Environmental memory alters the fitness effects of adaptive mutations in fluctuating environments

Abstract

Evolution in a static laboratory environment often proceeds via large-effect beneficial mutations that may become maladaptive in other environments. Conversely, natural settings require populations to endure environmental fluctuations. A sensible assumption is that the fitness of a lineage in a fluctuating environment is the time average of its fitness over the sequence of static conditions it encounters. However, transitions between conditions may pose entirely new challenges, which could cause deviations from this time average. To test this, we tracked hundreds of thousands of barcoded yeast lineages evolving in static and fluctuating conditions and subsequently isolated 900 mutants for pooled fitness assays in 15 environments. Here we find that fitness in fluctuating environments indeed often deviates from the time average, leading to fitness non-additivity. Moreover, closer examination reveals that fitness in one component of a fluctuating environment is often strongly influenced by the previous component. We show that this environmental memory is especially common for mutants with high variance in fitness across tested environments. We use a simple mathematical model and whole-genome sequencing to propose mechanisms underlying this effect, including lag time evolution and sensing mutations. Our results show that environmental fluctuations impact fitness and suggest that variance in static environments can explain these impacts.

The increasing scale of experimental evolution, thanks to new levels of throughput and parallelism, provides unprecedented opportunities to understand evolutionary dynamics and mechanisms. Unifying principles have emerged about evolution in a single environment, including that replicate populations show parallel adaptation in recurrent genes, operons or pathways^1–5, with successive mutations having a saturating effect on fitness, resulting in declining adaptability over time^6,7. However, laboratory studies have mostly examined static environments, which have relatively temporally constant and spatially uniform conditions and which often select for mutations that exhibit costly fitness tradeoffs if conditions change^8–12. Such tradeoffs are relevant in natural settings where populations must endure distinct and intermittently harsh conditions, unlike in continually replenished laboratory environments.

Experimental evolution in fluctuating environments, while relatively uncharted, is making strides towards bridging this gap. One review found that costly fitness tradeoffs arise less often in heterogeneous than homogenous environments¹³. Evidence also suggests that fluctuating environments produce more surprising and unpredictable results. At the population scale, fluctuations have been shown to lead to more variation across evolving replicates^14,15. At the individual level, a mutant’s fate can be sensitive to the timescale¹⁶ and order¹⁷ of fluctuations, and the molecular basis and fitness of mutations emerging from fluctuating environments can be different from those in static environments^18,19. These findings align with the theory that predicts that evolution is less deterministic in fluctuating environments^20,21.

The variety of evolutionary outcomes seen in fluctuating environments raises the possibility that fluctuations render an environment fundamentally different from the sum of its parts. If fitness is additive in a fluctuating environment, the fluctuations might be decomposed into static components, and fitness in each component simply averaged to predict the overall fitness in the fluctuating environment. However, a theoretical study showed a counterintuitive finding that temporal fluctuations do not always time average fitness effects²⁰. Supporting this result, there is growing empirical evidence of non-additive fitness in fluctuating environments. For example, a study of yeast gene-deletion mutants in two fluctuating environments found many instances of non-additivity, owing to both under- and overperformance in fluctuating environments¹⁶. Another study highlighted the fallibility of fitness assays across environmental gradients in predicting fitness in fluctuating conditions for a range of organisms, finding inconsistency between parameters obtained in static environments and performance in fluctuating environments²². While these results suggest that fluctuating environments may be inherently different from static environments, the mechanisms of non-additivity in fluctuating environments remain undefined.

One difference between fluctuating and static environments is the nature of the transitions they contain. For example, in laboratory batch culture, microorganisms grow from low density until depleting the resource, after which the culture is diluted into fresh medium, re-starting the cycle. If the medium is the same every cycle, we consider this a static environment. Yet even in such ‘static’ conditions, the dilution step requires a transition from a state of dormancy to growth, manifesting as a lag time. Batch culture evolution of yeast in a static glucose-limited environment led to the emergence of adaptive mutants that gained fitness advantage in the lag phase, with the magnitude of this advantage determined by the growth parameters of the previous cycle²³. Their fitness advantage was thus accrued during one cycle but realized during the next. This result suggests that a mutant’s lag time can depend on its pre-conditioning environment and raises the question of how fitness would change in a fluctuating environment, where medium composition changes from one cycle to the next. We expect lag phase to change if the carbon source changes, given that lag times between carbon sources were observed in classical studies of diauxic shifts²⁴, and have more recently been associated with growth trade-offs^25–27 and specificity of gene expression²⁸. In addition, epigenetic processes mediate phenotypic plasticity and memory in fluctuating environments^29–32, generating cell-to-cell variation that promotes survival in transiently stressful conditions^33,34. Mutations might alter such phenotypic effects, causing fitness relative to the ancestor to change in fluctuating environments.

Here we use high-throughput genome barcoding to investigate how differences between transitions in fluctuating and static environments cause changes in fitness, where we define fitness as a mutant’s change in relative frequency across growth and dilution timepoints, corrected by mean population fitness (Fig. 1). We first evolved clonal populations of Saccharomyces cerevisiae, each containing ~500,000 unique barcoded lineages, in static environments, including stressors and alternate carbon sources, as well as in temporally fluctuating pairwise combinations of these environments. We tracked barcoded evolutionary trajectories and subsequently selected a pool of 889 mutants for follow-up fitness assays in all environments. By comparing fitness in fluctuating environments to the average fitness in the component static environments, we see a spectrum of non-additivity, defined as the difference between fitness of a mutant in a fluctuating environment and its time-averaged fitness in the component static environments. Furthermore, frequency trajectories of individual mutants reveal striking changes in fitness in the components of fluctuating environments compared with the corresponding static environments. These changes are often hidden in overall fitness, to some extent, as they partially cancel each other. We show that these changes reveal a pattern based on fitness differences across static environments, whereby mutants with larger variance in fitness are more sensitive to transitions and exhibit more environmental memory, or a change in fitness in an individual component of a fluctuating environment compared with static environments with this component only. We use a simple mathematical model and whole-genome sequencing to propose mechanisms underlying this environmental sensitivity, including that mutations that cause higher fitness variance are environment specific and may shift lag times more in fluctuating environments. Our results show that environmental fluctuations alter fitness and fundamentally differentiate dynamics in static from fluctuating environments.

Fig. 1 |. Fitness assays test for non-additivity in mutants evolved from static and fluctuating environments.

a, We evolved the same barcoded library in five static conditions and five fluctuating pairs of these static conditions. We then isolated 889 mutants from the evolution experiments and performed pooled fitness assays in all environments, plus five additional fluctuating environments. b,c, After correcting for mean population fitness, we estimate a mutant’s fitness from the slope of its log frequency in static environments 1 (b) and 2 (c). d, The null hypothesis of additive fitness in a fluctuating environment is represented by the average of the slopes in b and c. Non-additive fitness might result if transitions in the fluctuating environment alter the fitness of a mutant. e, Non-additivity can be visualized by plotting observed fitness in a fluctuating environment versus the null hypothesis. Mutants with non-additive fitness will appear above or below the one-to-one line.

Results

Dataset generated by experimental evolution and fitness assays

To study how evolution and fitness depend on the environment, we began by evolving barcoded yeast in static and fluctuating environments. We propagated clonal populations containing ~500,000 uniquely barcoded lineages, as developed in a previous study³⁵, for ~168 generations in serial batch culture. We carried out evolutions in five static environments and five fluctuating pairwise combinations of these static environments (Fig. 1a, Table 1 and Methods; we included the remaining five pairwise combinations in later fitness assays). Static environments contained either glucose (Glu), S. cerevisiae’s preferred carbon source, or less-optimal alternate carbon sources galactose (Gal), which induces a classical diauxic shift in yeast³⁶, and lactate (Lac), an organic acid that might induce growth tradeoffs relative to sugar²⁷. In two environments, we supplemented the glucose condition with stressors known to affect S. cerevisiae fitness^37,38 (sodium chloride (NaCl) and hydrogen peroxide (H₂O₂)) (Table 1).

Table 1. Descriptions of static and fluctuating environments.

Environment	Composition	Evolved	Fitness measured	Multi-hit genes (number of hits)
				SNPs	Copy number variation
Static
Glu	SC + 1.5% glucose	•	•	ZAP1 (2)
Gal	SC + 1.5% galactose	•	•	ISN1 (2)
Lac	SC + 0.7% lactate	•	•	–
H2O2	SC + 1.5% glucose + 2.5 mM hydrogen peroxide	•	•	–
NaCl	SC + 1.5% glucose + 0.5 M sodium chloride	•	•	YNCB0007W (2), PAU8 (2)	ENA1–ENA2–ENA5 (18)
Fluctuating
Glu–Gal		•	•	ISN1 (2)
Glu–Lac		•	•	ARN2 (2), GRX3 (2), ISN1 (2)
Glu–H2O2		•	•	AFT1 (14), BOL2 (7), SNF5 (2), ZRT3 (2), RRP5 (2), ISN1 (2)
Glu–NaCl		•	•	–	ENA1–ENA2–ENA5 (7)
H2O2–NaCl		•	•	–	ENA1–ENA2–ENA5 (4)
Gal–Lac			•	No evolution	No evolution
Gal–H2O2			•	No evolution	No evolution
Gal–NaCl			•	No evolution	No evolution
Lac–H2O2			•	No evolution	No evolution
Lac–NaCl			•	No evolution	No evolution

We tracked changing barcode diversity during evolution and subsequently chose timepoints for reviving and isolating mutants (Supplementary Fig. 1). We created a pool of 889 uniquely barcoded mutants for fitness assays in all static and fluctuating environments. To measure fitness relative to the ancestor, we added the pool at 5% relative abundance to a preculture containing the ancestor strain, giving each barcoded lineage a starting frequency of ~5 × 10⁻⁵. We measured lineage frequencies over several cycles (eight generations per cycle) (Fig. 1b–d and Methods). Briefly, we define fitness as log frequency change, corrected by mean population fitness:

$$f_{i+1}=f_i{e}^{(s-\overline{s})}$$ (1)

Here $f_i+1$ represents the frequency of a lineage at timepoint $i+1$, which changes exponentially from timepoint $i$ if its fitness $s$ differs from mean population fitness $\overline{s}$, which we measure with barcoded neutral strains. We infer fitness in fluctuating environments separately for each component and define the overall fitness as the average of the two components.

To check the reproducibility of fitness assays, we included three biological replicates of each condition. Replicates are strongly correlated (Supplementary Fig. 2), but we exclude one of the ten fluctuating environments, Lac–H₂O₂, in analyses summarizing environments, because replicates in this environment are weakly correlated (Methods), but include it individually (Supplementary Figs. 2–5). To focus on mutants adaptive in their home evolution environments, we exclude those with fitness less than 0.05 in their home environment, or per-cycle fitness 5% greater than ancestral fitness, but results do not change for a higher threshold or for no threshold (Supplementary Fig. 6). Unsurprisingly, most mutants are adaptive in their home environment: excluding mutants below the adaptive threshold brings the size of the pool to 695 (78% of the initial pool). A comparison of mutants evolved from static versus fluctuating environments shows various patterns (Supplementary Fig. 7). Mutants evolved from static environments sometimes have higher fitness in their home environment than mutants evolved from fluctuating environments. Similarly, mutants from static environments sometimes have fitness tradeoffs, or higher fitness differences across environments, compared with mutants from fluctuating environments. Finally, mutants from fluctuating environments are more likely than mutants from static environments to be adaptive in all static environments, indicating that evolution in a fluctuating environment selects for generalist strategies that are more likely to be adaptive in conditions unseen during evolution.

Non-additive fitness and memory are common

To determine whether fitness in fluctuating environments is additive, we compare it with fitness in static environments, where we observe a diversity of behaviours within the pool (Supplementary Fig. 7). The null hypothesis of additive fitness in a fluctuating environment follows from the expectation that mutants will increase or decrease their frequency in a given condition regardless of the previous condition from which they were diluted (Methods). If mutants instead have non-additive fitness, this may indicate that transitions between different conditions have unique effects on mutants’ growth compared with transitions between the same condition (Fig. 1d). Indeed, previous studies have shown that environmental fluctuations can lead to changes in fitness, owing to either changes in the lag phase of growth^27,28 or other mechanisms^16,39 (Fig. 1e).

We find that non-additivity, or deviation from the time average, is common in our mutant pool (Fig. 2a). For brevity, we highlight three of the ten fluctuating environments, which include all five static environment components and which contain examples of mutants both overperforming and underperforming their time-averaged fitness (see Supplementary Fig. 4 for the remaining seven). To distinguish non-additivity from the effects of measurement noise, we compare observed non-additivity to the combined standard error of fitness measured in both static and fluctuating environments across all timepoints of biological replicates (a less conservative approach uses just the standard error across replicates; Supplementary Fig. 6 and Methods). We construct a significance score by subtracting the predicted time-averaged fitness from the observed fitness and dividing the resulting non-additivity by this standard error. We find that 30% of cases of non-additivity are significant at the 95% confidence level, or more than two standard deviations from the time average. The magnitude of non-additivity is greater than 0.25, or the median fitness of the pool in static environments, in 7% of cases, showing that fitness often deviates from additivity by a large magnitude.

Fig. 2 |. Non-additivity is common, but it masks even greater fitness changes.

a, Plotting fitness of the mutant pool in three fluctuating environments against the null hypothesis of the average of their fitness in the static environments reveals many cases of non-additivity, or differences between these two quantities. As explained in the text, we highlight three similar cases (not the same genotype) in green, magenta and blue, which correspond to colours in b–d. Data are presented as mean values of three replicates over two independent fitness assay experiments. Error bars represent the s.e.m., calculated by bootstrapping fitness measurements across all timepoints of all replicates (Methods). b, Frequency trajectories (solid lines; mean of three replicates) show that the static null prediction (dashed lines; also calculated from the replicate mean) is inaccurate and that overall non-additivity masks the totality of fitness change, or environmental memory. c, Frequency trajectories of non-additive mutants show reversals of the outcome expected based on static environment fitness. d, Frequency trajectories of additive mutants also show reversals, even if the overall trajectory and fitness are similar to what was expected. e, Non-additivity, or the difference between overall fluctuating fitness and the additive prediction, is plotted for all measurements in nine fluctuating environments. f, Memory, or the difference between fitness in fluctuating environment components and corresponding static environments, is greater in magnitude than non-additivity. g, Of the cases of non-additivity, 30% exceed a conservative 95% significance threshold (Methods). h, Of the cases of memory, 53% exceed the 95% significance threshold.

Even more striking than non-additive behaviours, mutants show large changes in fitness within components of fluctuating environments that may not be captured by non-additivity. To fully quantify the difference between static and fluctuating environments, we define environmental memory as the difference between observed fitness in each component of a fluctuating environment and fitness in the corresponding static environment. We expect zero memory if the fitness is fully defined by growth during the current cycle, but not if fitness is influenced by (that is, ‘remembers’) the previous cycle. We highlight several mutants with varying degrees of non-additivity that have dramatically different behaviours from expectations based on static environment fitness, leading to environmental memory (Fig. 2b–d). Observed frequency trajectories in the fluctuating environment (solid lines), excluding the first two cycles, are plotted against null expectation based on fitness in the component static environments and mean population fitness at each timepoint (dashed lines; Methods). In these plots, non-additivity appears as a deviation from the overall slope of the dashed line, while memory appears as a deviation from segments of the dashed line in individual components.

For example, the green plots in Fig. 2b (corresponding to green dots in Fig. 2a) show examples of mutants that have nearly additive fitness but exhibit memory, or slight changes within each component that are not fully captured by non-additivity. Figure 2c, however, shows mutants with highly non-additive fitness. In the leftmost plot, a mutant with high fitness in glucose and low fitness in galactose dramatically reverses its fitness in the fluctuating components, decreasing in frequency during the glucose cycle and increasing in frequency during the galactose cycle. The other plots in Fig. 2c show similarly dramatic fitness reversals. Fitness reversals even occur for mutants that have additive fitness (Fig. 2d; note that the finer scales in these plots show the high degree of additivity of these mutants’ fitness). In this case, overall trajectories reach the expected frequency, hiding memory in the overall measurement, as overperformance in one-half of the environment cancels underperformance in the other half. These results show not only that non-additivity in fluctuating environments is common, but also that even in cases in which the overall fitness across the whole fluctuating experiment is similar to the expectation, the component fitnesses often deviate sharply from the null expectation.

Unlike non-additivity, environmental memory includes the difference between observed and null in both halves of the fluctuating environment. Non-additivity (Fig. 2e) has a smaller magnitude than memory (Fig. 2f), which extends to roughly twice the range. As before, our conservative approach to determine significance compares memory with maximum possible measurement error (Methods), finding that 53% of measurements of memory (compared with 30% of non-additivity) are significant at the 95% confidence level (Fig. 2g,h; 41% of non-additivity and 66% of memory are significant under a less conservative approach; Supplementary Fig. 6). We confirm that memory is positively correlated across replicates (Supplementary Fig. 2) and that it cannot be explained by expected variation owing to noise in static environments or regression to the mean across timepoints (Supplementary Fig. 8 and Methods). The magnitude of memory in either component of a fluctuating environment is greater than 0.25 in 29% of cases (Supplementary Fig. 9; this is true of non-additivity in 7% of cases), illustrating that transitions in fluctuating environments lead to radical and widespread changes in fitness, making fluctuating environments inherently different from a sequence of static environments.

Memory correlates with fitness variance

Overall patterns of environmental memory reveal a tradeoff in which mutants gain fitness in one-half of a fluctuating environment but lose fitness in the other half. To visualize memory of the pool in each fluctuating environment, we first plot fitness in pairs of static environments, colouring mutants by fitness difference (Fig. 3a; distance from the equal-fitness dashed line). As shown in Fig. 3b–d, darker shades of blue denote higher fitness in the first environment, and darker shades of red indicate higher fitness in the second environment. We preserved this shading when plotting memory, or difference in fitness between each component of a fluctuating environment and the corresponding static environment. As shown in Fig. 3e, the null hypothesis, or no memory, sits at the origin of these plots. Data not on the origin can still represent additive fitness if they sit on the y = −x line because, in this case, fitness change in one-half of a fluctuating environment exactly cancels change in the other half. We observe not only that the measurements generally deviate from the origin, but also that they tend to cluster around the y = −x line, showing that fitness gains occur in one component of a fluctuating environment and losses occur in the other, and that they often match each other in magnitude (Fig. 3f–h). This negative trend appears in all ten fluctuating environments (Supplementary Fig. 4b), indicating that opposing fitness changes that are not fully captured by non-additivity are widespread and generic. Furthermore, mutants tend to gain fitness in the component corresponding to the static environment in which they do worse and lose fitness in the component corresponding to the static environment in which they excel, indicated by the recurrent pattern of blue dots in the upper left quadrant and red dots in the lower right quadrant. This surprising pattern suggests that memory is indeed caused by influence of the previous condition.

Fig. 3 |. Fitness in one component of a fluctuating environment influences fitness in the other component.

a, Plotting fitness across a pair of static environments indicates mutants that have higher fitness in the first environment (blue) and mutants that have higher fitness in the second environment (red). b–d, Fitness of the pool is shown in three pairs of static environments, where data show the mean of three replicates across two independent fitness assays: Glu versus Gal (b), Glu versus Lac (c) and H₂O₂ versus NaCl (d). e, Plotting the difference of fitness in one component of a fluctuating environment and fitness in the corresponding static environment shows memory, or how fitness changes in fluctuating environments. The y = −x line indicates mutants that change their fitness but are still additive. f–h, The change in fitness in the two components of fluctuating environments is negatively correlated, indicating that mutants gain fitness in one component and lose fitness in the other. The presence of blue dots in the upper left quadrants and red dots in the lower right quadrants indicates that fitness gains often occur in the environment with lower static fitness and fitness losses often occur in the environment with higher static fitness, suggesting that in a fluctuating environment, fitness is influenced by the previous condition: Glu versus Gal (f), Glu versus Lac (g) and H₂O₂ versus NaCl (h). i, We define fitness difference between two static environments as the distance from the equal-fitness line. j–l, Mutants with high mean fitness difference across all ten pairs are farther from the origin in these plots, meaning that they have more environmental memory: Glu versus Gal (j), Glu versus Lac (k) and H₂O₂ versus NaCl (l).

A possible explanation for one cycle of a fluctuating environment influencing fitness in the next is that a mutant may evolve to optimize transitions in a particular environment, whether static or fluctuating. In that case, a lineage’s physiological state at the end of one cycle might determine its transition to lag phase and growth in the following cycle, and thus lead to different consequences if the environment in the following cycle is the same or different. For mutants with bigger fitness differences across static environments, transitions between environments could foreseeably become more severe, leading to more changes in behaviour in a fluctuating environment. Indeed, the colour arrangement in Fig. 3f–h suggests that the fitness difference across a pair of static environments may correlate with fitness change when those two environments fluctuate. For example, dark red and dark blue dots, representing mutants with bigger fitness differences, tend to sit farther from the origin, indicating that they have more memory. There are some exceptions to this pattern, such as the dark red and blue dots clustered near the origin in Fig. 3f. These are mutants with large fitness differences in static Glu compared with static Gal, and which change their fitness in Glu–Gal relatively less than other mutants with similar fitness differences. However, calculating global mean fitness difference, rather than just local Glu–Gal fitness difference, reveals that these mutants have low global mean fitness difference. Overall, lower global mean fitness difference translates to less memory in fluctuating environments (or placement closer to the origin in these plots) (Fig. 3i–l).

As a more rigorous test of whether global mean fitness difference correlates with memory in a fluctuating environment regardless of local fitness difference, we calculate partial correlations of memory in each fluctuating environment with global mean fitness difference, controlling for and excluding local fitness difference. The partial correlations are positive and significant in nine out of ten fluctuating environments (all except for Lac–H₂O₂), even if static environments corresponding to the components of the focal fluctuating environment are excluded from the mean fitness difference (Supplementary Fig. 5 and Methods). This result shows that mutants with high fitness variance are uniquely sensitive to transitions in fluctuating environments and that a particular setting is not necessary to identify this characteristic sensitivity.

The result that bigger fitness differences in static environments propagate to bigger fitness changes in fluctuating environments can be summarized by plotting the mean fitness difference across all pairs of static environments against the mean fitness change across all fluctuating environments (Fig. 4a), with memory and non-additivity plotted separately in different colours. We confirm that fitness difference is an appropriate parameter to compare to fitness change by decomposing it into two independent parameters, both of which contribute towards explaining variation in fitness change in a general additive model (Supplementary Fig. 10). While both memory and non-additivity correlate with mean fitness difference, memory has a nearly one-to-one correlation, meaning that in fluctuating environments, a mutant will, on average, change its fitness by an amount nearly equal to its average fitness difference across static environments. While this is an average effect, it could manifest in a particular fluctuating environment as a mutant reversing its fitness, as we saw in the trajectories in Fig. 2c,d. In addition, the negative trends in Fig. 3f–h suggest that mutants compensate for fitness increases in one component of a fluctuating environment with fitness decreases in the other component, suggesting that fitness reversals could be common.

Fig. 4 |. Fitness reversals in fluctuating environments are common and recapitulated by a simple model of lag time evolution.

a, Two distributions, of mean memory and mean non-additivity, are shown. Data are presented as mean values of three replicates over two independent fitness assay experiments. Mean memory, or mean absolute difference between fitness in a static environment and fitness in the corresponding fluctuating component, correlates strongly with mean fitness difference across static environments. This nearly one-to-one correlation indicates that, on average, mutants change their fitness in a fluctuating environment by an amount nearly equal to their fitness difference across static environments. Mean non-additivity, or mean difference between fluctuating fitness and average static fitness, is a lower bound of mean memory. b, The frequency of fitness reversals in fluctuating environments is quantified by the fraction of the time that the other static environment fitness is a better predictor of fitness in half of a fluctuating environment, or 29% of overall cases. The top 10% of mutants by mean fitness difference more often reverse their fitness. c, Fitness in one replicate of a static environment is better predicted by a replicate of another static environment than another replicate of the same static environment 2% of the time. The same is true for replicates of fluctuating environment components in 13% of cases, a noisier control because it contains half as many timepoints. d, A simple model reproduces the correlation pattern shown in a. e, The model reproduces the difference between mutants with high and low mean fitness difference shown in b. f, The ancestor dominates growth in the model, in which mutants’ fitness is determined by comparative lag (dis) advantages, which shift towards the mean of their distribution across static environments when the environment fluctuates.

Fitness reversals are common in fluctuating environments

To determine how often fitness reversals occur, we asked which of the two static environments is a better predictor for fitness in a component of a fluctuating environment (for example, is static Glu fitness or static Gal fitness better at predicting the Glu component of fitness in fluctuating Glu–Gal?). We categorize the results as the same static environment being a better predictor (for example, static Glu better predicts fluctuating Glu), the other static environment being a better predictor (for example, static Gal better predicts fluctuating Glu), or a borderline case if the prediction and result vary by less than 0.05 (we choose this threshold as the median standard error of the fluctuating component fitness is 0.046). Overall, the other static environment is a better predictor than the same static environment in 29% of cases. In the top 10% of mutants ranked by mean fitness difference, this statistic increases to 39%, while for the bottom 10%, it decreases to 11% (Fig. 4b). As a control, we predict fitness in static environment replicates with either other replicates of the same static environment or replicates of another static environment; as a second control, we predict fitness in fluctuating environment component replicates with other replicates either from the same component or from the other component (Fig. 4c). We expect both controls to be noisy, as they use replicates rather than averages of replicates, and the second control to be especially noisy, as fluctuating environment component measurements contain half as many timepoints as static environment measurements. Indeed, the second control represents the noisiest upper bound (13%) as opposed to the first control (2%). In either case, fitness reversals in fluctuating environments occur more often than would be expected owing to measurement error. Most strikingly, mutants with the biggest fitness differences reverse their fitness most often, despite these reversals requiring greater change.

To explain potential mechanisms of fitness change and reversal in fluctuating environments, we use a simple mathematical model describing our fitness assays (Fig. 4d–f, Methods and Supplementary Note 1). We assume that, owing to a starting frequency orders of magnitude higher than that of the mutants, the ancestor dominates growth and sets the time to resource depletion, before which mutants increase or decrease their frequencies (Fig. 4f). We assume that sensitivity to transitions is more likely to affect lag than growth⁴⁰, and that mutants’ fitness changes are primarily due to changes in lag time compared with the ancestor, but that they retain the ancestor’s growth rate for a given environment. Mutants with more variance in fitness across static environments have a wider range of lag (dis)advantages. Guided by partial correlations between memory and global fitness differences as described above (Supplementary Fig. 5), we also assume that in a fluctuating environment, mutants shift their lag (dis)advantages proportionately to the width of the distribution across all static environments, regardless of local fitness difference in the pair of fluctuating environments. In addition, we eliminate differences in yield across environments as a cause of non-additivity and memory (Supplementary Note 1). These assumptions recapitulate the result that fitness change in fluctuating environments increases with mean fitness difference across static environments, and that memory exceeds non-additivity (Fig. 4d). We fit the overall result that the other static environment is a better predictor for fitness in a fluctuating environment component in 29% of cases by setting the shift in lag (dis)advantage to 80% of the distance towards the mean of a mutant’s distribution. The model also recapitulates that mutants with more variance in fitness reverse their fitness more often, as their larger fitness variance means the results are less likely to be borderline cases (Fig. 4e). These results suggest that lag time evolution could be a cause of fitness reversals in fluctuating environments, but further measurements are needed to support this hypothesis.

Environment-specific mutations appear associated with memory

In search of a genetic mechanism for lag time changes in mutants with high fitness variance in fluctuating environments, we whole-genome sequenced a subset of the mutant pool, obtaining 352 sequences (Methods). Most of our mutants contain only unique mutations, but several of the environments produced mutants with mutations in the same genes. Of such multi-hit genes, only five experienced more than five hits (Table 1). These five genes include ENA1–ENA2–ENA5, which in tandem encode a sodium efflux pump known to be necessary for resuming growth following transfer into a high-salt environment⁴¹ and here showed repeated copy number amplifications during evolution in a high-salt environment (18 out of 43 NaCl mutants, 7 out of 27 Glu–NaCl mutants, 3 out of 34 H₂O₂–NaCl mutants); in addition, the genes AFT1 and BOL2, part of an iron-sensing and uptake pathway^42,43, had single-nucleotide polymorphisms (SNPs) in 28 out of 72 mutants evolved in Glu–H₂O₂ (including heterozygous SNPs, and there were 7 additional mutants evolved in other environments with heterozygous SNPs in these genes). We also assayed 359 mutants for ploidy, 322 of which are adaptive (Methods), as the DNA barcoding process sometimes induces self-diploidization³, categorizing 160 out of 322 adaptive mutants as diploid. To narrow this list to pure diploids lacking other adaptive mutations, we eliminated the iron- and salt-related mutations from the identified diploids, leaving 138 ‘pure’ diploids (note that we do not eliminate diploids with low-frequency mutations, so we cannot be sure how much of their fitness is due to these mutations versus diploidy alone). In summary, highly repeated mutations fall into three groups: two that appear to have evolved to sense particular environments, and environment-nonspecific diploids.

We categorize these groups of mutations by plotting their mean fitness difference and mean memory. In agreement with a previous study showing that pure diploids benefit from low-variance, modest gains in fitness across a range of environments¹², we find that diploids have moderate fitness variance and memory (Fig. 5a). Iron-sensing mutants have high fitness variance and memory, while salt-sensing mutants have moderate fitness variance and memory. However, when the latter group is subdivided into those with high- and low-copy number amplifications, we see that more copy number amplifications lead to comparatively higher fitness variance and memory (Fig. 5b), showing that more extreme forms of this environment-sensing mutation increase fitness variance and memory. These results offer a mechanistic explanation of the adaptive strategy for a subset of mutants: having an ability to sense iron or salt in their environment gives them a high fitness advantage in the relevant environment but probably comes with a costly tradeoff, such as an increased lag, when the environment changes.

Fig. 5 |. Environment-sensing mutations are associated with higher fitness variance and memory.

a, Three classes of mutants are plotted by mean fitness difference and mean memory, both individually and with the overall mean indicated by labels (error bars are the standard error of the overall mean). Diploids (n = 138) have moderate mean fitness variance and memory. Iron-sensing mutants (n = 35) have higher fitness variance and memory, while salt mutants (n = 28) do not. b, Subdividing the pool of salt pump mutants into high (n = 3) and low (n = 25) copy number amplification reveals that more amplification leads to higher mean fitness variance and memory. A single SNP mutant was observed in the same set of genes as the copy number variants.

Environmental memory observed in mutants from previous study

The observation that fitness in one component of a fluctuating environment influences fitness in the other component suggests that the physiological state of a population at the end of its growth cycle influences its growth in the following cycle. This result agrees with previous measurements of yeast in static environments, which showed that fitness accrued in the final stage of the growth cycle is realized during the lag phase of the following cycle for a set of highly adaptive nutrient-sensing pathway mutants evolved from a minimal glucose-limited medium²³. Subsequent measurements revealed that these mutants are deleterious when the medium is supplemented with 0.5 M sodium chloride¹². Based on the findings of our study, we would expect that these glucose-sensing mutants’ large fitness variance would lead to environmental memory in fluctuations. To test this expectation, we grew those mutants in an environment fluctuating between optimal and high-salt conditions, indeed finding that their frequencies crashed in optimal conditions after exposure to high-salt conditions (Supplementary Fig. 11). These results echo the environmental memory presented in this study, in which we evolved and measured mutants in a complex instead of minimal medium. The agreement across differing types of medium and fluctuations (both stressors and alternate carbon sources) suggests a general mechanism that causes strains, particularly those with environment-sensing mutations, to change their lag phase in one condition after exposure to another.

Discussion

Natural environments are consistently perturbed by environmental fluctuations, and the amplitude and frequency of some fluctuations are expected to increase⁴⁴. An additional concern is the ability of emerging viruses, drug-resistant bacteria and mutating cancer cells to adapt to ever-shifting host environments. Predicting evolution in fluctuating environments is therefore important, but experiments have thus far mostly focused on adaptation to static conditions. Our study finds that fitness in a fluctuating environment can be profoundly altered by transitions that are lacking in static environments. Moreover, these changes are at least partially concealed by measurements of fitness across the complete cycle of fluctuating environments, owing to a tradeoff that causes fitness to increase in one component of a fluctuating environment and to decrease in the other component. We show that mutants with high fitness variance across environments are uniquely sensitive to transitions, reversing their fitness most often in fluctuating environments, even when this variance is measured across static environments not included in the fluctuating environment components. As a result, predicting evolution in fluctuating environments based on static environments may be difficult.

While extrapolating from static to fluctuating environments may be difficult, our study also suggests that changes in fluctuating environments may be governed by a global structure whereby a strain’s fitness variance in static environments predicts its fitness change in fluctuating environments. A related phenomenon apparently detrimental to predicting evolution, epistatic interactions between mutations, has also been elucidated by similar global patterns. Originally observed in empirical studies^6,45,46, these patterns reveal a structure whereby a strain’s background fitness predicts the fitness effect of a new mutation, leading to unifying models⁴⁷ that have recently been applied to a novel context of predicting ecological function from species interactions⁴⁸. The success of these global patterns in interpreting interactions between mutations and between species bodes well for the problem outlined here of interpreting interactions between environments.

Our data suggest that memory causes fitness in the previous condition to influence fitness in the current condition, resulting in a pattern in which greater differences in fitness across environments lead to greater fitness changes in fluctuating environments. While we observe this pattern universally (Supplementary Fig. 5), it is also true that some fluctuating environments induce more non-additivity and memory than others (Supplementary Fig. 9). Furthermore, memory across conditions, when varying the previous or current condition, shows heterogeneous positive and negative correlations (Supplementary Fig. 12). Altogether, these results suggest that while memory is strong and pervasive, and produces a pattern that appears generically across environments, it is also context dependent. Further investigation is needed to understand how memory manifests in various settings.

To further generalize the trend that we show between fitness variance in static environments and fitness change in fluctuating environments, more investigation is needed beyond our comparison of a set of recently evolved mutants with their ancestral strain. For example, other systems such as ecological communities approaching stable states should be examined for the existence of this pattern. We grew the mutants in our pool from very low relative frequencies in the presence of a majority of ancestor cells to prevent frequency-dependent effects, but studies of frequency-dependent interactions in communities have also shown evidence of additive^49,50 and non-additive^51,52 effects, as well as growth and lag tradeoffs that support long-term coexistence⁵³. Our study also did not address the effects of the timescale and order of fluctuations, nor did we examine environments fluctuating between more than two conditions. In all cases, mathematical models offer a promising tool for interpreting how outcomes may be altered by fluctuation- and frequency-dependent effects⁵⁴.

Our whole-genome sequencing results suggest that sensing mutations may lead to higher fitness variance and environmental memory. In contrast to previous studies^3,11, however, most of our sequenced mutants contain only unique mutations. This result might reflect a diversity of adaptive mechanisms in the evolutionary conditions, the relatively short timescale of the evolution experiments or undetected adaptations, such as aneuploidy⁵⁵ or epigenetic modifications. Epigenetically induced phenotypic heterogeneity could contribute to a bet-hedging strategy^32,33,56, increasing geometric fitness at the cost of arithmetic fitness across conditions⁵⁷. If such a generalist strategy decreases fitness differences across environments, considering our results, it should also decrease memory in fluctuating environments. Our finding that mean fitness difference correlates with memory independent of local fitness difference (Supplementary Fig. 5) suggests a mechanism underlying some mutants’ sensitivity to transitions and others’ lack thereof. Transcriptomic and epigenomic analysis of mutants in static and fluctuating environments could shed light on phenotypic plasticity or epigenetic mechanisms underlying memory.

Predicting the effects of increasing environmental fluctuations is an important challenge in ecology and evolutionary biology. Here we have shown that the widespread existence of memory in fluctuating environments makes them qualitatively different settings than just the sum of their component static environments. Our study shows large memory effects in single-celled eukaryotic microorganisms that reproduce asexually, and it remains to be seen whether our results can be extended to other types of microorganisms or multicellular organisms. We observe these memory effects as fitness changes in fluctuating environments, probably because the growth environment in one cycle influences the lag phase in the following cycle. These serial transfers impose a boom-and-bust growth cycle on yeast that is generic to natural ecological contexts in which populations expand by exhausting resources and subsequently enter a stationary phase, and an organism’s fitness is determined by its ability to reproduce before resources are depleted by the surrounding community. Transitions from one cycle to the next occur in both static and fluctuating environments in our experiments, but the latter impose more severe shifts, especially for mutants with greater fitness variance across static environments. This trend reveals that while null expectations about fitness in fluctuating environments are inadequate, their failure illuminates biological patterns and avenues for future investigation.

Methods

Long-term evolution experiments

Founding populations.

The barcoded yeast population used in this study was constructed in a previous study³⁵ and contains around half a million uniquely barcoded transformants. The library was created from an S288C derivative, BY4709, in which a ‘landing pad’ was inserted into a neutral location in the yeast genome that allows high-frequency, site-specific genomic integration of plasmids via the Cre–loxP recombination system. We created new stocks of this library and sequenced the barcode region to confirm a high diversity of ~500,000 barcodes before beginning batch culture experiments.

Evolution batch cultures.

We evolved the population in ten evolution conditions (Table 1), which are composed of static or fluctuating regimes of five environments: Glu, Gal, Lac, H₂O₂ and NaCl. We began evolution experiments by growing a single overnight 15 ml preculture containing the founding population in synthetic complete (SC) medium with 1.5% glucose (Glu medium). We then transferred 400 μl of this preculture to all evolution environments, containing 100 ml of various medium types. All cultures were evolved by serial batch culture in 500 ml Delong flasks (Bellco) at 30 °C and 223 rpm. We diluted cultures every 48 h 250× by inoculating 400 μl of culture into 100 ml fresh medium. The SC base medium (per litre: 2 g US Biological Drop-out Mix Complete, 6.7 g RPI yeast nitrogen base) was supplemented with either 1.5% d-glucose (RPI; Glu), 1.5% d-galactose (RPI; Gal) or 0.7% sodium dl-lactate (Sigma; Lac). In the remaining two environments, we supplemented the Glu medium with either 0.5 M sodium chloride (RPI; NaCl) or 2.5 mM hydrogen peroxide (Ward’s; H₂O₂). All media were prepared in the weeks before the experiments and stored at 4 °C until the final days before use, when we pre-warmed them in a 30 °C incubator. We tested hydrogen peroxide concentration in the H₂O₂ medium after weeks of storage using the MQuant peroxide test kit (for 1–3–10–30–100 mg l⁻¹) and found that the hydrogen peroxide had reduced to ~60% of the original concentration. After learning of this effect, we added hydrogen peroxide directly to media during the dilution and transfer step, rather than during medium preparation, in the subsequent fitness assays (described below). In contrast to short-term fitness assays, which included three biological replicates for each condition (as described below), evolution experiments contained one or two replicates. We evolved in all fluctuating environments with two replicates except for Glu–Gal, which had one replicate, and we evolved in static environments with one replicate, except for Glu and NaCl, both of which had two replicates. We propagated the cultures for 20–23 growth cycles and stored 2 ml saturated culture by aliquoting 1 ml cells into 1 ml 50% glycerol in two Eppendorf tubes and storing at −80 °C. The remainder of the cell culture was centrifuged, and the cell pellet was resuspended in 2 ml sorbitol solution (0.9 M sorbitol, 0.1 M Tris–HCl (pH 7.5), 0.1 M EDTA (pH 8.0)), aliquoted into two Eppendorf tubes and stored at −20 °C for genomic extraction.

Barcode amplicon and whole-genome sequencing

DNA extraction.

We extracted genomic DNA from each sample using the Norgen Fungi/Yeast Genomic DNA Isolation 96-Well Kit, supplemented with lyticase. In collaboration with Norgen sales representatives and research scientists, we modified this kit to use 96-well plates for all steps. We extracted DNA using ~10% of our spun-down samples, or about 10⁹ cells. Final DNA yield was assayed with a Biotek fluorescent plate reader and averaged ~4 μg per sample.

Barcode amplicon library preparation and sequencing.

To track changes in barcoded lineage frequency over the course of evolution, we conducted PCR amplification of the barcoded region with a two-step protocol. The primers used in the first step of amplification are the same as described in ref. 12, but with a different amplification protocol. In both steps of PCR, we performed three reactions per sample in the standard Q5 master mix (per 50 μl reaction):

• 10 μl 5× Q5 reaction buffer

• 1 μl 10 mM dNTPs

• 2.5 μl 10 μM forward primer

• 2.5 μl 10 μM reverse primer

• 0.5 μl Q5 High-Fidelity DNA Polymerase

• DNA

• Nuclease-free water (to 50 μl)

In the first step, we aimed for 100 ng of genomic DNA template (or approximately 1/1,000 of total DNA in a saturated 100 ml experiment) per reaction, but as we added equal volumes to all reactions, the actual amount was sometimes as low as 25 ng or as high as 250 ng. For the first cycle, we amplified the barcode region with the following programme:

1. 98 °C for 30 s

2. 98 °C for 10 s

3. 62 °C for 20 s

4. 72 °C for 30 s

5. Repeat steps 2–4 29× for a total of 30 cycles

6. 72 °C for 3 min

7. 4 °C hold

The sequences of the first-step primers are listed below. Note that these primers contain unique molecular identifiers, denoted by the sequence of ‘N’ nucleotides, which were used to control for PCR amplification bias in previous studies. In this study, we did not use the unique molecular identifiers.

Forward primers used were as follows (boldface sequences are unique, while other sequences bind to homologous regions):

Primer name	Sequence
F201	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN CGATGTT TAATATGGACTAAAGGAGGCTTTT
F202	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN ACAGTGT TAATATGGACTAAAGGAGGCTTTT
F203	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN TGACCAT TAATATGGACTAAAGGAGGCTTTT
F204	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN GCCAATT TAATATGGACTAAAGGAGGCTTTT
F205	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN ATCACGT TAATATGGACTAAAGGAGGCTTTT
F206	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN CAGATCT TAATATGGACTAAAGGAGGCTTTT
F207	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN GGCTACT TAATATGGACTAAAGGAGGCTTTT
F208	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN TAGCTTT TAATATGGACTAAAGGAGGCTTTT
F209	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN TTAGGCT TAATATGGACTAAAGGAGGCTTTT
F210	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN ACTTGAT TAATATGGACTAAAGGAGGCTTTT
F211	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN GATCAGT TAATATGGACTAAAGGAGGCTTTT
F212	TCGTCGGCAGCGTC AGATGTGTATAAGAGACAG NNNNNNNN CTTGTAT TAATATGGACTAAAGGAGGCTTTT

Reverse primers used were as follows:

Primer name	Sequence
R301	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN TATATACGC TCGAATTCAAGCTTAGATCTGATA
R302	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN CGCTCTATC TCGAATTCAAGCTTAGATCTGATA
R303	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN GAGACGTCT TCGAATTCAAGCTTAGATCTGATA
R304	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN ATACTGCGT TCGAATTCAAGCTTAGATCTGATA
R305	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN ACTAGCAGA TCGAATTCAAGCTTAGATCTGATA
R306	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN TGAGCTAGC TCGAATTCAAGCTTAGATCTGATA
R307	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN CTGCTACTC TCGAATTCAAGCTTAGATCTGATA
R308	GTCTCGTGGGCTCGG AGATGTGTATAAGAGACAG NNNNNNNN GCGTACGCA TCGAATTCAAGCTTAGATCTGATA

After checking amplification for ~25–50 randomly chosen reactions on a gel, we then diluted the step 1 product 500× into the second reaction, by diluting 25× into nuclease-free water, and then 20× into the same master mix listed above. The only difference between step 1 and 2 master mix was the primers–we used IDT for Illumina UD Indexes in the second step (https://support-docs.illumina.com/SHARE/AdapterSequences/Content/SHARE/AdapterSeq/Illumina_DNA/IDTIl-luminaUDIndexes.htm), with unique pairs of forward and reverse primers for each reaction to avoid error from index hopping or template switching⁵⁸. We then ran the following programme to attach the IDT indices to barcode amplicons:

1. 98 °C for 30 s

2. 98 °C for 10 s

3. 62 °C for 20 s

4. 72 °C for 30 s

5. Repeat steps 2–4 11× for a total of 12 cycles

6. 72 °C for 3 min

7. 4 °C hold

We again checked for amplification of randomly chosen reactions on a gel and pooled the step 2 product across the three reaction replicates, and then pooled samples in groups of 96 using 10–15 μl per sample. We then performed a standard PCR purification protocol in one column per sample, eluting into 100 μl nuclease-free water, and measured concentration with a Qubit fluorometer. The final concentration ranged from ~100 ng μl⁻¹ to 200 ng μl⁻¹. Our samples were then sent to Admera Health (https://www.admerahealth.com/) for quality control (qPCR and either Bioanalyzer or TapeStation) and sequencing. We used 2 × 150 paired-end sequencing along with index sequencing reads on Illumina machines using patterned flow cells (either HiSeq X or NovaSeq X). All amplicon samples were sequenced with at least 20% genomic DNA spiked in (either whole genomes or phi-X) to ensure adequate diversity on the flow cell.

Whole-genome library preparation and sequencing.

We prepared libraries with the Illumina DNA Prep kit (ILMN DNA LP (M) Tagmentation (96 samples, IPB)). We followed the manufacturer’s protocol, with the exception that we used one-fifth the normal volume of reagents, allowing us to use the kit for five times the normal amount of samples, based on lab members’ and others’ success with this modification to the protocol. We sent our libraries to Admera Health (https://www.admerahealth.com/) for quality control (qPCR and either Bioanalyzer or TapeStation) and sequencing. We used 2 × 150 paired-end sequencing along with index sequencing reads on NovaSeq X Illumina machines.

Tracking lineage dynamics during evolution

Processing amplicon sequencing data.

Using BarcodeCounter2 (ref. 59), sequencing reads from evolution timepoints were first aligned to the reference barcode region using Bowtie2. Based on this alignment, both condition and lineage barcodes were extracted. Reads were split into different files based on their multiplexing tags, which were unique for each sample. We then clustered reads using Bartender⁶⁰ with Hamming distance 2 and seed length 8. Examples of evolution trajectories can be seen in Supplementary Fig. 1, and full barcode count data for all evolution experiments are available on Github (https://github.com/clare-abreu/environmental_memory/tree/main/data/Evo_counts). To isolate mutants, we chose a single timepoint from each long-term evolution experiment where adaptive trajectories were sufficiently diverse or where the most adaptive lineages reached a frequency of ~10⁻³, for thawing and cell sorting. The logic here is that we wanted to isolate a diversity of adaptive mutants and thus did not want to choose an early timepoint where beneficial mutations had not yet occurred or a late timepoint where one or several adaptive mutants had taken over the population.

Isolation, selection and pooling of mutants for fitness assays

Cell sorting of thawed stocks.

After timepoints were chosen from each long-term evolution experiment, yeast clones were isolated from frozen glycerol samples from the chosen timepoints. Frozen stock (~50 μl, containing ~5 × 10⁶ cells) was diluted into 500 μl phosphate-buffered saline plus 1 μl propidium iodide and used for flow cytometry sorting. Single cells were sorted into 96-well plates with 100 μl yeast extract–peptone–dextrose (YPD) medium in each well. Five plates of cells (480 cells) were sorted for each evolutionary replicate (80 plates in total). Sorted cells were grown at 30 °C for 3 days without shaking and reached saturation by day 3. Saturated cell culture (~5 μl) was removed from each well and inoculated into a different 96-well plate, with 100 μl fresh YPD medium in each well. These replicated plates were grown at 30 °C for 2 days without shaking to reach saturation and used for subsequent barcode identification. The remainder of the saturated cell culture was mixed with 100 μl 50% glycerol and stored at −80 °C.

DNA barcode identification by Metagrid.

High-throughput barcode sequencing of the plates of isolated and grown cells was performed as in ref. 10, with the exception that cell lysis was performed by boiling 20 μl of saturated cell culture in 20 mM NaOH. After sequencing, some wells were eliminated owing to low coverage. Of the remaining wells, we eliminated those with less than 60% of reads mapping to the top barcode and those in which the number of reads of the top barcode was equal to or less than 1.5 times the number ofreads of the next barcode.

Selection and pooling of mutants.

From the ~3,700 wells in which we had identified single barcodes per well, we selected 889 clones for our mutant pool. We chose mutants with high fitness in their evolutionary trajectories based on Fitmut2 (ref. 61) inferences and ensured that no overlap existed between barcode sequences. We used default parameters for FitMut2, with 8 generations per cycle and a mutation rate of 10⁻⁵. Using FitMut2, we inferred the fitness, establishment time and likelihood that the mutants were adaptive (defined as the probability that their fitness is greater than 0) from lineage trajectories over the course of evolution (Supplementary Fig. 1). We wanted to include all mutants that appeared to be adaptive, so we selected mutants meeting any of the following criteria: (1) their inferred fitness from FitMut2 was greater than 0.51; mutants with fitness above 0.51 have large inferred fitness effects and constitute the tail of the distribution of fitness effects. In addition, previous work has found that auto-diploidization is a common mutation that tends to confer a smaller fitness advantage between 0.1 and 0.25 (ref. 3), which we indeed see in the distribution of fitness effects plots inferred from FitMut2 in our case. (2) The probability that they were adaptive was greater than 0.5; such mutants are more likely than not to be adaptive based on FitMut2 inference. (3) They reached a final frequency of 10⁻⁵; such mutants increased in frequency over the evolution with a large population size by an order of magnitude or more, and could have been missed by FitMut2. (4) They reached a frequency of 10⁻⁵ at the 6 cycles before the final one (to account for environments where a small number of barcoded lineages took over the population, reaching frequencies close to 1). In addition, we added ten randomly selected weakly adaptive mutants (defined to have probability adaptive between 0.125 and 0.5). On average, 89 clones were selected from each evolution condition, but counts ranged from a minimum of 40 (H₂O₂) to 120 (Glu, Glu–H₂O₂ and Glu–NaCl) clones per condition. We revived cultures from frozen glycerol replicate plates and allowed them to grow for 2 days in fresh SC medium before pipetting ~10 μl of each selected barcode into subpools, which we then consolidated into a final pool, weighting volumes to aim for equal frequency of all barcodes.

Short-term fitness assays

All fitness assays were performed using three biological replicates. As described previously^3,12,23, growth competitions were set up between a pool of barcoded mutants and a reference strain, although certain protocol details were changed. We grew three separate overnight pre-cultures in 25 ml SC + 1.5% glucose for each round of assays: (1) ancestor reference strain, (2) mutant barcode pool and (3) barcoded neutral strains with fitness equal to that of the ancestor. We then mixed these cultures at a 93:5:2 ratio (correcting for measured optical density). This ratio allows mutants to compete against the ancestor rather than against each other, helps to minimize the change in average fitness throughout the competition experiment and reduces the effect of any frequency-dependent fitness effects as well as any fitness-affecting interactions among the strains that may occur. The change in the frequency of each barcode over time reflects the fitness of the adaptive mutant possessing that barcode, relative to the rest of the population, which is primarily composed of the ancestor (we excluded later timepoints in some conditions in which the ancestor proportion decreased to less than 50%; Supplementary Fig. 12). We inoculated 400 μl of the mixed culture (~5 × 10⁷ cells) into 100 ml of fresh media in 500 ml DeLong flasks. As in the long-term evolution experiments, this culture was then grown at 30 °C in an incubator shaking at 223 rpm for 48 h. After 48 h of growth, 400 μl of saturated culture was transferred into fresh medium of the same type. In static environments, we transferred the serial dilution four more times, yielding five cycles over which to measure the rate at which a barcode’s frequency changed, and in fluctuating environments, we transferred five more times for six cycles.

After each transfer of 400 μl, the leftover culture was frozen for sequencing barcodes later. To prepare this culture for freezing, it was transferred to 50 ml conicals, spun down at 3,000 rpm for 5 min, resuspended in 2 ml of sorbitol freezing solution (0.9 M sorbitol, 0.1 M Tris–HCl (pH 7.5), 0.1 M EDTA (pH 8.0)), aliquoted into two wells of a 2 ml 96-well plate and stored at −20 °C.

We performed DNA extraction and library preparation with the same protocol described above for evolution experiments, with one exception: we used restriction digest to cut the ApaLI restriction site in the middle of the reference strain’s barcode region. This step prevents the ancestor from being sequenced, affording greater sequencing coverage to the mutant pool. We performed the digest after DNA extraction and again after the second step of the PCR, adding 1–2 μl ApaLI (NEB number R0507L) and 5 μl 10× Cutsmart to 43 μl samples and incubating at 37 °C for at least 2 h (or up to overnight).

Fitness inferences and data analysis

Processing amplicon sequencing data.

As with the sequencing data from evolution experiments, we first extracted barcodes with BarcodeCounter2 (ref. 59). We then used BarcodeCounter2 to map extracted barcodes to our known list of mutants in our pool.

Fitness inference.

We inferred fitness of mutants by solving equation (1) for all mutants at each timepoint for each condition and replicate: $f_{i+1}=f_i{e}^{(s-\overline{s})}$, where $f_{i+1}$ represents the frequency of a lineage at timepoint $i+1$, which changes exponentially from timepoint $i$ if its fitness $s$ differs from mean population fitness $\overline{s}$.

We measure mean population fitness at each timepoint using ~50 uniquely barcoded neutral strains, which were isolated and identified as neutral, or having fitness equal to that of the ancestor⁶². As we set the ancestor’s fitness to zero, we can solve for mean fitness by plugging the neutral strains’ frequencies $n$ into equation (1):

$$n_{i+1}=n_i{e}^{\left(0-\overline{s}\right)}$$ (2)

Solving for mean population fitness $\overline{s}$ gives:

$$\overline{s}=-\ln \left(\frac{n_{i+1}}{n_i}\right)$$ (3)

We take the average of equation (3) over all neutral lineages at each timepoint $i+1$ of each condition and replicate, and plug the result into equation (1) to determine the fitness of each mutant:

$$s=\ln \left(\frac{f_{i+1}}{f_i}\right)+\overline{s}=\ln \left(\frac{f_{i+1}}{f_i}\right)-\ln \left(\frac{n_{i+1}}{n_i}\right)$$ (4)

We then average this fitness across all timepoints for a given mutant, replicate and condition. We exclude the first timepoint, corresponding to the initial mixture of ancestor, neutrals and mutants described above, from all estimates. Static environment fitness assays include five subsequent timepoints, while fluctuating environment fitness assays include six subsequent timepoints, to grow the population in three cycles of each condition. In fluctuating environments, we exclude the second timepoint in addition to the first, assuming the first two cycles are a sort of ‘preculture’, with the exception of two fluctuating environments (Glu–H₂O₂ and Lac–H₂O₂) in which the barcoded pool reached a frequency greater than 50% in the final timepoint (Supplementary Fig. 12). In those conditions, we excluded the final timepoint and included the second timepoint. In addition, we excluded the final timepoint from the static environment H₂O₂ for the same reason.

In static environment inferences, we average fitness as calculated by equation (4) across all timepoints, while in fluctuating environment inferences, we infer fitness separately for each of the two components and define the overall fitness as the average of the two components. Each component consists of two different cycles, and we average these two estimates. In both static and fluctuating environment inferences, we then average fitness across all relevant cycles in all three replicates to get a mean fitness estimate for each mutant.

We calculate the standard deviation of each mutant’s fitness by assuming normally distributed errors and minimizing the negative log likelihood of a Gaussian distribution using the minimize function from the scipy.optimize module in Python, with the limited-memory Broyden–Fletcher–Goldfarb–Shanno with box constraints optimization method, setting the initial guess for mean fitness to 0 and the standard deviation to 0.1. To calculate the standard error of each mutant’s fitness, we bootstrapped this minimization with 250 trials, sampling with replacement from all fitness measurements across all timepoints.

In rare cases, some mutants were not detected at all timepoints, either because they went extinct or because no counts were sampled. We exclude such timepoints from our fitness inferences. In the case of static environments, if a mutant reached a detectable frequency at a later timepoint, we include this timepoint, dividing equation (4) by the number of cycles between detectable frequencies. This is not possible in fluctuating environments because inferring fitness separately for the two fluctuating environment components requires measuring frequency change between consecutive timepoints only.

Calculating static null predictions in fluctuating environments.

In Fig. 2b–d, we plot observed trajectories in fluctuating environments compared with predicted trajectories based on static environment fitness and mean population fitness at each timepoint (dashed lines, Fig. 2b–d). To plot these predicted trajectories, we used equation (1): $f_{i+1}=f_i{e}^{(s-\overline{s})}$. Given a mutant’s known initial frequency at timepoint 2 ($f_2$), we calculated and plotted the frequency at timepoint 3 ($f_3$) by plugging in that mutant’s fitness ($s$) in the static environment corresponding to the fluctuating environment component between timepoints 2 and 3, as well as mean population fitness ($\overline{s}$) at timepoint 3. Mean population fitness is calculated using equation (2), averaged over all neutral lineages.

Defining additive fitness.

Our null hypothesis for additive fitness in a fluctuating environment follows from the same logic used to infer fitness in a static environment. As in equation (1), frequency changes over two cycles in two environments (1 and 2):

$$f_2=f_1{e}^{(s_2-\overline{s_2})};f_1=f_0{e}^{(s_1-\overline{s_1})}$$ (5)

We then combine the two cycles into overall frequency changes:

$$f_2=f_o{e}^{((s_1+s_2)-(\overline{s_1}+\overline{s_2}))}$$ (6)

The null hypothesis that fitness in a fluctuating environment is the arithmetic mean comes from dividing by two to define fitness in the same per-cycle units as in static environments:

$$\frac{s_1+s_2}{2}=\frac{1}{2}\left(\ln \left(\frac{f_2}{f_0}\right)+(\overline{s_1}+\overline{s_2})\right)$$ (7)

To solve for mean fitness as in equation (4), we use barcoded neutral strain frequencies in each of the two cycles:

$$s_2=\ln \left(\frac{f_2}{f_1}\right)-\ln \left(\frac{n_2}{n_1}\right);s_1=\ln \left(\frac{f_1}{f_0}\right)-\ln \left(\frac{n_1}{n_0}\right)$$ (8)

This leads to the overall fitness in a fluctuating environment over two cycles:

$$\frac{s_1+s_2}{2}=\frac{1}{2}\left(\ln \left(\frac{f_2}{f_1}\right)+\ln \left(\frac{f_1}{f_0}\right)-\left(\ln \left(\frac{n_2}{n_1}\right)+\ln \left(\frac{n_1}{n_0}\right)\right)\right)=\frac{1}{2}\left(\ln \left(\frac{f_2}{f_0}\right)-\ln \left(\frac{n_2}{n_0}\right)\right)$$ (9)

In practice, we average fitness across cycles, as described above. We infer fitness separately for each of the two components of the fluctuating environment and define the overall fitness as the average of the two components. Each component consists of two different cycles, and we average these two estimates.

Defining adaptive fitness.

To focus our analyses on adaptive mutants, we chose an adaptive threshold of 0.05 and excluded mutants with fitness below this threshold in their home evolution environment. This threshold was based on the flattening of the curve in Supplementary Fig. 3a. However, results are qualitatively the same if no threshold is used or if an adaptive threshold of 0.1 is used (Supplementary Fig. 3).

Excluding data based on replicate-to-replicate correlations.

We compared replicate-to-replicate correlations of fitness to identify highly variable mutants or conditions (Supplementary Fig. 2). We exclude the Lac–H₂O₂ environment from this average, because fitness is weakly correlated in this environment—during experiments, growth in H₂O₂ after transfer from Lac was not visible for >24 h, suggesting long lag times or mortality. We exclude the Lac–H₂O₂ environment from analyses summarizing environments, but include it individually (Supplementary Figs. 2–5). We exclude 12 mutants with mean replicate-to-replicate fitness difference greater than 0.2 from analyses summarizing environments in Figs. 2 and 4, but results do not change if they are included (Supplementary Fig. 3b).

Comparison of measurement noise to non-additivity and memory.

To distinguish non-additivity and memory from the effects of measurement noise, we compared observed non-additivity and memory to that expected based on measurement uncertainty alone, as shown in Fig. 2e–h. To calculate the percentage of measurements of non-additivity (or memory) with a magnitude greater than would be expected from measurement noise alone, we construct a significance score, similar to a z-score, but for individual measurements. We divide the observed difference in fitness from that expected in a fluctuating environment (for example, non-additivity or memory) by the standard error resulting from the combination of standard errors due to predictions from static environments and measurements in fluctuating environments. For example, the significance score of non-additivity is:

$$\text{Non-additivity significance score}=\frac{|s_{{\text{fluct}}_{ij}}-(s_i+s_j)/2|}{\sqrt{{\text{s.e.m.}}_{{\text{fluct}}_{ij}}^2+\frac{1}{2}\sqrt{{\text{s.e.m.}}_i^2+{\text{s.e.m.}}_j^2}}}$$ (10)

where $s_{{\text{fluct}}_{ij}}$ is fitness in fluctuating environments $i$ and $j$, $s_i$ is fitness in static environment $i$, and s.e.m. is the standard error of the mean of the measured fitness. Similarly, the significance score of memory is:

$$\text{Memory significance score}=\frac{|s_{{\text{fluct}}_i}-s_i|}{\sqrt{{\text{s.e.m.}}_{{\text{fluct}}_i}^2+{\text{s.e.m.}}_i^2}}$$ (11)

where $s_{{\text{fluct}}_i}$ is fitness in the $i$th component of the fluctuating environment, $s_i$ is fitness in static environment $i$ and s.e.m. is the standard error of the mean of the measured fitness. To find the percentage of measurements of non-additivity or memory that is significant at the 95% confidence level, we calculate the percentage of significance scores that is greater than 1.96, or more than two standard deviations away from the prediction. In the more conservative version of this comparison (discussed in the main text), we used the bootstrapped standard error of fitness across all timepoints within all replicates, whereas a less conservative version of this comparison uses the standard error across replicates. The latter comparison has lower uncertainty (41% of cases of non-additivity are significant at the 95% confidence level versus 30% in the former comparison; 66% of cases of memory are significant at the 95% confidence level versus 53% in the former comparison) because the standard error across replicates averages over an entire frequency trajectory rather than including noise within each trajectory.

Partial correlation of fitness differences and fitness change.

We calculated partial correlations of memory in a given fluctuating environment with mean fitness difference, controlling for local fitness difference in the relevant pair of static environments, using the partial_corr method in the pingouin library in Python. We first calculated mean fitness difference across nine out of ten pairs of static environments, excluding the relevant pair. For example, in the case of memory in the Glu–Gal fluctuating environment, we excluded fitness difference between static Glu and static Gal. The partial correlation is positive and significant in nine out of ten fluctuating environments (Supplementary Fig. 8a; the exception is Lac–H₂O₂, in which biological replicates are very weakly correlated).

We then excluded more pairs to see whether memory in a given fluctuating environment is correlated with fitness difference across unrelated pairs of environments, controlling for fitness difference across the local pair of static environments. For example, we calculated the partial correlation of Glu–Gal memory with mean fitness difference across pairs composed of Lac, H₂O₂ and NaCl, controlling for Glu–Gal fitness difference. The correlations remain positive and significant in this case (Supplementary Fig. 8b), showing that we can expect more memory in unseen environments based on greater variance in fitness measured elsewhere.

General additive model to compare independent components of fitness difference.

We used the R library mgcv to construct and fit a general additive model to determine the effects of two independent components of mean fitness difference on mean memory. As shown in Supplementary Fig. 9, fitness difference, as plotted in a two-dimensional space of fitness in two static environments, is composed of distance from the origin and angle from the equal-fitness line. We confirmed that both variables significantly contribute to variation in mean memory (origin distance estimate: 0.55, P < 2 × 10⁻¹⁶; angle estimate: 0.34, P = 2.4 × 10⁻⁸), and we confirmed low correlation of these variables using the check_collinearity function.

Mathematical model of fitness assays

Figure 4d,e shows the results of a mathematical model of our fitness assays. In this model, which is derived in Supplementary Note 1, we assume that the ancestor dominates the population by having a starting frequency many orders of magnitude higher than that of the mutants, and so sets the time to resource depletion, before which mutants can increase in frequency. Mutants have positive fitness if they grow faster than the ancestor or during the ancestor’s lag time (equation (9), Supplementary Note 1):

$$s_i=r_i\text{Δ}{T}_{\text{L}}+\left(\frac{r_i-r_a}{r_a}\right)\ln (\text{DF})$$ (12)

Here $s_i$ is the fitness of mutant $i$, $r_i$ is its exponential growth rate, $\text{Δ}{T}_{\text{L}}$ is the difference between the mutant’s lag time and the ancestor’s lag time (if this quantity is positive, the mutant has a lag advantage over the ancestor), $r_a$ is the ancestor’s exponential growth rate and DF is the dilution factor at each timepoint (or 250 in our experiments).

We further assume that mutants retain the ancestor’s exponential growth rate in a given environment, and fitness is determined only by lag (dis)advantage:

$$s_i=r_i\text{Δ}{T}_{\text{L}}$$ (13)

Mutants with high fitness variance have bigger differences in fitness across environments and so have wider distributions of lag (dis) advantage across environments.

Memory in a fluctuating environment component, or the difference between fitness in fluctuating and static conditions, is determined by the difference in lag (dis)advantage between conditions:

$$s_{i\text{f}}-s_{i\text{s}}=r_i\left(\text{Δ}{T}_{\text{Lf}}-\text{Δ}{T}_{\text{Ls}}\right)$$ (14)

Here $s_{i\text{s}}$ is the mutant’s fitness in the static environment, $s_{i\text{f}}$ its fitness in the corresponding component of the fluctuating environment, $\text{Δ}{T}_{\text{Ls}}$ its lag (dis)advantage in the static environment and $\text{Δ}{T}_{\text{Lf}}$ its lag (dis)advantage in the corresponding component of the fluctuating environment. The mutant will have environmental memory if its lag (dis)advantage shifts in the fluctuating environment. As the ancestor’s lag time probably changes in fluctuating conditions, memory will happen if the mutant’s lag time changes differently than the ancestor’s in fluctuating conditions. For example, if the ancestor’s lag is 4 h in the static Glu and 6 h in the Glu component of Glu–Gal, while the mutant’s lag is 3 h and 5 h, respectively, there is no memory. But if the mutant’s lag is 3 h in both conditions, memory is nonzero and positive, meaning the mutant overperforms in fluctuating Glu compared with static Glu fitness.

To simulate fitness assays in static and fluctuating environments, we first sampled ancestor growth rates across five static environments from a random uniform distribution (0.3, 0.5). We then sampled lag advantages for a pool of 700 mutants by first sampling each mutant’s ‘home’ (or evolution condition origin) environment lag advantage from a random uniform distribution (0.5, 3) and setting the mean and standard deviation of its lag (dis)advantage distribution in all five static environments equal to 0.5 times its home advantage. This choice was based on the fact that we observe that mutants with higher mean fitness difference also have higher than average home environment fitness (Supplementary Fig. 4e,f).

We then simulated fitness in fluctuating environments by shifting a mutant’s lag (dis)advantage away from its static environment value and towards the mean ofthe mutant’s distribution. Guided by our finding that memory correlates with global fitness difference when controlling for local fitness difference (Supplementary Fig. 8), we shift proportionately to the width of the mutant’s distribution across all static environments. We fit the result that the wrong static environment is a better predictor for fitness in fluctuating environment components in 39% of cases by setting this shift to 80% of the distance from the local lag (dis)advantage to the mean of the distribution.

Whole-genome sequencing analysis

We selected 359 mutants for sequencing, including as many mutants with high mean memory as possible. Two samples were excluded because their barcoded regions did not match the appropriate barcode sequence, possibly owing to contamination, and an additional five were discarded owing to low (<20×) coverage, leaving 352 whole-genome sequences.

FASTQ processing.

For each sample, we received two fastq files, one for each read of the paired-end sequencing (fastqR1 and fastqR2). Reads were mapped using bwa to S. cerevisiae S288C reference genome R64-1-1 (https://downloads.yeastgenome.org/sequence/S288C_reference/genome_releases/), converted to BAM format and sorted using samtools. Read groups were fixed using the Picard tool AddOrReplaceRead-Groups. Duplicates were marked using the Picard tool MarkDuplicates and the BAM file indexed using samtools.

Single-nucleotide polymorphism and small indel variant calling.

Single-nucleotide polymorphism (SNP) and small indel variants were called using the HaplotypeCaller tool from GATK. GVCF files were then merged using GenomicsDBImport, and genotyping was performed on the combined gVCF data with GenotypeGVCFs to produce a single VCF file with the called variants for all samples. Average coverage for each sample was calculated using samtools, keeping only those with at least 20× coverage. Variants were then filtered to exclude ancestral genotypes and mitochondrial variants, and using GATK default filters for other filtering. Results were checked visually in IGV. We discarded variants that appeared erroneous due to poor alignment or coverage, particularly in repetitive regions, and marked true variants as homozygous or heterozygous, based on whether the variant appeared in closer to 50% or 100% of reads. Finally, variants were annotated using snpEff.

Copy number variant calling.

BAM files were searched for high-coverage regions with samtools and bedtools, selecting genome sites with more than 3× average coverage. To eliminate ancestral copy number variation, all selected sites were compared and results appearing in more than 15 samples were dropped. The remaining results were checked visually in IGV for copy number variation.

Ploidy assay

We conducted a ploidy test as in ref. 3. Saturated cultures from the 96-well plates also used for whole-genome sequencing were mixed; 5 μl was pipetted onto YPD + 20 μg ml⁻¹ benomyl (in DMSO) on rectangular agar plates, grown at room temperature for several days and then imaged. Under these conditions, diploid growth was strongly inhibited by benomyl, but haploid growth was less affected. We pipetted onto two agar plates per 96-well plate, using every other well, to avoid effects of nearest neighbours on colony growth.

Data availability

All sequencing data are deposited in Short Read Archive under Bio-Project identifier PRJNA1103172. The remaining data are available via GitHub at https://github.com/clare-abreu/environmental_memory. Barcoded yeast strains are available from the authors upon request. Source data are provided with this paper.