scholarly journals Weak approximations of Wright-Fisher equation

2021 ◽  
Vol 62 ◽  
pp. 23-26
Author(s):  
Gabrielė Mongirdaitė ◽  
Vigirdas Mackevičius
Keyword(s):  
Fisher Equation ◽  
Fisher Model ◽  
Weak Approximations

We construct weak approximations of the Wright-Fisher model and illustrate their accuracy by simulation examples.

scholarly journals Weak Approximations of the Wright–Fisher Process

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 125
Author(s):  
Vigirdas Mackevičius ◽  
Gabrielė Mongirdaitė
Keyword(s):  
Random Variables ◽  
Second Order ◽  
Fisher Equation ◽  
Discretization Schemes ◽  
Weak Approximations ◽  
Discretization Step ◽  
Fisher Process

In this paper, we construct first- and second-order weak split-step approximations for the solutions of the Wright–Fisher equation. The discretization schemes use the generation of, respectively, two- and three-valued random variables at each discretization step. The accuracy of constructed approximations is illustrated by several simulation examples.

scholarly journals A phylogenetic estimator of effective population size or mutation rate.

Genetics ◽  
1994 ◽  
Vol 136 (2) ◽  
pp. 685-692 ◽  
Author(s):  
Y X Fu
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
High Efficiency ◽  
Minimum Variance ◽  
Population Subdivision ◽  
Effective Population ◽  
Fisher Model ◽  
Mitochondrial Sequences

Abstract A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating theta by the new method is presented using the mitochondrial sequences from an American Indian population.

scholarly journals Fisher equation with turbulence in one dimension

2009 ◽  
Vol 238 (19) ◽  
pp. 2003-2015 ◽  
Author(s):  
Roberto Benzi ◽  
David R. Nelson
Keyword(s):  
One Dimension ◽  
Fisher Equation

scholarly journals A General Solution of the Wright–Fisher Model of Random Genetic Drift

2016 ◽  
Vol 27 (4) ◽  
pp. 467-492 ◽  
Author(s):  
Tat Dat Tran ◽  
Julian Hofrichter ◽  
Jürgen Jost
Keyword(s):  
General Solution ◽  
Genetic Drift ◽  
Random Genetic Drift ◽  
Fisher Model
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