Fitness Valleys Research Articles

Accelerated crossing of fitness valleys through division of labor and cheating in asexual populations

Complex traits can require the accumulation of multiple mutations that are individually deleterious. Their evolution requires a fitness valley to be crossed, which can take relatively long time spans. A new evolutionary mechanism is described that accelerates the emergence of complex phenotypes, based on a “division of labor” game and the occurrence of cheaters. If each intermediate mutation leads to a product that can be shared with others, the complex type can arise relatively quickly as an emergent property among cooperating individuals, without any given individual having to accumulate all mutations. Moreover, the emergence of cheaters that destroy cooperative interactions can lead to the emergence of individuals that have accumulated all necessary mutations on a time scale that is significantly faster than observed in the absence of cooperation and cheating. Application of this mechanism to somatic and microbial evolution is discussed, including evolutionary processes in tumors, biofilms, and viral infections.

Reconstructing the Dynamics of HIV Evolution within Hosts from Serial Deep Sequence Data

At the early stage of infection, human immunodeficiency virus (HIV)-1 predominantly uses the CCR5 coreceptor for host cell entry. The subsequent emergence of HIV variants that use the CXCR4 coreceptor in roughly half of all infections is associated with an accelerated decline of CD4+ T-cells and rate of progression to AIDS. The presence of a ‘fitness valley’ separating CCR5- and CXCR4-using genotypes is postulated to be a biological determinant of whether the HIV coreceptor switch occurs. Using phylogenetic methods to reconstruct the evolutionary dynamics of HIV within hosts enables us to discriminate between competing models of this process. We have developed a phylogenetic pipeline for the molecular clock analysis, ancestral reconstruction, and visualization of deep sequence data. These data were generated by next-generation sequencing of HIV RNA extracted from longitudinal serum samples (median 7 time points) from 8 untreated subjects with chronic HIV infections (Amsterdam Cohort Studies on HIV-1 infection and AIDS). We used the known dates of sampling to directly estimate rates of evolution and to map ancestral mutations to a reconstructed timeline in units of days. HIV coreceptor usage was predicted from reconstructed ancestral sequences using the geno2pheno algorithm. We determined that the first mutations contributing to CXCR4 use emerged about 16 (per subject range 4 to 30) months before the earliest predicted CXCR4-using ancestor, which preceded the first positive cell-based assay of CXCR4 usage by 10 (range 5 to 25) months. CXCR4 usage arose in multiple lineages within 5 of 8 subjects, and ancestral lineages following alternate mutational pathways before going extinct were common. We observed highly patient-specific distributions and time-scales of mutation accumulation, implying that the role of a fitness valley is contingent on the genotype of the transmitted variant.

Mutational Pathway Determines Whether Drug Gradients Accelerate Evolution of Drug-Resistant Cells

Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anticancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a nonuniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combating the emergence of resistance.

The impact of interspecific competition on lineage evolution and a rapid peak shift by interdemic genetic mixing in experimental bacterial populations

Epistatic interactions between genes in the genome constrain the accessible evolutionary paths of lineages. Two factors involving epistasis that can affect the evolutionary path and fate of lineages were investigated. The first factor concerns the impact of competition with another species lineage that has different epistatic constraints. Five enteric bacterial populations were evolved by point mutation in medium containing a single limiting resource. Single-species and two-species cultures were used to determine whether different asexual lineages have different capacities for producing variants due to epistatic constraints, and whether their survival is determined by local inter-lineage competition with different species. Local inter-lineage competition quickly resulted in one successful lineage, with another lineage becoming extinct before finding a higher peak. The second factor concerns a peak-shifting process, and whether the sexual recombination between different demes can cause peak shifts was investigated. An Escherichia coli population consisting of a male (Hfr) and female strain (F−) was evolved in a single limiting resource and compared to evolving populations containing the male or female strain alone. The E. coli sexual lineage was successful due to its ability to escape lower peaks and reach a higher peak, not because of a rapid approach to the nearest local peak the male or female asexual lineage could reach. The data in this study demonstrate that lineage survivability can be determined by the ability to produce beneficial mutations and checked by local competition between lineages of different species. Interspecific competition may prevent a population from evolving through crossing fitness valleys or adaptive ridges if it requires many generations to achieve peak shifts. The data also show that genomic recombination between different conspecific lineages can rapidly carry the combined lineage to a higher peak.

Comparing ungulate dietary proxies using discriminant function analysis

A variety of tooth-wear and morphological dietary proxies have been proposed for ungulates. In turn, they have been applied to fossil specimens with the purpose of reconstructing the diets of extinct taxa. Although these dietary proxies have been used in isolation and in combination, a consistent set of statistical analyses has never been applied to all of the available datasets. The purpose of this study is to determine how well the most commonly used dietary proxies classify ungulates as browsers, grazers, and mixed feeders individually and in combination. Discriminant function analysis is applied to individual dietary proxies (hypsodonty, mesowear, microwear, and several cranial dietary proxies) and to combinations thereof to compare rates of successful dietary classification. In general, the tooth-wear dietary proxies (mesowear and microwear) perform better than morphological dietary proxies, though none are strong proxies in isolation. The success rates of the cranial dietary proxies are not increased substantially when ruminants and bovids are analyzed separately, and significance among the three dietary guilds is reduced when controlling for phylogenetic relatedness. The combination of hypsodonty, mesowear, and microwear is found to have a high rate of successful dietary classification, but a combination of all commonly used proxies increases the success rate to 100%. In most cases, mixed feeders bear the greatest resemblance to browsers suggesting that a morphology intermediate to browsers and grazers may represent a fitness valley resulting from the inability to exploit both browse and graze efficiently. These results are important for future paleoecological studies and should be used as a guide for determining which dietary proxies are appropriate to the research question.

Reciprocal Sign Epistasis between Frequently Experimentally Evolved Adaptive Mutations Causes a Rugged Fitness Landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.

ESCAPING AN EVOLUTIONARY LOBSTER TRAP: DRUG RESISTANCE AND COMPENSATORY MUTATION IN A FLUCTUATING ENVIRONMENT

The fitness landscape concept aids intuition on adaptive evolution through low fitness genotypes. Evolutionary processes become complex when environments and therefore fitnesses fluctuate. Antibiotic resistance evolution in bacteria is an important example of such dynamics. Resistance bears a cost in the drug-free environment, but compensatory mutation can lower this cost, creating a fitness valley. With the drug present, the valley becomes a hill that is easily climbed. Once a population is dominated by resistant-compensated genotypes, reversion to sensitivity is difficult: this phenomenon has been described as an evolutionary lobster trap. With increasing frequencies of drug resistance among pathogenic bacteria, it is critical to understand how this trap can be escaped. Here, we develop stochastic models to investigate these dynamics. The residual fitness cost (the cost remaining after compensatory mutation has occurred) is a key parameter. Reversion to sensitivity is favored when the time spent in the absence of the drug relative to its presence is high compared to the residual fitness cost. Population sizes are also important: in large populations, resistant-compensated mutants appear in resistant-uncompensated or sensitive-compensated genotypes without fixation of these intermediates. This stochastic tunneling effect occurs when sufficient time is allowed by the rates of environmental fluctuation.

The Rate of Fitness-Valley Crossing in Sexual Populations

Biological traits result in part from interactions between different genetic loci. This can lead to sign epistasis, in which a beneficial adaptation involves a combination of individually deleterious or neutral mutations; in this case, a population must cross a "fitness valley" to adapt. Recombination can assist this process by combining mutations from different individuals or retard it by breaking up the adaptive combination. Here, we analyze the simplest fitness valley, in which an adaptation requires one mutation at each of two loci to provide a fitness benefit. We present a theoretical analysis of the effect of recombination on the valley-crossing process across the full spectrum of possible parameter regimes. We find that low recombination rates can speed up valley crossing relative to the asexual case, while higher recombination rates slow down valley crossing, with the transition between the two regimes occurring when the recombination rate between the loci is approximately equal to the selective advantage provided by the adaptation. In large populations, if the recombination rate is high and selection against single mutants is substantial, the time to cross the valley grows exponentially with population size, effectively meaning that the population cannot acquire the adaptation. Recombination at the optimal (low) rate can reduce the valley-crossing time by up to several orders of magnitude relative to that in an asexual population.

GENOME STRUCTURE AND THE BENEFIT OF SEX

We examine the behavior of sexual and asexual populations in modular multipeaked fitness landscapes and show that sexuals can systematically reach different, higher fitness adaptive peaks than asexuals. Whereas asexuals must move against selection to escape local optima, sexuals reach higher fitness peaks reliably because they create specific genetic variants that "skip over" fitness valleys, moving from peak to peak in the fitness landscape. This occurs because recombination can supply combinations of mutations in functional composites or "modules," that may include individually deleterious mutations. Thus when a beneficial module is substituted for another less-fit module by sexual recombination it provides a genetic variant that would require either several specific simultaneous mutations in an asexual population or a sequence of individual mutations some of which would be selected against. This effect requires modular genomes, such that subsets of strongly epistatic mutations are tightly physically linked. We argue that such a structure is provided simply by virtue of the fact that genomes contain many genes each containing many strongly epistatic nucleotides. We briefly discuss the connections with "building blocks" in the evolutionary computation literature. We conclude that there are conditions in which sexuals can systematically evolve high-fitness genotypes that are essentially unevolvable for asexuals.

Base Pairing Constraints Drive Structural Epistasis in Ribosomal RNA Sequences

It has long been accepted that the structural constraints stemming from the 3D structure of ribosomal RNA (rRNA) lead to coevolution through compensating mutations between interacting sites. State-of-the-art methods for detecting coevolving sites, however, while reaching high levels of specificity and sensitivity for Watson-Crick (WC) pairs of the helices defining the secondary structure, only scarcely reveal tertiary interactions occurring at the level of the 3D structure. In order to understand the relative failure of coevolutionary methods to detect such interactions, we analyze 2,682 interacting sites derived from high-resolution structures, which include a comprehensive data set of rRNA sequences from Archaea and Bacteria. We report a striking difference in the amount of coevolution between WC and non-WC pairs. In order to understand this pattern, we derive fitness landscapes from the geometry of base pairing interactions and construct neutral networks of substitutions for each type of interaction. These networks show that coevolution is a property of WC pairs because, unlike non-WC pairs, their landscapes exhibit fitness valleys, a single mutation in a WC pair resulting in a fitness drop. Second, we used the inferred neutral networks to estimate the level of constraint acting on each type of base pair and show that it correlates negatively with the observed rate of substitutions for all non-WC pairs. WC pairs appear as outliers, fixing more substitutions than expected according to their level of constraint. We here propose that the rate of substitution in WC pairs is due to coevolution resulting from constraints acting at intermediate levels of organization, namely the one of the helical stem with its forming WC pairs. In agreement with this hypothesis, we report a significant excess of intrahelical, inter-WC pairs coevolution compared with interhelices pairs. Altogether, these results show that detailed biochemical knowledge is required and has to be incorporated into evolutionary reasoning in order to understand the fine patterns of variation at the molecular level. They also demonstrate that coevolutionary analysis provides almost exclusively 2D information and only little 3D signal.

Crossing fitness valleys during the evolution of limpet homing behaviour

Abstract Evolution is often considered a gradual hill-climbing process, slowly increasing the fitness of organisms. Here I investigate evolution of homing behaviour in simulated intertidal limpets. While the simulation of homing is only a possible mechanism by which homing may have evolved, the process allows an investigation of how evolution may occur over different fitness landscapes. With some fitness landscapes, in order to evolve path integration as a homing mechanism, a temporary reduction in an organism’s fitness was required — since high developmental costs occurred before successful homing strategies evolved. Simple hill-climbing algorithms, therefore, only rarely resulted in the evolution of a functional homing behaviour. The inclusion of trail-following greatly increases the frequency of success of evolution of a path integration strategy. Initially an emergent homing behaviour is formed combining path integration with trail-following. This also demonstrates evolution through exaptation, since in the simulation, the original role of trail-following is likely to be unrelated to homing. Analysis of the fitness landscapes of homing in the presence of trail-following behaviour shows a high variability of fitness, which results in the formation of ‘stepping-stones’ of high fitness across fitness valleys. By using these stepping-stones, simple hill-climbing algorithms can reach the global maximum fitness value.

Compensatory evolution in mitochondrial tRNAs navigates valleys of low fitness

A long-standing controversy in evolutionary biology is whether or not evolving lineages can cross valleys on the fitness landscape that correspond to low-fitness genotypes, which can eventually enable them to reach isolated fitness peaks. Here we study the fitness landscapes traversed by switches between different AU and GC Watson-Crick nucleotide pairs at complementary sites of mitochondrial transfer RNA stem regions in 83 mammalian species. We find that such Watson-Crick switches occur 30-40 times more slowly than pairs of neutral substitutions, and that alleles corresponding to GU and AC non-Watson-Crick intermediate states segregate within human populations at low frequencies, similar to those of non-synonymous alleles. Substitutions leading to a Watson-Crick switch are strongly correlated, especially in mitochondrial tRNAs encoded on the GT-nucleotide-rich strand of the mitochondrial genome. Using these data we estimate that a typical Watson-Crick switch involves crossing a fitness valley of a depth of about 10(-3) or even about 10(-2), with AC intermediates being slightly more deleterious than GU intermediates. This compensatory evolution must proceed through rare intermediate variants that never reach fixation. The ubiquitous nature of compensatory evolution in mammalian mitochondrial tRNAs and other molecules implies that simultaneous fixation of two alleles that are individually deleterious may be a common phenomenon at the molecular level.

The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate.

The rate at which asexual populations cross fitness valleys

Complex traits often involve interactions between different genetic loci. This can lead to sign epistasis, whereby mutations that are individually deleterious or neutral combine to confer a fitness benefit. In order to acquire the beneficial genotype, an asexual population must cross a fitness valley or plateau by first acquiring the deleterious or neutral intermediates. Here, we present a complete, intuitive theoretical description of the valley-crossing process across the full spectrum of possible parameter regimes. We calculate the rate at which a population crosses a fitness valley or plateau of arbitrary width, as a function of the mutation rates, the population size, and the fitnesses of the intermediates. We find that when intermediates are close to neutral, a large population can cross even wide fitness valleys remarkably quickly, so that valley-crossing dynamics may be common even when mutations that directly increase fitness are also possible. Thus the evolutionary dynamics of large populations can be sensitive to the structure of an extended region of the fitness landscape — the population may not take directly uphill paths in favor of paths across valleys and plateaus that lead eventually to fitter genotypes. In smaller populations, we find that below a threshold size, which depends on the width of the fitness valley and the strength of selection against intermediate genotypes, valley-crossing is much less likely and hence the evolutionary dynamics are less influenced by distant regions of the fitness landscape.

Assessing the fitness landscape revolution

According to Pigliucci and Kaplan, there is a revolution underway in how we understand fitness landscapes. Recent models suggest that a perennial problem in these landscapes—how to get from one peak across a fitness valley to another peak—is, in fact, non-existent. In this paper I assess the structure and the extent of Pigliucci and Kaplan’s proposed revolution and argue for two points. First, I provide an alternative interpretation of what underwrites this revolution, motivated by some recent work on model-based science. Second, I show that the implications of this revolution need to carefully assessed depending on question being asked, for peak-shifting is not central to all evolutionary questions that fitness landscapes have been used to explore.

Natural Selection Fails to Optimize Mutation Rates for Long-Term Adaptation on Rugged Fitness Landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.

Exaptation and emergence as mechanisms to cross fitness valleys during evolution: an example using simulated homing behaviour

AbstractEvolution is often considered a gradual hill climbing process, slowly increasing the fitness of organisms. I investigate the evolution of homing behaviour in simulated intertidal limpets. In order to evolve path integration as a homing mechanism, a temporary reduction in an organism’s fitness is required – since high developmental costs occur before a successful homing strategy evolves. Simple hill-climbing algorithms, therefore, only rarely result in the evolution of a functional homing behaviour. The inclusion of a second behaviour (trail-following) greatly increases the frequency of success of evolution of a path integration strategy. Initially an emergent homing behaviour is formed combining path integration with trail following. This also demonstrates evolution through exaptation, since the original role of trail following is likely to be unrelated to homing. Analysis of the fitness landscapes of homing in the presence of trail-following behaviour shows a high variability of fitness, which results in the formation of ‘stepping-stones’ of high fitness across fitness valleys. By using these stepping-stones, simple hill-climbing algorithms can reach the global maximum fitness value.

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.

Adaptation increases the likelihood of diversification in an experimental bacterial lineage

Understanding the mechanisms and processes that generate biological diversity is a fundamental problem in evolution and ecology. In the past decade, the theory of evolutionary branching and adaptive diversification has provided new perspectives for understanding the evolution of diversity caused by ecological interactions. In models of adaptive diversification, the fitness landscapes change dynamically, so that the likelihood of diversification into different phenotypic clusters increases over time. In contrast, in models with static fitness landscapes, the likelihood of diversification decreases as populations climb fitness peaks, because crossing maladaptive fitness valleys becomes increasingly difficult. We used experimental evolution in bacteria to test how the likelihood of diversification changes over time in a bacterial lineage that has diversified in sympatry from a single ancestral strain. By analyzing the "fossil" record of this lineage, and restarting the lineage from different time points in the evolutionary past, we demonstrate that: (i) the lineage has initially undergone a phase of directional adaptation to the competitive environment, and (ii) during this phase, the likelihood of diversification increases significantly over time. These results suggest evolutionary branching caused by frequency-dependent competition as the main mechanism of diversification in our experimental populations.

Human Immunodeficiency Virus Type 1 Coreceptor Switching: V1/V2 Gain-of-Fitness Mutations Compensate for V3 Loss-of-Fitness Mutations

Human immunodeficiency virus type 1 (HIV-1) entry into target cells is mediated by the virus envelope binding to CD4 and the conformationally altered envelope subsequently binding to one of two chemokine receptors. HIV-1 envelope glycoprotein (gp120) has five variable loops, of which three (V1/V2 and V3) influence the binding of either CCR5 or CXCR4, the two primary coreceptors for virus entry. Minimal sequence changes in V3 are sufficient for changing coreceptor use from CCR5 to CXCR4 in some HIV-1 isolates, but more commonly additional mutations in V1/V2 are observed during coreceptor switching. We have modeled coreceptor switching by introducing most possible combinations of mutations in the variable loops that distinguish a previously identified group of CCR5- and CXCR4-using viruses. We found that V3 mutations entail high risk, ranging from major loss of entry fitness to lethality. Mutations in or near V1/V2 were able to compensate for the deleterious V3 mutations and may need to precede V3 mutations to permit virus survival. V1/V2 mutations in the absence of V3 mutations often increased the capacity of virus to utilize CCR5 but were unable to confer CXCR4 use. V3 mutations were thus necessary but not sufficient for coreceptor switching, and V1/V2 mutations were necessary for virus survival. HIV-1 envelope sequence evolution from CCR5 to CXCR4 use is constrained by relatively frequent lethal mutations, deep fitness valleys, and requirements to make the right amino acid substitution in the right place at the right time.