed the YPD- 30°C- evolved clones in SC 37°C because some of these clones have
very low fitness and 2490A- GFP1 has a lower fitness than 11470A- GFP1. We used the fitness differ-
ence measured between these two references in Johnson etal., 2021 to standardize the fitness
measurements YPD- 30°C- evolved clones in SC 37°C so that all fitness measurements in SC 37°C are
on the same scale. Fitness assays were performed and data was analyzed as described in Johnson
etal., 2021. Briefly, we maintained mixed cultures of our clones and fluorescent references for three
daily growth cycles, as described above, and measured the frequency of fluorescent cells at each
transfer using flow cytometry. We then calculated the fitness of each clone as the slope of the natural
log of the ratio between the frequencies of the nonreference and reference cell populations over time.
Finally, we calculated the mean and standard error of the fitness measurements for the two clones
associated with each population- timepoint.
Acknowledgements
We thank Sergey Kryazhimskiy, Alena Martsul, Andrew Murray, and members of the Desai lab for
useful discussions about experimental design and analysis. We thank Shreyas Gopalakrishnan, Juhee
Goyal, and Megan E Dillingham for their help with isolating the clones used in this experiment. We
thank Craig Miller and one anonymous reviewer for helpful discussion and comments during the revi-
sion process. This work was supported by an NSF Graduate Research Fellowship (to MSJ), the NSF
(PHY- 1914916), and the NIH (GM104239). Computational work was performed on the Cannon cluster
supported by the Research Computing Group at Harvard University.
Additional information
Funding
Funder Grant reference number Author
National Science
Foundation
Graduate Research
Fellowship
Milo S Johnson
National Science
Foundation
PHY-1914916 Michael M Desai
National Institutes of
Health
GM104239 Michael M Desai
The funders had no role in study design, data collection and interpretation, or the
decision to submit the work for publication.

Research article Evolutionary Biology
Johnson and Desai. eLife 2022;11:e76491. DOI: https://doi.org/10.7554/eLife.76491 21 of 24
Author contributions
Milo S Johnson, Conceptualization, Formal analysis, Investigation, Writing – original draft, Writing –
review and editing; Michael M Desai, Conceptualization, Resources, Supervision, Funding acquisition,
Investigation, Writing – original draft, Project administration, Writing – review and editing
Author ORCIDs
Milo S Johnson
http://orcid.org/0000-0003-0169-2494
Michael M Desai
http://orcid.org/0000-0002-9581-1150
Decision letter and Author response
Decision letter https://doi.org/10.7554/eLife.76491.sa1
Author response https://doi.org/10.7554/eLife.76491.sa2
Additional files
Supplementary files
• Supplementary file 1. Column- annotated underlying data for this project. Includes background
fitness, fitness effect, and modeling data from this experiment and Johnson etal., 2019.
• Supplementary file 2. Oligos used in this study.
• Transparent reporting form
Data availability
Raw sequencing data has been deposited in the GenBank SRA (accession: SRP351176). All code used
in this project is available on GitHub (https://github.com/mjohnson11/VTn_pipeline, copy archived at
swh:1:rev:02d2b41d54dd22487df1c75f9e381411c5ef0376). All figures are based on data included in
Supplementary File 1.
The following dataset was generated:
Author(s) Year Dataset title Dataset URL Database and Identifier
Johnson MS, Desai
MM
2021 Mutational robustness
changes during long- term
adaptation in laboratory
budding yeast populations
https://www. ncbi. nlm.
nih. gov/ bioproject/
PRJNA789529
NCBI BioProject,
PRJNA789529
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