scholarly journals The advance of Muller's ratchet in a haploid asexual population: approximate solutions based on diffusion theory

1993 ◽  
Vol 61 (3) ◽  
pp. 225-231 ◽  
Author(s):  
Wolfgang Stephan ◽  
Lin Chao ◽  
Joanne Guna Smale
Keyword(s):  
Diffusion Theory ◽  
Large Population ◽  
Approximate Solutions ◽  
Diffusion Approximations ◽  
Asexual Population ◽  
Muller's Ratchet ◽  
Expected Time ◽  
Equilibrium Size ◽  
Muller’S Ratchet ◽  
Asexual Populations

SummaryAsexual populations experiencing random genetic drift can accumulate an increasing number of deleterious mutations, a process called Muller's ratchet. We present here diffusion approximations for the rate at which Muller's ratchet advances in asexual haploid populations. The most important parameter of this process is n0 = N e−U/s, where N is population size, U the genomic mutation rate and s the selection coefficient. In a very large population, n0 is the equilibrium size of the mutation-free class. We examined the case n0 > 1 and developed one approximation for intermediate values of N and s and one for large values of N and s. For intermediate values, the expected time at which the ratchet advances increases linearly with n0. For large values, the time increases in a more or less exponential fashion with n0. In addition to n0, s is also an important determinant of the speed of the ratchet. If N and s are intermediate and n0 is fixed, we find that increasing s accelerates the ratchet. In contrast, for a given n0, but large N and s, increasing s slows the ratchet. Except when s is small, results based on our approximations fit well those from computer simulations.

scholarly journals Diffusion approximations in population genetics and the rate of Muller's ratchet

2021 ◽  
Author(s):  
Matteo Smerlak ◽  
Camila Braeutigam
Keyword(s):  
Population Genetics ◽  
Diffusion Theory ◽  
Diffusion Equations ◽  
Muller's Ratchet ◽  
Expected Time ◽  
Parameters Selection ◽  
Fisher Model ◽  
Muller’S Ratchet ◽  
Fixation Probabilities ◽  
Modern Population

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size---a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, including in regimes where selection and/or mutation are strong compared to genetic drift. As an illustration, we use a diffusion approximation of the Wright-Fisher model to improve estimates for the expected time to fixation of a strongly deleterious allele, i.e. the rate of Muller's ratchet.

ADAPTIVE EVOLUTION OF ASEXUAL POPULATIONS UNDER MULLER'S RATCHET

Evolution ◽  
2004 ◽  
Vol 58 (7) ◽  
pp. 1403 ◽  
Author(s):  
Doris Bachtrog ◽  
Isabel Gordo
Keyword(s):  
Adaptive Evolution ◽  
Muller's Ratchet ◽  
Muller’S Ratchet ◽  
Asexual Populations

scholarly journals Competition between continuously evolving lineages in asexual populations

2016 ◽  
Author(s):  
Noah Ribeck ◽  
Joseph S. Mulka ◽  
Luis Zaman ◽  
Brian D. Connelly ◽  
Richard E. Lenski
Keyword(s):  
Large Population ◽  
Current Theory ◽  
Simple Expression ◽  
Critical Threshold ◽  
Beneficial Mutation ◽  
Asexual Population ◽  
Simplifying Assumptions ◽  
Population Sizes ◽  
Asexual Populations

ABSTRACTIn an asexual population, the fate of a beneficial mutation depends on how its lineage competes against other mutant lineages in the population. With high beneficial mutation rates or large population sizes, competition between contending mutations is strong, and successful lineages can accumulate multiple mutations before any single one achieves fixation. Most current theory about asexual population dynamics either neglects this multiple-mutations regime or introduces simplifying assumptions that may not apply. Here, we develop a theoretical framework that describes the dynamics of adaptation and substitution over all mutation-rate regimes by conceptualizing the population as a collection of continuously adapting lineages. This model of “lineage interference” shows that each new mutant’s advantage over the rest of the population must be above a critical threshold in order to likely achieve fixation, and we derive a simple expression for that threshold. We apply this framework to examine the role of beneficial mutations with different effect sizes across the transition to the multiple-mutations regime.

scholarly journals Rapid fixation of deleterious alleles can be caused by Muller's ratchet

1997 ◽  
Vol 70 (1) ◽  
pp. 63-73 ◽  
Author(s):  
BRIAN CHARLESWORTH ◽  
DEBORAH CHARLESWORTH
Keyword(s):  
Analytical Approximation ◽  
Similar Process ◽  
Asexual Population ◽  
Single Chromosome ◽  
Muller's Ratchet ◽  
Analytical Approximations ◽  
Deleterious Alleles ◽  
Wide Range ◽  
Muller’S Ratchet ◽  
Parameter Values

Theoretical arguments are presented which suggest that each advance of Muller's ratchet in a haploid asexual population causes the fixation of a deleterious mutation at a single locus. A similar process operates in a diploid, fully asexual population under a wide range of parameter values, with respect to fixation within one of the two haploid genomes. Fixations of deleterious mutations in asexual species can thus be greatly accelerated in comparison with a freely recombining genome, if the ratchet is operating. In a diploid with segregation of a single chromosome, but no crossing over within the chromosome, the advance of the ratchet can be decoupled from fixation if mutations are sufficiently close to recessivity. A new analytical approximation for the rate of advance of the ratchet is proposed. Simulation results are presented that validate the assertions about fixation. The simulations show that none of the analytical approximations for the rate of advance of the ratchet are satisfactory when population size is large. The relevance of these results for evolutionary processes such as Y chromosome degeneration is discussed.

scholarly journals Muller's ratchet under epistatic selection.

Genetics ◽  
1994 ◽  
Vol 136 (4) ◽  
pp. 1469-1473 ◽  
Author(s):  
A S Kondrashov
Keyword(s):  
Previous Analysis ◽  
Random Drift ◽  
Asexual Population ◽  
Muller's Ratchet ◽  
Fitness Effects ◽  
Deleterious Alleles ◽  
Minimum Number ◽  
Muller’S Ratchet ◽  
Mean Fitness ◽  
Independent Effects

Abstract In a finite asexual population mean fitness may decrease by a process known as Muller's ratchet, which proceeds if all individuals with the minimum number of deleterious alleles are randomly lost. If these alleles have independent effects on fitness, previous analysis suggested that the rate of this decrease either remains constant or, if accumulation of mutations leads to the decline of the population size, grows. Here I show that this conclusion is quite sensitive to the assumption of independence. If deleterious alleles have synergistic fitness effects, then, as the ratchet advances, the frequency of the best available genotype will necessarily increase, making its loss less and less probable. As a result, sufficiently strong synergistic epistasis can effectively halt the action of Muller's ratchet. Instead of being driven extinct, a finite asexual population could then survive practically indefinitely, although with lower mean fitness than without random drift.

scholarly journals Defying Muller’s Ratchet: Ancient Heritable Endobacteria Escape Extinction through Retention of Recombination and Genome Plasticity

mBio ◽  
2016 ◽  
Vol 7 (3) ◽  
Author(s):  
Mizue Naito ◽  
Teresa E. Pawlowska
Keyword(s):  
Mycorrhizal Fungi ◽  
Arbuscular Mycorrhizal ◽  
Genome Plasticity ◽  
Escape Extinction ◽  
Muller's Ratchet ◽  
Evolutionary Forces ◽  
Slightly Deleterious Mutations ◽  
Muller’S Ratchet ◽  
Asexual Populations ◽  
Host Generation

ABSTRACT   Heritable endobacteria, which are transmitted from one host generation to the next, are subjected to evolutionary forces that are different from those experienced by free-living bacteria. In particular, they suffer consequences of Muller’s ratchet, a mechanism that leads to extinction of small asexual populations due to fixation of slightly deleterious mutations combined with the random loss of the most-fit genotypes, which cannot be recreated without recombination. Mycoplasma-related endobacteria (MRE) are heritable symbionts of fungi from two ancient lineages, Glomeromycota (arbuscular mycorrhizal fungi) and Mucoromycotina . Previous studies revealed that MRE maintain unusually diverse populations inside their hosts and may have been associated with fungi already in the early Paleozoic. Here we show that MRE are vulnerable to genomic degeneration and propose that they defy Muller’s ratchet thanks to retention of recombination and genome plasticity. We suggest that other endobacteria may be capable of raising similar defenses against Muller’s ratchet.

scholarly journals Muller’s Ratchet in Asexual Populations Doomed to Extinction

2018 ◽  
Author(s):  
Logan Chipkin ◽  
Peter Olofsson ◽  
Ryan C. Daileda ◽  
Ricardo B. R. Azevedo
Keyword(s):  
Process Model ◽  
Population Decline ◽  
Extinction Time ◽  
Deleterious Mutations ◽  
Multitype Branching Process ◽  
Muller's Ratchet ◽  
Constant Size ◽  
Muller’S Ratchet ◽  
Asexual Populations ◽  
Mutational Meltdown

AbstractAsexual populations are expected to accumulate deleterious mutations through a process known as Muller’s Ratchet. Lynch, Gabriel, and colleagues have proposed that the Ratchet eventually results in a vicious cycle of mutation accumulation and population decline that drives populations to extinction. They called this phenomenon mutational meltdown. Here, we analyze the meltdown using a multitype branching process model where, in the presence of mutation, populations are doomed to extinction. We find that extinction occurs more quickly in small populations, experiencing a high deleterious mutation rate, and mutations with more severe deleterious effects. The effects of mutational parameters on extinction time in doomed populations differ from those on the severity of Muller’s Ratchet in populations of constant size. We also 1nd that mutational meltdown, although it does occur in our model, does not determine extinction time. Rather, extinction time is determined by the expected impact of deleterious mutations on fitness.

scholarly journals Does Muller's ratchet work with selfing?

1978 ◽  
Vol 32 (3) ◽  
pp. 289-293 ◽  
Author(s):  
R. Heller ◽  
J. Maynard Smith
Keyword(s):  
Large Class ◽  
Deleterious Mutations ◽  
Asexual Population ◽  
Muller's Ratchet ◽  
Slightly Deleterious Mutations ◽  
Muller’S Ratchet

SUMMARYThe accumulation of deleterious mutations in a finite diploid selfing population is investigated. It is shown that the conditions for accumulation are very similar to those for the accumulation of mutations in an asexual population by ‘Muller's ratchet’. The ratchet is likely to operate in both types of population if there is a large class of slightly deleterious mutations.

scholarly journals The constraints of finite size in asexual populations and the rate of the ratchet

1995 ◽  
Vol 66 (3) ◽  
pp. 241-253 ◽  
Author(s):  
Damian D. G. Gessler
Keyword(s):  
Negative Binomial ◽  
Finite Size ◽  
Mutation Accumulation ◽  
Necessary Condition ◽  
Mutation Pressure ◽  
Actual Distribution ◽  
Muller's Ratchet ◽  
State Strength ◽  
Muller’S Ratchet ◽  
Asexual Populations

SummaryAn analysis of mutation accumulation in finite, asexual populations shows that by modeling discrete individuals, a necessary condition for mutation–selection balance is often not met. It is found that over a wide parameter range (whenever N e−μ/s < 1, where N is the population size, μ is the genome-wide mutation rate, and s is the realized strength of selection), asexual populations will fail to achieve mutation–selection balance. This is specifically because the steady-state strength of selection on the best individuals is too weak to counter mutation pressure. The discrete nature of individuals means that if the equilibrium level of mutation and selection is such that less than one individual is expected in a class, then equilibration towards this level acts to remove the class. When applied to the classes with the fewest mutations, this drives mutation accumulation. This drive is in addition to the well-known identification of the stochastic loss of the best class as a mechanism for Muller's ratchet. Quantification of this process explains why the distribution of the number of mutations per individual can be markedly hypodispersed compared to the Poisson expectation. The actual distribution, when corrected for stochasticity between the best class and the mean, is akin to a shifted negative binomial. The parameterization of the distribution allows for an approximation for the rate of Muller's ratchet when N e−μ/s < 1. The analysis is extended to the case of variable selection coefficients where incoming mutations assume a distribution of deleterious effects. Under this condition, asexual populations accumulate mutations faster, yet may be able to survive longer, than previously estimated.

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