The mean number of alleles in multigene families

1992 ◽  
Vol 24 (01) ◽  
pp. 1-19 ◽  
Author(s):  
G. A. Watterson
Keyword(s):  
Probability Distribution ◽  
Gene Conversion ◽  
Random Sample ◽  
Multigene Families ◽  
Explicit Formulas ◽  
Large Samples ◽  
The Mean

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.

The mean number of alleles in multigene families

1992 ◽  
Vol 24 (1) ◽  
pp. 1-19 ◽  
Author(s):  
G. A. Watterson
Keyword(s):  
Probability Distribution ◽  
Gene Conversion ◽  
Random Sample ◽  
Multigene Families ◽  
Explicit Formulas ◽  
Large Samples ◽  
The Mean

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (04) ◽  
pp. 759-769
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

1994 ◽  
Vol 31 (1) ◽  
pp. 235-243 ◽  
Author(s):  
David M. Lucantoni ◽  
Marcel F. Neuts
Keyword(s):  
Probability Distribution ◽  
Fundamental Period ◽  
Queueing Model ◽  
Explicit Formulas ◽  
Sample Paths ◽  
Mean Vectors ◽  
The Mean

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in the MAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for the MAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (4) ◽  
pp. 759-769 ◽  
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles.A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

Recent Probability Results for Extreme Ages

1970 ◽  
Vol 96 (3) ◽  
pp. 389-392
Author(s):  
John E. Walsh
Keyword(s):  
Probability Distribution ◽  
Random Sample ◽  
Joint Distribution ◽  
Probability Distributions ◽  
Sample Type ◽  
Age At Death ◽  
Estimation Of Parameters ◽  
Large Samples ◽  
Approximations To Distributions ◽  
Sample Case

AbstractConsider a very large number of persons, and probability distributions for the age at death of the last survivor, next to last survivor, etc. First, suppose that the persons are statistically independent with the same probability distribution for age at death (random sample case). Then, some approximations to distributions of extremes are often usable. These approximations are completely specified except for at most three parameters. This simplifies distribution estimation to estimation of the parameters. Moreover, previous large samples (possibly different sizes) from the same population of persons, and much of their data on extremes, can be used for estimation. Also, the sample results of ten remain applicable for the more general case of independence (or mild dependence) but possibly different distributions for the ages at death. Here, the average of these distributions is ‘sampled’. Very recent results show that distributions of extremes are of the sample type for any joint distribution of the ages at death. However, the distribution ‘sampled’ can be greatly different for the last survivor, next to last survivor, etc. This effectively limits estimation of parameters to previous groups having very nearly the same joint distribution and use of one observed extreme per group.

Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

1994 ◽  
Vol 31 (01) ◽  
pp. 235-243 ◽  
Author(s):  
David M. Lucantoni ◽  
Marcel F. Neuts
Keyword(s):  
Probability Distribution ◽  
Fundamental Period ◽  
Queueing Model ◽  
Explicit Formulas ◽  
Sample Paths ◽  
Mean Vectors ◽  
The Mean

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in theMAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for theMAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

scholarly journals Recombination and Gene Conversion in a 170-kb Genomic Region of Arabidopsis thaliana

Genetics ◽  
2002 ◽  
Vol 161 (3) ◽  
pp. 1269-1278 ◽  
Author(s):  
Bernhard Haubold ◽  
Jürgen Kroymann ◽  
Andreas Ratzka ◽  
Thomas Mitchell-Olds ◽  
Thomas Wiehe
Keyword(s):  
Genetic Diversity ◽  
Arabidopsis Thaliana ◽  
Linkage Disequilibrium ◽  
Gene Conversion ◽  
Genomic Sequence ◽  
Genomic Region ◽  
Resistance To Herbivory ◽  
Linkage Disequilibria ◽  
Coalescent Simulations ◽  
The Mean

Abstract Arabidopsis thaliana is a highly selfing plant that nevertheless appears to undergo substantial recombination. To reconcile its selfing habit with the observations of recombination, we have sampled the genetic diversity of A. thaliana at 14 loci of ~500 bp each, spread across 170 kb of genomic sequence centered on a QTL for resistance to herbivory. A total of 170 of the 6321 nucleotides surveyed were polymorphic, with 169 being biallelic. The mean silent genetic diversity (πs) varied between 0.001 and 0.03. Pairwise linkage disequilibria between the polymorphisms were negatively correlated with distance, although this effect vanished when only pairs of polymorphisms with four haplotypes were included in the analysis. The absence of a consistent negative correlation between distance and linkage disequilibrium indicated that gene conversion might have played an important role in distributing genetic diversity throughout the region. We tested this by coalescent simulations and estimate that up to 90% of recombination is due to gene conversion.

scholarly journals Probability Characteristics, Area Reduction, and Wind Directionality Effects of Extreme Pressure Coefficients of High-Rise Buildings

2021 ◽  
Vol 11 (15) ◽  
pp. 7121
Author(s):  
Shouke Li ◽  
Feipeng Xiao ◽  
Yunfeng Zou ◽  
Shouying Li ◽  
Shucheng Yang ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Pressure Coefficient ◽  
Wind Pressure ◽  
Extreme Pressure ◽  
Distribution Law ◽  
Distribution Fitting ◽  
Pressure Coefficients ◽  
High Rise ◽  
Area Reduction ◽  
The Mean

Wind tunnel tests are carried out for the Commonwealth Advisory Aeronautical Research Council (CAARC) high-rise building with a scale of 1:400 in exposure categories D. The distribution law of extreme pressure coefficients under different conditions is studied. Probability distribution fitting is performed on the measured area-averaged extreme pressure coefficients. The general extreme value (GEV) distribution is preferred for probability distribution fitting of extreme pressure coefficients. From the comparison between the area-averaged coefficients and the value from GB50009-2012, it is indicated that the wind load coefficients from GB50009-2012 may be non-conservative for the CAARC building. The area reduction effect on the extreme wind pressure is smaller than that on the mean wind pressure from the code. The recommended formula of the area reduction factor for the extreme pressure coefficient is proposed in this study. It is found that the mean and the coefficient of variation (COV) for the directionality factors are 0.85 and 0.04, respectively, when the orientation of the building is given. If the uniform distribution is given for the building’s orientation, the mean value of the directionality factors is 0.88, which is close to the directionality factor of 0.90 given in the Chinese specifications.

scholarly journals Sequence identity in an early chorion multigene family is the result of localized gene conversion.

Genetics ◽  
1991 ◽  
Vol 128 (3) ◽  
pp. 595-606
Author(s):  
B L Hibner ◽  
W D Burke ◽  
T H Eickbush
Keyword(s):  
Nucleotide Sequence ◽  
Gene Conversion ◽  
Nucleotide Sequence Identity ◽  
Early Period ◽  
Gene Families ◽  
Multigene Families ◽  
Coding Regions ◽  
Sequence Identity ◽  
Isolation And Characterization ◽  
Sequence Exchange

Abstract The multigene families that encode the chorion (eggshell) of the silk moth, Bombyx mori, are closely linked on one chromosome. We report here the isolation and characterization of two segments, totaling 102 kb of genomic DNA, containing the genes expressed during the early period of choriogenesis. Most of these early genes can be divided into two multigene families, ErA and ErB, organized into five divergently transcribed ErA/ErB gene pairs. Nucleotide sequence identity in the major coding regions of the ErA genes was 96%, while nucleotide sequence identity for the ErB major coding regions was only 63%. Selection pressure on the encoded proteins cannot explain this difference in the level of sequence conservation between the ErA and ErB gene families, since when only fourfold redundant codon positions are considered, the divergence within the ErA genes is 8%, while the divergence within the ErB genes (corrected for multiple substitutions at the same site) is 110%. The high sequence identity of the ErA major exons can be explained by sequence exchange events similar to gene conversion localized to the major exon of the ErA genes. These gene conversions are correlated with the presence of clustered copies of the nucleotide sequence GGXGGX, encoding paired glycine residues. This sequence has previously been correlated with gradients of gene conversion that extend throughout the coding and noncoding regions of the High-cysteine (Hc) chorion genes of B. mori. We suggest that the difference in the extent of the conversion tracts in these gene families reflects a tendency for these recombination events to become localized over time to the protein encoding regions of the major exons.

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