The use of gene frequencies in estimating the mean number of mates in a multiple-mate and stored-sperm system of mating

1977 ◽  
Vol 49 (4) ◽  
pp. 181-185 ◽  
Author(s):  
C. Johnson
Keyword(s):  
Gene Frequencies ◽  
The Mean ◽  
Multiple Mate

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

scholarly journals On sojourn times at particular gene frequencies

1975 ◽  
Vol 25 (2) ◽  
pp. 89-94 ◽  
Author(s):  
Edward Pollak ◽  
Barry C. Arnold
Keyword(s):  
Markov Chains ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Finite Population ◽  
Diffusion Method ◽  
Gene Frequencies ◽  
Sojourn Times ◽  
The Mean ◽  
Number Of Visits ◽  
Finite Markov Chains

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

scholarly journals Effects of dominance and size of population on response to mass selection

1961 ◽  
Vol 2 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Ken-Ichi Kojima
Keyword(s):  
Gene Frequency ◽  
Finite Size ◽  
Prediction Equation ◽  
Small Population ◽  
Mass Selection ◽  
Gene Frequencies ◽  
Random Drift ◽  
Expected Gain ◽  
The Mean ◽  
Frequency Changes

A theory of mass selection in a small population was developed, and the mean change in gene frequencies, the variance of gene frequency changes and the expected gain in the mean phenotypic value of an offspring population were formulated in terms of a generalized selection differential and the additive and dominance effects of genes.The magnitude of the variance of changes in gene frequency was compared with the magnitude of the variance expected from the genetic random drift in a population with the same gene frequency and of the same size in absence of selection. The former was found to be usually smaller than the latter when the gene frequency ranged from intermediate to high and when selection was directed for a high performance.The usual prediction equation for gain from selection in an infinite population was compared with the expected gain formula derived for a small population. The size of the population did not cause a serious difference between the two expected gains when there was no dominance effect of genes. Dominance alone could cause the usual prediction to be slightly more biased. The joint effects of the finite size of population and dominance gene action could amount to a considerable bias in the usual prediction equation. Such a bias can be, in the main, accounted for by the inbreeding depression.

GENIC HETEROZYGOSITY AND VARIATION IN PERMANENT TRANSLOCATION HETEROZYGOTES OF THE OENOTHERA BIENNIS COMPLEX

Genetics ◽  
1975 ◽  
Vol 79 (3) ◽  
pp. 493-512
Author(s):  
Morris Levy ◽  
Donald A Levin
Keyword(s):  
Clinal Variation ◽  
Oenothera Biennis ◽  
Gene Frequencies ◽  
Enzyme Loci ◽  
Entire Chromosome ◽  
Wild Strains ◽  
Translocation Heterozygosity ◽  
The Mean ◽  
Allozyme Genotype

ABSTRACT Genic heterozygosity and variation were studied in the permanent translocation heterozygotes Oenothera biennis I, Oe. biennis II, Oe. biennis III, Oe. strigosa, Oe. parviflora I, Oe. parviflora II, and in the related bivalent formers Oe. argillicola and Oe. hookeri. From variation at 20 enzyme loci, we find that translocation heterozygosity for the entire chromosome complex is accompanied by only moderate levels of genic heterozygosity: 2.8% in Oe. strigosa, 9.5% in Oe. biennis and 14.9% in Oe. parviflora. Inbred garden strains of Oe. argillicola exhibited 8% heterozygosity; neither garden nor wild strains of Oe. hookeri displayed heterozygosity and only a single allozyme genotype was found. The mean number of alleles per locus is only 1.30 in Oe. strigosa, 1.40 in Oe. biennis, and 1.55 in Oe. parviflora, compared to 1.40 in Oe. argillicola. Clearly, the ability to accumulate and/or retain heterozygosity and variability has not been accompanied by extraordinary levels of either. Clinal variation is evident at some loci in each ring-former. A given translocation complex may vary geographically in its allozymic constitution. From gene frequencies, Oe. biennis I, II, and III, Oe. strigosa and Oe. hookeri are judged to be very closely related, whereas Oe. argillicola seems quite remote; Oe. parviflora is intermediate to the two phylads. Gene frequencies also suggest that Oe. argillicola diverged from the Euoenothera progenitor about 1,000,000 years ago, whereas most of the remaining evolution in the complex has occurred within the last 150,000 years.

Mutant Alleles of Small Effect Are Primarily Responsible for the Loss of Fitness With Slow Inbreeding in Drosophila melanogaster

Genetics ◽  
1998 ◽  
Vol 148 (3) ◽  
pp. 1143-1158 ◽  
Author(s):  
B D H Latter
Keyword(s):  
Drosophila Melanogaster ◽  
Population Size ◽  
Effective Population ◽  
Gene Frequencies ◽  
Marker Loci ◽  
Laboratory Populations ◽  
Neutral Marker ◽  
The Mean ◽  
The Stability ◽  
Generation Period

AbstractMultilocus simulation is used to identify genetic models that can account for the observed rates of inbreeding and fitness decline in laboratory populations of Drosophila melanogaster. The experimental populations were maintained under crowded conditions for ~200 generations at a harmonic mean population size of Nh ~65–70. With a simulated population size of N = 50, and a mean selective disadvantage of homozygotes at individual loci ~1–2% or less, it is demonstrated that the mean effective population size over a 200-generation period may be considerably greater than N, with a ratio matching the experimental estimate of Ne/Nh ~1.4. The buildup of associative overdominance at electrophoretic marker loci is largely responsible for the stability of gene frequencies and the observed reduction in the rate of inbreeding, with apparent selection coefficients in favor of the heterozygote at neutral marker loci increasing rapidly over the first N generations of inbreeding to values ~5–10%. The observed decline in fitness under competitive conditions in populations of size ~50 in D. melanogaster therefore primarily results from mutant alleles with mean effects on fitness as homozygotes of sm ≤ 0.02. Models with deleterious recessive mutants at the background loci require that the mean selection coefficient against heterozygotes is at most hsm ~0.002, with a minimum mutation rate for a single Drosophila autosome 100 cM in length estimated to be in the range 0.05–0.25, assuming an exponential distribution of s. A typical chromosome would be expected to carry at least 100–200 such mutant alleles contributing to the decline in competitive fitness with slow inbreeding.

scholarly journals Comparing the means of inbred lines with the base population: a model with overdominant loci

1979 ◽  
Vol 33 (1) ◽  
pp. 89-92
Author(s):  
Francis Minvielle
Keyword(s):  
Inbred Line ◽  
Quantitative Trait ◽  
Inbred Lines ◽  
Base Population ◽  
Gene Frequencies ◽  
The Mean

SUMMARYFor one-, two- and n-locus models of a quantitative trait assumed to be determined by overdominant loci, it is shown that the mean of an inbred line will be equal to or larger than the mean of the base population if the original gene frequencies satisfy a condition which is generally a function of the degree of overdominance and of the genotypic values.

scholarly journals Improvement of litter size in a strain of mice at a selection limit

1971 ◽  
Vol 17 (3) ◽  
pp. 215-235 ◽  
Author(s):  
D. S. Falconer
Keyword(s):  
Litter Size ◽  
Inbred Lines ◽  
Original Strain ◽  
Residual Variance ◽  
Gene Frequencies ◽  
Additive Variance ◽  
Residual Variation ◽  
Number Of Genes ◽  
Recessive Genes ◽  
The Mean

SUMMARYA strain of mice that had ceased to respond to selection for high litter size was inbred with continued selection. Depression of the mean proved the existence of residual genetic variance. Four lines survived the inbreeding, and one reached 20 generations with a mean equal to the original strain, thus disproving overdominance as a major cause of the residual variation. The four selected inbred lines were crossed and a new strain derived from the cross was maintained in parallel with the original strain. The new strain showed an improvement of 1·5 mice per litter over the original strain. Thus selection with inbreeding was able to achieve an advance beyond the limit attained by the original selection.The hypothesis that the residual variation was due to genes with simple dominance was tested by seeing if it could account for the observations with reasonable values of the relevant parameters. The improvement made by the inbreeding and crossing required the elimination of about 30 recessive genes with effects (homozygote difference) of 0·5 phenotypic standard deviations and gene frequencies of 0·2. Consideration of the mean levels of the selected inbred lines in conjunction with the rate of depression found on inbreeding without selection showed that the selection with inbreeding had eliminated about 75% of the segregating reces-sives. The number of genes contributing to the residual variance was therefore about 40. The additive variance generated by these genes was just consistent with the estimate of zero from the realized heritability. Consideration of the original selection showed that about half the genes could have been still segregating when the response ceased. The hypothesis therefore requires the number of genes in the base population to have been about 80. The number of genes required, though large, does not seem impossible, and the hypothesis of genes with simple dominance can account for all the observations.

scholarly journals GENE FLOW AND LIFE HISTORY PATTERNS

Genetics ◽  
1979 ◽  
Vol 93 (1) ◽  
pp. 263-284
Author(s):  
John A Endler
Keyword(s):  
Life History ◽  
Gene Flow ◽  
Egg Laying ◽  
Square Root ◽  
Gene Frequencies ◽  
Local Conditions ◽  
Breeding Sites ◽  
Shifting Balance ◽  
The Mean ◽  
Dispersal Distances

ABSTRACT Dispersal distances overestimate the gene-flow scale l (the square-root of the mean squared distance travelled from birth to reproduction) when egg laying is concentrated early in dispersal and when there is mortality during dispersal. If egg laying follows a square-root normal distribution in time, as it does in several Drosophila species, then l is reduced to about 0.6 of that estimated from dispersal alone, unless egg laying is concentrated in a very brief period. If mortality is such that the half-life is earlier than the mean fecundity day, then l will be reduced still more relative to the dispersal estimate, and will be very sensitive to small changes in mortality. Overestimating l yields overestimates of the amount of selection needed to maintain geographic differences in gene frequencies. If mortality increases in suboptimal habitats, then the neighborhood size will be smaller in those areas, because increased mortality decreases l. This means that l is smallest, allowing the greatest differentiation and genetic innovation, precisely where it is most needed. This lends support to WRIGHT'S shifting balance hypothesis. If l is adjusted to local conditions, then we do not necessarily expect a positive relationship between environmental and genetic heterogeneity. Data from Drosophila pseudoobscura are used to make the models realistic, and it is shown that l depends on the distances among traps or breeding sites. It is therefore essential to know the geometry of breeding sites and the life history parameters to estimate l.

scholarly journals GENETIC VARIANCE AND CORRELATION AFTER SELECTION FOR TWO TRAITS BY INDEX, INDEPENDENT CULLING LEVELS AND EXTREME SELECTION

Genetics ◽  
1980 ◽  
Vol 94 (3) ◽  
pp. 763-775
Author(s):  
G L Bennett ◽  
L A Swiger
Keyword(s):  
Computer Simulation ◽  
Genetic Correlation ◽  
Genetic Variance ◽  
Multivariate Methods ◽  
Selection Methods ◽  
Gene Frequencies ◽  
Genetic Variances ◽  
Independent Culling ◽  
The Mean ◽  
The Stability

ABSTRACT Three two-trait selection methods were analyzed for their effects on genetic variance and correlation by multivariate methods, two-locus methods and computer simulation. The two-trait selection methods studied were independent culling levels (ICL), index (IND) and extreme (EXT) selection. The effects of the selection methods on genetic variance and correlation were partitioned into permanent effects due to changes in gene frequencies and temporary effects due to nonrandom association of alleles at different loci. Multivariate methods were used to predict temporary effects from a single generation of selection by each method and from several generations of index selection. Two-locus theory was used to determine the stability and rank of temporary effects on genetic correlation for all three methods. Predictions were compared to computer simulation results. When selection increased the means of both traits, EXT had the lowest (closest to,—l.O) genetic correlation and highest variances, while ICL tended to have the highest (closest to 1.0) genetic correlation. When selection increased the mean of one trait and decreased the mean cjf the other, EXT had the highest genetic variances and correlation, while ICL had the lowest genetic variances and correlation.

scholarly journals The Consequences of Fluctuating Selection for Isozyme Polymorphisms in Daphnia

Genetics ◽  
1987 ◽  
Vol 115 (4) ◽  
pp. 657-669
Author(s):  
Michael Lynch
Keyword(s):  
Necessary Conditions ◽  
Natural Populations ◽  
Temporal Distribution ◽  
Fluctuating Selection ◽  
Gene Frequencies ◽  
Daphnia Population ◽  
Mean And Variance ◽  
The Mean ◽  
Selection For ◽  
Temporal Sequences

ABSTRACT Temporal sequences of allele frequencies in natural populations of Daphnia are analyzed to obtain the mean and variance of the selection coefficient for both asexual and sexual phases. In general, the alleles at enzyme loci appear to be quasi-neutral. Although significant variation exists for the estimated selection coefficients, the means are in all cases close to zero. Estimates of the variance of selection intensity are applied to existing models to demonstrate the implications of fluctuating selection for the spatial and temporal distribution of gene frequencies in Daphnia. The empirical and analytical results are shown to provide a possible solution to some previously puzzling aspects of Daphnia population genetic surveys. Neither genetic drift nor diversifying selection are necessary conditions for the local diversification of gene frequencies.

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