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

2019 ◽  
Vol 130 ◽  
pp. 13-49 ◽  
Author(s):  
Atish Agarwala ◽  
Daniel S. Fisher
Keyword(s):  
Fitness Landscapes ◽  
High Dimensional ◽  
Adaptive Walks

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 Inevitability of Red Queen evolution driven by organismic complexity and simple feedback via environmental modification

2021 ◽  
Author(s):  
Daniel S Fisher
Keyword(s):  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
High Dimensional ◽  
Red Queen ◽  
Future Evolution ◽  
Population Growth Rates ◽  
Slowing Down ◽  
Rate Of Increase ◽  
Evolutionary Trajectories ◽  
Low Dimensional

Evolution in complex high-dimensional phenotype spaces can be very different than the caricature of uphill evolutionary trajectories in a low-dimensional fitness landscape. And slight modifications of the environment can have large consequences for the future evolution. Here, the simplest approximation of evolution, an almost-always clonal population evolving by small effect mutations under deterministic "adaptive" dynamics, is studied. The complexities of organisms and their interactions with their environments are caricatured by population growth rates being smoothly varying random functions in very high dimensional phenotype spaces. In a fixed environment, there are huge numbers of fitness maxima, yet evolutionary trajectories wander around amongst saddles, gradually slowing down but still wandering widely and without committing to any maximum. But with even very small changes of the environment caused by the phenotypic changes, after an initial transient the evolution continues forever without further slowing down. In this Red Queen "phase" the apparent rate of increase of the fitness saturates (at a feedback strength-dependent rate) and the trajectories perpetually wander over large phenotypic distances. Organismic complexities, caricatured by a large number of constraints on the molecular-level phenotype, together with the simplest possible interactions of the organisms with their environment, are shown to be sufficient to cause such Red Queen dynamics. Arguments are made for the ubiquity of such behavior.

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 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.

scholarly journals Analysis of statistical correlations between properties of adaptive walks in fitness landscapes

2020 ◽  
Vol 7 (1) ◽  
pp. 192118
Author(s):  
Sandro M. Reia ◽  
Paulo R. A. Campos
Keyword(s):  
Experimental Evolution ◽  
Fitness Landscape ◽  
Shortest Paths ◽  
Fitness Landscapes ◽  
The Other ◽  
Attraction Basin ◽  
Statistical Correlations ◽  
Adaptive Walks ◽  
Nk Landscapes ◽  
The Relationship

The fitness landscape metaphor has been central in our way of thinking about adaptation. In this scenario, adaptive walks are idealized dynamics that mimic the uphill movement of an evolving population towards a fitness peak of the landscape. Recent works in experimental evolution have demonstrated that the constraints imposed by epistasis are responsible for reducing the number of accessible mutational pathways towards fitness peaks. Here, we exhaustively analyse the statistical properties of adaptive walks for two empirical fitness landscapes and theoretical NK landscapes. Some general conclusions can be drawn from our simulation study. Regardless of the dynamics, we observe that the shortest paths are more regularly used. Although the accessibility of a given fitness peak is reasonably correlated to the number of monotonic pathways towards it, the two quantities are not exactly proportional. A negative correlation between predictability and mean path divergence is established, and so the decrease of the number of effective mutational pathways ensures the convergence of the attraction basin of fitness peaks. On the other hand, other features are not conserved among fitness landscapes, such as the relationship between accessibility and predictability.

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