scholarly journals The distribution of epistasis on simple fitness landscapes

2018 ◽  
Author(s):  
Christelle Fraïsse ◽  
John J. Welch
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Null Model ◽  
Large Data ◽  
Fitness Landscapes ◽  
Mutational Bias ◽  
Data Set ◽  
Epistatic Interactions ◽  
Standing Variation ◽  
Mean And Variance

AbstractFitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information about the overall distribution is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effects sizes, mutational bias, and maladaptation of the wild-type. We illustrate our approach by reanalysing a large data set of mutant effects in a yeast snoRNA. Though characterized by some strong epistatic interactions, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have little effect on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape, and the distribution of mutations, and so it is expected to vary in consistent ways between new mutations, standing variation, and fixed mutations.

scholarly journals The distribution of epistasis on simple fitness landscapes

2019 ◽  
Vol 15 (4) ◽  
pp. 20180881 ◽  
Author(s):  
Christelle Fraïsse ◽  
John J. Welch
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Null Model ◽  
Fitness Landscapes ◽  
Mutational Bias ◽  
Variable Effect ◽  
Epistatic Effects ◽  
Standing Variation ◽  
Mean And Variance ◽  
Nucleolar Rna

Fitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA (small nucleolar RNA). Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.

scholarly journals Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

2018 ◽  
Author(s):  
Atish Agarwala ◽  
Daniel S. Fisher
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Broad Class ◽  
Fitness Landscapes ◽  
High Dimensional ◽  
General Function ◽  
Long Distance ◽  
Future Evolution ◽  
Adaptive Mutations ◽  
Adaptive Walks

AbstractThe dynamics of evolution is intimately shaped by epistasis — interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of “ruggedness” are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness “seascapes” cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

scholarly journals Cancer progression models and fitness landscapes: a many-to-many relationship

2017 ◽  
Author(s):  
Ramon Diaz-Uriarte
Keyword(s):  
Cancer Progression ◽  
Fitness Landscape ◽  
Simulated Data ◽  
Directed Acyclic Graphs ◽  
Fitness Landscapes ◽  
Gene Interactions ◽  
Cross Sectional ◽  
Data Set ◽  
Large Variability ◽  
Acyclic Graphs

AbstractThe identification of constraints, due to gene interactions, in the order of accumulation of mutations during cancer progression can allow us to single out therapeutic targets. Cancer progression models (CPMs) use genotype frequency data from cross-sectional samples to try to identify these constraints, and return Directed Acyclic Graphs (DAGs) of genes. On the other hand, fitness landscapes, which map genotypes to fitness, contain all possible paths of tumor progression. Thus, we expect a correspondence between DAGs from CPMs and the fitness landscapes where evolution happened. But many fitness landscapes —e.g., those with reciprocal sign epistasis— cannot be represented by CPMs. Using simulated data under 500 fitness landscapes, I show that CPMs’ performance (prediction of genotypes that can exist) degrades with reciprocal sign epistasis. There is large variability in the DAGs inferred from each landscape, which is also affected by mutation rate, detection regime, and fitness landscape features, in ways that depend on CPM method. And the same DAG is often observed in very different landscapes, which differ in more than 50% of their accessible genotypes. Using a pancreatic data set, I show that this many-to-many relationship affects the analysis of empirical data. Fitness landscapes that are widely different from each other can, when evolutionary processes run repeatedly on them, both produce data similar to the empirically observed one, and lead to DAGs that are very different among themselves. Because reciprocal sign epistasis can be common in cancer, these results question the use and interpretation of CPMs.

scholarly journals The fitness landscape of the codon space across environments

2018 ◽  
Author(s):  
Inès Fragata ◽  
Sebastian Matuszewski ◽  
Mark A. Schmitz ◽  
Thomas Bataillon ◽  
Jeffrey D. Jensen ◽  
...  
Keyword(s):  
Amino Acid ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Synonymous Mutations ◽  
Landscape Studies ◽  
Fitness Effects ◽  
Bayesian Monte Carlo ◽  
The Relationship

AbstractFitness landscapes map the relationship between genotypes and fitness. However, most fitness landscape studies ignore the genetic architecture imposed by the codon table and thereby neglect the potential role of synonymous mutations. To quantify the fitness effects of synonymous mutations and their potential impact on adaptation on a fitness landscape, we use a new software based on Bayesian Monte Carlo Markov Chain methods and reestimate selection coefficients of all possible codon mutations across 9 amino-acid positions in Saccharomyces cerevisiae Hsp90 across 6 environments. We quantify the distribution of fitness effects of synonymous mutations and show that it is dominated by many mutations of small or no effect and few mutations of larger effect. We then compare the shape of the codon fitness landscape across amino-acid positions and environments, and quantify how the consideration of synonymous fitness effects changes the evolutionary dynamics on these fitness landscapes. Together these results highlight a possible role of synonymous mutations in adaptation and indicate the potential mis-inference when they are neglected in fitness landscape studies.

scholarly journals High-order epistasis in catalytic power of dihydrofolate reductase gives rise to a rugged fitness landscape in the presence of trimethoprim selection

2018 ◽  
Author(s):  
Yusuf Talha Tamer ◽  
Ilona K. Gaszek ◽  
Haleh Abdizadeh ◽  
Tugce Altinusak Batur ◽  
Kimberly Reynolds ◽  
...  
Keyword(s):  
Dihydrofolate Reductase ◽  
Biochemical Parameters ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Computational Study ◽  
Binding Pocket ◽  
Resistance Mechanisms ◽  
Fitness Landscapes ◽  
High Order ◽  
Catalytic Power

ABSTRACTEvolutionary fitness landscapes of certain antibiotic target enzymes have been comprehensively mapped showing strong high order epistasis between mutations, but understanding these effects at the biochemical and molecular levels remained open. Here, we carried out an extensive experimental and computational study to quantitatively understand the evolutionary dynamics of Escherichia coli dihydrofolate reductase (DHFR) enzyme in the presence of trimethoprim induced selection. Biochemical and structural characterization of resistance-conferring mutations targeting a total of ten residues spanning the substrate binding pocket of DHFR revealed distinct resistance mechanisms. Next, we experimentally measured biochemical parameters (Km, Ki, and kcat) for a mutant library carrying all possible combinations of six resistance-conferring DHFR mutations and quantified epistatic interactions between them. We found that the epistasis between DHFR mutations is high-order for catalytic power of DHFR (kcat and Km), but less prevalent for trimethoprim affinity (Ki). Taken together our data provide a concrete illustration of how epistatic coupling at the level of biochemical parameters can give rise to complex fitness landscapes, and suggest new strategies for developing mutant specific inhibitors.

scholarly journals The influence of higher-order epistasis on biological fitness landscape topography

2017 ◽  
Author(s):  
Daniel M. Weinreich ◽  
Yinghong Lan ◽  
Jacob Jaffe ◽  
Robert B. Heckendorn
Keyword(s):  
Natural Selection ◽  
Fitness Landscape ◽  
Higher Order ◽  
Fitness Landscapes ◽  
Epistatic Interactions ◽  
Epistatic Effects

AbstractThe effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We explore whether natural selection may have contributed to this finding, and conclude by highlight opportunities for further work dissecting the influence that epistasis of all orders has on the efficiency of natural selection.

scholarly journals On the deformability of an empirical fitness landscape by microbial evolution

2018 ◽  
Vol 115 (44) ◽  
pp. 11286-11291 ◽  
Author(s):  
Djordje Bajić ◽  
Jean C. C. Vila ◽  
Zachary D. Blount ◽  
Alvaro Sánchez
Keyword(s):  
Environmental Effects ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
Microbial Evolution ◽  
Fitness Landscapes ◽  
Complex Genetics ◽  
Evolutionary Innovation ◽  
Genotype Space ◽  
Evolutionary Trajectories

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli. Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

scholarly journals A family of fitness landscapes modeled through gene regulatory networks

2021 ◽  
Author(s):  
Chia-Hung Yang ◽  
Samuel V. Scarpino
Keyword(s):  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Fitness Function ◽  
Fitness Landscapes ◽  
Relative Fitness ◽  
Landscape Models ◽  
Fitness Value ◽  
Gene Regulatory

AbstractOver 100 years, Fitness landscapes have been a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other and are related according to relative fitness. Despite the high dimensionality of such real-world landscapes, empirical studies are often limited in their ability to quantify the fitness of different genotypes beyond point mutations, while theoretical works attempt statistical/mechanistic models to reason the overall landscape structure. However, most classical fitness landscape models overlook an instinctive constraint that genotypes leading to the same phenotype almost certainly share the same fitness value, since the information of genotype-phenotype mapping is rarely incorporated. Here, we investigate fitness landscape models through the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as the phenotypes. With the assumption that regulatory mediators/products exhibit binary states, we prove topographical features of GRN fitness landscape models such as accessibility and connectivity insensitive to the choice of the fitness function. Furthermore, using graph theory, we deduce a mesoscopic structure underlying GRN fitness landscape models that retains necessary information for evolutionary dynamics with minimal complexity. We also propose an algorithm to construct such a mesoscopic backbone which is more efficient than the brute-force approach. Combined, this work provides mathematical implications for fitness landscape models with high-dimensional genotype-phenotype mapping, yielding the potential to elucidate empirical landscapes and their resulting evolutionary processes in a manner complementary to existing computational studies.

scholarly journals Effect of Host Species on Topography of the Fitness Landscape for a Plant RNA Virus

2016 ◽  
Vol 90 (22) ◽  
pp. 10160-10169 ◽  
Author(s):  
Héctor Cervera ◽  
Jasna Lalić ◽  
Santiago F. Elena
Keyword(s):  
Host Species ◽  
Evolutionary Biology ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Rna Virus ◽  
Fitness Landscapes ◽  
Content Type ◽  
Fine Grained ◽  
Novel Host ◽  
Fitness Tradeoffs

ABSTRACTAdaptive fitness landscapes are a fundamental concept in evolutionary biology that relate the genotypes of individuals to their fitness. In the end, the evolutionary fate of evolving populations depends on the topography of the landscape, that is, the numbers of accessible mutational pathways and possible fitness peaks (i.e., adaptive solutions). For a long time, fitness landscapes were only theoretical constructions due to a lack of precise information on the mapping between genotypes and phenotypes. In recent years, however, efforts have been devoted to characterizing the properties of empirical fitness landscapes for individual proteins or for microbes adapting to artificial environments. In a previous study, we characterized the properties of the empirical fitness landscape defined by the first five mutations fixed during adaptation of tobacco etch potyvirus (TEV) to a new experimental host,Arabidopsis thaliana. Here we evaluate the topography of this landscape in the ancestral hostNicotiana tabacum. By comparing the topographies of the landscapes for the two hosts, we found that some features remained similar, such as the existence of fitness holes and the prevalence of epistasis, including cases of sign and reciprocal sign epistasis that created rugged, uncorrelated, and highly random topographies. However, we also observed significant differences in the fine-grained details between the two landscapes due to changes in the fitness and epistatic interactions of some genotypes. Our results support the idea that not only fitness tradeoffs between hosts but also topographical incongruences among fitness landscapes in alternative hosts may contribute to virus specialization.IMPORTANCEDespite its importance for understanding virus evolutionary dynamics, very little is known about the topography of virus adaptive fitness landscapes, and even less is known about the effects that different host species and environmental conditions may have on this topography. To bridge this gap, we evaluated the topography of a small fitness landscape formed by all genotypes that result from every possible combination of the first five mutations fixed during adaptation of TEV to the novel hostA. thaliana. To assess the effect that host species may have on this topography, we evaluated the fitness of every genotype in both the ancestral and novel hosts. We found that both landscapes share some macroscopic properties, such as the existence of holes and being highly rugged and uncorrelated, yet they differ in microscopic details due to changes in the magnitude and sign of fitness and epistatic effects.

Fitness Landscape Models

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Statistical Physics ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Real Life ◽  
Extinction Rate ◽  
Epistatic Interactions ◽  
Nk Model ◽  
Energy Models ◽  
Landscape Models ◽  
A Genome

Kauffman (1993, 1995; Kauffman and Levin 1987; Kauffman and Johnsen 1991) has proposed and studied in depth a class of models referred to as NK models, which are models of random fitness landscapes on which one can implement a variety of types of evolutionary dynamics and study the development and interaction of species. (The letters N and K do not stand for anything; they are the names of parameters in the model.) Based on the results of extensive simulations of NK models, Kauffman and co-workers have suggested a number of possible connections between the dynamics of evolution and the extinction rate. To a large extent it is this work which has sparked recent interest in biotic mechanisms for mass extinction. In this chapter we review Kauffman's work in detail. An NK model is a model of a single rugged landscape, which is similar in construction to the spin-glass models of statistical physics (Fischer and Hertz 1991), particularly p-spin models (Derrida 1980) and random energy models (Derrida 1981). Used as a model of species fitness the NK model maps the states of a model genome onto a scalar fitness W. This is a simplification of what happens in real life, where the genotype is first mapped onto phenotype and only then onto fitness. However, it is a useful simplification which makes simulation of the model for large systems tractable. As long as we bear in mind that this simplification has been made, the model can still teach us many useful things. The NK model is a model of a genome with N genes. Each gene has A alleles. In most of Kauffman's studies of the model he used A = 2, a binary genetic code, but his results are not limited to this case. The model also includes epistatic interactions between genes—interactions whereby the state of one gene affects the contribution of another to the overall fitness of the species. In fact, it is these epistatic interactions which are responsible for the ruggedness of the fitness landscape.

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