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.

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 The Rate of Compensatory Evolution

Genetics ◽  
1996 ◽  
Vol 144 (1) ◽  
pp. 419-426 ◽  
Author(s):  
Wolfgang Stephan
Keyword(s):  
Diffusion Theory ◽  
Secondary Structures ◽  
Compensatory Mutation ◽  
Weak Selection ◽  
Mutation Pressure ◽  
Theory Of Evolution ◽  
Compensatory Evolution ◽  
Expected Time ◽  
Individual Fitness ◽  
Shifting Balance

Abstract A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, kc, is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, kc, depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, kc, is given by the rate at which favorable combinations of double mutantS are produced by compensatory mutation. For r > 0, kc, decreases exponentially with r. In contrast, kc, becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to Wright'S shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.

Muller’s ratchet of the Y chromosome with gene conversion

Genetics ◽  
2021 ◽  
Author(s):  
Takahiro Sakamoto ◽  
Hideki Innan
Keyword(s):  
Gene Duplication ◽  
Gene Conversion ◽  
Y Chromosome ◽  
Conversion Rate ◽  
Single Copy ◽  
Duplicated Genes ◽  
Fitness Effect ◽  
Muller's Ratchet ◽  
Y Chromosomes ◽  
Muller’S Ratchet

Abstract Muller’s ratchet is a process in which deleterious mutations are fixed irreversibly in the absence of recombination. The degeneration of the Y chromosome, and the gradual loss of its genes, can be explained by Muller’s ratchet. However, most theories consider single-copy genes, and may not be applicable to Y chromosomes, which have a number of duplicated genes in many species, which are probably undergoing concerted evolution by gene conversion. We developed a model of Muller’s ratchet to explore the evolution of the Y chromosome. The model assumes a non-recombining chromosome with both single-copy and duplicated genes. We used analytical and simulation approaches to obtain the rate of gene loss in this model, with special attention to the role of gene conversion. Homogenization by gene conversion makes both duplicated copies either mutated or intact. The former promotes the ratchet, and the latter retards, and we ask which of these counteracting forces dominates under which conditions. We found that the effect of gene conversion is complex, and depends upon the fitness effect of gene duplication. When duplication has no effect on fitness, gene conversion accelerates the ratchet of both single-copy and duplicated genes. If duplication has an additive fitness effect, the ratchet of single-copy genes is accelerated by gene duplication, regardless of the gene conversion rate, whereas gene conversion slows the degeneration of duplicated genes. Our results suggest that the evolution of the Y chromosome involves several parameters, including the fitness effect of gene duplication by increasing dosage and gene conversion rate.

A genealogical approach to variable-population-size models in population genetics

1986 ◽  
Vol 23 (02) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly
Keyword(s):  
Population Genetics ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Process Models ◽  
Moran Model ◽  
Fisher Model ◽  
Variable Population ◽  
Exchangeable Model ◽  
Necessary And Sufficient ◽  
Variable Population Size

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

Amazon molly and Muller's ratchet

Nature ◽  
1995 ◽  
Vol 375 (6527) ◽  
pp. 111-112 ◽  
Author(s):  
Leo W. Beukeboom ◽  
Rolf P. Weinzierl ◽  
Nico K. Michiels
Keyword(s):  
Muller's Ratchet ◽  
Amazon Molly ◽  
Muller’S Ratchet

scholarly journals Drastic Fitness Loss in Human Immunodeficiency Virus Type 1 upon Serial Bottleneck Events

1999 ◽  
Vol 73 (4) ◽  
pp. 2745-2751 ◽  
Author(s):  
Eloisa Yuste ◽  
Sonsoles Sánchez-Palomino ◽  
Concha Casado ◽  
Esteban Domingo ◽  
Cecilio López-Galíndez
Keyword(s):  
Human Immunodeficiency Virus ◽  
Human Immunodeficiency Virus Type ◽  
Virus Type ◽  
Field Isolate ◽  
Plaque Assay ◽  
Muller's Ratchet ◽  
Immunodeficiency Virus ◽  
Muller’S Ratchet ◽  
Hiv 1

ABSTRACT Muller’s ratchet predicts fitness losses in small populations of asexual organisms because of the irreversible accumulation of deleterious mutations and genetic drift. This effect should be enhanced if population bottlenecks intervene and fixation of mutations is not compensated by recombination. To study whether Muller’s ratchet could operate in a retrovirus, 10 biological clones were derived from a human immunodeficiency virus type 1 (HIV-1) field isolate by MT-4 plaque assay. Each clone was subjected to 15 plaque-to-plaque passages. Surprisingly, genetic deterioration of viral clones was very drastic, and only 4 of the 10 initial clones were able to produce viable progeny after the serial plaque transfers. Two of the initial clones stopped forming plaques at passage 7, two others stopped at passage 13, and only four of the remaining six clones yielded infectious virus. Of these four, three displayed important fitness losses. Thus, despite virions carrying two copies of genomic RNA and the system displaying frequent recombination, HIV-1 manifested a drastic fitness loss as a result of an accentuation of Muller’s ratchet effect.

scholarly journals Rapid fitness losses in mammalian RNA virus clones due to Muller's ratchet.

1992 ◽  
Vol 89 (13) ◽  
pp. 6015-6019 ◽  
Author(s):  
E. Duarte ◽  
D. Clarke ◽  
A. Moya ◽  
E. Domingo ◽  
J. Holland
Keyword(s):  
Rna Virus ◽  
Muller's Ratchet ◽  
Muller’S Ratchet
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