Dynamics of Finite Populations I. The Expected Time to Fixation or Loss and the Probability of Fixation of an Allele in a Haploid Population of Variable Size

Biometrics ◽  
1972 ◽  
Vol 28 (2) ◽  
pp. 373 ◽  
Author(s):  
R. D. Cook ◽  
R. F. Nassar
Keyword(s):  
Finite Populations ◽  
Variable Size ◽  
Expected Time ◽  
Haploid Population ◽  
Probability Of Fixation

The time back to the most recent common ancestor in exchangeable population models

2004 ◽  
Vol 36 (01) ◽  
pp. 78-97 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Size ◽  
Common Ancestor ◽  
Large Population ◽  
Upper Bounds ◽  
Population Models ◽  
Recent Common Ancestor ◽  
Coalescent Theory ◽  
Expected Time ◽  
Most Recent Common Ancestor ◽  
Haploid Population

A class of haploid population models with population size N, nonoverlapping generations and exchangeable offspring distribution is considered. Based on an analysis of the discrete ancestral process, we present solutions, algorithms and strong upper bounds for the expected time back to the most recent common ancestor which hold for arbitrary sample size n ∈ {1,…,N}. New insights into the asymptotic behaviour of the expected time back to the most recent common ancestor for large population size are presented relating the results to coalescent theory.

scholarly journals Random selective advantages of genes and their probabilities of fixation

1973 ◽  
Vol 21 (3) ◽  
pp. 215-219 ◽  
Author(s):  
Louis Jensen
Keyword(s):  
Finite Population ◽  
Selective Advantage ◽  
Rare Gene ◽  
Haploid Population ◽  
Selection Intensities ◽  
Image Position ◽  
Ultimate Probability ◽  
Random Fluctuations ◽  
Probability Of Fixation

SUMMARYThe question of what is meant by random fluctuations in selection intensities in a finite population is re-examined. The model presented describes the change in the frequency of a gene in a haploid population of size M. It is assumed that in any generation the adaptive values of A and a are equally likely to be 1 + s: 1 or 1: 1 + s. If s is the selective advantage and x the frequency of gene A, then the first two moments of the change in frequency are found to be m(Δx) = x(1 − x)(1 − 2x) θ/2M andwhere E(s2) = θ/M. The ultimate probability of fixation is computed, showing that variability in selection increases the chance of fixation of a rare gene. A more general form for m(Δx) also is obtained. This form is compared with the equation currently used in describing random fluctuations in selection intensities.

The time back to the most recent common ancestor in exchangeable population models

2004 ◽  
Vol 36 (1) ◽  
pp. 78-97 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Population Size ◽  
Common Ancestor ◽  
Large Population ◽  
Upper Bounds ◽  
Population Models ◽  
Recent Common Ancestor ◽  
Coalescent Theory ◽  
Expected Time ◽  
Most Recent Common Ancestor ◽  
Haploid Population

A class of haploid population models with population size N, nonoverlapping generations and exchangeable offspring distribution is considered. Based on an analysis of the discrete ancestral process, we present solutions, algorithms and strong upper bounds for the expected time back to the most recent common ancestor which hold for arbitrary sample size n ∈ {1,…,N}. New insights into the asymptotic behaviour of the expected time back to the most recent common ancestor for large population size are presented relating the results to coalescent theory.

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