Muller plot of allele dynamics

Figure 1A shows the dynamics across 20,000 generations of 42 spontaneous mutations that arose and reached detectable frequencies in the Ara−1 population of the LTEE. Each mutation is identified by the name of the gene in which it occurred (e.g., topA) or, for mutations in intergenic regions, by the adjacent genes (e.g., yedW-yedX). In a few cases, a numeral follows the name of a gene to distinguish mutations that affected the same gene (e.g., several pykF alleles). Twenty-five of these 42 mutations—all of them with labels preceded by dots (e.g., topA at the left and rpsD on the right)—eventually reached fixation (or nearly so) in the population. In other words, these mutations were on the line of descent leading to fully sequenced clones from generations 30,000 and 40,000. The other 17 mutations were transient (e.g., fabR on the left). That is, these alleles reached detectable frequencies—and in a few cases even achieved majority status (e.g., acs-nrfA between generations 8500 and 12,500)—but they later went extinct. Trajectories for each mutation are also shown separately in Figure S3.

Not all mutations were tracked

Figure 1A contains a great deal of data, but when interpreting these dynamics it is important to realize that some information is missing because only a subset of all mutations was targeted in our genotyping assays. Many alleles were undoubtedly rare and transient; if an allele was not moderately abundant (at least several percent) in one of the generational samples that were deeply sequenced (Barrick and Lenski 2009), and if it was not on the line of descent leading to the clones sequenced in later generations (Barrick et al. 2009), then we could not design a targeted genotyping assay to detect it. Moreover, even some alleles that were known to fix in the population could not be accurately quantified using our genotyping method, (e.g., new transposon insertions and other structural mutations) and so information for those mutations is also missing from Figure 1A. We attempted to assay all 37 mutations in the 20,000-generation clone, REL8593A, that were on the line of descent leading to clones sequenced at 30,000 and 40,000 generations (Barrick et al. 2009). However, 12 assays failed: 6 of the failures were structural mutations mediated by insertion-sequence elements, 1 was a 1-bp insertion, and 5 were SNPs. Including mutations off the line of descent, REL8593A has 45 mutations in total, comprising 29 SNPs and 16 insertions, deletions, and other rearrangements (Barrick et al. 2009). The fact that a single clone had almost twice as many mutations as the number successfully tracked in that same clone implies that many other variants were overlooked. In the future, improved estimates of the cumulative number of polymorphisms might be derived by more frequent whole-population sequencing, especially if these data are analyzed using methods that can ably detect both SNPs and non-SNP mutations (Deatherage et al. 2015).

Pure drift cannot explain evolutionary rate

Random genetic drift alone cannot explain the large number of fixations observed or, for that matter, even one fixation. Each LTEE population began from a single haploid cell, and therefore any variant arose as a new mutation with an initial frequency of 1/N, where N is the population size. For a neutral mutation that eventually fixes in a population, the expected time to fix by random drift alone (i.e., without hitchhiking) is on the order of N generations (Kimura 1983). In the LTEE, N fluctuates between ∼5 × 10⁶ and ∼5 × 10⁸ as a consequence of the daily dilutions and regrowth (Lenski et al. 1991). These numbers are far too large to allow mutations to fix by pure drift in 20,000 generations, much less within the many fewer generations observed for the earliest fixations.

Beneficial drivers

We also know that mean fitness increased over the course of the LTEE. It increased in an almost step-like manner over the first few thousand generations (Lenski et al. 1991; Lenski and Travisano 1994), implying a series of fixations of beneficial driver mutations under positive selection, and it has continued to increase more gradually during the subsequent tens of thousands of generations (de Visser and Lenski 2002; Wiser et al. 2013). We also know or infer that particular mutations were beneficial because isogenic strains were constructed to measure the fitness effects of single evolved mutations, because similar mutations affecting the same gene reached high frequencies or fixed in many replicate LTEE populations, or both. These known or suspected beneficial drivers include 15 of the mutations in Figure 1A including topA (Crozat et al. 2005, 2010; Woods et al. 2011), fabR (Woods et al. 2011; Deatherage et al. 2015), spoT (Cooper et al. 2003; Woods et al. 2011), three in pykF (Woods et al. 2006, 2011; Barrick et al. 2009), mrdB (Woods et al. 2006), mrdA (Woods et al. 2006), malT (Pelosi et al. 2006), infB (Barrick et al. 2009), fis (Crozat et al. 2005), nadR (Woods et al. 2006; Barrick et al. 2009), pcnB (Barrick et al. 2009), iclR (Barrick and Lenski 2009), and rpsD (Barrick et al. 2009). It is likely that additional mutations in Figure 1A were also beneficial drivers, while some others may have been neutral or weakly deleterious hitchhikers that achieved transiently high frequency or fixation by virtue of beneficial mutations present in the same genomes.

Clonal interference

Clonal interference refers to the effect of competition between beneficial mutations that occur in different lineages in the same asexual population; its effects are clearly seen in Figure 1A as wedges that open, expand, and then close. Owing to the absence of genetic exchange, two or more beneficial mutations that arise contemporaneously, but in different lineages, cannot be combined in the same genome. Instead, one will eventually prevail and the others must go extinct. The winning lineage might prevail because its initial driver mutation is more beneficial than the initial drivers in the contending lineages. However, the winner might also depend on the effects of later beneficial mutations that arise in one or more of the contending lineages. Such an outcome is especially likely if the initial drivers in the different lineages have similar fitness effects, because that similarity means it would take longer for one lineage to exclude the other, thus providing more time for later beneficial mutations to occur and affect the outcome.

One interference wedge is seen near the very start as a mutation in fabR rises in frequency over the first 1000 generations, but that lineage declines precipitously during the next 500 generations before disappearing entirely (Figure 1A). Five more wedges rise and fall between generations 1000 and 2500. Strikingly, three of them involve different mutations in one gene, pykF. Yet another mutation in pykF later went to fixation in this population (Schneider et al. 2000; Barrick et al. 2009), but it is not shown here because the type of mutation—an insertion of an IS150 element—was not amenable to the method for detecting genetic polymorphisms used in this study. Moreover, different pykF mutations fixed in all 12 LTEE populations (Woods et al. 2006). Thus, there were numerous parallel increases of pykF mutations, both within and across populations, and this parallel evolution provides strong evidence that these were beneficial mutations.

Some additional interference wedges are also present later in the Muller plot including, most notably, an extremely large one that begins with a mutation in rpsA around generation 5000. This lineage became numerically dominant by generation 8000; it remained the majority for thousands of generations before a precipitous decline and sharp recovery between ∼11,000 and 13,000 generations; and it finally petered out to extinction by generation 15,000. We will return to this episode in a later section on Evidence for frequency dependence.

Rapid increases in mutation frequencies

Except for the period from 5000 to 15,000 generations, most mutations that fixed in the Ara−1 population did so very quickly, usually within a few thousand generations. Although these dynamics are visually striking, they are not unexpectedly fast. Three issues come into play when we consider these dynamics. First, the alleles tracked in the Muller plot arose by mutation long before they are shown as being present. Only alleles with frequencies well above 1% could be reliably detected using our methods, but when any new mutation occurred its frequency was 1/N, a mere 0.0000002–0.00002% depending on when the mutational event happened in the transfer cycle. In any case, each successful allele had to reach at least 0.00002% after surviving the first transfer event, which took place within the first day after it arose. Thus, mutations were hidden from view until they had increased in frequency by 50,000-fold or more.

Second, the fitness effects of beneficial mutations that evolved in the LTEE, and which have been measured by constructing and competing isogenic strains, are typically between ∼1% and ∼10% depending on the mutation (Barrick et al. 2009). Assuming a constant fitness difference, the logarithm of the ratio of the beneficial mutant to its progenitor should increase linearly (Dykhuizen and Hartl 1983). For a mutation that confers a 10% advantage, it takes only ∼33 generations (doublings, as used in the LTEE) to rise from 1:100 to 1:10, another 33 generations to increase from 1:10 to 1:1 (i.e., 50%), another to go from 1:1 to 10:1, and one more to achieve near fixation at 100:1. For this mutation, the entire “visible” process would occur in ∼130 generations; however, the time steps in Figure 1A are 500 generations each, and so the fixation would likely be manifest in a single interval. For a mutation that gives a 1% benefit, each order-of-magnitude change in the ratio would take 10-fold longer, or ∼330 generations. In that case, the visible fixation process would require ∼1300 generations, which still falls within a mere three time steps in the Muller plot.

Third, in many of the fixation events, the initial rate of increase in a lineage was much steeper than the final rate. For example, the lineage with the ybaL allele went from undetectable in the 2000-generation sample to being the vast majority by generation 2500, but it did not fix until after generation 5000. Stated the other way, many lineages are unexpectedly persistent, such as the lineage that carried the spoT allele but lacked the yegI and ybaL mutations, which hung on at low frequency from 2500 to 5000 generations. We can posit two explanations for this effect. First, as a consequence of clonal interference, a lineage that has a new beneficial mutation is initially competing primarily with its progenitor, but over time that lineage will increasingly compete against other lineages with different beneficial alleles, thereby slowing its ascent (Lang et al. 2011).

A second possibility is frequency-dependent selection, such that the unexpectedly persistent lineage has acquired some mutation that gives it a fitness advantage when it is rare; for example, it may more efficiently use a metabolic byproduct of the other lineage. This advantage when rare allows the lineage to survive longer than it otherwise could; in the absence of on-going evolution, its advantage when rare would allow it to persist forever. However, in this scenario the new majority lineage evolves, sooner or later, additional beneficial mutations that overcome the minority type’s advantage when rare, thus completing the extinction of the once-dominant lineage by the successor lineage. Incidentally, a somewhat different scenario occurred in another of the LTEE populations. In that population, two lineages stably coexisted by frequency-dependent selection. Both continued to fix beneficial mutations, and their relative abundance fluctuated dramatically over time. However, neither gained a sufficient advantage to drive the other extinct, and they have coexisted now for tens of thousands of generations (Rozen and Lenski 2000; Le Gac et al. 2012).

Nested fixations and cohorts that fix together

In the Muller plot (Figure 1A), we see many examples of nested fixations, in which one mutation begins its sweep to fixation in the background of a prior mutation that has not yet completed its own sweep to fixation. For example, before the topA allele has fixed, the spoT mutation has begun its rise; similarly, the ybaL mutation begins to spread before the yegI mutation has fixed. These nested fixations are not surprising; like clonal interference, they imply that mutations with fairly large beneficial effects are sufficiently common, given the population size, that more than one highly beneficial mutation is often present in contending subpopulations at the same time.

In other cases, however, we see what appear to be simultaneous fixations of two or more mutant alleles—what have been called “cohorts” (Lang et al. 2013). One conspicuous example involved four mutations in the mrdA, malT, nagC, and infB genes that rose together starting at ∼3000 generations in the background carrying the ybaL mutant allele. Another case started at ∼12,500 generations with three mutations in the pcnB, arcB, and ebgR genes that spread and fixed together.

These quasisimultaneous fixations may, at first glance, seem surprising. In fact, however, there are several plausible explanations for their occurrence, as explained below. An important consideration is that most of the time these mutant alleles spent rising in frequency occurred before they reached a frequency at which they could be detected; thus, the relevant dynamics for determining the order in which the mutations happened were hidden from our view. Also, the hypotheses below are not mutually exclusive; instead, two or more of the processes might be involved in any given cohort fixation.

Evidence for frequency dependence

We now turn to the striking dynamics that occurred in this population between 5000 and 15,000 generations (Figure 1A). To better resolve the dynamics, including especially the linkage relationships among various alleles, we genotyped 90 clonal isolates sampled from generations 7500 (Figure 1B) and 10,000 (Figure 1C) for the presence or absence of the various mutations. The earliest discernible events involved the simultaneous rise of two distinct clades from within the blue-colored background that bears a cohort of four mutations (including mrdA) that eventually fixed (Figure 1A). One of the two clades began with a mutation in the rpsA gene; it is aqua-colored at first, then various shades of green as more mutations accumulated with time (Figure 1A). The nested pattern of the first two mutations in rpsA and acs-nrfA was evident in the clones from generation 7500 (Figure 1B), but by generation 10,000 these two mutations were fully concordant (Figure 1C). Three more mutations—in atoS, nuoG, and nuoM—emerged as distinct subclades in the later sample, but they did not persist (Figure 1C). The other main clade appeared first as a cohort of four mutations (including gltB); it is shown in chartreuse initially, with shades of yellow, red, pink, and purple used as more mutations arose (Figure 1A). In the clones sampled at 7500 generations, it was impossible to discern the order of those first four mutations, although the next three mutations that arose in this lineage were already present as nested subsets at that point (Figure 1B). By generation 10,000, six mutations in this clade had become fully concordant; two mutations that would eventually fix (pflC and nadR-2) were nested, as were four others that did not persist (Figure 1C). Following their appearances after 5000 generations, both major clades increased in number, with the one that carried the rpsA mutation becoming the clear majority by 8000 generations and remaining so for most of the next few thousand generations. It then experienced a precipitous decline, a sharp recovery, and another precipitous decline, followed by its extinction. We confirmed that these sharp fluctuations were not artifacts of our genotyping method by also using pyrosequencing to track three diagnostic alleles that distinguished the two clades (Figure S4). By the end of this episode, at least 14 mutations (from gltB to iclR, and probably others not detected by our methods) had piled up on the line of descent before the lineage that ultimately prevailed finally drove the other clade extinct by 15,000 generations.

Hypothetical scenario with frequency-dependent fitness:

We hypothesized that a negative frequency-dependent interaction stabilized the relative abundance of the two clades, while beneficial mutations within each clade buffeted their abundances until, eventually, one drove the other extinct (Figure 2). Under the null hypothesis, the relative fitness of members of the two clades, taken at the same point in time, does not depend on their relative abundance in the population (Figure 2A). The alternative is that each type has an advantage when rare, such that there is a stable equilibrium (i.e., a relative fitness equal to unity) at some intermediate frequency (Figure 2B). Now imagine that beneficial mutations occur in both lineages that alter the shape of the fitness function (Figure 2C). We show these changes as affecting the intercept, but not the slope of the fitness function, as though the mutations provide a general benefit that does not affect the frequency-dependent interaction; however, one can imagine similar scenarios where the slope changes. In the scenario illustrated, the initial equilibrium frequency of clade C2 is ∼0.2. A beneficial mutation in clade C1 drives the equilibrium frequency of C2 down to ∼0.05 (green line), and then a later beneficial mutation in C2 drives its equilibrium frequency up to ∼0.5 (blue line); finally, though, another mutation in C1 pushes the equilibrium frequency of C2 into negative territory (red line) and C2 then goes extinct, assuming it gets no further beneficial mutations, because it is less fit than C1 at all frequencies (Figure 2C).

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Figure 2

Hypothetical scenario showing the interplay between negative frequency dependence and ongoing beneficial mutations. (A) Null case, in which the fitness of clade C2 relative to clade C1 is independent of their relative frequencies. (B) Static negative frequency dependence, where the fitness of C2 relative to C1 declines as the frequency of C2 in the population increases. (C) Dynamic frequency dependence, where ongoing mutations in each clade provide generic fitness benefits. Although the mutations do not affect the frequency-dependent interaction per se, they affect the location and existence of the stable equilibrium. In the example shown here, the first beneficial mutation (green line) occurs in C1 and lowers the equilibrium frequency of C2; the second beneficial mutation (blue line) occurs in C2 and raises its equilibrium frequency; and a third beneficial mutation (red line) occurs in C1 that eliminates the equilibrium and drives C2 extinct.

Experimental tests of frequency dependence:

We ran competition experiments to test whether representatives of the two lineages exhibited frequency-dependent interactions at two time points. We chose clones from the 7500-generation sample that represented the most derived genotypes within clades C1 and C2; they differed by at least nine mutations (Figure 1B). We competed them head-to-head starting at three different ratios, with 12-fold replication for each ratio. We calculated their relative fitness as the ratio of their realized growth rates during the competition assay. We saw no evidence of frequency dependence (Figure 3A); of course, we cannot exclude the possibility of a very small effect, on the order of 1% or less. It is also noteworthy that there was no detectable difference in fitness between the two competitors, even though they differed by so many mutations and both were increasing in abundance relative to the overall population in which they arose (Figure 1A).

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Figure 3

Changing nature of interaction between clones from two clades over time. (A) Clonal isolates from clades C1 and C2 sampled from population Ara−1 at 7500 generations show no frequency-dependent interaction. Although they differ by at least nine mutations, there is no significant difference in their fitness at any of the three initial ratios tested. (B) Clonal isolates from the same clades at 10,000 generations show a strong negative frequency-dependent interaction, with the fitness of the C2 clone declining as its frequency increases. The C2 clone has a significant advantage at all three initial ratios tested, although there may be a stable equilibrium with C2 at a frequency above those tested. Although C2 eventually drove C1 extinct, ongoing beneficial mutations evidently affected the dynamics (Figure 1A). Error bars show 95% confidence intervals.

We repeated this experiment except using the most derived genotypes from clades C1 and C2 at 10,000 generations. In particular, the C1 clone had a mutation in nuoM, and the C2 clone had a mutation in nadR that was the latest mutation that subsequently fixed in the Ara−1 population. In this case, we observed strong frequency dependence; the C2 clone had a fitness advantage of 5.4% when its starting frequency was 10%, an advantage of 2.9% when its initial frequency was 50%, and an advantage of 0.9% when it started at 90% (Figure 3B). Although the C2 clone was fitter than the C1 clone at all three initial ratios tested, the trend suggests the possibility of stable coexistence with C1 at an equilibrium frequency of <5%. Note, however, that this hypothetical equilibrium frequency does not match the frequency of clade C1 observed in the 10,000-generation sample, when it was roughly half the total population (Figure 1A). This discrepancy is not surprising, though, because the competitions involved single representatives from two clades that were continuing to evolve and adapt over time. The important point to take away from the frequency-dependent interaction is this: as clade C2 spread, its advantage over C1 diminished. The frequency dependence thus helps to explain, at least in part, why this selective sweep took so much longer, and involved many more mutations, than other sweeps that both preceded and followed it.