The geometry of random genetic drift VI. A random selection diffusion model

1980 ◽  
Vol 12 (1) ◽  
pp. 50-58 ◽  
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
B. H. Voorhees
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Genetic Drift ◽  
Random Selection ◽  
Jacobi Field ◽  
Random Genetic Drift ◽  
Field Equations ◽  
Frequency Space ◽  
Quadratic Dependence ◽  
Selection Parameters

The ray solution of Felsenstein'sn-allele random selection diffusion process is given for small values of the selection parameters. This solution holds away from, but not near, the boundary of frequency space. The solution is possible only because the coefficients of the associated Jacobi field equations agree uniformly with those for the case of zero selection up to fourth powers in the selection parameters, whilst the covariance of the diffusion has only quadratic dependence.

The geometry of random genetic drift VI. A random selection diffusion model

1980 ◽  
Vol 12 (01) ◽  
pp. 50-58
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
B. H. Voorhees
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Genetic Drift ◽  
Random Selection ◽  
Jacobi Field ◽  
Random Genetic Drift ◽  
Field Equations ◽  
Frequency Space ◽  
Quadratic Dependence ◽  
Selection Parameters

The ray solution of Felsenstein's n-allele random selection diffusion process is given for small values of the selection parameters. This solution holds away from, but not near, the boundary of frequency space. The solution is possible only because the coefficients of the associated Jacobi field equations agree uniformly with those for the case of zero selection up to fourth powers in the selection parameters, whilst the covariance of the diffusion has only quadratic dependence.

The geometry of random drift II. The symmetry of random genetic drift

1977 ◽  
Vol 9 (2) ◽  
pp. 250-259 ◽  
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
G. Mark Lathrop ◽  
Kenneth Morgan
Keyword(s):  
Velocity Field ◽  
Genetic Drift ◽  
Gene Frequency ◽  
Radial Symmetry ◽  
Divergence Times ◽  
Random Genetic Drift ◽  
Initial State ◽  
Random Drift ◽  
Arithmetic Average ◽  
Frequency Space

It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.

The geometry of random drift II. The symmetry of random genetic drift

1977 ◽  
Vol 9 (02) ◽  
pp. 250-259 ◽  
Author(s):  
Peter L. Antonelli ◽  
Jared Chapin ◽  
G. Mark Lathrop ◽  
Kenneth Morgan
Keyword(s):  
Velocity Field ◽  
Genetic Drift ◽  
Gene Frequency ◽  
Radial Symmetry ◽  
Divergence Times ◽  
Random Genetic Drift ◽  
Initial State ◽  
Random Drift ◽  
Arithmetic Average ◽  
Frequency Space

It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.

CYTO-NUCLEAR EPISTASIS: TWO-LOCUS RANDOM GENETIC DRIFT IN HERMAPHRODITIC AND DIOECIOUS SPECIES

Evolution ◽  
2006 ◽  
Vol 60 (4) ◽  
pp. 643 ◽  
Author(s):  
Michael J. Wade ◽  
Charles J. Goodnight
Keyword(s):  
Genetic Drift ◽  
Random Genetic Drift ◽  
Dioecious Species

scholarly journals Influence of Random Genetic Drift on Human Immunodeficiency Virus Type 1envEvolution During Chronic Infection

Genetics ◽  
2004 ◽  
Vol 166 (3) ◽  
pp. 1155-1164 ◽  
Author(s):  
Daniel Shriner ◽  
Raj Shankarappa ◽  
Mark A. Jensen ◽  
David C. Nickle ◽  
John E. Mittler ◽  
...  
Keyword(s):  
Human Immunodeficiency Virus ◽  
Human Immunodeficiency Virus Type ◽  
Virus Type ◽  
Genetic Drift ◽  
Chronic Infection ◽  
Random Genetic Drift ◽  
Immunodeficiency Virus

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

scholarly journals Evolution of gene regulatory networks by means of selection and random genetic drift

2018 ◽  
Author(s):  
Antonios Kioukis ◽  
Pavlos Pavlidis
Keyword(s):  
Natural Selection ◽  
Positive Selection ◽  
Genetic Drift ◽  
Regulatory Networks ◽  
Fitness Landscape ◽  
Random Genetic Drift ◽  
Maturation Period ◽  
Evolutionary Forces ◽  
Gene Regulatory

The evolution of a population by means of genetic drift and natural selection operating on a gene regulatory network (GRN) of an individual has not been scrutinized in depth. Thus, the relative importance of various evolutionary forces and processes on shaping genetic variability in GRNs is understudied. Furthermore, it is not known if existing tools that identify recent and strong positive selection from genomic sequences, in simple models of evolution, can detect recent positive selection when it operates on GRNs. Here, we propose a simulation framework, called EvoNET, that simulates forward-in-time the evolution of GRNs in a population. Since the population size is finite, random genetic drift is explicitly applied. The fitness of a mutation is not constant, but we evaluate the fitness of each individual by measuring its genetic distance from an optimal genotype. Mutations and recombination may take place from generation to generation, modifying the genotypic composition of the population. Each individual goes through a maturation period, where its GRN reaches equilibrium. At the next step, individuals compete to produce the next generation. As time progresses, the beneficial genotypes push the population higher in the fitness landscape. We examine properties of the GRN evolution such as robustness against the deleterious effect of mutations and the role of genetic drift. We confirm classical results from Andreas Wagner’s work that GRNs show robustness against mutations and we provide new results regarding the interplay between random genetic drift and natural selection.

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