The genetic variability of polygenic characters under optimizing selection, mutation and drift

SUMMARYThe effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.

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The maintenance of the genetic variability of polygenic characters by heterozygous advantage

Genetics Research ◽

10.1017/s0016672300012799 ◽

1973 ◽

Vol 22 (1) ◽

pp. 9-12 ◽

Cited By ~ 15

Author(s):

M. G. Bulmer

Keyword(s):

Genetic Variability ◽

Population Size ◽

Finite Population ◽

Stable Equilibrium ◽

The Other ◽

Gene Substitution ◽

Optimal Value ◽

Selection For ◽

As If

SUMMARYThe results of a previous paper on the effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci have been extended to include the possibility that, in addition to selection for an optimal value, there may be independent selection in favour of heterozygotes; it is assumed for simplicity that at each locus the heterozygote has the same advantage, s, over each of the homozygotes. Under selection alone there is a stable equilibrium if s > ca2, where c is a measure of the intensity of the optimizing selection and a is the effect of a gene substitution. Under the additional forces exerted by mutation and by drift due to finite population size each locus behaves independently of the other loci as if it had a heterozygous advantage equal to (s − ca2).

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Selection of new inversions in multi-locus genetic systems

Genetics Research ◽

10.1017/s0016672300013343 ◽

1973 ◽

Vol 21 (2) ◽

pp. 167-183 ◽

Cited By ~ 52

Author(s):

Brian Charlesworth ◽

Deborah Charlesworth

Keyword(s):

Sex Differences ◽

Selection Pressure ◽

Stable Equilibrium ◽

Large Population ◽

Approximate Expression ◽

Rate Of Change ◽

Initial Population ◽

Square Root ◽

Locus System ◽

Selection Of

SUMMARYAn approximate expression, is derived for the rate of change in frequency of an inversion introduced at a low initial frequency into a multi-locus system at equilibrium under recombination and selection. It is shown that this expression gives accurate predictions of the rate of progress of the inversion, even if the initial population is perturbed somewhat from equilibrium. Extensions to the cases where there are sex differences in recombination and selection are considered. An implication of the results is that selection pressure for newly arisen inversions depends on the existence of a stable equilibrium with linkage disequilibrium. The expected chance of survival of a new inversion in a large population is shown to be approximately one half the square root of the loss in fitness due to recombination.

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RATE OF DECREASE OF GENETIC VARIABILITY IN A TWO-DIMENSIONAL CONTINUOUS POPULATION OF FINITE SIZE

Genetics ◽

10.1093/genetics/70.4.639 ◽

1972 ◽

Vol 70 (4) ◽

pp. 639-651

Author(s):

Takeo Maruyama

Keyword(s):

Genetic Variability ◽

Finite Size ◽

Local Property ◽

Essential Difference ◽

Two Dimensional ◽

Habitat Size ◽

One Dimensional ◽

Homologous Genes ◽

Rate Of Decay ◽

Continuous Population

ABSTRACT The rate of decay of genetic variability was investigated for two-dimensional continuous populations of finite size. The exact value of the rate involves a rather complicated expression (formula (4-1)). However, numerical examples indicate that in a population habitat size L × L and density D, the rate is approximately equal to (see PDF) where σ2 is the variance of dispersion distance assuming isotropical migration. The value given in (2) is equal to that of a panmictic population of size DL 2. It is remarkable that whether the rate assumes the value given by (1) or by (2) depends only on Dσ2 (a local property), which is independent of the habitat size. Since, in a one-dimensional population, this depends on both Dσ2 and the habitat size, there is an essential difference between the two types of population structure.—The function giving the probability of two homologous genes separated by a given distance being different alleles was also obtained, (formula (5-1)).

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Microtwinning Evidence For The Apparent Five-Fold Symmetry in T2(Al6Li3Cu)

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125178 ◽

1987 ◽

Vol 45 ◽

pp. 24-25

Author(s):

Kenneth S. Vecchio ◽

David B. Williams

Keyword(s):

Stable Equilibrium ◽

Equilibrium Phase ◽

Convergent Beam Electron Diffraction ◽

Icosahedral Structure ◽

Cubic Crystals ◽

Icosahedral Phases ◽

Heat Treated ◽

Zero Layer ◽

Convergent Beam ◽

Zr Alloy

Since the discovery in 1984 by Shechtman et al. of crystals which display apparent five-fold symmetry, extensive effort has been given to establishing a theoretical basis for the existence of icosahedral phases (eg.2.). Several other investigations have been centered on explaining these observations based on twinning of cubic crystals (eg.3.). Recently, the existence of a stable, equilibrium phase T2Al6 Li3Cu) possessing an icosahedral structure has been reported in the Al-Li-Cu system(4-6).In the present study an Al-2.6wt.%Li-l.5wt.%Cu-0.lwt.%Zr alloy was heat treated at 300°C for 100hrs. to produce large T2 precipitates. Convergent Beam Electron Diffraction (CBED) patterns were obtained from two-fold, three-fold, and apparent five-fold axes of T2 particles. Figure 1 shows the five-fold symmetric zero layer CBED pattern obtained from T2 particles.

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