Exploiting the Adaptation Dynamics to Predict the Distribution of Beneficial Fitness Effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depends on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remains nearly a constant for exponentially decaying distributions and increases when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold good for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.     

The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa

Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.     

The Evolutionarily Stable Distribution of Fitness Effects

The distribution of fitness effects (DFE) of new mutations is a key parameter in determining the course of evolution. This fact has motivated extensive efforts to measure the DFE or to predict it from first principles. However, just as the DFE determines the course of evolution, the evolutionary process itself constrains the DFE. Here, we analyze a simple model of genome evolution in a constant environment in which natural selection drives the population toward a dynamic steady state where beneficial and deleterious substitutions balance. The distribution of fitness effects at this steady state is stable under further evolution and provides a natural null expectation for the DFE in a population that has evolved in a constant environment for a long time. We calculate how the shape of the evolutionarily stable DFE depends on the underlying population genetic parameters. We show that, in the absence of epistasis, the ratio of beneficial to deleterious mutations of a given fitness effect obeys a simple relationship independent of population genetic details. Finally, we analyze how the stable DFE changes in the presence of a simple form of diminishing-returns epistasis.     

The Consistency of Beneficial Fitness Effects of Mutations across Diverse Genetic Backgrounds

Parallel and convergent evolution have been remarkably common observations in molecular adaptation but primarily in the context of the same genotype adapting to the same conditions. These phenomena therefore tell us about the stochasticity and limitations of adaptation. The limited data on convergence and parallelism in the adaptation of different genotypes conflict as to the importance of such events. If the effects of beneficial mutations are highly context dependent (i.e., if they are epistatic), different genotypes should adapt through different mutations. Epistasis for beneficial mutations has been investigated but mainly through measurement of interactions between individually beneficial mutations for the same genotype. We examine epistasis for beneficial mutations at a broader genetic scale by measuring the fitness effects of two mutations beneficial for the ssDNA bacteriophage ID11 in eight different, related genotypes showing 0.3-3.7% nucleotide divergence from ID11. We found no evidence for sign epistasis, but the mutations tended to have much smaller or no effects on fitness in the new genotypes. We found evidence for diminishing-returns epistasis; the effects were more beneficial for lower-fitness genotypes. The patterns of epistasis were not determined by phylogenetic relationships to the original genotype. To improve our understanding of the patterns of epistasis, we fit the data to a model in which each mutation had a constant, nonepistatic phenotypic effect across genotypes and the phenotype-fitness map had a single optimum. This model fit the data well, suggesting that epistasis for these mutations was due to nonlinearity in the phenotype-fitness mapping and that the likelihood of parallel evolution depends more on phenotype than on genotype.     

Perceptual Adaptation to the Correction of Natural Astigmatism

Background

The visual system adjusts to changes in the environment, as well as to changes within the observer, adapting continuously to maintain a match between visual coding and visual environment. We evaluated whether the perception of oriented blur is biased by the native astigmatism, and studied the time course of the after-effects following spectacle correction of astigmatism in habitually non-corrected astigmats.

Methods and Findings

We tested potential shifts of the perceptual judgments of blur orientation in 21 subjects. The psychophysical test consisted on a single interval orientation identification task in order to measure the perceived isotropic point (astigmatism level for which the image did not appear oriented to the subject) from images artificially blurred with constant blur strength (B = 1.5 D), while modifying the orientation of the blur according to the axis of natural astigmatism of the subjects. Measurements were performed after neutral (gray field) adaptation on naked eyes under full correction of low and high order aberrations. Longitudinal measurements (up to 6 months) were performed in three groups of subjects: non-astigmats and corrected and uncorrected astigmats. Uncorrected astigmats were provided with proper astigmatic correction immediately after the first session. Non-astigmats did not show significant bias in their perceived neutral point, while in astigmatic subjects the perceived neutral point was significantly biased, typically towards their axis of natural astigmatism. Previously uncorrected astigmats shifted significantly their perceived neutral point towards more isotropic images shortly (2 hours) after astigmatic correction wear, and, once stabilized, remained constant after 6 months. The shift of the perceived neutral point after correction of astigmatism was highly correlated with the amount of natural astigmatism.

Conclusions

Non-corrected astigmats appear to be naturally adapted to their astigmatism, and astigmatic correction significantly changes their perception of their neutral point, even after a brief period of adaptation.     

A Comparison of Models to Infer the Distribution of Fitness Effects of New Mutations

Knowing the distribution of fitness effects (DFE) of new mutations is important for several topics in evolutionary genetics. Existing computational methods with which to infer the DFE based on DNA polymorphism data have frequently assumed that the DFE can be approximated by a unimodal distribution, such as a lognormal or a gamma distribution. However, if the true DFE departs substantially from the assumed distribution (e.g., if the DFE is multimodal), this could lead to misleading inferences about its properties. We conducted simulations to test the performance of parametric and nonparametric discretized distribution models to infer the properties of the DFE for cases in which the true DFE is unimodal, bimodal, or multimodal. We found that lognormal and gamma distribution models can perform poorly in recovering the properties of the distribution if the true DFE is bimodal or multimodal, whereas discretized distribution models perform better. If there is a sufficient amount of data, the discretized models can detect a multimodal DFE and can accurately infer the mean effect and the average fixation probability of a new deleterious mutation. We fitted several models for the DFE of amino acid-changing mutations using whole-genome polymorphism data from Drosophila melanogaster and the house mouse subspecies Mus musculus castaneus. A lognormal DFE best explains the data for D. melanogaster, whereas we find evidence for a bimodal DFE in M. m. castaneus.     

Using Species Distribution Models to Predict Potential Landscape Restoration Effects on Puma Conservation

A mosaic of intact native and human-modified vegetation use can provide important habitat for top predators such as the puma (Puma concolor), avoiding negative effects on other species and ecological processes due to cascade trophic interactions. This study investigates the effects of restoration scenarios on the puma’s habitat suitability in the most developed Brazilian region (São Paulo State). Species Distribution Models incorporating restoration scenarios were developed using the species’ occurrence information to (1) map habitat suitability of pumas in São Paulo State, Southeast, Brazil; (2) test the relative contribution of environmental variables ecologically relevant to the species habitat suitability and (3) project the predicted habitat suitability to future native vegetation restoration scenarios. The Maximum Entropy algorithm was used (Test AUC of 0.84 ± 0.0228) based on seven environmental non-correlated variables and non-autocorrelated presence-only records (n = 342). The percentage of native vegetation (positive influence), elevation (positive influence) and density of roads (negative influence) were considered the most important environmental variables to the model. Model projections to restoration scenarios reflected the high positive relationship between pumas and native vegetation. These projections identified new high suitability areas for pumas (probability of presence >0.5) in highly deforested regions. High suitability areas were increased from 5.3% to 8.5% of the total State extension when the landscapes were restored for ≥ the minimum native vegetation cover rule (20%) established by the Brazilian Forest Code in private lands. This study highlights the importance of a landscape planning approach to improve the conservation outlook for pumas and other species, including not only the establishment and management of protected areas, but also the habitat restoration on private lands. Importantly, the results may inform environmental policies and land use planning in São Paulo State, Brazil.     

Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization.     

Viral Adaptation to an Antiviral Protein Enhances the Fitness Level to Above That of the Uninhibited Wild Type

Viruses often evolve resistance to antiviral agents. While resistant strains are able to replicate in the presence of the agent, they generally exhibit lower fitness than the wild-type strain in the absence of the inhibitor. In some cases, resistant strains become dependent on the antiviral agent. However, the agent rarely, if ever, elevates dependent strain fitness above the uninhibited wild-type level. This would require an adaptive mechanism to convert the antiviral agent into a beneficial growth factor. Using an inhibitory scaffolding protein that specifically blocks φX174 capsid assembly, we demonstrate that such mechanisms are possible. To obtain the quintuple-mutant resistant strain, the wild-type virus was propagated for approximately 150 viral life cycles in the presence of increasing concentrations of the inhibitory protein. The expression of the inhibitory protein elevated the strain''s fitness significantly above the uninhibited wild-type level. Thus, selecting for resistance coselected for dependency, which was characterized and found to operate on the level of capsid nucleation. To the best of our knowledge, this is the first report of a virus evolving a mechanism to productively utilize an antiviral agent to stimulate its fitness above the uninhibited wild-type level. The results of this study may be predictive of the types of resistant phenotypes that could be selected by antiviral agents that specifically target capsid assembly.While viruses often acquire resistance to antiviral agents, resistance mutants generally exhibit lower fitness than the wild-type strain in the absence of the inhibitor (6, 16, 17, 25) and can develop a dependency on the antiviral agent (1, 19). However, the molecular mechanism of dependency rarely, if ever, involves the productive use of the antiviral agent to elevate fitness above the uninhibited wild-type level. Many studies are conducted with animal viruses, often in clinical settings, which can impose restraints on the experimental durations. Thus, prolonged exposure to antiviral agents may be required for the emergence of a multiply mutant strain that has evolved mechanisms to productively utilize inhibitors.Due to its rapid replication, bacteriophage φX174 has become an attractive model system for evolutionary studies (2, 3, 23, 24). Selective pressures can be applied for hundreds of infection cycles in a relatively short period of time. Using the atomic structure of assembly intermediates as a guide (8, 9, 15), viral scaffolding proteins that inhibit virion assembly have been designed (4). The molecular mechanism of inhibition was characterized, and resistance mutants were isolated via one-step genetic selections (4). In this study we report the isolation of a more robust resistant mutant. The quintuple mutant was generated by propagating φX174 for approximately 150 life cycles in the presence of increasing concentrations of the inhibitory protein, which was derived from the external scaffolding D protein. This protein forms asymmetric dimers that direct procapsid assembly. A conformational switch at glycine residue 61 (G61) in α-helix 3 is critical for productive dimer formation. In one subunit, α-helix 3 is bent 30°, whereas it assumes a straight conformation in the other subunit. All amino acid substitutions for G61 inhibit the ability to undergo the requisite conformational switch. The severity of the conferred dominant lethal phenotypes directly correlates with the side chain sizes of the substituted amino acids (4, 5).The inhibitory proteins most likely remove assembly intermediates by lowering the thermodynamic barriers that normally prevent off-pathway reactions (4, 5). Both off-pathway reactions and proper assembly involve D-D protein interactions across what will become the twofold axes of symmetry in the virion (8, 9). In the procapsid crystal structure, α-helix 3 of the D₂, D₃, and D₄ subunits mediates these interactions. Mutants resistant to the dominant lethal proteins were isolated in one-step genetic selections, and mutations mapped to either the coat or internal scaffolding proteins. These mutations may indirectly reinstate the avidity of the D protein electrostatic bonding partners required for productive morphogenesis (4, 5). However, the resistance phenotype is weak. To isolate a more robust phenotype, wild-type φX174 was continually cultured through exponential phase cells expressing an inhibitory D protein. Results from this analysis indicate that the selection for resistance coselected for a level of dependence. The inhibitory protein stimulates resistant strain fitness significantly above the uninhibited wild-type level and appears to be required for efficient capsid nucleation. These results suggest that the virus evolved a mechanism to convert this potent antiviral agent into a beneficial factor and may be predictive of the types of resistant phenotypes that could be selected by antiviral agents that specifically target capsid assembly.     

Distribution of Fitness Effects Caused by Single-Nucleotide Substitutions in Bacteriophage f1

Empirical knowledge of the fitness effects of mutations is important for understanding many evolutionary processes, yet this knowledge is often hampered by several sources of measurement error and bias. Most of these problems can be solved using site-directed mutagenesis to engineer single mutations, an approach particularly suited for viruses due to their small genomes. Here, we used this technique to measure the fitness effect of 100 single-nucleotide substitutions in the bacteriophage f1, a filamentous single-strand DNA virus. We found that approximately one-fifth of all mutations are lethal. Viable ones reduced fitness by 11% on average and were accurately described by a log-normal distribution. More than 90% of synonymous substitutions were selectively neutral, while those affecting intergenic regions reduced fitness by 14% on average. Mutations leading to amino acid substitutions had an overall mean deleterious effect of 37%, which increased to 45% for those changing the amino acid polarity. Interestingly, mutations affecting early steps of the infection cycle tended to be more deleterious than those affecting late steps. Finally, we observed at least two beneficial mutations. Our results confirm that high mutational sensitivity is a general property of viruses with small genomes, including RNA and single-strand DNA viruses infecting animals, plants, and bacteria.MUTATIONAL fitness effects are relevant to many evolutionary processes. For instance, they determine the fraction of mutations that evolves neutrally (Ohta 1992), the amount of genetic variation at the mutation–selection balance (Haldane 1937), processes of fitness decay, such as Muller''s ratchet (Butcher 1995), mutational meltdown (Lynch et al. 1993), or lethal mutagenesis (Bull et al. 2007), the ability of organisms to fix beneficial mutations and evolve novel functions (Wagner 2005), or the origin of sex and recombination (Peck et al. 1997; de Visser et al. 2003). Considerable progress has been made in characterizing mutational fitness effects using model organisms or studying genetic variation in natural populations (Eyre-Walker and Keightley 2007). For instance, mutation–accumulation experiments suggest that the average effect of spontaneous deleterious mutations is 1% or lower (Kibota and Lynch 1996) in Escherichia coli, while roughly 90% of engineered gene knockouts are viable (Baba et al. 2006) and transposon insertions reduce fitness by 3% or less on average (Elena et al. 1998). In yeast, mutation–accumulation and chemical mutagenesis experiments have shown that mutations reduce fitness by 1–4% on average in diploid strains (Zeyl and de Visser 2001; Szafraniec et al. 2003; Joseph and Hall 2004). In nematodes most mutations have fitness effects lower than 1% (Keightley and Caballero 1997; Davies et al. 1999), in Drosophila the average effect of mutations ranges from 0.5 to 3.5% (Mukai et al. 1972; Ohnishi 1977; Fernández and López-Fanjul 1996; Fry et al. 1999), and, in humans, most segregating amino acid substitutions have fitness effects lower than 10% (Eyre-Walker and Keightley 2007).Although mutation–accumulation studies provide valuable information about the average effects of deleterious mutations, their power to infer the entire distribution of mutational effects, including neutral and lethal mutations, is more limited. Also, excluding bias due to selection can be problematic, and the precise location and nature of each mutation is often unknown. On the other hand, studies based on engineering mutations have been generally restricted to large deletions or insertions, which are probably infrequent in nature compared to point mutations. A direct and powerful approach that helps us to solve these difficulties consists of introducing single-nucleotide substitutions by site-directed mutagenesis. Due to their small genome sizes, viruses are excellent systems for achieving this goal. In previous work, this technique has been used for studying mutational fitness effects in several RNA viruses (Sanjuán et al. 2004; Carrasco et al. 2007; Domingo-Calap et al. 2009). However, less is known for DNA viruses—but see Domingo-Calap et al. (2009). Here, we use this approach to characterize the distribution of mutational fitness effects in the bacteriophage f1, an inovirus of the bacteriophage m13 clade, making two important improvements over previous work: first, the number of mutations tested is higher (100) and second, the contribution of experimental error to the observed distribution is explicitly accounted for. We show that one-fifth of single-nucleotide substitutions are lethal, while viable ones reduce fitness by 11% on average and can be described by a heavy-tail two-parameter distribution such as the log-normal. Interestingly, the fraction of beneficial mutations is unexpectedly high. We also compare the average effects of different mutation types and of mutations affecting different genes.