Ultimate probability of fixation and time to fixation or loss of a gene under a variable fitness model

1974 ◽  
Vol 44 (6) ◽  
pp. 247-254 ◽  
Author(s):  
R. F. Nassar ◽  
R. D. Cook
Keyword(s):  
Ultimate Probability ◽  
Probability Of Fixation

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.

scholarly journals The Probability of Fixation in Populations of Changing Size

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 723-733 ◽  
Author(s):  
Sarah P Otto ◽  
Michael C Whitlock
Keyword(s):  
Diffusion Equation ◽  
Adaptive Evolution ◽  
Process Model ◽  
Branching Process ◽  
Approximate Solutions ◽  
Logistic Growth ◽  
Beneficial Mutations ◽  
Demographic Models ◽  
Deleterious Alleles ◽  
Probability Of Fixation

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

scholarly journals Vanishing GC-Rich Isochores in Mammalian Genomes

Genetics ◽  
2002 ◽  
Vol 162 (4) ◽  
pp. 1837-1847 ◽  
Author(s):  
Laurent Duret ◽  
Marie Semon ◽  
Gwenaël Piganeau ◽  
Dominique Mouchiroud ◽  
Nicolas Galtier
Keyword(s):  
Gc Content ◽  
Synonymous Substitution ◽  
Equilibrium Analysis ◽  
Large Excess ◽  
Substitution Pattern ◽  
Origin And Evolution ◽  
Evolutionary Force ◽  
Mammalian Genomes ◽  
Human Polymorphism ◽  
Probability Of Fixation

AbstractTo understand the origin and evolution of isochores—the peculiar spatial distribution of GC content within mammalian genomes—we analyzed the synonymous substitution pattern in coding sequences from closely related species in different mammalian orders. In primate and cetartiodactyls, GC-rich genes are undergoing a large excess of GC → AT substitutions over AT → GC substitutions: GC-rich isochores are slowly disappearing from the genome of these two mammalian orders. In rodents, our analyses suggest both a decrease in GC content of GC-rich isochores and an increase in GC-poor isochores, but more data will be necessary to assess the significance of this pattern. These observations question the conclusions of previous works that assumed that base composition was at equilibrium. Analysis of allele frequency in human polymorphism data, however, confirmed that in the GC-rich parts of the genome, GC alleles have a higher probability of fixation than AT alleles. This fixation bias appears not strong enough to overcome the large excess of GC → AT mutations. Thus, whatever the evolutionary force (neutral or selective) at the origin of GC-rich isochores, this force is no longer effective in mammals. We propose a model based on the biased gene conversion hypothesis that accounts for the origin of GC-rich isochores in the ancestral amniote genome and for their decline in present-day mammals.

Probability of Fixation of Nonfunctional Genes at Duplicate Loci

1973 ◽  
Vol 107 (955) ◽  
pp. 362-372 ◽  
Author(s):  
Masatoshi Nei ◽  
Arun K. Roychoudhury
Keyword(s):  
Duplicate Loci ◽  
Probability Of Fixation
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