Adaptive tracking with antagonistic pleiotropy results in seemingly neutral molecular evolution

Abstract

The neutral theory of molecular evolution, positing that most amino acid substitutions in protein evolution are neutral, is supported by vast comparative genomic data. However, here we report that the key premise of the theory—beneficial mutations are extremely scarce—is violated. Deep mutational scanning data from 12,267 amino acid-altering mutations in 24 prokaryotic and eukaryotic genes reveal that >1% of these mutations are beneficial, predicting that >99% of amino acid substitutions would be adaptive. This observation demands a new theory that is compatible with both the high beneficial mutation rate and the comparative genomic data considered consistent with the neutral theory. We propose such a theory named adaptive tracking with antagonistic pleiotropy. In this theory, virtually all beneficial mutations observed are environment-specific. Frequent environmental changes and mutational antagonistic pleiotropy across environments render most of the beneficial mutations seen at one time deleterious soon after and hence rarely fixed. Consequently, despite the occurrence of adaptive tracking—continuous adaptation to a changing environment fueled by beneficial mutations, neutral substitutions prevail. We show that this theory is supported by population genetics simulation, empirical observations, and experimental evolution, and has implications for the adaptedness of natural populations as well as the tempo and mode of evolution.

The neutral theory of molecular evolution^1-3 is often regarded as the sole conceptual revolution in evolutionary biology since the establishment of the modern synthesis in the 1940s⁴. The neutral theory attempts to explain empirical patterns of protein and gene sequence evolution. It asserts that most amino acid or nonsynonymous nucleotide substitutions are selectively neutral instead of advantageous and are the result of random genetic drift. Compared with the modern synthesis, the neutral theory more easily explains the molecular clock³, which refers to the approximate constancy in the rate of amino acid substitution in a protein across evolutionary lineages⁵. It also explains the generally slower sequence evolution of functionally more important genes or gene segments than their less important counterparts³. A derivative of the neutral theory known as the nearly neutral theory emphasizes the prevalence of slightly deleterious mutations in addition to strongly deleterious and neutral mutations⁶. We will not distinguish between the two theories unless necessary, because they both maintain that most amino acid or nonsynonymous nucleotide substitutions are non-adaptive. While initially controversial⁷, the neutral theory has withstood over 50 years of empirical tests, especially by the vast population and comparative genomic data collected in the last two decades, so is now commonly (albeit not universally^8,9) considered an accurate description of the evolutionary process for most genes and proteins^10,11.

The neutral theory relies on the key premise that, relative to neutral mutations, beneficial mutations are extremely rare. This is because, in a diploid population with an effective population size of $N_{\mathrm{e}}$, the fixation probability of a beneficial mutation with a fitness advantage of $s$ (and a dominance of 0.5) relative to that of a neutral mutation is approximately $4N_{\mathrm{e}S}$ (ref. ¹²). If $s$ is on average 0.0025 and $N_{\mathrm{e}}$ is 10⁷, $4N_{\mathrm{e}S}$ = 10⁵. Hence, under these parameters, for the neutral theory to hold, neutral mutations must be at least 10⁵ times as frequent as beneficial mutations. Given that most nonsynonymous mutations are deleterious¹³, the neutral theory requires beneficial nonsynonymous mutations to be much rarer than one per 10⁵ nonsynonymous mutations. Here we show that the fraction of nonsynonymous mutations that are beneficial far exceeds this value. We propose a model explaining why patterns of molecular evolution appear to conform to the neutral theory despite the violation of its key premise. We then provide evidence for this model and discuss its broad implications.

RESULTS

Proportion of beneficial mutations

Deep mutational scanning of individual genes followed by mutant fitness quantification enables estimating the distribution of fitness effects (DFE) of mutations¹⁴. For instance, the DFE of coding mutations in 21 representative genes of the yeast Saccharomyces cerevisiae was recently quantified under YPD, a commonly used rich medium for culturing yeast in the laboratory^15,16. We estimated from this dataset that 1.58% of the 6,306 nonsynonymous mutations examined are significantly beneficial, with a median $s$ of 0.011, at nominal P < 0.05 (Extended Data Fig. 1a). The above fraction becomes 1.49% at a false discovery rate (FDR) of 0.05. Although beneficial ones account for a tiny proportion of nonsynonymous mutations, they would make up almost all nonsynonymous substitutions because their fixation probabilities are orders of magnitude greater than those of other nonsynonymous mutations under yeast’s $N_{\mathrm{e}}$ of 10⁷ (ref. ¹⁷) (Fig. 1a). The DFE allows inferring Ω, the expected fixation probability of a nonsynonymous mutation relative to that of a neutral mutation (equivalent to the nonsynonymous to synonymous substitution rate ratio ω if synonymous mutations are neutral), and α, the fraction of nonsynonymous substitutions that are advantageous. We inferred that Ω = 1.4×10⁴ (Fig. 1b) and α = 1-1.5×10⁻²² > 0.99 (Fig. 1c). The α value indicates that virtually every nonsynonymous and hence amino acid substitution would be adaptive, rejecting the neutral theory. Qualitatively similar results on Ω and α were obtained even when we treated all non-significant fitness effects of mutations as 0 (Fig. 1bc), assumed a tenfold reduction in the beneficial mutation rate (Fig. 1bc), or called beneficial mutations more stringently (Extended Data Fig. 1bc).

Fig. 1. Empirical distributions of fitness effects (DFEs) of nonsynonymous mutations refute the neutral theory for functional genes.

a, The DFE of nonsynonymous mutations in 21 yeast genes (blue curve) and the corresponding DFE of nonsynonymous substitutions (orange curve). The green curve shows the fixation probabilities of mutations (right Y-axis) with fitness effects $s$. The diagram on the left shows a broad range of $s$, whereas the diagram on the right amplifies the region with very small $\mid s\mid$ under the assumption of a flat DFE of nonsynonymous mutations in this region. Fitness effects of individual beneficial nonsynonymous mutations in the 21 yeast genes are provided in Extended Data Fig. 1a. b, Inferred nonsynonymous substitution rate relative to the neutral expectation ($\Omega$) under various DFEs of nonsynonymous mutations. Original, originally estimated DFE of nonsynonymous mutations; Significant, originally estimated DFE with all non-significant fitness effects set to 0; Original/10, “original” DFE with a tenfold reduction of the beneficial mutation rate; Significant/10, “significant” DFE with a tenfold reduction of the beneficial mutation rate. c, Inferred 1-α under various DFEs of nonsynonymous mutations, where α is the fraction of nonsynonymous substitutions that are beneficial. $N_{\mathrm{e}}$ is assumed to be 10⁷, which is appropriate for yeast. When the DFE for a gene is available from multiple environments, we use here the data from the environment to which the strains are expected to be best adapted (listed first in Data S1). Data S1 also shows results for other environments and under other $N_{\mathrm{e}}$ values.

We then investigated all other available DFEs of nonsynonymous mutations in cellular organisms, including those of 5,016 nonsynonymous mutations in yeast HSP82 ¹⁸, 490 nonsynonymous mutations in yeast UBI4 ¹⁹, and 455 nonsynonymous mutations in Escherichia coli folA ²⁰. All analyses yielded very large Ω and α values (Fig. 1bc, Extended Data Fig. 1bc, Data S1). Hence, the DFEs of a total of 12,267 nonsynonymous mutations in 24 genes of a prokaryotic model and a eukaryotic model demonstrate that the proportion of beneficial mutations far exceeds what the neutral theory permits. Under these DFEs, the above conclusion largely holds even when there is strong clonal interference as in asexual populations (Extended Data Fig. 1de) or when $N_{\mathrm{e}}$ is much smaller as in large mammals ($N_{\mathrm{e}}$ = 10⁴; Extended Data Fig. 1fg).

Consistently, according to yeast high-resolution lineage tracking in a glucose-limited minimal medium, over 2% of mutations have fitness advantages of ≥ 2% ²¹. Similarly, 6.8% of random transposon insertions in E. coli are advantageous in a glucose-limited minimal medium²². Furthermore, a yeast mutation accumulation (MA) experiment found that 5.75% of non-neutral mutations are beneficial²³. Even larger fractions of beneficial mutations have been reported from MA experiments of the green alga Chlamydomonas reinhardtii^24,25 and flowering plant Arabidopsis thaliana²⁶.

Relevance to natural evolution

Some environments used in the quantification of the above DFEs are laboratory conditions to which the laboratory strains of yeast or E. coli are at least partially adapted. Indeed, the inferred Ω and α of the 21 yeast genes are lower in YPD than in three less used laboratory conditions that are apparently stressful to yeast (Data S1). Nonetheless, it is unlikely that the laboratory strains are fully adapted to the common laboratory conditions, at which point the fraction of beneficial mutations should become effectively zero. One wonders how similar natural populations are to laboratory strains in the extent of adaptation to their respective environments. The fitness trajectory of E. coli in Lenski’s long-term evolution experiment (LTEE) in a constant environment suggests that a complete adaptation will take much more than 50,000 generations²⁷. Consistently, while ω declined over time in the above LTEE, it still reached ~3 from the 40,000^th to 50,000^th generation²⁸. We note that, although many synonymous mutations are non-neutral^29,30, they differ from nonsynonymous mutations in that they do not alter protein sequences; hence, ω can still quantify selection acting on protein sequences and ω > 1 indicates adaptive protein sequence evolution³⁰. A yeast LTEE³¹ also found that adaptations in various constant environments continued after 5,000 generations for most strains tested (Table S1). Because it is generally highly unlikely for a natural environment to be constant for so long as in these LTEEs, observations from the LTEEs suggest that, in nature, organisms are typically far from fully adapted to an environment before the environment changes. Hence, organisms are presumably always adapting to their (changing) environments and our estimated DFEs are in principle relevant to natural evolution.

Adaptive tracking with antagonistic pleiotropy

Our inference of Ω >>1 from the yeast and E. coli DFEs (Fig. 1b) means a much higher nonsynonymous substitution rate than the neutral expectation, implying that functional genes evolve substantially faster than functionless DNA sequences such as pseudogenes, contradicting common observations³². What went wrong in our inference of Ω? We assumed that the fitness effect of a mutation stays unchanged during its time to fixation. However, even for a newly arisen mutant with a fitness advantage as large as 1% (and a dominance of 0.5), the expected time to fixation³³ exceeds ~2,000 generations as long as $N_{\mathrm{e}}$ ≥ 10⁴. During this time, the environment could have changed multiple times, altering the mutant fitness. In particular, antagonistic pleiotropy across environments—a mutation is beneficial in some environments but deleterious in others—is thought to be common^18,20,34-42. It is thus plausible that the vast majority of beneficial mutations observed in any environment are overall deleterious in the multiple environments they encounter in the time to potential fixation, so cannot reach fixation. While environment-independent beneficial mutations are possible, they are expected to be extremely rare because such mutations should have long been fixed. The relative abundance of environment-specific beneficial mutations, coupled with the scarcity of environment-independent beneficial mutations, means that, although a population is continuously adapting to its changing environment (i.e., adaptive tracking⁴³), the beneficial mutations fueling the adaptation do not reach fixation. By contrast, some nonsynonymous mutations have minimal impacts on protein structure/function and are neutral or nearly so regardless of the environment. These (nearly) neutral mutations will thus constitute most of the substitutions. Under the above model of adaptive tracking with antagonistic pleiotropy, or the adaptive tracking model for short, the evolutionary process is adaptive, yet the substitutions are mostly neutral (Extended Data Fig. 2).

Evolution under the adaptive tracking model

To investigate whether the adaptive tracking model can reconcile the relative abundance of advantageous mutations with seemingly neutral patterns of molecular evolution, we used SLiM⁴⁴ to perform forward population genetics simulations of diploid, sexually reproducing populations. With the mutation rate and other relevant parameters fixed (e.g., $N_{\mathrm{e}}$ = 10⁴), we compared the simulation outcomes of four models: (1) all mutations are neutral as in pseudogenes (Pseudo); (2) 10% of mutations are neutral while the remaining are deleterious, mimicking genes obeying the neural theory (Neutral); (3) 10% of mutations are neutral while 98% and 2% of the remaining mutations are respectively deleterious and beneficial, as in an adaptation to a constant environment (Adaptive); and (4) same as the preceding model, except that the environment changes on average every 50 generations (AdapTrack). Under AdapTrack, upon each environmental change, the signs of the fitness effects of 16% of non-neutral mutations are randomly reassigned according to their intrinsic probabilities of being beneficial (Pben ranges between 0 and 25%; see Methods), whereas the rest of non-neutral mutations are always deleterious (Pben = 0). The above parameters are chosen to maintain the expected fraction of non-neutral mutations that are beneficial at 2% in any environment. The expected mutational effect size is adjusted by the “harshness” of the environment.

The simulation showed that Neutral and AdapTrack populations have almost identical (derived) allele frequency spectra, whereas Adaptive populations harbor more high-frequency alleles (Fig. 2a). The fraction of neutral polymorphisms is highly similar between Neutral and AdapTrack populations (Fig. 2b). AdapTrack populations contain a tiny fraction of polymorphisms whose derived alleles are beneficial in the present environment, whereas Adaptive populations contain a larger fraction of beneficial polymorphisms (Fig. 2b). As expected, over 95% of substitutions are beneficial in Adaptive populations despite that only 1.8% of mutations are advantageous (Fig. 2c). By contrast, the vast majority of substitutions are neutral under both Neutral and AdapTrack (Fig. 2c). The estimated Ω exceeds 3 under Adaptive but is ~0.1 under Neutral and AdapTrack (Fig. 2d).

Fig. 2. Derived allele frequency spectra, polymorphisms, substitutions, and substitution rates under various evolutionary models simulated.

a-d, Allele frequency spectra (a), polymorphisms (b), substitutions (c), and $\Omega$, substitution rate relative to the neutral expectation (d) under Pseudo, Neutral, Adaptive, and AdapTrack models. Here, $N_{\mathrm{e}}$ =10⁴, and the environment alters on average every 50 generations under AdapTrack. e-h, Allele frequency spectra (e), polymorphisms (f), substitutions (g), and $\Omega$ (h) under AdapTrack with different $N_{\mathrm{e}}$. i-l, Allele frequency spectra (i), polymorphisms (j), substitutions (k), and $\Omega$ (l) under AdapTrack with different mean durations (L) per condition in a changing environment. m-p, Allele frequency spectra (m), polymorphisms (n), ubstitutions (o), and $\Omega$ (p) under AdapTrack with different numbers of distinct conditions (M) in a cyclically changing environment. In (b), (f), (j), and (n), the value above a bar is the number of polymorphic sites relative to the number for the bar showing an underlined value of 1.00. In (d), (h), (l), and (p), the lower and upper edges of a box represent the first (Q1) and third (Q3) quartiles, respectively, the horizontal line inside the box indicates the median, the whiskers extend to the most extreme values inside inner fences from Q1 – 1.5 × (Q3 – Q1) to Q3 + 1.5 × (Q3 – Q1), and the dots show outliers. Under AdapTrack, because of environmental changes, the classification of beneficial vs. deleterious polymorphisms is based on the present environment and the classification of beneficial vs. deleterious substitutions is based on the geometric mean fitness over all generations from the appearance of the mutation to its fixation. All results shown are based on 30 simulation replications per parameter set.

We kept $N_{\mathrm{e}}$ constant across environments in our simulation, because varying $N_{\mathrm{e}}$ across environments according to environmental harshness hardly alters the outcome (Extended Data Fig. 3a-d). If the higher importance of a gene or gene segment is reflected by a lower fraction of neutral mutations³, AdapTrack generates lower evolutionary rates for more important genes or gene segments (Extended Data Fig. 3e-h), as predicted by the neutral theory³. Allowing P_ben to have a wider or narrower range than the default value does not qualitatively alter the outcome of AdapTrack so long as the upper limit of P_ben is below 50% (Extended Data Fig. 3i-l). To mimic continuous environmental changes, we simulated a scenario where the probability of an environmental change correlates inversely with its magnitude but found the outcome qualitatively unchanged (Extended Data Fig. 3m-p). In all above simulations, we considered semidominant mutations. Similar results were obtained when the dominance of a mutation varied across environments depending on the sign of $s$ (Extended Data Fig. 3q-t).

To further explore the AdapTrack model, we varied several parameters. We found that, as $N_{\mathrm{e}}$ reduces and selection weakens, the allele frequency spectrum right-shifts (Fig. 2e), the fraction of deleterious polymorphisms increases (Fig. 2f), and the fraction of deleterious substitutions (Fig. 2g) and Ω (Fig. 2h) both increase, resembling the classic predictions of the nearly neutral theory⁶.

The mean duration of each condition in a changing environment, when varying between L = 2 and 50 generations, has almost no effect on the simulation outcome (Fig. 2i-l). When L reaches 100 generations, however, $\Omega$ starts to rise due to increased fixations of temporarily beneficial mutations in long-lasting environments (Fig. 2k-l). Notwithstanding, $\Omega$ << 1 (Fig. 2l) and α < 0.2 (Fig. 2k) even when L reaches 100 generations, suggesting broad applicability of AdapTrack.

The natural environment often exhibits cyclic changes in certain aspects such as seasonal changes in temperature and precipitation. We thus investigated the impact of the number of distinct conditions (M) in a cyclically changing environment under AdapTrack when the expected duration per condition remains 50 generations (Fig. 2m-p). We found that α (Fig. 2o) and $\Omega$ (Fig. 2p) both increase as M decreases, because of the rise of the probability that a non-neutral mutation is overall beneficial with smaller M. However, given so many varying environmental factors that are not perfectly correlated, it is unlikely that there are < 10 distinct conditions that a population encounters in the wild. Hence, even under cyclic environmental changes, molecular evolution under AdapTrack is seemingly neutral.

The molecular clock is only approximate and can vary depending on $N_{\mathrm{e}}$ ⁴⁵. In our simulation, we found the substitution rate per year to be much less sensitive to the variation of $N_{\mathrm{e}}$ under Neutral and AdapTrack when compared with that under Adaptive (Fig. 3abc). Similarly, the substitution rate per year is much less sensitive to the variation of the fraction of non-neutral mutations that are beneficial (Fben) under AdapTrack than under Adaptive (Fig. 3de). These results indicate that AdapTrack is as good as Neutral and much better than Adaptive in the ability to explain the molecular clock.

Fig. 3. The molecular clock is insensitive to variations in effective population size (${\mathit{N}}_{\mathbf{e}}$) (top row) and fraction of beneficial mutations among non-neutral mutations (F_ben) (bottom row) under Neutral or AdapTrack, relative to that under Adaptive.

a-e, Accumulation of nucleotide substitutions with time under Neutral (a), AdapTrack (b, d), and Adaptive (c, e) models of simulated evolution. Each curve shows the mean trajectory of 30 replicates under the same $N_{\mathrm{e}}$ (a-c) or F_ben (d, e), with the shaded area showing the central 95% of the data distribution. Because the numbers of substitutions are very large in (c) and (e), the shaded areas are too small to see in these panels. The slope of the fitted line is estimated for replicates with the same $N_{\mathrm{e}}$ or F_ben, and CV refers to the coefficient of variation of the slope across evolution under different $N_{\mathrm{e}}$ (top row) or F_ben (bottom row) values.

The primary difference in the population dynamics of mutations between Neutral (Fig. 4a) and AdapTrack (Fig. 4b) is that strongly non-neutral mutations rarely reach high frequencies under Neutral but occasionally reach high frequencies under AdapTrack because they can be strongly beneficial when the environment is right. A comparison between an AdapTrack population rotating among infinitely many different environments (Fig. 4b) and one rotating among 20 different environments (Fig. 4c) shows that, in the latter population, strongly non-neutral mutations can not only reach high frequencies but also maintain high frequencies for a relatively long time. Fitness is almost constant under Neutral (Fig. 4d) but fluctuates under AdapTrack—changes abruptly as the environment changes, gradually rises as the environment stays, and changes abruptly again as the environment changes again (Fig. 4ef). The sharp upward or downward fitness shift at the time of an environmental change is caused by the difference between the total fitness effect of past substitutions and present polymorphisms in the new environment and that in the preceding environment.

Fig. 4. Mutational and fitness trajectories under Neutral and AdapTrack models in a population genetics simulation with ${\mathit{N}}_{\mathbf{e}}$ = 10⁴.

a-c, Mutational trajectories between the 80,000^th and 110,000^th generation under Neutral (a), AdapTrack with an infinite number of environments (b), and AdapTrack with a cyclically changing environment composed of 20 distinct conditions (c), respectively. d-f, Fitness trajectories between the 90,000^th and 92,000^th generation under Neutral (d), AdapTrack with an infinite number of environments (e), and AdapTrack with a cyclically changing environment composed of 20 distinct conditions (f), respectively. Note that the Y-axis scale varies in (d)-(f). In (e) and (f), distinct but temporally adjacent environments are shaded differently.

Overall, the simulations demonstrate that, under a wide range of parameters, the adaptive tracking model with a relatively high proportion of beneficial mutations (1.8%) in each environment yields evolutionary patterns resembling those predicted by the neutral theory and nearly neutral theory.

Evidence for the adaptive tracking model

Our adaptive tracking model assumes that antagonistic pleiotropy across environments is common. Indeed, based on the yeast multiple-environment DFEs in ref. ¹⁵ (four environments) and ref. ¹⁸ (six environments), among nonsynonymous mutations that are significantly beneficial in at least one environment, 70.3% and 51.9% are respectively significantly detrimental in at least one other environment. For two reasons, these are likely conservative estimates. First, because fitness measurement errors are several orders of magnitude greater than the sensitivity of natural selection, antagonistic pleiotropy is undoubtedly underestimated from the measured DFEs. For example, if statistical significance is not required, the above two fractions increase to 98.5% and 99.6%, respectively. Second, the number of environments encountered by yeast in nature is substantially greater than those examined in the two studies, and the probability of antagonistic pleiotropy should rise with the number of environments considered.

Furthermore, in Drosophila melanogaster, allele frequencies at many loci fluctuate seasonally and parallelly in multiple populations^46,47, suggesting mutational antagonistic pleiotropy across seasons as well as adaptive tracking. Importantly, the fly genes that experienced seasonal selections do not show higher nonsynonymous substitution rates than control genes that were not subject to such selections (Extended Data Fig. 4, Table S2), as predicted by our adaptive tracking model (Fig. 2d).

Testing the adaptive tracking model using experimental evolution

The adaptive tracking model predicts that $\Omega$ and by extension ω are smaller during adaptation in a changing environment than in corresponding constant environments (Fig. 2d). This was indeed observed in a yeast evolution experiment where the changing environment was composed of five dissimilar media⁴⁰. The evolutionary dynamics of mutations further confirmed that the ω disparity between evolution in changing and constant environments arose from antagonistic pleiotropy⁴⁰ (see also Extended Data Fig. 5). Nevertheless, a comparable experiment did not find this disparity in ω when the five constituent media of the changing environment were similar⁴⁰, raising the question of the commonness of antagonistic pleiotropy in a changing environment. To address this question, we performed yeast experimental evolution involving 100 different media randomly grouped into 10 sets of 10 media (Table S3). For each set, we performed experimental evolution in a changing environment that shifted among the 10 randomly ordered media (with a duration of 80 generations per medium), as well as separate constant-environment evolution in each of the 10 media (Fig. 5a). Each evolution experiment had 12 replicates, each of which underwent 800 asexual generations of evolution. In total, we evolved 1320 populations, including 1200 in constant environments (10 sets × 10 media × 12 replicates) and 120 in changing environments (10 sets × 12 replicates), all initiated from the same diploid progenitor.

Fig. 5. Yeast experimental evolution in changing and corresponding constant environments.

a, Schematics of experimental evolution in 10 changing environments each rotating among 10 different media and in the corresponding 100 constant environments, respectively. b, Fraction of beneficial substitutions (F_b) in each changing environment (red line) and corresponding constant environments (blue dots), respectively. Each panel represents one set of 10 media. Symbols of the box plot follow Fig. 2d. P values are from two-tailed t-tests comparing the 10 blue dots with the red line. c, F_b is significantly lower in the changing environments than in the corresponding constant environments. For each set of environments, the red dot represents F_b in the changing environment, whereas the connected blue dot represents the mean F_b in the corresponding 10 constant environments. A pair of red and blue dots are connected by a solid line when their F_b difference is significant (P < 0.05 in panel b), or a dotted line when the difference is not significant. P-value indicated is from a two-tailed paired t-test of the difference between the red and blue dots in the 10 pairs. d, Nonsynonymous to synonymous substitution rate ratio (ω) is significantly lower in changing than in the corresponding constant environments. Each red dot represents ω in a changing environment, whereas the connected blue dot represents the mean ω in the corresponding 10 constant environments. A pair of red and blue dots are connected by a solid line when their ω difference is significant (P < 0.05 in a two-tailed t-test), or a dotted line when the difference is not significant. P-value indicated is from a two-tailed paired t-test of the difference between the red and blue dots in the 10 pairs. The numbers below the 10 diagrams in (b) and those next to the red dots in (c) and (d) correspond to the 10 changing environments in the left diagram of (a).

Following prior studies^41,48-50, we sequenced the genomes of the progenitor and a single clone of each population at the end of the experimental evolution to an average of 40× coverage. A total of 10,877 single-nucleotide variants (SNVs) were detected in coding regions, including 8,202 nonsynonymous, 1,880 synonymous, and 795 nonsense SNVs, as well as 1,046 insertions/deletions (indels) encompassing 782 frame-shifting and 264 frame-conserving indels (Table S4). For convenience, we refer to these accumulated mutations in the sequenced clones as “substitutions”, although they may not have been fixed in the corresponding populations; this treatment does not affect the conclusion from the following analysis (see Methods).

In addition to predicting a lower ω mentioned above, the adaptive tracking model predicts a lower fraction of beneficial substitutions in changing environments than in corresponding constant environments (Fig. 2c). An additional SLiM simulation of the evolution of asexual yeast populations for 800 generations confirmed that these predictions hold even under the above definition of “substitutions” (Extended Data Fig. 6). We focused our analysis on coding substitutions due to the paucity of beneficial noncoding substitutions in yeast experimental evolution⁴¹. By convention^51,52, if a gene is hit by multiple substitutions across replicates of the same treatment, substitutions in the gene are considered beneficial (see Methods for justification). For each changing or constant environment, we computed for each of the 12 replicates the ratio of its number of substitutions in multi-hit genes to the total number of its substitutions. We then averaged this ratio across the 12 replicates and used it as a measure of the fraction of beneficial substitutions (F_b) in the environment. F_b of the changing environment is lower than the median F_b of the 10 corresponding constant environments in nine of the 10 sets of environments (P = 0.02; two-tailed binomial test; Fig. 5b). For five sets of environments, F_b differs significantly between the changing environment and the corresponding constant environments (nominal P < 0.05, two-tailed t-test), and in all five sets F_b is smaller in the changing than constant environments (Fig. 5b). When the 10 sets of environments are considered together, F_b in a changing environment is significantly lower than the mean F_b in the corresponding constant environments (P = 0.005; two-tailed paired t-test; Fig. 5c). Similar results were obtained if only nonsynonymous and null substitutions (P = 0.005, two-tailed paired t-test; Extended Data Fig. 7a) or only nonsynonymous substitutions (P = 0.008, two-tailed paired t-test; Extended Data Fig. 7b) were considered potentially beneficial. Furthermore, as one might predict, F_b in a changing environment increases with the mean similarity across the 10 media in the changing environment (Spearman’s ρ = 0.55, one-tailed P < 0.05; Extended Data Fig. 7c).

Consistent with the finding from the earlier evolution experiment in five dissimilar media⁴⁰, ω in the changing environment is lower than the mean ω in the 10 corresponding constant environments in all 10 sets of environments examined (P = 0.002, two-tailed binomial test; Fig. 5d; Table S5). Individually, five sets of experiments show significantly lower ω in the changing environment than in the corresponding constant environments (nominal P < 0.05, two-tailed t-test; Fig. 5d). When all 10 sets are considered together, ω in a changing environment is significantly lower than the mean ω in the corresponding constant environments (P = 0.004, two-tailed paired t-test; Fig. 5d).

Together, the above results from our yeast experimental evolution strongly support the adaptive tracking model. Two samples may have been cross-contaminated if they share multiple substitutions. We did not observe any two samples sharing more than two substitutions but found six pairs of samples each sharing two substitutions. Similar results were obtained when these 12 samples were excluded (Extended Data Fig. 7d-g). Despite the observation of lower F_b and ω in changing than constant environments in our experiment, signals of adaptive evolution such as ω > 1 are still present in some populations evolving in changing environments. This is probably because each of our changing environments contained only 10 different media; population genetics simulations showed that ω declines to below 1 as the number of different media increases⁴⁰.

DISCUSSION

Our analysis of the DFEs of nonsynonymous mutations showed that the key premise of the neutral theory is violated, questioning the general validity of the theory. In retrospect, the rejection of the neutral theory for functional genes is unsurprising. Given that $N_{\mathrm{e}}$ of natural populations of most species exceeds 10⁴, the neutral theory cannot hold unless beneficial mutations are extremely rare relative to neutral mutations, which occurs probably only when a population is fully or nearly fully adapted to its environment (i.e., at or near a local or global peak in the fitness landscape). However, the prolonged adaptations to constant environments revealed by LTEEs imply that the above situation is exceedingly rare in nature because the environment would have changed before the population reaches a fitness peak or its vicinity. Our model of adaptive tracking with antagonistic pleiotropy reconciles the apparent contradiction between the violation of the key premise of the neutral theory and the consistency of many molecular evolutionary patterns with the theory, as demonstrated by our population genetics simulations. The key prediction of our model that frequent environmental changes prevent the fixation of beneficial mutations is strongly supported by our yeast experimental evolution.

Our model of adaptive tracking with antagonistic pleiotropy relies on three conditions with theoretical^33,42 and empirical^{15,16,18-26,34-41,47} support: (1) beneficial mutations are abundant at virtually any time, (2) beneficial mutations are largely environment-specific, and (3) the duration of a constant environment is shorter than the typical fixation time of beneficial mutations. While our model is a special form of fluctuating selection, prior studies of fluctuating selection^53-64 did not reconcile nor recognize the contradiction between the abundance of beneficial mutations in short-term evolution and the low ω observed in long-term evolution. See Extended Data Fig. 8 and Supplementary Discussion for additional comparisons between our model and other models^65-67.

While the long-term evolutionary outcome may look similar, the underlying evolutionary process is different between the neutral and adaptive tracking models, with the paucity and abundance of positive selection in the former and latter, respectively. Consequently, the two models make some distinct predictions. For example, our population genetics simulation showed that, compared with the neutral model (Fig. 4a), the adaptive tracking model predicts that a strongly non-neutral mutant can occasionally reach a relatively high frequency if it happens to be fit in the environment, but the frequency usually quickly drops when the environment changes (Fig. 4b). This is reminiscent of the thrifty gene hypothesis of diabetes⁶⁸, which proposes that human alleles that reached high frequencies by positive selection in an ancestral environment become disease-causing in the modern environment due to antagonistic pleiotropy. If the adaptive tracking model is generally true, such instances may not be rare. Furthermore, the allele frequency spikes (Fig. 4bc) suggest signals of selective sweeps in populations under the adaptive tracking model, as was confirmed by selection tests of SLiM-simulated data (Extended Data Fig. 9). Besides analysis of time series population genomic data⁴⁷, selection tests may be an important method for differentiating adaptive tracking from neutral evolution in nature.

The adaptive tracking model implies that natural populations are often only partially adapted to their environments and that the adaptedness of a present-day population depends on the time and magnitude of the last environmental change. Consequently, the most abundant genotype may not be the fittest genotype in the present environment. The adaptive tracking model illustrates the prevalence of adaptive evolution resulting from frequent changes of the environment but also its limitation because of mutational antagonistic pleiotropy across environments and the lengthiness of the adaptation process.

An approximately constant pace of nucleotide or amino acid substitution is usually considered evidence for neutral evolution, but this association is broken in the adaptive tracking model where continuous adaptation to successive environments is coupled with clock-like molecular evolution (Fig. 3). In the adaptive tracking model, population fitness shifts abruptly with environmental changes and then rises by adaptation, so it zigzags at relatively fine temporal scales (Fig. 4ef). However, mean population fitness at grand temporal scales may look approximately constant as if it is at stasis (Fig. 4ef), giving a false impression of no adaptation. These features suggest the difficulty in accurately inferring the mode from the tempo of evolution (of genomes or phenotypes) and the essentiality of using an appropriate time scale in investigating evolutionary mechanisms.

Our study focused on the impact of temporal environmental changes on molecular evolution. The environment of a population may also be spatially heterogenous such that a mutant has variable fitness in different parts of the geographic distribution of the population⁶⁹. Under this scenario, it is possible that antagonistic pleiotropy prevents the fixation of a mutant that is beneficial in some but detrimental in other parts of the distribution, creating seemingly neutral evolutionary patterns. Our pilot SLiM simulation of such a scenario supports this prediction (Extended Data Fig. 10).

We focused our analysis on nonsynonymous mutations in this study because the neutral theory was originally concerned with the evolution of protein and protein-coding sequences^1,2. In principle, mutations in non-coding regions (e.g., regulatory sequences) can have opposite fitness effects in different environments, so the adaptive tracking model may also apply to certain non-coding genomic regions; measuring multi-environment DFEs of non-coding mutations can help answer this question.

One caveat of our study is that all available DFEs are from unicellular organisms, despite that a relatively high rate of advantageous mutations is also found from A. thaliana MA experiments²⁶ and that the seasonal evolution of fruit flies^46,47 supports the adaptive tracking model. While there is no obvious reason suggesting drastically different DFEs between unicellular and multicellular organisms, future characterization of DFEs in multicellular organisms is highly desired. Compared with unicellular organisms, multicellular organisms generally have longer generations and smaller $N_{\mathrm{e}}$, but their combined effect on the importance of adaptive tracking is unclear when the time scale of environmental changes is considered (see Methods and Supplementary Discussion). Other topics of relevance include the potentially high genetic load associated with environmental changes under the adaptive tracking model and the role of phenotypic plasticity^43,70-72 in dealing with environmental changes (see Supplementary Discussion). It will be important to study these subjects in the future.

METHODS

Fixation probability and expected time to fixation

In a diploid population with an effective population size of $N_{\mathrm{e}}$ and population size of $N$, the fixation probability of a beneficial mutation^3,12 with a current frequency of $1/(2N)$, selection coefficient of $s$, and dominance of 0.5 is $\frac{1-e^{-2s{N}_{\mathrm{e}}∕N}}{1-e^{-4N_{\mathrm{e}}s}}\approx 2s{N}_{\mathrm{e}}∕N$, whereas the fixation probability of a neutral mutation of the same current frequency is $1/(2N)$. Hence, the ratio of the above two fixation probabilities is approximately $4N_{\mathrm{e}}$. The expected time to fixation of a newly arisen beneficial mutation³³ is $2\text{ln}(2N_{\mathrm{e}}-)/s$ generations when $s$ >> 0. When $s$ = 0.01, this time is 2.0×10³ generations under $N_{\mathrm{e}}$ = 10⁴ and 3.4×10³ generations under $N_{\mathrm{e}}$ = 10⁷.

Empirical DFEs

We focused on the evolution of cellular organisms because viral evolution is already known to be frequently subject to positive selection. Many DFE datasets of cellular organisms have been generated from deep mutational scanning of protein-coding genes, but not all of them are suitable for our analysis. Specifically, DFEs of mutations in antibiotic resistance genes under antibiotic-containing environments were excluded because they often include mutations with very large $s$ and may not represent DFEs of typical genes in nature. DFEs of fewer than 100 nonsynonymous mutations were excluded because such small datasets cannot yield reliable estimates of DFEs of beneficial nonsynonymous mutations. When multiple DFEs of the same gene in the same species were available, we used the largest dataset in our analysis. Applying the above criteria in a literature search, we found four studies^15,18-20 that either reported the DFE of point mutations or provided sequencing read count data that could be used to estimate the DFE of point mutations.

It is important to recognize potential caveats of the four DFE datasets used. First, Shen et al. generated the DFE from 21 yeast genes in four different media¹⁵. The 21 genes studied have diverse functions and expression levels; they detectably reduce fitness when deleted but are all nonessential. Although it was suggested that mutant fitness might have been generally underestimated in this dataset due to the use of a potentially biased wild-type control⁷³, subsequent experiments using unbiased controls confirmed the original results¹⁶. Specifically, our analysis of mutant fitness verified or re-estimated by a more robust method for 17 of the 21 genes¹⁶ yielded qualitatively similar results (Ω = 3,272 and α = 1-1.13×10⁻⁷ > 0.99) as those from the original mutant fitness of the 21 genes. Second, in the study of mutations in yeast HSP82 (also known as HSP90), HSP82 was placed on a low-copy plasmid and its expression was driven by a constitutive, low-expression ADH promoter that reduced Hsp82 protein levels to near-critical levels, potentially amplifying the fitness effects of mutations¹⁸. Mutant fitness was measured in SD medium lacking tryptophan to select for cells carrying the plasmid. Mutations in yeast UBI4, which encodes ubiquitin, was studied by expressing the only ubiquitin gene from a high-copy plasmid under the control of a galactose-regulated promoter¹⁹. The authors stated that the use of the high-copy plasmid allowed expressing ubiquitin at near-physiological levels because multiple ubiquitin genes exist in the wild-type genome¹⁹. Mutant fitness was measured in SD medium with G418 and ampicillin. To study the folA gene in E. coli, which encodes dihydrofolate reductase (DHFR), Thompson et al.²⁰ used a non-native promoter to drive the expression of the gene that was placed on a plasmid. The DHFR abundance in the experiment was controlled at approximately 10% of the endogenous protein level to enlarge the mutational fitness effect, which was measured in M9 medium with 50 mg/mL chloramphenicol. The various caveats of the DFE data suggest that Ω and α will be somewhat overestimated from the HSP82 and folA datasets, approximately unbiasedly estimated from the UBI4 dataset, and reliably estimated from the 21-gene dataset.

Note that including only nonessential genes in the DFE data should not bias our estimation of Ω and α appreciably. Specifically, because <20% of genes are essential in both E. coli⁷⁴ and yeast⁷⁵, even if all nonsynonymous mutations in essential genes are selectively purged due to strong deleterious effects, the overall Ω of all genes would still be >0.8 times the Ω estimated from nonessential genes, which would still exceed 1 substantially. If a fraction of nonsynonymous mutations in essential genes can be fixed, Ω of all genes would be even closer to that estimated from nonessential genes. As for α, if we assume that there are no beneficial mutations in essential genes and that the deleterious portion of essential genes’ DFE is the same as that of nonessential genes, one can derive α of all genes α_all > 4α_est/(5-α_est), where α_est is the α estimated from nonessential genes. Because α_est is very close to 1, let us write α_est = 1-d, where 0 < d <<1. It can be shown that α_all > 1-5d/(4+d) > α_est-0.25d. Hence, αall is only slightly lower than α_est. If some beneficial nonsynonymous mutations exist in essential genes and/or deleterious nonsynonymous mutations are more deleterious when occurring in essential than nonessential genes, α_all would be even closer to α_est.

Estimating Ω and α from empirical DFEs

We directly retrieved the DFE of nonsynonymous mutations of 21 yeast genes from ref. ¹⁵. The data also included standard errors of the mutant fitness estimated from replicate measurements and P-values under the null hypothesis of equality between wild-type and mutant fitness. However, the other three studies presented fitness effects of single amino acid changes that may be due to single or multiple nucleotide changes. We therefore retrieved the raw read counts from either the authors or online data repositories and recalculated the fitness effects of single nonsynonymous mutations on the background of the wild type. For each mutant, we computed its relative abundance at each time point of the competition by dividing its number of reads by that of the wild type. We then fitted a linear model where the log-transformed relative mutant abundance is a function of time (in unit of generation) and the slope represents the logarithm of mutant fitness relative to the wild type. When experimental replicates were available (i.e., ref. ¹⁸ and ref. ²⁰), we incorporated data from all replicates and included replicate identity as a categorical variable in the linear regression. The P-value of the regression slope is used to determine whether the mutant fitness differs significantly from 1.

For a diploid population, given the DFE of nonsynonymous mutations, the nonsynonymous substitution rate relative to the neutral expectation is $\Omega =\frac{d_{\mathrm{N}}}{d_{\text{neutral}}}=\frac{\frac{1}{n}{\sum }_{i=1}^{n}P(s_i,N_{\mathrm{e}})}{\frac{1}{2N_{\mathrm{e}}}}$, where $i$ represents the $i$^th mutation in the $n$ nonsynonymous mutations included in the DFE, $s_{\mathrm{i}}$ is the fitness advantage of the $i$^th mutation, $P(s_i,N_e)=\frac{1-e^{-2s_i}}{1-e^{-4N_e{s}_i}}$ is the fixation probability of the $i$^th mutation when it first appears in the population, under the assumption that the mutation has a dominance of 0.5 and the population size $N$ equals $N_{\mathrm{e}}$, and $\frac{1}{2N_{\mathrm{e}}}$ is the fixation probability of a newly arisen neutral mutation under $N=N_{\mathrm{e}}$. The fraction of beneficial substitutions among all nonsynonymous substitutions is calculated by $\alpha =\frac{{\sum }_{\text{beneficial nonsynonymous}}P(s_i,N_e)}{{\sum }_{\text{all nonsynonymous}}P(s_j,N_e)}$

$N_{\mathrm{e}}$ was set at 10⁷ in the main analysis (Fig. 1bc), because 10⁷ is approximately the empirically estimated $N_{\mathrm{e}}$ of yeast¹⁷ and is smaller than the $N_{\mathrm{e}}$ of E. coli⁷⁶, which only makes the $\Omega$ and α estimates conservative. We also varied $N_{\mathrm{e}}$ (from 10⁴ to 10⁸), with the results shown in Extended Data Fig. 1f-g and Data S1.

In addition to estimating $\Omega$ and α from the observed DFEs (referred to as “original” in Fig. 1bc), we estimated $\Omega$ and α from DFEs where all non-significant fitness effects (i.e., nominal P ≥ 0.05) are set to 0 (referred to as “significant” in Fig. 1bc). We also applied a more stringent criterion of FDR = 0.05 or 0.01, but the results were not qualitatively different (Extended Data Fig. 1bc). Furthermore, we estimated $\Omega$ and α by considering a 10-fold reduction in beneficial mutation rate relative to that in the original DFE (referred to as “original/10” in Fig. 1bc). Specifically, mutations were separately sampled from the beneficial and non-beneficial portions of the original DFE such that the fraction of beneficial mutations in 10,000 sampled mutations is ten-fold lower than that in the original DFE. The sampling was repeated 100 times to allow the estimation of $\Omega$ and α. We similarly estimated $\Omega$ and α by considering a 10-fold reduction in beneficial mutation rate relative to that in the significant DFE (referred to as “significant/10” in Fig. 1bc).

The above calculation of $\Omega$ assumed the strong-selection weak-mutation scheme. However, when multiple beneficial mutations are present simultaneously in a population, they may have to compete for fixation (especially when the recombination rate is low), making $\Omega$ smaller than computed under the strong-selection weak-mutation scheme. The most extreme scenario is represented by asexual populations (i.e., no recombination) where clonal interference leads to the fixation of only the most beneficial mutation present in the population. We thus used the previously derived formula⁷⁷ to calculate the average fixation probability of a beneficial mutation under clonal interference: $P_{\mathrm{b}}(\gamma ,\mu ,N_e)=\gamma {\int }_0^{\infty }2s{e}^{-\psi (s,\gamma ,\mu ,N_e)-\gamma s}ds$, where $\gamma$ is the rate parameter of the exponential distribution that fits the DFE of beneficial nonsynonymous mutations; α is the rate of beneficial nonsynonymous mutations; and $\psi (s,\gamma ,\mu ,N_e)=\frac{\mu }{s}{N}_e\text{ln}(N_e)e^{-\gamma s}\cdot 2(s+\frac{1}{\gamma })$. The fixation probabilities of non-beneficial mutations are calculated by $P(s_i,N_e)=\frac{1-e^{-2s_i}}{1-e^{-4N_e{s}_i}}$ Finally, we calculate $\Omega =\frac{d_{\mathrm{N}}}{d_{\text{neutral}}}=\frac{2N_{\mathrm{e}}}{n}[N_{\mathrm{b}}{P}_{\mathrm{b}}(\gamma ,\mu ,N_e)+{\sum }_{\text{non}-\text{beneficial nonsynonymous}}P(s_i,N_{\mathrm{e}})]$ and $\alpha =\frac{N_{\mathrm{b}}{P}_{\mathrm{b}}(\gamma ,\mu ,N_e)}{N_{\mathrm{b}}{P}_{\mathrm{b}}(\gamma ,\mu ,N_e)+{\sum }_{\text{non}-\text{beneficial nonsynonymous}}P(s_j,N_e)}$, where $N_{\mathrm{b}}$ is the number of beneficial nonsynonymous mutations (Extended Data Fig. 1de). In YPD, the yeast mutation rate is 2×10⁻¹⁰ per site per generation⁷⁸, which is 2.4×10⁻³ per genome per generation. In the DFE of the 21 yeast genes in YPD, the fraction of beneficial nonsynonymous mutations (regardless of statistical significance) among all mutations is ~5%. Thus, the beneficial mutation rate μ is 1.2×10⁻⁴ per genome per generation. We estimated from the beneficial nonsynonymous mutations in the 21 yeast genes that $\gamma$ = 179.2 and used this value in the estimation of $\Omega$ and α under clonal interference.

Population genetics simulations by SLiM

SLiM is a computer program for forward population genetics simulation⁴⁴. The default parameters in our diploid simulation were as follows: $N_{\mathrm{e}}$ = 10⁴, mutation rate μ = 10⁻⁷ per site per generation, number of pairs of chromosomes = 16, size of each chromosome = 10⁴ nucleotides, and recombination rate = 10⁻⁴ per site per generation and is equal across all sites (so the recombination rate per chromosome per generation is 1). Parameters were initially chosen to mimic S. cerevisiae evolution in nature but were then adjusted to speed up the simulation. For example, the $N_{\mathrm{e}}$ used was 10³ times smaller and the μ used was about 10³ times greater such that the $N_{\mathrm{e}}\mu$ used was close to that in yeast. The default length of each simulation was 200,000 generations. Because the initial population was genetically homogeneous, we used simulated data from the 80,000^th to 200,000^th generation to ensure that the data represented equilibrium states. For the AdapTrack model with population size of 5×10⁴, longer simulations were performed to ensure the attainment of population equilibrium, and data from the 240,000^th to 360,000^th generation were used for analysis.

We simulated the basic set of models, including Pseudo, Neutral, Adaptive, and AdapTrack (Fig. 2a-d). In Pseudo, all mutations are neutral. In Neutral, Adaptive, and AdapTrack, when a new mutation arises, a random number determines whether it is neutral (with a default probability of 10%) or non-neutral (with a default probability of 90%). When it is non-neutral, the size of the selection coefficient (∣$s$∣) is sampled from an exponential distribution with a mean of 0.01. Under the Neutral model, the sign of $s$ is negative. Under the Adaptive model, the sign of $s$ is randomly determined to be either positive (with a 2% probability) or negative (with a 98% probability). Under AdapTrack, for a non-neutral mutation, we first decide if it is always deleterious (with probability P₀). If the mutation is not always deleterious, we assign it to be beneficial with probability P_ben, where P_ben is randomly drawn from a uniform distribution U(0, P_max), where P_max represents the maximal probability of being beneficial. The sampled P_ben will be associated with the specific mutation. To keep the overall probability of being beneficial at 2% for all non-neutral mutations, P₀ and P_max must satisfy the equation (1-P₀)(P_max/2) = 0.02. That is, P₀ = 1-0.04/P_max. In the basal AdapTrack model, P₀ = 84% and Pmax = 25%. In each generation, there is a 2% probability that the environment changes, so the average duration of a constant environment is 50 generations. Different environments have different “harshness” (H), which is sampled from a normal distribution with mean = 1 and standard deviation = 0.15 (H is set to 0 if the sampled value is negative). When the environment changes, the selection coefficients of all existing non-neutral mutations will be reassigned. After the determination of the expected size of the selection coefficient (∣$s$∣) of a mutation described earlier, the actual size of the selection coefficient in a specific environment is sampled from the gamma distribution Gamma $\left(k=10,\theta =\frac{\mid s\mid H}{10}\right)$, so that the expected size of the selection coefficient in the environment equals $\mid s\mid H$. Finally, if the mutation is always deleterious, the sign of the selection coefficient is negative; otherwise, the sign of the selection coefficient is assigned positive with a probability of P_ben and negative with a probability of (1- P_ben).

Note that although we did not explicitly simulate a class of neutral mutations that become beneficial under the right environment, such cases occasionally occur in our simulation because the selection coefficient of a mutation varies depending on the environment. For example, a non-neutral mutation with a tiny $s$ in the present environment (e.g., $s$ ≈ −1/$N_{\mathrm{e}}$) may have $s$ >> 1/$N_{\mathrm{e}}$in the next environment. This is equivalent to a present-day, effectively neutral mutation becoming beneficial in the future.

We also evaluated how varying $N_{\mathrm{e}}$ may affect the simulation outcome. We used environmental “harshness” (H) to control population size (Extended Data Fig. 3a-d). Specifically, we set the carrying capacity (N_K) of an environment by N_K = N_e×10^(1-H), where $N_{\mathrm{e}}$ is the default population size. Then the population size in the next generation is given by N_next = N_cur [1 + 0.2×(1 - N_cur/N_K)], where N_cur is the current population size. We set N_next = N_K when N_next computed using the preceding formula is smaller than both N_K and N_cur or when N_next exceeds both N_K and N_cur.

We also simulated several versions of AdapTrack by varying relevant parameters, including the effective population size ($N_{\mathrm{e}}$= 500, 1000, 5000, 10000, and 50000; see Fig. 2e-h), mean duration of a constant condition in a changing environment (L = 2, 25, 50, 100, and 200 generations; see Fig. 2i-l), number of distinct conditions in a cyclically changing environment (M = 2, 5, 10, 20, and infinity; see Fig. 2m-p), fraction of beneficial mutations among non-neutral mutations (F_ben = 1%, 2%, 4%, and 8%; see Fig. 3), fraction of neutral mutations (F_neu = 5%, 10%, 15%, 20%, and 25%; see Extended Data Fig. 3e-h), and levels of antagonistic pleiotropy (P_max = 0.15, 0.25, 0.35, 0.45 and 0.50; see Extended Data Fig. 3i-l). We did not consider P_max > 0.5 because this would generate mutations that are overall beneficial across environments; such mutations should have been fixed long ago.

To capture more realistic environmental changes in nature, where smaller environmental changes are likely more common than larger environmental changes, we modeled an environmental change with a varying magnitude every generation. Specifically, we sampled from an exponential distribution (with mean = 1/2, 1/4, 1/6, 1/8, or 1/10) the probability with which a beneficial mutation will become deleterious (P_bd) and used P_bd as an indicator of the magnitude of the environmental change; if the sampled value is greater than 1, the sampling process will be repeated until the sampled value is lower than 1. To ensure that the overall probability of being beneficial is 2% for all non-neutral mutations, P_bd and the probability of a deleterious mutation becoming beneficial (P_db) must satisfy 0.02P_bd = 0.14P_db in every generation, where 0.02 is the fraction of non-neutral mutations that are beneficial and 0.14 = 0.16 - 0.02 is the fraction of non-neutral mutations that are sometimes deleterious. Then, based on P_db and P_bd, $s$ is reassigned as mentioned earlier (see Extended Data Fig. 3m-p).

To investigate how the dominance of mutations affects the simulation outcome, instead of assigning a dominance coefficient (h) of 0.5 to all mutations, we considered a more realistic scenario where the h value of a mutation varies across environments depending on whether the mutation is beneficial or detrimental in the environment. That is, we set h = 0.25 when the mutation is deleterious and 0.75 when it is beneficial (see Extended Data Fig. 3q-t), because deleterious mutations tend to be recessive and beneficial mutations tend to be dominant^79,80; neutral mutations have h = 0.5.

The type of antagonistic pleiotropy so far investigated has temporally antagonistic selections acting on individual mutations. We also investigated whether an antagonistic pleiotropy model where the selections are spatially instead of temporally antagonistic can generate seemingly neutral molecular evolution (see Extended Data Fig. 10). Specifically, we set up 20 geographic areas, each with a distinct, constant environment. The population size in each region was set at 500 to maintain a total size of 10,000 individuals. The individuals will migrate among the 20 areas every generation, with an average migration rate of 20 individuals per generation between each pair of areas.

Analyzing SLiM simulation results

To draw the (derived) allele frequency spectrum, we picked 20 timepoints evenly from the last 20,000 generations in each of 30 simulation replications, resulting in 600 frequency spectra under each model. The average of these 600 allele frequency spectra was presented.

To analyze polymorphisms, substitutions, and $\Omega$, we used the data from the final generation of each of the 30 simulation replicates. Substitutions that occurred in the generations considered were counted (i.e., between the 80,000^th and 200,000^th generation when $N_{\mathrm{e}}$ < 50,000 and between the 240,000^th and 360,000^th generation when $N_{\mathrm{e}}$ = 50,000). Under AdapTrack, the classification of beneficial vs. deleterious polymorphisms was based on the fitness in the present environment, while non-neutral substitutions were classified as beneficial or deleterious based on the geometric mean fitness across all generations from the appearance of the mutation to its fixation.

Molecular clock is typically investigated by comparing the per year substitution rate across evolutionary lineages. We computed the substitution rate per site per year under different $N_{\mathrm{e}}$ (500, 1000, 5000, and 10,000) in Neutral, Adaptive, and AdapTrack under the assumption that the generation time is proportional to $N_{\mathrm{e}}$^−0.33 (ref. ⁸¹). We similarly compared the substitution rate per site per year under varying F_ben (0.01, 0.02, 0.04, and 0.08) in Adaptive and AdapTrack. Under each set of parameters, we replicated the evolutionary simulation 30 times and estimated the mean substitution rate using the substitutions accumulated between the 80,000^th and 200,000^th generation. We then reported the coefficient of variation in per year substitution rate among the four sets of simulations with different $N_{\mathrm{e}}$ or F_ben (Fig. 3).

To draw mutational trajectories under Neutral or AdapTrack (see Fig. 4a-c), we picked one replicate under each model and showed the allele frequency trajectories of 1000 randomly chosen mutations between the 80,000^th and 110,000^th generation. Each of the chosen mutations must not be fixed before the 80,000^th generation, must not arise after the 110,000^th generation, and must persist in the population for at least 200 generations. The fitness trajectories (see Fig. 4d-f) show the mean fitness of the population relative to that of the original wild type in the environment of the time shown.

Detecting signals of positive selection under AdapTrack

Although the evolutionary outcome of the adaptive tracking model resembles that of the neutral model in many aspects (e.g., $\Omega$, α, and clock-like molecular evolution), positive selection occurs in the former but not in the latter, prompting us to investigate the possibility of detecting signals of positive selection in AdapTrack populations simulated by SLiM. Specifically, we used $N_{\mathrm{e}}$ = 10⁴, mutation rate μ = 5.5×10⁻⁷ per site per generation, number of pairs of chromosomes = 1, size of each chromosome = 10⁵ nucleotides, and recombination rate = 5×10⁻⁷ per site per generation (and equal across all sites), such that the simulated population genomic data correspond to those from a 5-Mb segment of the human genome. We simulated five different models each for 100,000 generations and replicated the simulation 30 times under each model: Pseudo, Neutral, AdapTrack with an infinite number of environments, AdapTrack with 20 rotating environments, and Adaptive, as described earlier. Simulated data were recorded every 1,000 generations from the 80,000^th to 100,000^th generation, resulting in 20 × 30 = 600 datasets per model. Tajima’s D (ref. ⁸²), Fu and Li’s D (ref. ⁸³), Fay and Wu’s H (ref. ^84,85), Zeng et al.’s E (ref. ⁸⁵), and Garud et al.’s H12 (ref. ⁸⁶) were computed using a sliding window method from all simulated individuals. The length and step size of the sliding window was 10,000 and 1,000 bp for the first four statistics, and 4,000 and 500 bp for H12, respectively. Statistics computed from all sliding windows at all 600 timepoints were lumped for comparisons among the five models (Extended Data Fig. 9).

Nonsynonymous substitution rates (d_N) of fly genes under antagonistic selections

Rudman et al. identified 110 candidate genes that overlap with single-nucleotide polymorphisms with top parallel evolution signals in the experimental evolution of flies in a natural setting⁴⁷ (Table S2). Those genes likely represent targets of antagonistic selections during seasonal environmental changes. We compared the rates of nonsynonymous substitution (d_N) of these genes with those of 110 negative control genes randomly picked from genomic regions with no parallel evolution signals (Table S2). The dN values were calculated using PAML⁸⁷ from orthologs between D. melanogaster and D. simulans. To identify orthologs in D. simulans, we BLASTed coding sequences of the 220 D. melanogaster genes against genomic coding sequences of D. simulans downloaded from the NCBI genome assembly database (https://www.ncbi.nlm.nih.gov/assembly/), setting the E-value threshold at 10⁻¹⁰. If the query was partially matched to the subject, the subject was inspected manually to ensure the orthologous relationship. If multiple hits were detected, the hit with the lowest E-value was chosen. The orthologous coding sequences between D. melanogaster and D. simulans were then aligned using MACSE v2 (ref. ⁸⁸). Of the final set of orthologs, 90 of the 110 genes under antagonistic selections and 100 of the 110 negative control genes remained, and their d_N values are shown in the violin plot in Extended Data Fig. 4.

Strains and media for yeast experimental evolution

In a previous study, three replicate populations of the diploid yeast strain BY4743 were propagated for 600 generations in a synthetic complete (SC) medium with 2% glucose. From each replicate, three colonies were randomly picked, and their growth rates in the SC medium were measured using BioTek Gen5 Microplate Reader. The strain with the highest growth rate was chosen as the progenitor for the present evolution experiment. For this study, we employed 100 different media based on SC medium (or YPD when SC ingredients reacted with the additive and caused precipitation), each modified by altering carbon sources, nitrogen sources, nutrient depletion, toxins, and metabolites (Table S3). As the progenitor strain was previously adapted to the SC medium, most beneficial mutations occurred in our experiments likely targeted the specific added or depleted components of the 100 media rather than the shared SC medium background. For media containing chemicals requiring storage at −20°C, fresh preparations were made biweekly to prevent degradation.

Experimental evolution

We randomly grouped the 100 media into 10 sets of 10 media. For each set of media, we performed 12 replicates of experimental evolution in a changing environment that rotated among the 10 media in a random order, with population growth in each medium for 80 generations. For each set of media, we also performed 12 replicates of 800 generations of experimental evolution in the constant environment of each of the 10 media. In total, (10 constant + 1 changing) × 12 replicates × 10 sets = 1,320 populations were evolved. Each 500 μl yeast population was cultured at 30 °C with 220 rpm shaking in an incubating shaker. We used 96-deep-well plates to perform experimental evolution. Every 24 hrs (8 generations), after cultures reached stationary phase, we transferred 2 μl stationary culture into 500 μl fresh culture medium. At the end of the experiment, a single clone of each population was picked and stored at −80 °C for future analysis.

Library construction and genome sequencing

A total of 1321 clones from the 1320 experimental evolution populations and the progenitor were genome sequenced. For each clone, cultures were grown overnight in the SC medium, and genomic DNA was extracted from ~10⁷ cells using a MasterPure Yeast DNA Purification Kit (Lucigen; MPY80200). Sequencing libraries were prepared with the Nextera DNA Flex kit (Illumina; 20018705). Samples were sequenced using the Illumina HiSeq X platform with paired-end 150-nt reads. About 2 million read pairs were generated from each library, providing an average sequencing depth of ~40×.

Substitution identification

We aligned sequencing reads to the S. cerevisiae reference genome (R64-3-1) using Burrows-Wheeler Aligner⁸⁹ with default settings. Duplicate reads were removed with Picard tools (http://broadinstitute.github.io/picard/). SNVs and indels were called using the Genome Analysis Toolkit (GATK)⁹⁰. Each variant called had a minimum of five supporting reads. We focused our analysis on coding variants for the reason provided in the main text. Substitutions in evolved populations were identified by comparing the ancestral with evolved populations. All identified substitutions (SNVs and indels) in the coding region are listed in Table S4. The sequencing data of the 1200 populations evolved in 100 constant environments were generated as part of a larger project⁴¹ but were reanalyzed here.

Estimation of the fraction of beneficial substitutions

Because the number of substitutions per population in the experimental evolution was two to three orders of magnitude smaller than the number of genes in the yeast genome, without positive selection, it is highly unlikely that the same gene was hit by a substitution in two or more of the 12 replicate populations per treatment. We therefore followed convention to assume that substitutions in multi-hit genes are beneficial, where a multi-hit gene is a gene that harbors at least one substitution in at least two of the 12 replicates of an evolution experiment. For each changing or constant environment, we computed for each of the 12 replicates the ratio of its number of substitutions in multi-hit genes to the total number of its substitutions. We then averaged this ratio across the 12 replicates and used it as a measure of the fraction of beneficial substitutions (F_b) in the environment.

To assess the validity of the above method, we repeated the above analysis 1000 times using the same number of randomly generated substitutions as observed in experimental evolution. The average F_b was 0.014 (SD = 0.024), less than 10% of that observed in the actual experimental evolution (Fig. 5b), suggesting that the vast majority of our inferred beneficial substitutions are true positives.

Estimation of ω

ω is the number of nonsynonymous substitutions per nonsynonymous site divided by the number of synonymous substitutions per synonymous site between homologous gene sequences and is widely used to measure selection acting on protein-coding genes. Although many synonymous mutations are non-neutral^29,30, they do not affect the protein sequence. Hence, in principle, ω can still measure selection acting on protein sequences. It was previously reported that selection on mRNA folding strength could affect ω depending on the GC content of the gene⁹¹. However, because the GC content is not different between the experiments in constant and changing environments, ω is comparable between these experiments as a measure of selection on protein sequences.

We followed a previous study⁴⁰ to estimate ω. Specifically, we estimated the numbers of synonymous and nonsynonymous sites in the yeast genome using the modified Nei–Gojobori method⁹², which accounts for the transition bias, or the transition-to-transversion mutation ratio (Ts/Tv). Using an estimated Ts/Tv of 0.84 from an MA study of yeast⁷⁸, we estimated that there are S = 2,218,694 synonymous sites and N = 6,839,923 nonsynonymous sites in the yeast genome. We then respectively counted the total number of synonymous (S_SNV) and nonsynonymous (N_SNV) SNVs in the 12 replicates of an experiment, which allowed estimating ω = (N_SNV/N)/(SSNV/S). We then compared ω between a changing environment and the corresponding 12 constant environments.

Potential effects of using a clone to identify “substitutions”

We used a single clone to identify “substitutions”, which may contain low-frequency neutral or deleterious mutations. The sequencing data from constant-environment evolution experiments were obtained from a recent study⁴¹ where a single clone per population was sequenced due to the prohibitively high cost of sequencing over 3000 populations. To allow comparing with these data, we decided to similarly sequence one clone per population from changing-environment evolution experiments. Because some of the identified “substitutions” are actually unfixed and because “beneficial substitutions” should on average have lower frequencies in changing environments (due to antagonistic selections) than in constant environments, treating all identified beneficial alleles as beneficial substitutions likely overestimates beneficial substitutions more in changing than in constant environments. Hence, our finding of a lower fraction of beneficial substitutions in changing environments than in constant environments (Fig. 5bc) is conservative; that is, the actual difference is expected to be even bigger than shown in Fig. 5bc. Similarly, treating unfixed mutations as “substitutions” will overestimate ω in changing environments more than in constant environments. Hence, our finding of a lower ω in changing environments than in constant environments (Fig. 5d) is conservative; that is, the actual difference is expected to be even bigger than shown in Fig. 5d. In addition, in an earlier, much smaller experiment evolution study of constant and changing environments, we sequenced populations and obtained qualitatively similar results⁴⁰.

Similarity among the 10 media in each changing environment

To evaluate the similarity in adaptive genetic changes between two evolved lines, we calculated their Dice’s similarity coefficient by 2∣X∩Y∣/(∣X∣+∣Y∣), where ∣X∣ and ∣Y∣ are the numbers of putatively adaptive (multi-hit) genes in the two lines, respectively, and ∣X∩Y∣ is the number of putatively adaptive genes shared between the two lines. Dice’s coefficient ranges from 0 (no overlap in adaptive genes) to 1 (complete overlap). To assess the similarity among the 10 environments in each set of environments, we performed the following calculations. First, for each replicate (e.g., replicate 1 in environment 1 of the first set of environments), we computed its pairwise Dice’s coefficient in putatively adaptive genes with all other replicates from the other 9 environments, resulting in 12 × 9 = 108 coefficients. The average of these 108 values was taken as Dice’s coefficient for this replicate. Second, we repeated this process for all 12 replicates in the environment and averaged the 12 Dice’s coefficients in environment 1 to obtain Dice’s coefficient for the environment. Third, we repeated the above process for all 10 environments in the set and took their average as the similarity among the 10 environments in the set.

Other fluctuating selection models

In the quasi-neutral model^65,66, a mutant is subject to fluctuating selection with the mean $s$ over many generations approximating 0. This model may be considered an extreme version of the adaptive tracking model with P_ben = 0.5. While it is possible for a non-neutral mutation to have its mean $s$ close to 0, this is unlikely the case for all beneficial mutations observed at any time. Compared with regular adaptive tracking, in the quasi-neutral model, high-frequency polymorphisms tend to be long-lived instead of transient. Furthermore, because the quasi-neutral model resembles adaptive tracking with P_ben = 0.5, simulations (Extended Data Fig. 3k) suggest that it should yield a substantially higher fraction of adaptive substitutions than that under regular adaptive tracking. To verify this prediction, we simulated AdapTrack with the following parameters: 10% of mutations are neutral, P₀ = 96% of non-neutral mutations are always deleterious, and the remaining 4% of non-neutral mutations have P_ben = 0.5. Using this set of parameters ensured that, in any environment, the expected fractions of neutral, deleterious, and beneficial mutations equal their corresponding values in our regular AdapTrack simulation. We observed much higher $\Omega$ and α (Extended Data Fig. 8) than those under regular AdapTrack. The observation of an α of ~0.7 suggests that the quasi-neutral model cannot explain the seemingly neutral molecular evolution observed from the vast comparative genomic data.

We further simulated a fluctuating positive selection model, where non-neutral mutations are either consistently deleterious or having an expected $s$ > 0. That is, we used the following parameters in AdapTrack: 10% of mutations are neutral, P₀ = 97.33% of non-neutral mutations are always deleterious, and the remaining 2.66% of non-neutral mutations each have a P_ben value that is randomly sampled from a uniform distribution between 0.5 and 1. Using this set of parameters ensured that, in any environment, the expected fractions of neutral, deleterious, and beneficial mutations equal their corresponding values in our regular AdapTrack simulation. We observed higher $\Omega$ and α than those under the quasi-neutral model (Extended Data Fig. 8). The observation of a $\Omega$ of ~2.5 and an α > 0.9 suggests that the fluctuating positive selection model cannot explain the seemingly neutral molecular evolution observed from the vast comparative genomic data.

Adaptive tracking in populations of multicellular vs. unicellular organisms

Compared with unicellular organisms, multicellular organisms tend to have smaller $N_{\mathrm{e}}$ but longer generations. The time to fixation of a newly arisen beneficial mutation³³ is expected to be $2\text{ln}(2N_{\mathrm{e}}$-1)/$s$ generations when $s$ >> 0. Because generation time (in absolute time) is approximately $k{N}_{\mathrm{e}}$^−0.33, where $k$ is a positive constant⁸¹, the absolute time to fixation of a newly arisen beneficial mutation is $2k{N}_{\mathrm{e}}$^−0.33ln(2$N_{\mathrm{e}}-1$)/$s$, which is a decreasing function of $N_{\mathrm{e}}$. Hence, the absolute time to fixation is expected to be longer in multicellular than in unicellular populations, potentially making the adaptive tracking model more important for multicellular than unicellular organisms. However, environmental changes at very short time scales relative to the generation time of the species concerned may not trigger its adaptive tracking, because of the little chance for allele frequencies to respond to such brief environmental changes. From this perspective, adaptive tracking may be less common for multicellular than unicellular organisms.

Extended Data

Extended Data Fig. 1. Distribution of individual mutational fitness effects and inferred Ω and 1-α under various conditions.

a, Fitness effects of individual beneficial nonsynonymous mutations in the 21 yeast genes. Each dot represents the point estimate of the fitness effect of a mutation, with its standard error shown by the error bar. Red indicates a significant fitness effect (nominal P < 0.05), whereas grey indicates a non-significant fitness effect. b–c, Inferred $\Omega$ (b) and 1-α (c) when various statistical stringencies are applied in calling significant fitness effects of mutations. Under a statistical cutoff, $\Omega$ and 1-α are estimated by setting all non-significant fitness effects at 0. d–e, Inferred $\Omega$ (d) and 1-α (e) when asexual populations are considered. f–g, Inferred $\Omega$ (f) and 1-α (g) when the effective population size ($N_{\mathrm{e}}$) is 10⁴. See Fig. 1bc for symbol definitions.

Extended Data Fig. 2. Conceptual illustration of (a) neutral, (b) adaptive, and (c) adaptive tracking models of molecular evolution in sexual populations.

In each panel, the left diagram shows mutant frequencies over time, whereas the right diagram shows fractions of deleterious, neutral, and beneficial mutations (upper bar) and substitutions (lower bar), respectively. All three models assume that most mutations are deleterious. The neutral model assumes negligible beneficial mutations, so most substitutions are due to random fixations of neutral mutations. The adaptive model allows a non-negligible fraction of beneficial mutations, resulting in substitutions being largely beneficial and driven to fixation by positive selection. The adaptive tracking (with antagonistic pleiotropy) model allows a non-negligible fraction of beneficial mutations but assumes that these beneficial mutations soon become deleterious when the environment changes and thereby cannot reach fixation; consequently, most substitutions are neutral.

Extended Data Fig. 3. Derived allele frequency spectra, polymorphisms, substitutions, and substitution rates under various evolutionary models simulated, with conditions not considered in Fig. 2.

a–d, Allele frequency spectra (a), polymorphisms (b), substitutions (c), and $\Omega$ (d) under AdapTrack with a constant or fluctuating population size (indicated by “fluc”). e–h, Allele frequency spectra (e), polymorphisms (f), substitutions (g), and $\Omega$ (h) under AdapTrack with different fractions of neutral mutations that reflect different levels of gene importance. i–l, Allele frequency spectra (i), polymorphisms (j), substitutions (k), and $\Omega$ (l) under AdapTrack with different ranges of the probability that a sometimes-beneficial mutation can be beneficial in an environment. m–p, Allele frequency spectra (m), polymorphisms (n), substitutions (o), and $\Omega$ (p) under AdapTrack in which the magnitude of an environmental change that occurs every generation follows an exponential distribution (see Methods). The larger the mean of the exponential distribution, the greater the mean and variance of the magnitude of the environment changes. q–t, Allele frequency spectra (q), polymorphisms (r), substitutions (s), and $\Omega$ (t) under Neutral, Adaptive, and AdapTrack with or without dominance. With dominance (indicated by “dom”), the coefficient of dominance of a mutation in an environment is h = 0.75 if the mutation is beneficial in the environment, 0.50 if the mutation is neutral, and 0.25 if the mutation is deleterious. Without dominance, h = 0.50 regardless of the mutational fitness effect.

Extended Data Fig. 4. Nonsynonymous substitution rates (d_N) of 90 fly genes likely under parallel seasonal (antagonistic) selections and those of 100 negative control genes.

The violin plot shows the frequency distribution, with the red dot representing the mean and the top and bottom horizontal bars respectively indicating the maximal and minimal values. Genes under antagonistic selections have significantly lower d_N than the negative control genes (P = 0.0025, t-test).

Extended Data Fig. 5. Population dynamics of nonsynonymous SNVs in a changing environment and corresponding constant environments.

a–b, Data from ref. 40 are reanalyzed to generate nonsynonymous SNV frequency trajectories in five representative populations evolving in an antagonistic changing environment (a) and in five populations evolving in corresponding constant environments (b). In (a), the environment changed every 224 generations from one to the next of the five environments shown in (b). In (a), each line shows the allele frequency trajectory of a nonsynonymous mutation at the beginning of the experimental evolution, four time points marking the four environmental changes, and the end of the experimental evolution. In (b), each line shows the allele frequency trajectory of a nonsynonymous mutation at the same time points as in (a). Trajectories of all nonsynonymous SNVs in each population are displayed, and different SNVs are shown using different colors.

Extended Data Fig. 6. Results from a SLiM simulation mimicking the asexual, diploid yeast experimental evolution.

$N_{\mathrm{e}}$ = 4×10⁵, genome size = 1.6×10⁵, mutation rate = 1×10⁻⁷ per site per generation, and other conditions followed the basal AdapTrack and Adaptive models. The simulation was run for 800 generations, and the environment changed every 80 generations under AdapTrack but remained constant under Adaptive. a, Fractions of “substitutions” belonging to various categories, where “substitutions” refer to mutational differences between the progenitor and a single sampled individual at the end of the simulation. b, $\Omega$ computed from the “substitutions” above defined. Shown are the results from 100 simulation replications. In (b), the lower and upper edges of a box represent the first (Q1) and third (Q3) quartiles, respectively, the horizontal line inside the box indicates the median, the whiskers extend to the most extreme values inside inner fences from Q1 – 1.5 × (Q3 – Q1) to Q3 + 1.5 × (Q3 – Q1), and the dots show outliers.

Extended Data Fig. 7. Additional comparisons of beneficial substitutions and ω between yeast experimental evolution in constant and changing environments.

a–b, The fraction of beneficial substitutions is significantly lower in changing environments than in corresponding constant environments. Same as Fig. 5c, except that only nonsynonymous SNVs, nonsense SNVs, and frame-shifting indels (a), or only nonsynonymous SNVs (b) are considered in identifying beneficial substitutions. c, The fraction of beneficial substitutions in a changing environment increases with the similarity among the 10 media making up the changing environment. Each dot represents one of the 10 changing environments. Spearman’s correlation and associated one-tailed P-value are presented. d–f, Same as Fig. 5c except that the 12 potentially contaminated populations are excluded. Results are obtained when all substitution types (d), only nonsynonymous SNVs, nonsense SNVs, and frame-shifting indels (e), or only nonsynonymous SNVs (f) are considered in identifying beneficial substitutions. g, ω is significantly lower in changing environments than in constant environments, as in Fig. 5d, except that the 12 potentially contaminated populations are excluded.

Extended Data Fig. 8. Results of SLiM simulations under AdapTrack and other models of fluctuating selection.

a-d, Derived allele frequency spectra (a), polymorphisms (b), substitutions (c), and $\Omega$ (d). Under the quasi-neutral model (QuasiNeu), beneficial mutations are subject to fluctuating selection with zero expected selection coefficients across environments. Under the fluctuating positive selection model (FluPosSel), beneficial mutations are subject to fluctuating selection with positive expected selection coefficients across environments.

Extended Data Fig. 9. Signals of selective sweeps in SLiM simulated data.

a-e, Distributions of Tajima’s D (a), Fu and Li’s D (b), Fay and Wu’s H (c), Zeng et al.’s E (d), and Garud et al.’s H12 (e) for populations simulated under five different models. Each distribution, presented as a violin plot, is based on the aggregated data from 20 timepoints of each of 30 simulation replications. A t-test is conducted between Neutral and AdapTrack (inf env) or AdapTrack (20 env) as well as between Adaptive and AdapTrack (inf env) or AdapTrack (20 env). Here, “inf env” stands for infinite number of environments whereas “20 env” stands for 20 rotating environments. *, P < 0.05, **, P < 0.005; ***, P < 0.0005. In the violin plot, the white dot represents the median, the dark rectangular spans from the first (Q1) to third (Q3) quartile, and the dark vertical line represents the range of the distribution after removing outliers that lie outside the domain from Q1 – 1.5 × (Q3 – Q1) to Q3 + 1.5 × (Q3 – Q1).

Extended Data Fig. 10. Results of SLiM simulations under AdapTrack with temporal vs. spatial heterogeneity in fitness effects of mutations.

a-d, Derived allele frequency spectra (a), polymorphisms (b), substitutions (c), and $\Omega$ (d). We consider the average fitness across all environments when classifying beneficial and deleterious polymorphisms/substitutions under the spatial heterogeneity model. The results of the simulation of temporal heterogeneity are from Fig. 2a-d.

Data Availability

The Illumina sequencing data have been deposited to NCBI SRA under the accession number PRJNA1181288. Data for generating figures can be downloaded from Zenodo (https://doi.org/10.5281/zenodo.17149945 ⁹³).

Code Availability

Custom code can be downloaded from Github (https://github.com/song88180/Adaptive_Tracking_with_Antagonistic_Pleiotropy/releases/tag/v1).