Experiments on the role of deleterious mutations as stepping stones in adaptive evolution

Significance

It might seem obvious that deleterious mutations must impede evolution. However, a later mutation may interact with a deleterious predecessor, facilitating otherwise inaccessible adaptations. Although such interactions have been reported before, it is unclear whether they are rare and inconsequential or, alternatively, are important for sustaining adaptation. We studied digital organisms—computer programs that replicate and evolve—to compare adaptation in populations where deleterious mutations were disallowed with unrestricted controls. Control populations achieved higher fitness values because some deleterious mutations acted as stepping stones across otherwise impassable fitness valleys. Deleterious mutations can thus sometimes play a constructive role in adaptive evolution.

Abstract

Many evolutionary studies assume that deleterious mutations necessarily impede adaptive evolution. However, a later mutation that is conditionally beneficial may interact with a deleterious predecessor before it is eliminated, thereby providing access to adaptations that might otherwise be inaccessible. It is unknown whether such sign-epistatic recoveries are inconsequential events or an important factor in evolution, owing to the difficulty of monitoring the effects and fates of all mutations during experiments with biological organisms. Here, we used digital organisms to compare the extent of adaptive evolution in populations when deleterious mutations were disallowed with control populations in which such mutations were allowed. Significantly higher fitness levels were achieved over the long term in the control populations because some of the deleterious mutations served as stepping stones across otherwise impassable fitness valleys. As a consequence, initially deleterious mutations facilitated the evolution of complex, beneficial functions. We also examined the effects of disallowing neutral mutations, of varying the mutation rate, and of sexual recombination. Populations evolving without neutral mutations were able to leverage deleterious and compensatory mutation pairs to overcome, at least partially, the absence of neutral mutations. Substantially raising or lowering the mutation rate reduced or eliminated the long-term benefit of deleterious mutations, but introducing recombination did not. Our work demonstrates that deleterious mutations can play an important role in adaptive evolution under at least some conditions.

Evolutionary biologists usually assume that increased performance, including the origin of new traits, arises via a hill-climbing process, such that a population evolves toward a local fitness peak. Mutational paths through fitness valleys are often viewed as inaccessible (1, 2), and even nonlethal deleterious mutations are seen as dead ends that can be ignored when considering the rate of improvement and the distribution of adaptive outcomes (3). Wright’s shifting-balance theory offers one possible dynamic for a sexually reproducing metapopulation (comprising many demes or subpopulations) to traverse a fitness valley, but its efficacy is disputed (4). In asexually reproducing organisms, however, there exists a simpler mechanism for crossing a fitness valley. Provided that a deleterious mutation is not lethal, the genome carrying it has some expected “half life” and a corresponding chance of reproducing one or more times before going extinct (2, 5–10). Occasionally, the mutant subpopulation might acquire a second, hypercompensatory mutation that provides a net advantage (11, 12). Although such mutations are expected to be rare, new detrimental mutations are constantly generated, thus providing a multitude of potential stepping stones. If the second mutation would also have been deleterious had it appeared without the preceding mutation, then the beneficial combination is said to have a “sign-epistatic” interaction (3, 13)—two wrongs, in effect, make a right. In a sexual population, such interacting mutations will often find themselves becoming dissociated so long as they are rare, making it difficult for them to spread unless they are tightly linked (5, 6). In an asexual population, however, the fortuitous combination, once formed, will be stably inherited, thereby providing a simple way to traverse a fitness valley (5–10).

Previous research on a variety of systems, both biological and computational, has documented many examples of epistatic interactions between mutations (3, 6, 11, 14–24), including a few cases of mutational pairs that are individually deleterious but jointly beneficial (11, 12). Nonetheless, it remains unclear, even in digital systems, whether these cases have a significant impact on the rate of adaptive evolution or, alternatively, are mere curiosities of little overall importance. Even theoretical studies are often limited to simple two-mutation, two-allele models of evolution, which may not capture the more complex adaptive dynamics on a high-dimensional fitness landscape.

Here, we use the Avida platform (version 2.6; http://devolab.msu.edu) to study the importance of deleterious mutations in adaptive evolution (11, 25). In Avida, self-replicating computer programs called digital organisms compete for energy that allows them to execute the behaviors encoded by their genomes. Each single-instruction processing unit, or SIP, of energy allows a digital organism to execute one instruction in its genome. As populations of digital organisms evolve, they may become more efficient, requiring fewer SIPs to replicate, and they may acquire new computational functions that allow them to obtain more SIPs. As in nature, selection acts on the phenotype rather than directly on the genome, and many or most mutations have deleterious effects, whereas beneficial mutations are less common (19). Mutations in digital organisms often interact epistatically rather than multiplicatively, once again as observed in many natural systems (3, 14–18, 21–24). The digital organisms in this study live on a toroidal grid; when an organism replicates, its progeny is placed at random in one of the nine neighboring cells (including that occupied by the parent), replacing the previous occupant. Thus, population size remains constant. In our analyses, we typically focus on the most abundant genotype in a population at the end of an experimental run. We refer to this genotype as the “final dominant.” We also examine the “line of descent” that includes every organism along the lineage from the initial ancestor to the final dominant (11, 12, 25).

Lenski et al. (11) previously found instances of deleterious mutations acting as stepping stones while using Avida to examine the origin of a complex logic function called “bitwise equals” (EQU). Five of 23 replicate populations that evolved EQU had a deleterious mutation on the line of descent immediately before evolving the EQU phenotype. Reversion of those deleterious, penultimate mutations eliminated the EQU phenotype in three of the five cases, indicating that those three mutations contributed to the EQU function despite the fact that they reduced fitness on the backgrounds in which they first appeared. Cowperthwaite et al. (12) found similar stepping stones in simulations of evolving RNA sequences. Two other studies with digital organisms suggested that deleterious mutations could play an important role in adaptation on rugged fitness landscapes (26), even in sexual populations (27). However, none of these previous studies examined whether the stepping stones were important or even essential for sustained adaptation or, alternatively, were mere detours occasionally followed by evolving populations but of little or no consequence for long-term fitness gains.

To address this issue, we first examined the dynamics of adaptation in 50 populations of digital organisms that evolved under four mutation treatments (described in the next paragraph). We seeded populations with a hand-written ancestral organism whose genome consisted of a copy loop with instructions required for self-replication and a string of initially nonfunctional instructions that change under the influences of mutation, drift, and selection as the organisms adapt to their environment. Our experiments thus correspond to a low-fitness population with extensive opportunities for adaptation to a novel environment. Genome length was held constant at 50 instructions to facilitate and automate certain analyses. Each offspring had a 25% chance of having a single point mutation, which would change the instruction at a random site to one of 25 alternative instructions. The fitness landscape thus contained 26⁵⁰ distinct genotypes, with the fitness of each depending on the expression of the resulting genomic program and the fit of that program to the environment, including its ability to produce offspring, its speed of replication, and its success in performing one or more Boolean logic operations that provide additional SIPs. The small genome size and high mutation rate are roughly comparable with some RNA viruses. This genetic landscape and these parameters are sufficiently complex to shed light on evolution under circumstances beyond those amenable to formal theory or conventional population-genetic simulations. Moreover, the computational environment of digital organisms allows us to perform experiments that are impossible with biological systems.

Throughout this study, including in all treatment and control populations, we disallowed double mutations to facilitate classifying each mutation as beneficial, neutral, deleterious, or lethal. Before a mutant offspring was placed into the population, its fitness was evaluated in an isolated test environment, thus taking advantage of an opportunity that exists in a computational realm but not in a biological one, namely, to measure the effect of a mutation before it impacts a population’s evolution (Fig. S1A). Our initial experiments included a control treatment, where all mutation types were allowed, and three other treatments that eliminated deleterious mutations: Revert Deleterious (RvD), Replace Deleterious (RpD), and Replace Deleterious and Lethal (RpDL). Besides eliminating deleterious mutations, these treatments also affected the overall mutation rate and the distribution of fitness effects (Fig. S1 B–D). All other parameters were identical across treatments, including the ancestral genotype, selective environment, population size (10,000), and duration (250,000 updates, typically ∼45,000 generations) (Supporting Information).

After comparing the effects of these treatments, we examine a case study in more detail, and we perform replay experiments starting from adjacent genotypes to quantify the effects of individual deleterious mutations on subsequent adaptation. Further, we compare the effects of reverting or replacing deleterious mutations with the effects of similar treatments applied to neutral mutations. Finally, we explore how mutation rate and sexual reproduction influence the effects of deleterious mutations on long-term adaptation.

Results and Discussion

Effects of Reverting and Replacing Deleterious Mutations.

If deleterious mutations merely impede adaptive evolution, then populations that evolve in the treatments that prevent deleterious mutations should achieve higher mean fitness than control populations. However, if enough deleterious mutations serve as evolutionary stepping stones, then the control populations should reach higher fitness levels.

We ran three experimental treatments and one control treatment, as illustrated in Fig. S1. In the RvD treatment (Fig. S1B), each deleterious (but not lethal) mutation was reverted, as if it had never occurred. In the RpD treatment (Fig. S1C), each deleterious mutation was replaced with a random beneficial, neutral, or lethal mutation. In the RpDL treatment (Fig. S1D), each deleterious or lethal mutation was replaced with a random beneficial or neutral mutation. Finally, in the control treatment, all mutations were allowed to enter the population normally.

Fig. 1 shows the fitness trajectories for 50 populations under all four treatments. The control populations, which experienced deleterious mutations, reached higher fitness values, on average, than the treatment populations. We performed three Mann–Whitney tests to compare the fitness values of the final most-abundant genotypes in the control populations with the corresponding values for each alternative treatment; the difference was significant in every case (all P < 0.02). Differences among the three treatments that prevented deleterious mutations were more subtle, but also significant (P = 0.0283; Kruskal–Wallis test). The RvD treatment, in which deleterious mutations were reverted (thus reducing the total mutation rate), attained lower fitness levels than the two treatments where deleterious mutations were replaced (P = 0.0098 and P = 0.0575 versus RpDL and RpD, respectively, Mann–Whitney tests). The two replacement treatments did not differ significantly (P = 0.5510, Mann–Whitney test). Therefore, deleterious mutations in fact accelerated adaptive evolution by acting as stepping stones that facilitated the exploration of rugged fitness landscapes.

Fig. 1.

Fitness trajectories under four treatments affecting the entry of deleterious mutations into evolving populations. Black lines show log₁₀-transformed population mean fitness for 50 replicate populations in each treatment; red lines show the corresponding median across replicates. (A) Each deleterious (but not lethal) mutation was reverted, as if it had never occurred (RvD). (B) Each deleterious mutation was replaced with a random beneficial, neutral, or lethal mutation (RpD). (C) Each deleterious or lethal mutation was replaced with a random beneficial or neutral mutation (RpDL). (D) Control populations, in which all mutations were allowed to enter the population normally. Treatments that prevented deleterious mutations significantly impeded long-term adaptation. See text for statistical analyses.

Case Study and Evolutionary Replays.

To examine the importance of stepping stones in greater detail, we focused on the evolution of a particular function, EQU, which is the most complex (and most valuable) operation in the experimental environment and was the focal trait in the study by Lenski et al. (11). In our experiments, 28 of the 50 control populations evolved the EQU function whereas 16 or fewer of 50 did so for each treatment that precluded deleterious mutations. We performed Fisher’s exact tests comparing the frequency of evolving EQU in control populations with the corresponding frequencies under the other treatments, and we found significant differences in all three cases (all P < 0.05), consistent with the effects observed on overall fitness.

We next chose one deleterious mutation in one replicate population as a case study for in-depth analysis. That mutation reduced fitness by ∼9% when it first occurred (Fig. 2A). We refer to this mutation as A. The subsequent mutation on the line of descent, N, was neutral and played no adaptive role, as evidenced by constructing and comparing genotypes with and without that mutation and finding no differences in fitness or any other trait. The next mutation, B, interacted with the earlier deleterious mutation A to generate the ability to perform EQU for the first time in that population. However, mutation B was nearly lethal on its own; it reduced fitness by ∼99% in constructed genotypes without mutation A. This example thus presents a deleterious mutation that clearly served as a stepping stone (Fig. 2B). However, it is unclear from this single outcome whether other paths from the previous genotype could have produced the EQU function without this or any other deleterious mutation.

Fig. 2.

Analysis of a mutational sequence in a control population, showing a deleterious mutation acting as a stepping stone. (A) Fitness values (W) for four successive genotypes on the line of descent and constructions of the four other possible combinations of the same three mutations. The initially deleterious mutation, A, was beneficial only when combined with B; similarly, B was beneficial only when combined with A. The other mutation, N, was neutral and had no effect on fitness either alone or in combination with A, B, or both. All fitness values are expressed relative to the immediate progenitor (abn). (B) Fitness landscape of the four genotypes, excluding the neutral mutation. Genotypes ab, Ab, and AB all appeared on the line of descent whereas aB was constructed. Mutations A and B display a sign-epistatic fitness interaction.

To address that issue, we replayed evolution in the test case starting from two adjacent genotypes on the line of descent, one carrying the first deleterious mutation (Ab) and the other its immediate progenitor (ab). We ran 20 replicates starting from each genotype for 20,000 updates (∼3,500 generations) under the RpD treatment that disallowed subsequent deleterious mutations. A duration of 20,000 updates was sufficiently long to provide insight into the adaptive potential of these genotypes, while limiting the computational resources required to perform these experiments to a reasonable level. All 20 replays that started from Ab evolved EQU whereas none of the replays starting from ab did. Therefore, the deleterious mutation A was crucial for the evolution of EQU in that lineage (P ≪ 0.0001, Fisher's exact test).

We also performed 20 replays with the same progenitor genotype (ab), except using the control protocol, in which deleterious mutations could serve as stepping stones. Thirteen of these populations evolved EQU, a highly significant difference from the outcome under the RpD treatment (P < 0.0001, Fisher's exact test). Nine populations that reevolved EQU acquired the same pair of sign-epistatic mutations as in the original population whereas three replays evolved a different sign-epistatic pair. The remaining population followed a more complex route involving several intermediates, each with the same fitness defect, before acquiring a mutation that finally produced EQU. Thus, this lineage drifted across multiple stepping stones, illustrating the added effect of a neutral network (2, 28, 29).

We then expanded this replay approach to include all cases among the original control populations that satisfied the following conditions: at least one pair of mutations interacted sign-epistatically, the first mutation in that pair was substantially deleterious in the background in which it first arose (>1% fitness loss), and that same mutation was present and had become beneficial in the most abundant genotype of the final population. A total of 36 cases fulfilled these criteria. For each of these cases, we used the RpD protocol to evolve 20 populations starting from the deleterious mutant and 20 starting from its immediate progenitor, and we compared them after 20,000 updates (Fig. 3). Overall, the fitness values were significantly higher in populations founded by the deleterious mutants than in those founded by their progenitors (P = 0.0223, Wilcoxon signed-ranks test comparing medians, across replicates, of log-transformed fitness of the final dominant in each population). We also performed Mann–Whitney tests for each pair of genotypes, using a Bonferroni correction (30) to adjust the overall false-positive rate to α = 0.05 across all 36 tests. There were significant differences in 11 cases, and, in all of them, the populations started with the deleterious mutant achieved higher fitness; it is extremely unlikely that, by chance, all 11 significant contrasts would occur in the same direction (P = 0.0010, binomial test). In six cases, the mutant-derived populations reached much higher fitness in at least some replays whereas, in five cases, they achieved only slightly higher levels but did so consistently across most or all of the replays (Table S1). Thus, many of the deleterious mutations that served as stepping stones were not merely rare events of no lasting importance; instead, they opened up adaptive routes that were otherwise inaccessible.

Fig. 3.

Median final fitness values for populations founded by genotypes with (y axis) or without (x axis) each of 36 initially deleterious mutations. The mutations were all of large effect (>1% fitness loss), and each later became beneficial in one of the original control populations via sign-epistatic interactions with subsequent mutations. We used each mutant to found 20 new populations, and we used its immediate progenitor (lacking the deleterious mutation) to found an additional 20 populations; the new populations evolved for 20,000 updates. All subsequent deleterious mutations were replaced (RpD treatment) in every population. The median fitness values for the final dominant genotypes in the 20 replicate populations are shown. The dashed line corresponds to the null hypothesis that final fitness values would be unaffected by the initial deleterious mutation. Values below the line indicate that the mutation impeded long-term adaptation; values above the line imply that the deleterious mutation promoted long-term adaptation. The symbols indicate whether the treatments with and without the initial mutation differed significantly (P < 0.05, Mann–Whitney test with Bonferroni correction; see Table S1). Filled square, significant difference; open square, no significant difference. See text for further statistical analyses.

Effects of Reverting and Replacing Neutral Mutations.

The finding that deleterious mutations can act as important stepping stones for adaptive evolution raises the question of whether neutral mutations play a similar role. To address that question, we performed additional experiments in which we reverted (RvN) or replaced (RpN) neutral mutations using the same experimental design described above. As before, we also controlled for the inflated load of lethal mutations in the RpN treatment by including a treatment in which we replaced both neutral and lethal (RpNL) mutations.

One might expect that eliminating neutral mutations would slow adaptive evolution even more than eliminating deleterious mutations, on the grounds that neutral mutations have a longer half life than deleterious mutations and thus neutral mutations should persist as stepping stones for longer periods. On the other hand, there are fewer neutral than deleterious mutations in this system (19). Also, neutral mutations typically have fewer phenotypic effects than deleterious ones, and having some effects—even if they are deleterious—may be important for the epistatic interactions that allow stepping-stone mutations to promote adaptation. Both the RpN and RvN treatments yielded significantly lower fitness levels than did the control (P = 0.0127 and P = 0.0015, respectively, Mann–Whitney tests), but the difference between the RpNL treatment and control was not significant (P = 0.2626). On balance, the effects of excluding neutral mutations (Fig. 4) were similar to the effects of excluding deleterious mutations (Fig. 1). There were no significant differences between the fitness levels for the RpN and RpD treatments or the RpNL and RpDL treatments (P = 0.7433 and P = 0.2398, respectively, Mann–Whitney tests). However, the RvD treatment produced significantly lower fitness levels than did the RvN treatment (P = 0.0490). It is important to note, however, that the RvD treatment resulted in a lower overall mutation rate than the RvN treatment because more mutations are deleterious than neutral in this system (19). More generally, the fact that excluding either neutral or deleterious mutations caused comparable reductions in final fitness levels suggests that both contribute variation that is important for sustaining long-term adaptive evolution. Perhaps some fitness peaks are more accessible by neutral mutations and others by deleterious mutations.

Fig. 4.

Fitness trajectories under four treatments affecting the entry of neutral mutations into evolving populations. Black lines show log₁₀-transformed population mean fitness for 50 replicate populations in each treatment; red lines show the corresponding median across replicates. (A) Each neutral mutation was reverted, as if it had never occurred (RvN). (B) Each neutral mutation was replaced with a random beneficial, deleterious, or lethal mutation (RpN). (C) Each neutral or lethal mutation was replaced with a random beneficial or deleterious mutation (RpNL). (D) Control populations, in which all mutations were allowed to enter the population normally. The RvN and RpN treatments significantly impeded long-term adaptation; the RpNL treatment tended toward lower fitness than the control treatment, but the difference was not significant. See text for statistical analyses.

Deleterious mutations occurred under the RvN, RpN, and RpNL treatments, and they would often have replaced neutral mutations under the RpN and RpNL treatments. Therefore, we investigated whether deleterious mutations ameliorated the absence of neutral mutations in these treatments by acting as stepping stones. As before, we identified all those mutations that reduced fitness by >1%, belonged to a sign-epistatic pair, and remained in the final dominant genotype. For the 50 replicates in each treatment, we found 200 such mutations in the RvN lineages, 247 in the RpN lineages, and 95 in the RpNL lineages, compared with only 36 in the control lineages.

The RpN treatment had the most deleterious mutations among the three treatments that prevented neutral mutations, and so we examined to what extent those deleterious mutations had contributed to the realized fitness gains under this treatment. We performed paired sets of replay experiments, as before, starting from genotypes either with or without the initial deleterious mutation in the 247 sign-epistatic mutations (Table S2). However, these replays were conducted under the RpD treatment, such that neutral mutations were allowed but further deleterious mutations were precluded, to assess the influence of the initial deleterious mutation only. Twenty-two of the 247 sets of replays achieved significantly higher fitness in the populations seeded with the deleterious mutants whereas seven of the deleterious mutants led to significantly lower fitness (all P < 0.05 after Bonferroni correction). Across all 247 sets of replays, the populations that started with the deleterious mutants evolved significantly higher fitness than those started with the progenitor (P = 0.0019, Wilcoxon signed-rank test). Thus, the replacement of neutral mutations by deleterious ones tended to facilitate adaptation in the RpN populations, evidently because the populations found mutational paths involving sign-epistatic interactions. In contrast, populations that evolved under the RvN treatment, where neutral mutations were reverted (but not replaced), experienced an overall lower mutation rate and fewer deleterious mutations than those under the RpN treatment.

We performed another set of experiments in which both deleterious and neutral mutations were reverted or replaced to assess their combined effects on long-term adaptation. We thus eliminated the opportunity for evolving populations to use any stepping stones that were not immediately adaptive; therefore, adaptation could proceed only by a strict hill-climbing process. As expected, these populations achieved much lower fitness levels than the control populations that had access to deleterious and neutral mutations (Fig. 5, all P ≪ 0.0001, Mann–Whitney test).

Fig. 5.

Fitness trajectories under treatments affecting the entry of both neutral and deleterious mutations into evolving populations. Black lines show log₁₀-transformed population mean fitness for 50 replicate populations in each treatment; red lines show the corresponding median across replicates. (A) Each neutral or deleterious (but not lethal) mutation was reverted, as if it had never occurred. (B) Each neutral or deleterious mutation was replaced with a random beneficial or lethal mutation. (C) Each neutral, deleterious or lethal mutation was replaced with a random beneficial mutation (if one was found within 100 attempts). (D) Control populations, in which all mutations were allowed to enter the population normally. The treatments that prevented both neutral and deleterious mutations significantly impeded long-term adaptation relative to treatments that prevented only neutral or deleterious mutations. See text for statistical analyses.

Effect of Mutation Rate on Use of Stepping Stones.

All of the experiments above were performed with the mutation rate similar to the rate used in a previous study (11) that motivated our work; specifically, organisms had a 25% chance of a single point mutation per replication cycle in our experiments. To examine the effect of mutation rate on the propensity of evolving populations to use deleterious mutations as stepping stones, we ran experiments at both lower and higher mutation rates, with the probability of mutation per replication set to 8% and 75%, respectively; other parameters were unchanged. We ran only the control and RpD treatments, but we increased the number of replicates to 200 for each treatment to improve statistical power.

At the lower mutation rate, the median log-transformed fitness at the end of the runs was slightly lower for the RpD treatment than for the controls, but the difference was not significant (P = 0.0743, Mann–Whitney test) (Fig. S2). At the higher mutation rate, the median log fitness was actually slightly higher for the RpD treatment than for the controls although this difference was also not significant (P = 0.1786, Mann–Whitney test) (Fig. S3). Thus, the extent to which evolving populations use deleterious mutations as stepping stones is sensitive to the mutation rate and appears to reach some maximum at an intermediate rate. Evolution via stepping stones may occur less often at lower mutation rates because a deleterious mutation is more likely to be eliminated before the appearance of a potential compensatory mutation. This interpretation is consistent with results from numerical simulations (12). We were more surprised, however, that, at higher mutation rates, the use of stepping stones did not produce a measurable increase in final fitness. Previous theoretical studies have implicitly assumed that the rate of compensatory adaptation increases with the mutation rate (5–9). In that case, one would expect that deleterious mutations would be more important at higher mutation rate than at lower rates. One possible explanation for this unexpected result is that higher mutation rates drive populations toward flatter areas of the fitness landscape, with a greater proportion of mutations being neutral (31) and thus fewer opportunities for compensatory changes. Further work will be necessary to determine whether this explanation is correct.

Effect of Recombination on Use of Stepping Stones.

We also briefly explored the role of deleterious mutations as stepping stones in sexual populations. Recombination will tend to separate deleterious mutations from subsequent mutations that interact epistatically with them, and so we expected recombination to reduce or eliminate the utility of deleterious mutations as stepping stones in adaptive evolution. We implemented haploid recombination in Avida as described elsewhere (32). In brief, sexual digital organisms copied their genomes (potentially introducing mutations) just as asexual organisms did. However, before each sexual offspring was placed in the population, a random segment of its genome was replaced by a corresponding segment from another sexual offspring that was also about to be placed in the population. In the corresponding reversion treatment, deleterious mutations were reverted before recombination occurred. That is, for each incipient sexual offspring, we first tested whether it contained a deleterious mutation relative to its own parent, and, if so, the mutation was reverted before recombination and placement of the sexual offspring into the population.

The reversion treatment significantly depressed the final fitness levels relative to the control populations in the sexual populations (P < 0.0001, Mann–Whitney test). This result implies that many sign-epistatic interactions involved mutations that were sufficiently close that their linkage was not completely disrupted by recombination events. Previous work with digital organisms (32) has shown that recombination led to the evolution of more modular genomes, in which interacting sites tended to be physically close on the genome. This modularity may protect sign-epistatic interactions against disruption by recombination. A related study with Avida has confirmed that some initially deleterious mutations are indeed retained in sexual populations because they become beneficial after the appearance of linked sign-epistatic mutations (27). Not surprisingly, however, the difference between the reversion and control treatments was smaller in the sexual populations (Fig. S4) than in the asexual populations (Fig. 1), presumably because some sign-epistatic interactions were disrupted by recombination.

Recombination might also generate additional deleterious mutations—or, more precisely, expose mutations with deleterious effects—if some neutral mutations become detrimental when moved into other genetic backgrounds. Given the role of deleterious mutations as stepping stones in long-term adaptation, one might then imagine that sexual populations should evolve higher fitness than asexual ones because sexual populations experience more of these potential stepping stones. However, we found no evidence of such an effect; sexual and asexual populations in the control treatments achieved comparable final fitness values (P = 0.6124, Mann–Whitney test). Thus, any potential benefits of sexual reproduction were offset by costs, including the disruption of beneficial interactions between mutations.

Conclusions and Synthesis.

At first glance, it seems entirely reasonable to think that adaptation by natural selection proceeds through the appearance and fixation of beneficial mutations, and indeed many studies assume that adapting populations must follow paths of beneficial mutations through genotype space. For example, Weinreich et al. (3) considered only those paths involving sequential beneficial mutations in an empirical study on the evolution of antibiotic resistance in bacteria. In theoretical work, Poelwijk et al. (1) assumed that populations can cross fitness valleys and thereby reach higher fitness peaks only by simultaneous mutations, recombination, or relaxed selection. Other studies have considered the role of random drift on neutral networks in allowing access to otherwise inaccessible fitness peaks, but these studies also ignored the role of deleterious mutations as potential stepping stones (1–3, 13, 14, 26, 33). Of course, if a strictly uphill trajectory is mutationally accessible, then an evolving population will be more likely to take that path than one that involves a deleterious intermediate state, all else being equal. However, strictly uphill trajectories may not exist for every population; even when they exist, they may not be readily accessible depending on the number of mutations and their effects. An earlier study (11) using Avida found many cases where deleterious mutations were present on the line of descent and showed that, in some cases, these mutations played important roles in the evolution of complex new functions. Following that work, several theoretical studies (5, 8, 9, 12, 34) examined the role of deleterious mutations in crossing fitness valleys. However, these studies did not address whether this phenomenon was a mere curiosity—something that might occasionally happen, but without substantial or lasting effect on the process of adaptation—or, alternatively, whether deleterious mutations might be important for sustaining long-term adaptation. Here, we took advantage of the possibility in Avida (unlike organic systems) of testing the fitness effects of mutations before they are placed in a population, and then reverting or replacing some of them to preclude all deleterious mutations. These experiments demonstrate that deleterious mutations can, in fact, substantially increase fitness gains over long periods. However, the generality of this effect remains unclear and worthy of future empirical and theoretical investigation. We show that the effect is sensitive to mutation rate, with the long-term benefit of deleterious mutations highest at an intermediate mutation rate in this system. We also show that the effect is diminished, but not eliminated, by recombination in this system.

Materials and Methods

Treatments to Exclude Deleterious Mutations.

We used three treatments to preclude the occurrence of deleterious mutations that might act as stepping stones during adaptive evolution (Fig. S1A). These treatments differed in their impact on the overall mutation rate and the distribution of fitness effects (Fig. S1 B–D).

The RvD treatment reverted any nonlethal deleterious mutation to its previous state. Lethal mutations were not reverted because they cannot act as stepping stones. Deleterious mutations make up a large proportion of all mutations (typically about half in evolved genomes), and therefore this treatment reduced the overall mutation rate (Fig. S1B). To account for this effect on the mutation rate, the RpD treatment replaced a nonlethal deleterious mutation with another mutation by randomly sampling potential mutations until one belonging to a permissible class—beneficial, neutral, or lethal—was found. The RpD treatment thus maintained the overall mutation rate. However, this treatment increased the load of lethal mutations because they generally comprised the largest proportion of the permissible classes (Fig. S1C). The RpDL treatment addressed the increased load of lethal mutations by replacing both deleterious and lethal mutations, again maintaining the overall mutation rate but allowing only two classes of mutations, neutral and beneficial (Fig. S1D).

Two exceptions sometimes occurred that are not covered above. First, in the RpD and RpDL treatments, we tested a maximum of 100 candidate replacements before stopping the search to find a mutation belonging to an allowed class. This threshold was never reached under the RpD treatment because lethal alternative mutations were always abundant. However, in the RpDL treatment, the two largest classes of mutation (deleterious and lethal) were disallowed, and this threshold was occasionally reached. We examined 1,092,337 attempted replacements at 200 uniformly spaced updates across the 50 RpDL populations, and only 281 (<0.03%) failed to identify an acceptable replacement. In these rare cases, the original mutant was eliminated to prevent any deleterious mutations from entering the population. The second exception occurred in all treatments, including the controls. We occasionally encountered a mutant that, when tested in isolation, produced an offspring that was not an exact copy of itself, even if the mutation rate was set to zero. This type of unstable genotype can occur when an organism’s self-replication process is damaged. For example, a point mutation might cause the organism to copy only part of its genome, or to copy part of its genome more than once. We disallowed mutations that produced unstable genotypes in all treatments, including the control treatment, because our analyses were predicated on single mutations occurring in genomes of constant length.

Measuring the Fitness of Digital Organisms.

In the isolated test environment, and with additional mutations prevented, we evaluated each candidate mutant’s fitness by allowing it to execute its genome. We measured two aspects of its performance: the rate at which it acquired SIPs (single-instruction processing units) and the number of instructions executed to replicate itself. The ratio of these two numbers is a close approximation to the organism’s absolute fitness. If digital organism A has twice the fitness of organism B, then A will, on average, produce twice as many offspring as B in the same amount of time. This expectation is not frequency-dependent; i.e., it is independent of the relative abundance of A and B. Note also that previous work has shown that the outcome of direct competition is quantitatively consistent with the calculated differences in fitness except at very high mutation rates (31), where differences in offspring viability may become important; this effect is minimal at the mutation rates used in our study.

An organism obtained additional SIPs if, in the course of executing its genomic program, it performed one or more of nine distinct one- and two-input logic operations, according to the multiplicative schedule in Table S3. If a mutant could not self-replicate (within an allotted maximum time), the mutation was categorized as lethal. Otherwise, we classified the mutation as beneficial, neutral, or deleterious based on whether the mutant’s fitness was higher than, equal to, or lower than that of its immediate progenitor.

Reversion and Replacement of Neutral Mutations.

The RvN, RpN, and RpNL treatments followed the same procedures as the RvD, RpD, and RpDL treatments, respectively, except that neutral mutations were reverted or replaced rather than deleterious mutations. For the RvN and RpN treatments, mutations that changed fitness by <1% were considered to be neutral whereas, for the RpNL treatment, mutations were treated as neutral only if they did not affect fitness at all. Other experiments suggested that the exact definition of neutrality was immaterial to our general conclusions.

Reversion and Replacement in Sexual Populations.

Sexual recombination in digital organisms was implemented as described elsewhere (27, 32). In brief, an organism first produced an asexual copy of its genome. Then, two copies from different parents exchanged a section of their genomes to produce two offspring; we used two randomly chosen crossover points to define that section.

Potential mutations were tested for deleterious effects, and reversions were performed after genomes were copied but before recombination events. Therefore, mutations were judged as deleterious or not only against the background of the parent in which they arose. We did not perform replacement (rather than reversion) treatments in sexual populations.

Data Analyses and Statistics.

Analyses and statistics were performed in Python, using the libraries numpy, scipy, and matplotlib. Wilcoxon signed-rank tests were performed in R. All statistical tests were two-tailed. To correct for multiple tests in the replay experiments, we adjusted P values using the Dunn–Sidak method of the Bonferroni correction (30).