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 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 Escherichia coli with a Tunable Point Mutation Rate for Evolution Experiments

2020 ◽  
Vol 10 (8) ◽  
pp. 2671-2681 ◽  
Author(s):  
Nicholas A. Sherer ◽  
Thomas E. Kuhlman
Keyword(s):  
Escherichia Coli ◽  
Point Mutation ◽  
Mutation Rate ◽  
Fitness Landscape ◽  
Genetically Engineered ◽  
Mutation Rates ◽  
Nucleotide Polymorphisms ◽  
Beneficial Mutations ◽  
Beneficial Effects ◽  
Evolution Experiment

The mutation rate and mutations’ effects on fitness are crucial to evolution. Mutation rates are under selection due to linkage between mutation rate modifiers and mutations’ effects on fitness. The linkage between a higher mutation rate and more beneficial mutations selects for higher mutation rates, while the linkage between a higher mutation rate and more deleterious mutations selects for lower mutation rates. The net direction of selection on mutations rates depends on the fitness landscape, and a great deal of work has elucidated the fitness landscapes of mutations. However, tests of the effect of varying a mutation rate on evolution in a single organism in a single environment have been difficult. This has been studied using strains of antimutators and mutators, but these strains may differ in additional ways and typically do not allow for continuous variation of the mutation rate. To help investigate the effects of the mutation rate on evolution, we have genetically engineered a strain of Escherichia coli with a point mutation rate that can be smoothly varied over two orders of magnitude. We did this by engineering a strain with inducible control of the mismatch repair proteins MutH and MutL. We used this strain in an approximately 350 generation evolution experiment with controlled variation of the mutation rate. We confirmed the construct and the mutation rate were stable over this time. Sequencing evolved strains revealed a higher number of single nucleotide polymorphisms at higher mutations rates, likely due to either the beneficial effects of these mutations or their linkage to beneficial mutations.

scholarly journals Diminishing Returns of Population Size in the Rate of RNA Virus Adaptation

2000 ◽  
Vol 74 (8) ◽  
pp. 3566-3571 ◽  
Author(s):  
Rosario Miralles ◽  
Andrés Moya ◽  
Santiago F. Elena
Keyword(s):  
Population Size ◽  
Mutation Rate ◽  
Rna Viruses ◽  
Present Report ◽  
Cell System ◽  
Viral Population ◽  
Speed Limit ◽  
Clonal Interference ◽  
Beneficial Mutations

ABSTRACT Whenever an asexual viral population evolves by adapting to new environmental conditions, beneficial mutations, the ultimate cause of adaptation, are randomly produced and then fixed in the population. The larger the population size and the higher the mutation rate, the more beneficial mutations can be produced per unit time. With the usually high mutation rate of RNA viruses and in a large enough population, several beneficial mutations could arise at the same time but in different genetic backgrounds, and if the virus is asexual, they will never be brought together through recombination. Thus, the best of these genotypes must outcompete each other on their way to fixation. This competition among beneficial mutations has the effect of slowing the overall rate of adaptation. This phenomenon is known as clonal interference. Clonal interference predicts a speed limit for adaptation as the population size increases. In the present report, by varying the size of evolving vesicular stomatitis virus populations, we found evidence clearly demonstrating this speed limit and thus indicating that clonal interference might be an important factor modulating the rate of adaptation to an in vitro cell system. Several evolutionary and epidemiological implications of the clonal interference model applied to RNA viruses are discussed.

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 Intra-Population Competition during Adaptation to Increased Temperature in an RNA Bacteriophage

2021 ◽  
Vol 22 (13) ◽  
pp. 6815
Author(s):  
María Arribas ◽  
Ester Lázaro
Keyword(s):  
Large Population ◽  
Error Rates ◽  
Viral Population ◽  
Population Bottlenecks ◽  
Beneficial Mutations ◽  
The Family ◽  
Rapid Changes ◽  
Occasional Occurrence ◽  
Population Sizes ◽  
Population Competition

Evolution of RNA bacteriophages of the family Leviviridae is governed by the high error rates of their RNA-dependent RNA polymerases. This fact, together with their large population sizes, leads to the generation of highly heterogeneous populations that adapt rapidly to most changes in the environment. Throughout adaptation, the different mutants that make up a viral population compete with each other in a non-trivial process in which their selective values change over time due to the generation of new mutations. In this work we have characterised the intra-population dynamics of a well-studied levivirus, Qβ, when it is propagated at a higher-than-optimal temperature. Our results show that adapting populations experienced rapid changes that involved the ascent of particular genotypes and the loss of some beneficial mutations of early generation. Artificially reconstructed populations, containing a fraction of the diversity present in actual populations, fixed mutations more rapidly, illustrating how population bottlenecks may guide the adaptive pathways. The conclusion is that, when the availability of beneficial mutations under a particular selective condition is elevated, the final outcome of adaptation depends more on the occasional occurrence of population bottlenecks and how mutations combine in genomes than on the selective value of particular mutations.

scholarly journals The emergence of a birth-dependent mutation rate in asexuals: causes and consequences

2021 ◽  
Author(s):  
Florian Patout ◽  
Raphael Forien ◽  
Matthieu Alfaro ◽  
Julien Papaix ◽  
Lionel Roques
Keyword(s):  
Mutation Rate ◽  
Birth Rate ◽  
Fitness Landscape ◽  
Large Population ◽  
Reaction Diffusion ◽  
Weak Selection ◽  
Positive Dependence ◽  
Evolutionary Trajectories ◽  
Complex Landscape ◽  
Phenotype Distribution

In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the 'replicator-mutator equation' often neglect this generation-time effect. In this study, we investigate the emergence of a positive dependence between the birth rate and the mutation rate in models of asexual adaptation and the consequences of this dependence. We show that it emerges naturally at the population scale, based on a large population limit of a stochastic time-continuous individual-based model with elementary assumptions. We derive a reaction-diffusion framework that describes the evolutionary trajectories and steady states in the presence of this dependence. When this model is coupled with a phenotype to fitness landscape with two optima, one for birth, the other one for survival, a new trade-off arises in the population. Compared to the standard approach with a constant mutation rate, the symmetry between birth and survival is broken. Our analytical results and numerical simulations show that the trajectories of mean phenotype, mean fitness and the stationary phenotype distribution are in sharp contrast with those displayed for the standard model. The reason for this is that the usual weak selection limit does not hold in a complex landscape with several optima associated with different values of the birth rate. Here, we obtain trajectories of adaptation where the mean phenotype of the population is initially attracted by the birth optimum, but eventually converges to the survival optimum, following a hook-shaped curve which illustrates the antagonistic effects of mutation on adaptation.

scholarly journals The Evolution of Recombination: Removing the Limits to Natural Selection

Genetics ◽  
1997 ◽  
Vol 147 (2) ◽  
pp. 879-906 ◽  
Author(s):  
Sarah Perin Otto ◽  
Nick H Barton
Keyword(s):  
Natural Selection ◽  
Mutation Rate ◽  
Recombination Rate ◽  
Evolutionary Change ◽  
Fixation Probability ◽  
Beneficial Mutation ◽  
Beneficial Mutations ◽  
Adaptive Mutations ◽  
Tight Linkage ◽  
Selection For

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ2  Sδr/r when linkage is tight and λ2  S  3δr/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.

ACCELERATING THE EMERGENCE OF ORDER IN SWARMING SYSTEMS

2019 ◽  
Vol 23 (01) ◽  
pp. 1950015 ◽  
Author(s):  
YANDONG XIAO ◽  
CHULIANG SONG ◽  
LIANG TIAN ◽  
YANG-YU LIU
Keyword(s):  
Large Population ◽  
Unmanned Vehicles ◽  
Global Alignment ◽  
Multi Agent Systems ◽  
Vicsek Model ◽  
Contemporary Science ◽  
Speed Up ◽  
Multi Agent ◽  
Noise Robust ◽  
And Control

Our ability to understand and control the emergence of order in swarming systems is a fundamental challenge in contemporary science. The standard Vicsek model (SVM) — a minimal model for swarming systems of self-propelled particles — describes a large population of agents reaching global alignment without the need of central control. Yet, the emergence of order in this model takes time and is not robust to noise. In many real-world scenarios, we need a decentralized protocol to guide a swarming system (e.g., unmanned vehicles or nanorobots) to reach an ordered state in a prompt and noise-robust manner. Here, we find that introducing a simple adaptive rule based on the heading differences of neighboring particles in the Vicsek model can effectively speed up their global alignment, mitigate the disturbance of noise to alignment, and maintain a robust alignment under predation. This simple adaptive model of swarming systems could offer new insights in understanding the prompt and flexible formation of animals and help us design better protocols to achieve fast and robust alignment for multi-agent systems.

scholarly journals Mitotic recombination counteracts the benefits of genetic segregation

2007 ◽  
Vol 274 (1615) ◽  
pp. 1301-1307 ◽  
Author(s):  
Mohammad A Mandegar ◽  
Sarah P Otto
Keyword(s):  
Sexual Reproduction ◽  
Mitotic Recombination ◽  
Beneficial Mutation ◽  
Homozygous Carrier ◽  
Genetic Segregation ◽  
Homozygous Genotype ◽  
Speed Up ◽  
Extensive Body ◽  
Asexual Populations ◽  
Cost Of Sex

The ubiquity of sexual reproduction despite its cost has lead to an extensive body of research on the evolution and maintenance of sexual reproduction. Previous work has suggested that sexual reproduction can substantially speed up the rate of adaptation in diploid populations, because sexual populations are able to produce the fittest homozygous genotype by segregation and mating of heterozygous individuals. In contrast, asexual populations must wait for two rare mutational events, one producing a heterozygous carrier and the second converting a heterozygous to a homozygous carrier, before a beneficial mutation can become fixed. By avoiding this additional waiting time, it was shown that the benefits of segregation could overcome a twofold cost of sex. This previous result ignores mitotic recombination (MR), however. Here, we show that MR significantly hastens the spread of beneficial mutations in asexual populations. Indeed, given empirical data on MR, we find that adaptation in asexual populations proceeds as fast as that in sexual populations, especially when beneficial alleles are partially recessive. We conclude that asexual populations can gain most of the benefit of segregation through MR while avoiding the costs associated with sexual reproduction.

DIFFUSION OF A POPULATION OF INTERACTING REPLICATORS IN SEQUENCE SPACE

2002 ◽  
Vol 05 (04) ◽  
pp. 457-461 ◽  
Author(s):  
BÄRBEL M. R. STADLER
Keyword(s):  
Simple Model ◽  
Population Size ◽  
Computer Simulations ◽  
Mutation Rate ◽  
Sequence Space ◽  
Finite Population ◽  
Fitness Landscape ◽  
Diffusion Constant ◽  
Sequence Length

We consider a simple model for catalyzed replication. Computer simulations show that a finite population moves in sequence space by diffusion analogous to the behavior of a quasispecies on a flat fitness landscape. The diffusion constant depends linearly on the per position mutation rate and the ratio of sequence length and population size.

Sign in / Sign up

Export Citation Format

Share Document