scholarly journals Active Information Requirements for Fixation on the Wright-Fisher Model of Population Genetics

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Robert Marks ◽  
Daniel Andrés Díaz Pachón
Keyword(s):  
Population Genetics ◽  
Information Requirements ◽  
Fisher Model

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.

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

1986 ◽  
Vol 23 (2) ◽  
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.

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 A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci

2016 ◽  
Author(s):  
Léandra King ◽  
John Wakeley ◽  
Shai Carmi
Keyword(s):  
Population Genetics ◽  
Large Scale ◽  
Weak Correlation ◽  
Effective Population ◽  
Statistical Population ◽  
Demographic Models ◽  
Empirical Estimates ◽  
Fisher Model ◽  
Pairwise Differences ◽  
Coalescence Times

AbstractThe population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, Tajima’s estimator (), which is the average number of pairwise differences, is not consistent and therefore its variance does not vanish even as n → ∞. The non-zero variance of results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by all genealogies. We derive the correlation coefficient under a diploid, discrete-time, Wright-Fisher model, and we also derive a simple, closed-form lower bound. We also obtain empirical estimates of the correlation of coalescence times under demographic models inspired by large-scale human genealogies. While the effect we de scribe is small , it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.

A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

1998 ◽  
Vol 30 (2) ◽  
pp. 493-512 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Genetics ◽  
Markov Chains ◽  
Population Size ◽  
Mutation Rate ◽  
Convergence Theorem ◽  
Population Models ◽  
Fisher Model

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models.For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate ̃θ := θ(1-s/2), if the population size N is large and if the time is measured in units of (2-s)N generations.

Evolutionary Genomics of High Fecundity

2020 ◽  
Vol 54 (1) ◽  
pp. 213-236
Author(s):  
Bjarki Eldon
Keyword(s):  
Population Genetics ◽  
Population Genetic ◽  
Reference Model ◽  
Evolutionary Genomics ◽  
Whole Genome Sequencing Data ◽  
Sequencing Data ◽  
High Fecundity ◽  
Large Numbers ◽  
Fisher Model ◽  
Evolutionary Studies

Natural highly fecund populations abound. These range from viruses to gadids. Many highly fecund populations are economically important. Highly fecund populations provide an important contrast to the low-fecundity organisms that have traditionally been applied in evolutionary studies. A key question regarding high fecundity is whether large numbers of offspring are produced on a regular basis, by few individuals each time, in a sweepstakes mode of reproduction. Such reproduction characteristics are not incorporated into the classical Wright–Fisher model, the standard reference model of population genetics, or similar types of models, in which each individual can produce only small numbers of offspring relative to the population size. The expected genomic footprints of population genetic models of sweepstakes reproduction are very different from those of the Wright–Fisher model. A key, immediate issue involves identifying the footprints of sweepstakes reproduction in genomic data. Whole-genome sequencing data can be used to distinguish the patterns made by sweepstakes reproduction from the patterns made by population growth in a population evolving according to the Wright–Fisher model (or similar models). If the hypothesis of sweepstakes reproduction cannot be rejected, then models of sweepstakes reproduction and associated multiple-merger coalescents will become at least as relevant as the Wright–Fisher model (or similar models) and the Kingman coalescent, the cornerstones of mathematical population genetics, in further discussions of evolutionary genomics of highly fecund populations.

scholarly journals Information Geometry and Population Genetics: The Mathematical Structure of the Wright - Fisher Model

2018 ◽  
Vol 45 (1-2) ◽  
Author(s):  
Ranjita Pandey
Keyword(s):  
Population Genetics ◽  
Mathematical Structure ◽  
Information Geometry ◽  
Fisher Model

by Julian Hofrichter, Jurgen Jost and Tat Dat Tran

A convergence theorem for markov chains arising in population genetics and the coalescent with selfing

1998 ◽  
Vol 30 (02) ◽  
pp. 493-512 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Genetics ◽  
Markov Chains ◽  
Population Size ◽  
Mutation Rate ◽  
Convergence Theorem ◽  
Population Models ◽  
Fisher Model

A simple convergence theorem for sequences of Markov chains is presented in order to derive new ‘convergence-to-the-coalescent’ results for diploid neutral population models. For the so-called diploid Wright-Fisher model with selfing probability s and mutation rate θ, it is shown that the ancestral structure of n sampled genes can be treated in the framework of an n-coalescent with mutation rate ̃θ := θ(1-s/2), if the population size N is large and if the time is measured in units of (2-s)N generations.

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