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.

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.

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.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

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 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.

scholarly journals Derivation of the mean highest reversal floor and expected number of stops in lift systems

1979 ◽  
Vol 3 (4) ◽  
pp. 275-279 ◽  
Author(s):  
N.A. Alexandris ◽  
G.C. Barney ◽  
C.J. Harris
Keyword(s):  
Expected Number ◽  
The Mean

STOCHASTIC PREDATION MODEL WITH DEPLETION

1979 ◽  
Vol 111 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Guy L. Curry ◽  
Richard M. Feldman
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Expected Number ◽  
Numerical Comparisons ◽  
Prey Depletion

AbstractA stochastic model is developed for the expected number of prey taken by a single predator when prey depletion is apparent. The so-called “random predator equation” with prey exploitation of Royama and Rogers is compared with the stochastic model. The numerical comparisons illustrate situations where the deterministic model provides adequate and inadequate approximations.

A stochastic model for polymer degradation

1972 ◽  
Vol 9 (1) ◽  
pp. 43-53 ◽  
Author(s):  
S. K. Srinivasan ◽  
K. M. Mehata
Keyword(s):  
Stochastic Model ◽  
General Model ◽  
Polymer Degradation ◽  
Mean Square ◽  
Product Density ◽  
The Mean ◽  
Number Of Segments

The stochastic model for breaking of molecular segments proposed by Bithell is analysed and some results relating to the distribution of the number of fragments are obtained by using a slightly more general model which allows multiple ruptures. The product density technique is employed to derive the mean and mean square number of segments at any time t and the number of segments with length greater than y at time of production.

scholarly journals A Novel Theoretical Probabilistic Model for Opportunistic Routing with Applications in Energy Consumption for WSNs

Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 8058
Author(s):  
Christian E. Galarza ◽  
Jonathan M. Palma ◽  
Cecilia F. Morais ◽  
Jaime Utria ◽  
Leonardo P. Carvalho ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Consumption ◽  
Stochastic Model ◽  
Opportunistic Networks ◽  
Opportunistic Routing ◽  
Opportunistic Network ◽  
Expected Number ◽  
Successful Transmission ◽  
Network Parameters ◽  
Proposed Model

This paper proposes a new theoretical stochastic model based on an abstraction of the opportunistic model for opportunistic networks. The model is capable of systematically computing the network parameters, such as the number of possible routes, the probability of successful transmission, the expected number of broadcast transmissions, and the expected number of receptions. The usual theoretical stochastic model explored in the methodologies available in the literature is based on Markov chains, and the main novelty of this paper is the employment of a percolation stochastic model, whose main benefit is to obtain the network parameters directly. Additionally, the proposed approach is capable to deal with values of probability specified by bounded intervals or by a density function. The model is validated via Monte Carlo simulations, and a computational toolbox (R-packet) is provided to make the reproduction of the results presented in the paper easier. The technique is illustrated through a numerical example where the proposed model is applied to compute the energy consumption when transmitting a packet via an opportunistic network.

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