A test for Y‐linked additive and epistatic effects on surviving bacterial infections in Drosophila melanogaster

Y‐ and W‐chromosomes offer a theoretically powerful way for sexual dimorphism to evolve. Consistent with this possibility, Drosophila melanogaster Y‐chromosomes can influence gene regulation throughout the genome; particularly immune‐related genes. In order for Y‐linked regulatory variation (YRV) to contribute to adaptive evolution it must be comprised of additive genetic variance, such that variable Ys induce consistent phenotypic effects within the local gene pool. We assessed the potential for Y‐chromosomes to adaptively shape gram‐negative and gram‐positive bacterial defence by introgressing Ys across multiple genetic haplotypes from the same population. We found no Y‐linked additive effects on immune phenotypes, suggesting a restricted role for the Y to facilitate dimorphic evolution. We did find, however, a large magnitude Y by background interaction that induced rank order reversals of Y‐effects across the backgrounds (i.e. sign epistasis). Thus, Y‐chromosome effects appeared consistent within backgrounds, but highly variable among backgrounds. This large sign epistatic effect could constrain monomorphic selection in both sexes, considering that autosomal alleles under selection must spend half of their time in a male background where relative fitness values are altered. If the pattern described here is consistent for other traits or within other XY (or ZW) systems, then YRV may represent a universal constraint to autosomal trait evolution.     

Selection for distinct gene expression properties favours the evolution of mutational robustness in gene regulatory networks

Mutational robustness is a genotype's tendency to keep a phenotypic trait with little and few changes in the face of mutations. Mutational robustness is both ubiquitous and evolutionarily important as it affects in different ways the probability that new phenotypic variation arises. Understanding the origins of robustness is specially relevant for systems of development that are phylogenetically widespread and that construct phenotypic traits with a strong impact on fitness. Gene regulatory networks are examples of this class of systems. They comprise sets of genes that, through cross‐regulation, build the gene activity patterns that define cellular responses, different tissues or distinct cell types. Several empirical observations, such as a greater robustness of wild‐type phenotypes, suggest that stabilizing selection underlies the evolution of mutational robustness. However, the role of selection in the evolution of robustness is still under debate. Computer simulations of the dynamics and evolution of gene regulatory networks have shown that selection for any gene activity pattern that is steady and self‐sustaining is sufficient to promote the evolution of mutational robustness. Here, I generalize this scenario using a computational model to show that selection for different aspects of a gene activity phenotype increases mutational robustness. Mutational robustness evolves even when selection favours properties that conflict with the stationarity of a gene activity pattern. The results that I present support an important role for stabilizing selection in the evolution of robustness in gene regulatory networks.     

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single‐gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.     

Long-term adaptation of epistatic genetic networks

Gene networks are likely to govern most traits in nature. Mutations at these genes often show functional epistatic interactions that lead to complex genetic architectures and variable fitness effects in different genetic backgrounds. Understanding how epistatic genetic systems evolve in nature remains one of the great challenges in evolutionary biology. Here we combine an analytical framework with individual-based simulations to generate novel predictions about long-term adaptation of epistatic networks. We find that relative to traits governed by independently evolving genes, adaptation with epistatic gene networks is often characterized by longer waiting times to selective sweeps, lower standing genetic variation, and larger fitness effects of adaptive mutations. This may cause epistatic networks to either adapt more slowly or more quickly relative to a nonepistatic system. Interestingly, epistatic networks may adapt faster even when epistatic effects of mutations are on average deleterious. Further, we study the evolution of epistatic properties of adaptive mutations in gene networks. Our results show that adaptive mutations with small fitness effects typically evolve positive synergistic interactions, whereas adaptive mutations with large fitness effects evolve positive synergistic and negative antagonistic interactions at approximately equal frequencies. These results provide testable predictions for adaptation of traits governed by epistatic networks and the evolution of epistasis within networks.     

Strong Epistatic Selection on the RNA Secondary Structure of HIV

A key question in evolutionary genomics is how populations navigate the adaptive landscape in the presence of epistasis, or interactions among loci. This problem can be directly addressed by studying the evolution of RNA secondary structures, for which there is constraint to maintain pairing between Watson-Crick (WC) sites. Replacement of a nucleotide at one site of a WC pair reduces fitness by disrupting binding, which can be restored via a compensatory replacement at the interacting site. Here, I present the first genome-scale analysis of epistasis on the RNA secondary structure of human immunodeficiency virus type 1 (HIV-1). Comparison of polymorphism frequencies at ancestrally conserved sites reveals that selection against replacements is ∼2.7 times stronger at WC than at non-WC sites, such that nearly 50% of constraint can be attributed to epistasis. However, almost all epistatic constraint is due to selection against conversions of WC pairs to unpaired (UP) nucleotides, whereas conversions to GU wobbles are only slightly deleterious. This disparity is also evident in pairs with second-site compensatory replacements; conversions from UP nucleotides to WC pairs increase median fitness by ∼4.2%, whereas conversions from GU wobbles to WC pairs only increase median fitness by ∼0.3%. Moreover, second-site replacements that convert UP nucleotides to GU wobbles also increase median fitness by ∼4%, indicating that such replacements are nearly as compensatory as those that restore WC pairing. Thus, WC peaks of the HIV-1 epistatic adaptive landscape are connected by high GU ridges, enabling the viral population to rapidly explore distant peaks without traversing deep UP valleys.     

A SHIFT FROM MAGNITUDE TO SIGN EPISTASIS DURING ADAPTIVE EVOLUTION OF A BACTERIAL SOCIAL TRAIT

Although the importance of epistasis in evolution has long been recognized, remarkably little is known about the processes by which epistatic interactions evolve in real time in specific biological systems. Here, we have characterized how the epistatic fitness relationship between a social gene and an adapting genome changes radically over a short evolutionary time frame in the social bacterium Myxococcus xanthus. We show that a highly beneficial effect of this social gene in the ancestral genome is gradually reduced—and ultimately reversed into a deleterious effect—over the course of an experimental adaptive trajectory in which a primitive form of novel cooperation evolved. This reduction and reversal of a positive social allelic effect is driven solely by changes in the genetic context in which the gene is expressed as new mutations are sequentially fixed during adaptive evolution, and explicitly demonstrates a significant evolutionary change in the genetic architecture of an ecologically important social trait.     

Epistatic interactions between ancestral genotype and beneficial mutations shape evolvability in Pseudomonas aeruginosa

The idea that interactions between mutations influence adaptation by driving populations to low and high fitness peaks on adaptive landscapes is deeply ingrained in evolutionary theory. Here, we investigate the impact of epistasis on evolvability by challenging populations of two Pseudomonas aeruginosa clones bearing different initial mutations (in rpoB conferring rifampicin resistance, and the type IV pili gene network) to adaptation to a medium containing l ‐serine as the sole carbon source. Despite being initially indistinguishable in fitness, populations founded by the two ancestral genotypes reached different fitness following 300 generations of evolution. Genome sequencing revealed that the difference could not be explained by acquiring mutations in different targets of selection; the majority of clones from both ancestors converged on one of the following two strategies: (1) acquiring mutations in either PA2449 (gcsR, an l ‐serine‐metabolism RpoN enhancer binding protein) or (2) protease genes. Additionally, populations from both ancestors converged on loss‐of‐function mutations in the type IV pili gene network, either due to ancestral or acquired mutations. No compensatory or reversion mutations were observed in RNA polymerase (RNAP) genes, in spite of the large fitness costs typically associated with mutations in rpoB. Although current theory points to sign epistasis as the dominant constraint on evolvability, these results suggest that the role of magnitude epistasis in constraining evolvability may be underappreciated. The contribution of magnitude epistasis is likely to be greatest under the biologically relevant mutation supply rates that make back mutations probabilistically unlikely.     

The causes of epistasis

Since Bateson's discovery that genes can suppress the phenotypic effects of other genes, gene interactions-called epistasis-have been the topic of a vast research effort. Systems and developmental biologists study epistasis to understand the genotype-phenotype map, whereas evolutionary biologists recognize the fundamental importance of epistasis for evolution. Depending on its form, epistasis may lead to divergence and speciation, provide evolutionary benefits to sex and affect the robustness and evolvability of organisms. That epistasis can itself be shaped by evolution has only recently been realized. Here, we review the empirical pattern of epistasis, and some of the factors that may affect the form and extent of epistasis. Based on their divergent consequences, we distinguish between interactions with or without mean effect, and those affecting the magnitude of fitness effects or their sign. Empirical work has begun to quantify epistasis in multiple dimensions in the context of metabolic and fitness landscape models. We discuss possible proximate causes (such as protein function and metabolic networks) and ultimate factors (including mutation, recombination, and the importance of natural selection and genetic drift). We conclude that, in general, pleiotropy is an important prerequisite for epistasis, and that epistasis may evolve as an adaptive or intrinsic consequence of changes in genetic robustness and evolvability.     

A Developmental Systems Perspective on Epistasis: Computational Exploration of Mutational Interactions in Model Developmental Regulatory Networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.     

GENETIC ARCHITECTURE AND POSTZYGOTIC REPRODUCTIVE ISOLATION: EVOLUTION OF BATESON–DOBZHANSKY–MULLER INCOMPATIBILITIES IN A POLYGENIC MODEL

The Bateson–Dobzhansky–Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high‐fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F₁ hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F₂ and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.     

Evolutionary rescue by compensatory mutations is constrained by genomic and environmental backgrounds

Since deleterious mutations may be rescued by secondary mutations during evolution, compensatory evolution could identify genetic solutions leading to therapeutic targets. Here, we tested this hypothesis and examined whether these solutions would be universal or would need to be adapted to one's genetic and environmental makeups. We performed experimental evolutionary rescue in a yeast disease model for the Wiskott–Aldrich syndrome in two genetic backgrounds and carbon sources. We found that multiple aspects of the evolutionary rescue outcome depend on the genotype, the environment, or a combination thereof. Specifically, the compensatory mutation rate and type, the molecular rescue mechanism, the genetic target, and the associated fitness cost varied across contexts. The course of compensatory evolution is therefore highly contingent on the initial conditions in which the deleterious mutation occurs. In addition, these results reveal biologically favored therapeutic targets for the Wiskott–Aldrich syndrome, including the target of an unrelated clinically approved drug. Our results experimentally illustrate the importance of epistasis and environmental evolutionary constraints that shape the adaptive landscape and evolutionary rate of molecular networks.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

DYNAMICS OF HYBRID INCOMPATIBILITY IN GENE NETWORKS IN A CONSTANT ENVIRONMENT

After an ancestral population splits into two allopatric populations, different mutations may fix in each. When pairs of mutations are brought together in a hybrid offspring, epistasis may cause reduced fitness. Such pairs are known as Bateson–Dobzhansky–Muller (BDM) incompatibilities. A well-known model of BDM incompatibility due to Orr suggests that the fitness load on hybrids should initially accelerate, and continue to increase as the number of potentially incompatible substitutions increases (the "snowball effect"). In the gene networks model, which violates a key assumption of Orr's model (independence of fixation probabilities), the snowball effect often does not occur. Instead, we describe three possible dynamics in a constant environment: (1) Stabilizing selection can constrain two allopatric populations to remain near-perfectly compatible. (2) Despite constancy of environment, punctuated evolution may obtain; populations may experience rare adaptations asynchronously, permitting incompatibility. (3) Despite stabilizing selection, developmental system drift may permit genetic change, allowing two populations to drift in and out of compatibility. We reinterpret Orr's model in terms of genetic distance. We extend Orr's model to the finite loci case, which can limit incompatibility. Finally, we suggest that neutral evolution of gene regulation in nature, to the point of speciation, is a distinct possibility.     

Epistasis from functional dependence of fitness on underlying traits

Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.     

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.     

A simple model of co-evolutionary dynamics caused by epistatic selection

Epistasis is the dependency of the effect of a mutation on the genetic background in which it occurs. Epistasis has been widely documented and implicated in the evolution of species barriers and the evolution of genetic architecture. Here we propose a simple model to formalize the idea that epistasis can also lead to co-evolutionary patterns in molecular evolution of interacting genes. This model epistasis is represented by the influence of one gene substitution on the fitness rank of the resident allele at another locus. We assume that increasing or decreasing fitness rank occur equally likely. In simulations we show that this form of epistasis leads to co-evolution in the sense that the length of an adaptive walk between interacting loci is highly correlated. This effect is caused by episodes of elevated rate of evolution in both loci simultaneously. We find that the influence of epistasis on these measures of co-evolutionary dynamics is relatively robust to the details of the model. The main factor influencing the correlation in evolutionary rates is the probability that a substitution will have an epistatic effect, but the strength of epistasis or the asymmetry of the initial fitness ranks of the alleles have only a minor effect. We suggest that covariance in rates of evolution among loci could be used to detect epistasis among loci.     

Compensatory mutations are repeatable and clustered within proteins

Compensatory mutations improve fitness in genotypes that contain deleterious mutations but have no beneficial effects otherwise. As such, compensatory mutations represent a very specific form of epistasis. We show that intragenic compensatory mutations occur non-randomly over gene sequence. Compensatory mutations are more likely to appear at some sites than others. Moreover, the sites of compensatory mutations are more likely than expected by chance to be near the site of the original deleterious mutation. Furthermore, compensatory mutations tend to occur more commonly in certain regions of the protein even when controlling for clustering around the site of the deleterious mutation. These results suggest that compensatory evolution at the protein level is partially predictable and may be convergent.     

Fitness landscapes emerging from pharmacodynamic functions in the evolution of multidrug resistance

Adaptive evolution often involves beneficial mutations at more than one locus. In this case, the trajectory and rate of adaptation is determined by the underlying fitness landscape, that is, the fitness values and mutational connectivity of all genotypes under consideration. Drug resistance, especially resistance to multiple drugs simultaneously, is also often conferred by mutations at several loci so that the concept of fitness landscapes becomes important. However, fitness landscapes underlying drug resistance are not static but dependent on drug concentrations, which means they are influenced by the pharmacodynamics of the drugs administered. Here, I present a mathematical framework for fitness landscapes of multidrug resistance based on Hill functions describing how drug concentrations affect fitness. I demonstrate that these ‘pharmacodynamic fitness landscapes’ are characterized by pervasive epistasis that arises through (i) fitness costs of resistance (even when these costs are additive), (ii) nonspecificity of resistance mutations to drugs, in particular cross‐resistance, and (iii) drug interactions (both synergistic and antagonistic). In the latter case, reciprocal drug suppression may even lead to reciprocal sign epistasis, so that the doubly resistant genotype occupies a local fitness peak that may be difficult to access by evolution. Simulations exploring the evolutionary dynamics on some pharmacodynamic fitness landscapes with both constant and changing drug concentrations confirm the crucial role of epistasis in determining the rate of multidrug resistance evolution.     

Pleiotropy and the low cost of individual traits promote cooperation

The evolution of cooperation is thought to be promoted by pleiotropy, whereby cooperative traits are coregulated with traits that are important for personal fitness. However, this hypothesis faces a key challenge: what happens if mutation targets a cooperative trait specifically rather than the pleiotropic regulator? Here, we explore this question with the bacterium Pseudomonas aeruginosa, which cooperatively digests complex proteins using elastase. We empirically measure and theoretically model the fate of two mutants—one missing the whole regulatory circuit behind elastase production and the other with only the elastase gene mutated—relative to the wild‐type (WT). We first show that, when elastase is needed, neither of the mutants can grow if the WT is absent. And, consistent with previous findings, we show that regulatory gene mutants can grow faster than the WT when there are no pleiotropic costs. However, we find that mutants only lacking elastase production do not outcompete the WT, because the individual cooperative trait has a low cost. We argue that the intrinsic architecture of molecular networks makes pleiotropy an effective way to stabilize cooperative evolution. Although individual cooperative traits experience loss‐of‐function mutations, these mutations may result in weak benefits, and need not undermine the protection from pleiotropy.     

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.