scholarly journals PROBABILITY OF FIXATION AND MEAN FIXATION TIME OF AN OVERDOMINANT MUTATION

Genetics ◽  
1973 ◽  
Vol 74 (2) ◽  
pp. 371-380
Author(s):  
Masatoshi Nei ◽  
A K Roychoudhury
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Finite Population ◽  
Retardation Factor ◽  
Fixation Time ◽  
Selection Intensity ◽  
Infinite Population ◽  
Probability Of Fixation

ABSTRACT The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.

scholarly journals GENETIC VARIATION IN A HETEROGENEOUS ENVIRONMENT. I. TEMPORAL HETEROGENEITY AND THE ABSOLUTE DOMINANCE MODEL

Genetics ◽  
1974 ◽  
Vol 78 (2) ◽  
pp. 757-770
Author(s):  
Philip W Hedrick
Keyword(s):  
Genetic Variation ◽  
Temporal Variation ◽  
Gene Frequency ◽  
Environmental Heterogeneity ◽  
Finite Population ◽  
Environmental Variation ◽  
Dominance Model ◽  
Infinite Population ◽  
The Absolute ◽  
Absolute Dominance

ABSTRACT The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.

Long-term Response: 2. Finite Population Size and Mutation

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Population Size ◽  
Quantitative Trait ◽  
Finite Population ◽  
Initial Response ◽  
Optimal Selection ◽  
Selection Intensity ◽  
Effective Population ◽  
Additive Variance ◽  
Term Response

In a finite population, drift is often more important than selection in removing any initial additive variance. This chapter examines the joint impact of selection, drift, and mutation on the long-term response in a quantitative trait. One key result is the remarkable finding of Robertson that the expected long-term response from any initial additive variance is bounded above by the product of twice the effective population size times the initial response. This result implies that the optimal selection intensity for long-term response it to save half of the population in each generation.

scholarly journals The effect of initial reverse selection upon total selection response

1964 ◽  
Vol 5 (1) ◽  
pp. 68-79 ◽  
Author(s):  
J. S. Allan ◽  
Alan Robertson
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Initial Period ◽  
Low Frequency ◽  
Selection Response ◽  
Selection Intensity ◽  
Forward Selection ◽  
Frequency Distributions ◽  
Gene Effect ◽  
Recessive Genes

A computer has been used to investigate the effect of an initial period of reverse selection on the subsequent response of a population to renewed forward selection with the same population size and selection intensity. As the computer was used to derive gene frequency distributions, there was no random element in the results obtained. A theoretical solution to the problem was obtained for genes with small effects.The process can be adequately described by the duration of the reverse selection (expressed in terms of the population size N), the product of population size and gene effect, Ns, and the initial gene frequency. If the duration of reverse selection, t, is less than N/2, the loss in selection advance due to the reverse selection is roughly t/N, though slightly greater than this for genes with low frequency. The ‘point of no return’ after which it is impossible, with the same population size and selection intensity, to return even to the starting frequency is 1·4N generations for genes with small effect and this declines as the gene effect increases.Some extension of results to recessive genes is also given.

scholarly journals Coevolution does not slow the rate of loss of heterozygosity in a stochastic host-parasite model with constant population size

2020 ◽  
Author(s):  
Ailene MacPherson ◽  
Matthew J. Keeling ◽  
Sarah P. Otto
Keyword(s):  
Genetic Variation ◽  
Natural Selection ◽  
Population Size ◽  
Finite Population ◽  
Extensive Literature ◽  
Stochastic Perturbations ◽  
Frequency Dependent Selection ◽  
Infinite Population ◽  
Negative Frequency Dependent Selection ◽  
Host Parasite

AbstractCoevolutionary negative frequency dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the effect of matching-alleles (MAM) coevolution on the maintenance of genetic variation has not been explicitly modelled in a finite population. The dynamics of the MAM in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. We find that while this is largely true in finite populations two additional phenomena arise. The first of these effects is that of coevolutionary natural selection on stochastic perturbations in host and pathogen allele frequencies. While this may increase or decrease genetic variation, depending on the parameter conditions, the net effect is small relative to that of the second phenomena. Following fixation in the pathogen, the MAM becomes one of directional selection, which in turn rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.

scholarly journals Palliating the impact of fixation of a major gene on the genetic variation of artificially selected polygenes

2006 ◽  
Vol 88 (2) ◽  
pp. 105-118 ◽  
Author(s):  
LEOPOLDO SÁNCHEZ ◽  
ARMANDO CABALLERO ◽  
ENRIQUE SANTIAGO
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Selective Sweep ◽  
Major Gene ◽  
Optimal Path ◽  
Fixation Time ◽  
Selection Intensity ◽  
Effective Population ◽  
The Impact ◽  
Polygenic Variation

Selective sweeps of variation caused by fixation of major genes may have a dramatic impact on the genetic gain from background polygenic variation, particularly in the genome regions closely linked to the major gene. The response to selection can be restrained because of the reduced selection intensity and the reduced effective population size caused by the increase in frequency of the major gene. In the context of a selected population where fixation of a known major gene is desired, the question arises as to which is the optimal path of increase in frequency of the gene so that the selective sweep of variation resulting from its fixation is minimized. Using basic theoretical arguments we propose a frequency path that maximizes simultaneously the effective population size applicable to the selected background and the selection intensity on the polygenic variation by minimizing the average squared selection intensity on the major gene over generations up to a given fixation time. We also propose the use of mating between carriers and non-carriers of the major gene, in order to promote the effective recombination between the major gene and its linked polygenic background. Using a locus-based computer simulation assuming different degrees of linkage, we show that the path proposed is more effective than a similar path recently published, and that the combination of the selection and mating methods provides an efficient way to palliate the negative effects of a selective sweep.

scholarly journals A population genetical model for sequence evolution under multiple types of mutation

1989 ◽  
Vol 54 (3) ◽  
pp. 231-237 ◽  
Author(s):  
Masaru Iizuka
Keyword(s):  
Population Size ◽  
Dna Sequence ◽  
Phylogenetic Relationships ◽  
Finite Population ◽  
Theoretical Study ◽  
Deleterious Mutation ◽  
Sequence Evolution ◽  
Infinite Population ◽  
Neutral Mutation ◽  
Dna Sequence Evolution

SummaryDNA sequencing and restriction mapping provide us with information on DNA sequence evolution within populations, from which the phylogenetic relationships among the sequences can be inferred. Mutations such as base substitutions, deletions, insertions and transposable element insertions can be identified in each sequence. Theoretical study of this type of sequence evolution has been initiated recently. In this paper, population genetical models for sequence evolution under multiple types of mutation are developed. Models of infinite population size with neutral mutation, infinite population size with deleterious mutation and finite population size with neutral mutation are considered.

scholarly journals Fixation time of overdominant alleles influenced by random fluctuation of selection intensity

1972 ◽  
Vol 20 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Tomoko Ohta ◽  
Motoo Kimura
Keyword(s):  
Population Size ◽  
Random Fluctuation ◽  
Fixation Time ◽  
Selection Intensity ◽  
Selection Coefficient ◽  
Polymorphic Variants ◽  
The Mean

SUMMARYIt was demonstrated that the number of generations until fixation or loss of an overdominant alleles is influenced by random fluctuation of selection coefficients. When 2 < Vs, where is the mean selection coefficient against either homozygote and Vs is the between -generation variance of the selection coefficient, overdominance generally accelerates rather than retards fixation of segregating alleles. This finding should have important bearing on our consideration of the behaviour of polymorphic variants which are nearly neutral but have very slight overdominance. When the population size (Ne) is extremely large, not only Ne but also /Vs have to be considered in discussing the effectiveness of overdominance.

scholarly journals Distribution of linkage disequilibrium with selection and finite population size

1979 ◽  
Vol 33 (1) ◽  
pp. 29-48 ◽  
Author(s):  
P. J. Avery ◽  
W. G. Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Large Expansion ◽  
Large Populations ◽  
The Difference ◽  
Successive Generations ◽  
Stable Points

SUMMARYThe effects of finite population size, occurring either as a bottleneck in a single generation followed by a large expansion or in all generations, are considered for models of two linked heterotic loci. Linkage is assumed to be tight because it is required if there is to be stable linkage disequilibrium, D ǂ 0, in infinitely large populations. (D is the difference between gamete frequencies and the product of the gene frequencies.)If a substantial perturbation of frequencies occurs as a result of a bottleneck but the population is subsequently very large, D may take hundreds of generations to return to its stable point. In finite populations, the distribution of D can be ⋃-shaped, unimodal or bimodal. The correlation of D in successive generations is higher with tight linkage and is little affected by selection or the size of the population.The utility of infinite population studies of linkage disequilibrium and its stable points is questioned, and considerable pessimism is expressed about the possibilities of distinguishing selection and sampling effects at linked loci.

scholarly journals EFFECTS OF POPULATION SIZE AND SELECTION INTENSITY ON SHORT-TERM RESPONSE TO SELECTION FOR POSTWEANING GAIN IN MICE

Genetics ◽  
1973 ◽  
Vol 73 (3) ◽  
pp. 513-530
Author(s):  
J P Hanrahan ◽  
E J Eisen ◽  
J E Legates
Keyword(s):  
Population Size ◽  
Selection Response ◽  
Selection Intensity ◽  
Realized Heritability ◽  
Family Selection ◽  
Effective Population ◽  
Population Sizes ◽  
Selection For ◽  
Selection Intensities ◽  
Term Response

ABSTRACT The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

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