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Epistasis and Shapes of Fitness Landscapes  [PDF]
Niko Beerenwinkel,Lior Pachter,Bernd Sturmfels
Mathematics , 2006,
Abstract: The relationship between the shape of a fitness landscape and the underlying gene interactions, or epistasis, has been extensively studied in the two-locus case. Gene interactions among multiple loci are usually reduced to two-way interactions. We present a geometric theory of shapes of fitness landscapes for multiple loci. A central concept is the genotope, which is the convex hull of all possible allele frequencies in populations. Triangulations of the genotope correspond to different shapes of fitness landscapes and reveal all the gene interactions. The theory is applied to fitness data from HIV and Drosophila melanogaster. In both cases, our findings refine earlier analyses and reveal previously undetected gene interactions.
Epistasis and constraints in fitness landscapes  [PDF]
Luca Ferretti,Daniel Weinreich,Benjamin Schmiegelt,Atsushi Yamauchi,Yutaka Kobayashi,Fumio Tajima,Guillaume Achaz
Quantitative Biology , 2015,
Abstract: Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, their characterization relies on simple measures of their structure, which can be used as statistics in empirical applications. Here we propose two new sets of measures that explicitly capture two relevant features of fitness landscapes: epistasis and constraints. The first set contains new measures for epistasis based on the correlation of fitness effects of mutations. They have a natural interpretation, capture well the interaction between mutations, can be obtained analytically for most landscape models and can therefore be used to discriminate between different models. The second set contains measures of evolutionary constraints based on "chains" of forced mutations along fitness-increasing paths. Some of these measures are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. We further characterize the relationships of these measures to the ones that were previous proposed (e.g. number of peaks, roughness/slope, fraction of non-additive components, etc). Finally, we show how these measures can help uncovering the amount and the nature of epistatic interactions in two experimental landscapes.
Effects of Epistasis and Pleiotropy on Fitness Landscapes  [PDF]
Bj?rn ?stman
Quantitative Biology , 2013,
Abstract: The factors that influence genetic architecture shape the structure of the fitness landscape, and therefore play a large role in the evolutionary dynamics. Here the NK model is used to investigate how epistasis and pleiotropy -- key components of genetic architecture -- affect the structure of the fitness landscape, and how they affect the ability of evolving populations to adapt despite the difficulty of crossing valleys present in rugged landscapes. Populations are seen to make use of epistatic interactions and pleiotropy to attain higher fitness, and are not inhibited by the fact that valleys have to be crossed to reach peaks of higher fitness.
Inferring fitness landscapes by regression produces biased estimates of epistasis  [PDF]
Jakub Otwinowski,Joshua B. Plotkin
Quantitative Biology , 2014, DOI: 10.1073/pnas.1400849111
Abstract: The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as many genotypes as possible, measure their fitnesses, and fit a statistical model of the landscape that includes additive and pairwise interactive effects between loci. Here we elucidate the pitfalls of using such regressions, by studying artificial but mathematically convenient fitness landscapes. We identify two sources of bias inherent in these regression procedures that each tends to under-estimate high fitnesses and over-estimate low fitnesses. We characterize these biases for random sampling of genotypes, as well as for samples drawn from a population under selection in the Wright-Fisher model of evolutionary dynamics. We show that common measures of epistasis, such as the number of monotonically increasing paths between ancestral and derived genotypes, the prevalence of sign epistasis, and the number of local fitness maxima, are distorted in the inferred landscape. As a result, the inferred landscape will provide systematically biased predictions for the dynamics of adaptation. We identify the same biases in a computational RNA-folding landscape, as well as in regulatory sequence binding data, treated with the same fitting procedure. Finally, we present a method that may ameliorate these biases in some cases.
Epistasis and the structure of fitness landscapes: are experimental fitness landscapes compatible with Fisher's model?  [PDF]
Fran?ois Blanquart,Thomas Bataillon
Quantitative Biology , 2015,
Abstract: The fitness landscape defines the relationship between genotypes and fitness in a given environment, and underlies fundamental quantities such as the distribution of selection coefficient, or the magnitude and type of epistasis. A better understanding of variation of landscape structure across species and environments is thus necessary to understand and predict how populations adapt. An increasing number of experiments access the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring fitness of these genotypes. Yet these empirical landscapes represent a very small sample of the vast space of all possible genotypes, and this sample is biased by the protocol used to identify mutations. Here we develop a rigorous and flexible statistical framework based on Approximate Bayesian Computation to address these concerns, and use this framework to fit a broad class of phenotypic fitness models (including Fisher's model) to 24 empirical landscapes representing 9 diverse biological systems. In spite of uncertainty due to the small size of most published empirical landscapes, the inferred landscapes have similar structure in similar biological systems. Surprisingly, goodness of fit tests reveal that this class of phenotypic models, which has been successful so far in interpreting experimental data, is a plausible model in only 3 out of 9 biological systems. In most cases, including notably the landscapes of drug resistance, Fisher's model is not able to explain the structure of empirical landscapes and patterns of epistasis.
Learning genetic epistasis using Bayesian network scoring criteria
Xia Jiang, Richard E Neapolitan, M Michael Barmada, Shyam Visweswaran
BMC Bioinformatics , 2011, DOI: 10.1186/1471-2105-12-89
Abstract: Although BNs are a promising tool for learning epistatic relationships from data, we cannot confidently use them in this domain until we determine which scoring criteria work best or even well when we try learning the correct model without knowledge of the number of SNPs in that model.We evaluated the performance of 22 BN scoring criteria using 28,000 simulated data sets and a real Alzheimer's GWAS data set. Our results were surprising in that the Bayesian scoring criterion with large values of a hyperparameter called α performed best. This score performed better than other BN scoring criteria and MDR at recall using simulated data sets, at detecting the hardest-to-detect models using simulated data sets, and at substantiating previous results using the real Alzheimer's data set.We conclude that representing epistatic interactions using BN models and scoring them using a BN scoring criterion holds promise for identifying epistatic genetic variants in data. In particular, the Bayesian scoring criterion with large values of a hyperparameter α appears more promising than a number of alternatives.The advent of high-throughput genotyping technology has brought the promise of identifying genetic variations that underlie common diseases such as hypertension, diabetes mellitus, cancer and Alzheimer's disease. However, our knowledge of the genetic architecture of common diseases remains limited; this is in part due to the complex relationship between the genotype and the phenotype. One likely reason for this complex relationship arises from gene-gene and gene-environment interactions. So an important challenge in the analysis of high-throughput genetic data is the development of computational and statistical methods to identify gene-gene interactions. In this paper we apply Bayesian network scoring criteria to identifying gene-gene interactions from genome-wide association study (GWAS) data.As background we review gene-gene interactions, GWAS, Bayesian networks, and modeling
Reciprocal Sign Epistasis between Frequently Experimentally Evolved Adaptive Mutations Causes a Rugged Fitness Landscape  [PDF]
Daniel J. Kvitek,Gavin Sherlock
PLOS Genetics , 2011, DOI: 10.1371/journal.pgen.1002056
Abstract: 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.
Epistasis and Entropy  [PDF]
Kristina Crona
Quantitative Biology , 2015,
Abstract: Epistasis is a key concept in the theory of adaptation. Indicators of epistasis are of interest for large system where systematic fitness measurements may not be possible. Some recent approaches depend on information theory. We show that considering shared entropy for pairs of loci can be misleading. The reason is that shared entropy does not imply epistasis for the pair. This observation holds true also in the absence of higher order epistasis. We discuss a refined approach for identifying pairwise interactions using entropy.
Mapping the Fitness Landscape of Gene Expression Uncovers the Cause of Antagonism and Sign Epistasis between Adaptive Mutations  [PDF]
Hsin-Hung Chou,Nigel F. Delaney,Jeremy A. Draghi,Christopher J. Marx
PLOS Genetics , 2014, DOI: doi/10.1371/journal.pgen.1004149
Abstract: How do adapting populations navigate the tensions between the costs of gene expression and the benefits of gene products to optimize the levels of many genes at once? Here we combined independently-arising beneficial mutations that altered enzyme levels in the central metabolism of Methylobacterium extorquens to uncover the fitness landscape defined by gene expression levels. We found strong antagonism and sign epistasis between these beneficial mutations. Mutations with the largest individual benefit interacted the most antagonistically with other mutations, a trend we also uncovered through analyses of datasets from other model systems. However, these beneficial mutations interacted multiplicatively (i.e., no epistasis) at the level of enzyme expression. By generating a model that predicts fitness from enzyme levels we could explain the observed sign epistasis as a result of overshooting the optimum defined by a balance between enzyme catalysis benefits and fitness costs. Knowledge of the phenotypic landscape also illuminated that, although the fitness peak was phenotypically far from the ancestral state, it was not genetically distant. Single beneficial mutations jumped straight toward the global optimum rather than being constrained to change the expression phenotypes in the correlated fashion expected by the genetic architecture. Given that adaptation in nature often results from optimizing gene expression, these conclusions can be widely applicable to other organisms and selective conditions. Poor interactions between individually beneficial alleles affecting gene expression may thus compromise the benefit of sex during adaptation and promote genetic differentiation.
Tools for efficient epistasis detection in genome-wide association study
Xiang Zhang, Shunping Huang, Fei Zou, Wei Wang
Source Code for Biology and Medicine , 2011, DOI: 10.1186/1751-0473-6-1
Abstract: We have developed a set of three efficient programs, FastANOVA, COE and TEAM, that support epistasis test in a variety of problem settings in GWAS. These programs utilize permutation test to properly control error rate such as family-wise error rate (FWER) and false discovery rate (FDR). They guarantee to find the optimal solutions, and significantly speed up the process of epistasis detection in GWAS.A web server with user interface and source codes are available at the website http://www.csbio.unc.edu/epistasis/ webcite. The source codes are also available at SourceForge http://sourceforge.net/projects/epistasis/ webcite.Genome-wide association study (GWAS) examines the genetic variants across the entire genome to identify genetic factors associated with observed phenotypes. It has been shown to be a promising design to locate genetic factors causing phenotypic differences [1,2]. Since most traits of interest are complex, finding gene-gene interaction has received increasing attention in recent years [3,4]. Unlike single-locus approaches, which test and estimate the association between the phenotype and one marker (or SNP) at a time, two-locus epistasis detection approaches search for associations between the phenotype and each SNP-pair.In general, there are two challenges in epistasis detection. The first is to develop statistical test that can effectively capture the interaction between SNPs. The second challenge is to reduce the computational burden since there are an extremely large number of SNP-pairs need to be tested in the whole genome. The computational challenge is further compounded by the multiple testing problem. Controlling family-wise error rate (FWER) and false discovery rate (FDR) are two standard approaches for controlling error rates [5]. With large number of SNPs correlated, permutation test is preferred over simple Bonferroni correction [6], which is often to conservative. The idea of permutation procedure is to randomly shuffle the phenotype
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