scholarly journals Punctuated equilibrium as the default mode of evolution of large populations on fitness landscapes dominated by saddle points in the weak-mutation limit

2020 ◽  
Author(s):  
Yuri Bakhtin ◽  
Mikhail I. Katsnelson ◽  
Yuri I. Wolf ◽  
Eugene V. Koonin
Keyword(s):  
Fitness Landscape ◽  
Large Population ◽  
Saddle Points ◽  
Biological Evolution ◽  
Punctuated Equilibrium ◽  
Fitness Landscapes ◽  
Phenotypic Change ◽  
Beneficial Mutation ◽  
Effective Population ◽  
Default Mode

AbstractPunctuated equilibrium is a mode of evolution in which phenetic change occurs in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but no major phenotypic change occurs. Punctuated equilibrium has been originally proposed within the framework of paleobiology, to explain the lack of transitional forms that is typical of the fossil record. Theoretically, punctuated equilibrium has been linked to self-organized criticality (SOC), a model in which the size of ‘avalanches’ in an evolving system is power-law distributed, resulting in increasing rarity of major events. We show here that, under the weak-mutation limit, a large population would spend most of the time in stasis in the vicinity of saddle points in the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe time (Ne, effective population size), when a new beneficial mutation is fixed in the evolving population, which moves to a different saddle, or on much rarer occasions, from a saddle to a local peak. Thus, punctuated equilibrium is the default mode of evolution under a simple model that does not involve SOC or other special conditions.SignificanceThe gradual character of evolution is a key feature of the Darwinian worldview. However, macroevolutionary events are often thought to occur in a non-gradualist manner, in a regime known as punctuated equilibrium, whereby extended periods of evolutionary stasis are punctuated by rapid transitions between states. Here we analyze a mathematical model of population evolution on fitness landscapes and show that, for a large population in the weak-mutation limit, the process of adaptive evolution consists of extended periods of stasis, which the population spends around saddle points on the landscape, interrupted by rapid transitions to new saddle points when a beneficial mutation is fixed. Thus, punctuated equilibrium appears to be the default regime of biological evolution.

scholarly journals Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape

2021 ◽  
Vol 118 (4) ◽  
pp. e2015665118
Author(s):  
Yuri Bakhtin ◽  
Mikhail I. Katsnelson ◽  
Yuri I. Wolf ◽  
Eugene V. Koonin
Keyword(s):  
Fitness Landscape ◽  
Large Population ◽  
Saddle Points ◽  
Selection Coefficient ◽  
Beneficial Mutation ◽  
Effective Population ◽  
Phenotypic Changes ◽  
Self Organized ◽  
Evolving System ◽  
Self Organized Criticality

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe/s time (Ne, effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of “avalanches” in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

scholarly journals The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

2021 ◽  
Author(s):  
Yipei Guo ◽  
Ariel Amir
Keyword(s):  
Mutation Rate ◽  
Fitness Landscape ◽  
Large Population ◽  
Beneficial Mutation ◽  
Clonal Interference ◽  
Beneficial Mutations ◽  
Speed Up ◽  
Fixation Probabilities ◽  
Population Competition ◽  
Open Question

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation (SSWM) regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and how it affects the form of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the form of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the functional form of the fitness trajectory, while an enhancement of the beneficial mutation rate does the opposite of slowing down the form of the dynamics. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs. change in fraction of beneficial mutations).

scholarly journals A Survey of Advances in Landscape Analysis for Optimisation

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 40
Author(s):  
Katherine Mary Malan
Keyword(s):  
Fitness Landscape ◽  
Biological Evolution ◽  
Fitness Landscapes ◽  
Landscape Analysis ◽  
Theoretical Idea ◽  
Automated Algorithm ◽  
Algorithm Configuration ◽  
Practical Tool ◽  
Abstract Notion

Fitness landscapes were proposed in 1932 as an abstract notion for understanding biological evolution and were later used to explain evolutionary algorithm behaviour. The last ten years has seen the field of fitness landscape analysis develop from a largely theoretical idea in evolutionary computation to a practical tool applied in optimisation in general and more recently in machine learning. With this widened scope, new types of landscapes have emerged such as multiobjective landscapes, violation landscapes, dynamic and coupled landscapes and error landscapes. This survey is a follow-up from a 2013 survey on fitness landscapes and includes an additional 11 landscape analysis techniques. The paper also includes a survey on the applications of landscape analysis for understanding complex problems and explaining algorithm behaviour, as well as algorithm performance prediction and automated algorithm configuration and selection. The extensive use of landscape analysis in a broad range of areas highlights the wide applicability of the techniques and the paper discusses some opportunities for further research in this growing field.

scholarly journals On the (un-)predictability of a large intragenic fitness landscape

2016 ◽  
Author(s):  
Claudia Bank ◽  
Sebastian Matuszewski ◽  
Ryan T. Hietpas ◽  
Jeffrey D. Jensen
Keyword(s):  
Amino Acid ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Specific Information ◽  
Theoretical Approaches ◽  
Elevated Salinity ◽  
Theoretical Predictions ◽  
Experimental Approaches ◽  
Deterministic Processes ◽  
Negative Epistasis

AbstractThe study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with NGS methods enable accurate and extensive studies of the fitness effects of mutations – allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape, and its implications for the predictability and repeatability of evolution.Here, we present a uniquely large multi-allelic fitness landscape comprised of 640 engineered mutants that represent all possible combinations of 13 amino-acid changing mutations at six sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multi-allelic fitness landscape. Using subsets of the data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino-acid specific epistatic hotspots, and that inference is additionally confounded by the non-random choice of mutations for experimental fitness landscapes.Author SummaryThe study of fitness landscapes is fundamentally concerned with understanding the relative roles of stochastic and deterministic processes in adaptive evolution. Here, the authors present a uniquely large and complete multi-allelic intragenic fitness landscape of 640 systematically engineered mutations in yeast Hsp90. Using a combination of traditional and recently proposed theoretical approaches, they study the accessibility of the global fitness peak, and the potential for predictability of the fitness landscape topography. They report local ruggedness of the landscape and the existence of epistatic hotspot mutations, which together make extrapolation and hence predictability inherently difficult, if mutation-specific information is not considered.

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 Biophysical principles predict fitness landscapes of drug resistance

2016 ◽  
Vol 113 (11) ◽  
pp. E1470-E1478 ◽  
Author(s):  
João V. Rodrigues ◽  
Shimon Bershtein ◽  
Anna Li ◽  
Elena R. Lozovsky ◽  
Daniel L. Hartl ◽  
...  
Keyword(s):  
Drug Resistance ◽  
Protein Quality ◽  
Fitness Landscape ◽  
Catalytic Efficiency ◽  
Fitness Landscapes ◽  
Resistance Mutations ◽  
Chlamydia Muridarum ◽  
Complete Set ◽  
Essential Enzyme

Fitness landscapes of drug resistance constitute powerful tools to elucidate mutational pathways of antibiotic escape. Here, we developed a predictive biophysics-based fitness landscape of trimethoprim (TMP) resistance for Escherichia coli dihydrofolate reductase (DHFR). We investigated the activity, binding, folding stability, and intracellular abundance for a complete set of combinatorial DHFR mutants made out of three key resistance mutations and extended this analysis to DHFR originated from Chlamydia muridarum and Listeria grayi. We found that the acquisition of TMP resistance via decreased drug affinity is limited by a trade-off in catalytic efficiency. Protein stability is concurrently affected by the resistant mutants, which precludes a precise description of fitness from a single molecular trait. Application of the kinetic flux theory provided an accurate model to predict resistance phenotypes (IC50) quantitatively from a unique combination of the in vitro protein molecular properties. Further, we found that a controlled modulation of the GroEL/ES chaperonins and Lon protease levels affects the intracellular steady-state concentration of DHFR in a mutation-specific manner, whereas IC50 is changed proportionally, as indeed predicted by the model. This unveils a molecular rationale for the pleiotropic role of the protein quality control machinery on the evolution of antibiotic resistance, which, as we illustrate here, may drastically confound the evolutionary outcome. These results provide a comprehensive quantitative genotype–phenotype map for the essential enzyme that serves as an important target of antibiotic and anticancer therapies.

Algebraic Theory of Recombination Spaces

1997 ◽  
Vol 5 (3) ◽  
pp. 241-275 ◽  
Author(s):  
Peter F. Stadler ◽  
Günter P. Wagner
Keyword(s):  
Nearest Neighbor ◽  
Fitness Landscape ◽  
Algebraic Theory ◽  
Algebraic Approach ◽  
Search Space ◽  
Space Structure ◽  
Fitness Landscapes ◽  
Mathematical Representation ◽  
Laplacian Operator ◽  
Fourier Decomposition

A new mathematical representation is proposed for the configuration space structure induced by recombination, which we call “P-structure.” It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental “genotypes” the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier decomposition of fitness landscapes into a superposition of “elementary landscapes.” This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination, the elementary landscapes are exactly the p-spin functions (Walsh functions), that is, the same as the elementary landscapes of the string point mutation spaces (i.e., the hypercube). This supports the notion of a strong homomorphism between string mutation and recombination spaces. However, the effective nearest neighbor correlations on these elementary landscapes differ between mutation and recombination and among different recombination operators. On average, the nearest neighbor correlation is higher for one-point recombination than for uniform recombination. For one-point recombination, the correlations are higher for elementary landscapes with fewer interacting sites as well as for sites that have closer linkage, confirming the qualitative predictions of the Schema Theorem. We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator.

scholarly journals Genetic diversity, demographic history and neo-sex chromosomes in the Critically Endangered Raso lark

2020 ◽  
Vol 287 (1922) ◽  
pp. 20192613 ◽  
Author(s):  
Elisa G. Dierickx ◽  
Simon Yung Wa Sin ◽  
H. Pieter J. van Veelen ◽  
M. de L. Brooke ◽  
Yang Liu ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Population Size ◽  
Sex Chromosomes ◽  
Demographic History ◽  
Large Population ◽  
Effective Population ◽  
Island Species ◽  
Population Sizes ◽  
Approaches To Study ◽  
Genetic Signatures

Small effective population sizes could expose island species to inbreeding and loss of genetic variation. Here, we investigate factors shaping genetic diversity in the Raso lark, which has been restricted to a single islet for approximately 500 years, with a population size of a few hundred. We assembled a reference genome for the related Eurasian skylark and then assessed diversity and demographic history using RAD-seq data (75 samples from Raso larks and two related mainland species). We first identify broad tracts of suppressed recombination in females, indicating enlarged neo-sex chromosomes. We then show that genetic diversity across autosomes in the Raso lark is lower than in its mainland relatives, but inconsistent with long-term persistence at its current population size. Finally, we find that genetic signatures of the recent population contraction are overshadowed by an ancient expansion and persistence of a very large population until the human settlement of Cape Verde. Our findings show how genome-wide approaches to study endangered species can help avoid confounding effects of genome architecture on diversity estimates, and how present-day diversity can be shaped by ancient demographic events.

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 Challenges to assessing connectivity between massive populations of the Australian plague locust

2011 ◽  
Vol 278 (1721) ◽  
pp. 3152-3160 ◽  
Author(s):  
Marie-Pierre Chapuis ◽  
Julie-Anne M. Popple ◽  
Karine Berthier ◽  
Stephen J. Simpson ◽  
Edward Deveson ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Large Population ◽  
Movement Ecology ◽  
Effective Population ◽  
Continental Scale ◽  
Australian Continent ◽  
Population Structuring ◽  
Population Sizes ◽  
Approximate Bayesian ◽  
Australian Plague Locust

Linking demographic and genetic dispersal measures is of fundamental importance for movement ecology and evolution. However, such integration can be difficult, particularly for highly fecund species that are often the target of management decisions guided by an understanding of population movement. Here, we present an example of how the influence of large population sizes can preclude genetic approaches from assessing demographic population structuring, even at a continental scale. The Australian plague locust, Chortoicetes terminifera , is a significant pest, with populations on the eastern and western sides of Australia having been monitored and managed independently to date. We used microsatellites to assess genetic variation in 12 C. terminifera population samples separated by up to 3000 km. Traditional summary statistics indicated high levels of genetic diversity and a surprising lack of population structure across the entire range. An approximate Bayesian computation treatment indicated that levels of genetic diversity in C. terminifera corresponded to effective population sizes conservatively composed of tens of thousands to several million individuals. We used these estimates and computer simulations to estimate the minimum rate of dispersal, m , that could account for the observed range-wide genetic homogeneity. The rate of dispersal between both sides of the Australian continent could be several orders of magnitude lower than that typically considered as required for the demographic connectivity of populations.

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