scholarly journals The distribution of the fraction of the genome identical by descent in finite random mating populations

1980 ◽  
Vol 35 (2) ◽  
pp. 131-155 ◽  
Author(s):  
P. Stam
Keyword(s):  
Probability Distribution ◽  
Explicit Expression ◽  
Recurrence Relations ◽  
Present Model ◽  
Random Mating ◽  
Expected Number ◽  
Identical By Descent ◽  
Mating Population ◽  
Theoretical Results ◽  
Order Identity

SUMMARYThe probability distribution of the heterogenic (non-identical by descent) fraction of the genome in a finite monoecious random mating population has been derived. It was assumed that in any generation the length of both heterogenic and homogenic segments are exponentially distributed. An explicit expression is given for the expected number of ‘external junctions’ (sites that mark the end of a heterogenic segment) per unit map length in any generation. The latter necessitates the introduction of two higher-order identity relations between three genes, and their recurrence relations. Theoretical results were compared with the outcome of a series of simulation runs (showing a very good fit), as well as with the results predicted by Fisher's ‘theory of junctions’. In contrast to Fisher's approach, which only applies when the average heterogeneity is relatively small, the present model applies to any generation.

The distribution of heterogeneity in finite random mating populations

1980 ◽  
Vol 12 (1) ◽  
pp. 9-10
Author(s):  
P. Stam
Keyword(s):  
Probability Distribution ◽  
Explicit Expression ◽  
Recurrence Relations ◽  
Present Model ◽  
Random Mating ◽  
Expected Number ◽  
Identical By Descent ◽  
Mating Population ◽  
Theoretical Results ◽  
Order Identity

The probability distribution of the heterogenic (non-identical by descent) fraction of the genome in a finite monoecious random mating population has been derived. It was assumed that in any generation both the lengths of heterogenic and homogenic segments are exponentially distributed. An explicit expression is given for the expected number of ‘external junctions’ (sites that mark the end of a heterogenic segment) per unit map length in any generation. The latter necessitates the introduction of two higher-order identity relations between three genes, and their recurrence relations. Theoretical results were compared with the outcome of a series of simulation runs (showing a very good fit), as well as with the results predicted by Fisher's ‘theory of junctions’. In contrast to Fisher's approach, which only applies when the average heterogeneity is relatively small, the present model applies to any generation.

The distribution of heterogeneity in finite random mating populations

1980 ◽  
Vol 12 (01) ◽  
pp. 9-10
Author(s):  
P. Stam
Keyword(s):  
Probability Distribution ◽  
Explicit Expression ◽  
Recurrence Relations ◽  
Present Model ◽  
Random Mating ◽  
Expected Number ◽  
Identical By Descent ◽  
Mating Population ◽  
Theoretical Results ◽  
Order Identity

The probability distribution of the heterogenic (non-identical by descent) fraction of the genome in a finite monoecious random mating population has been derived. It was assumed that in any generation both the lengths of heterogenic and homogenic segments are exponentially distributed. An explicit expression is given for the expected number of ‘external junctions’ (sites that mark the end of a heterogenic segment) per unit map length in any generation. The latter necessitates the introduction of two higher-order identity relations between three genes, and their recurrence relations. Theoretical results were compared with the outcome of a series of simulation runs (showing a very good fit), as well as with the results predicted by Fisher's ‘theory of junctions’. In contrast to Fisher's approach, which only applies when the average heterogeneity is relatively small, the present model applies to any generation.

scholarly journals Average Number of Nucleotide Differences in a Sample From a Single Subpopulation: A Test for Population Subdivision

Genetics ◽  
1987 ◽  
Vol 117 (1) ◽  
pp. 149-153
Author(s):  
Curtis Strobeck
Keyword(s):  
Monte Carlo Simulation ◽  
Population Structure ◽  
Random Mating ◽  
Population Subdivision ◽  
Expected Number ◽  
Migration Rates ◽  
Mating Population ◽  
Unbiased Estimates ◽  
Increasing Function ◽  
Stepping Stone Model

ABSTRACT Unbiased estimates of θ = 4Nµ in a random mating population can be based on either the number of alleles or the average number of nucleotide differences in a sample. However, if there is population structure and the sample is drawn from a single subpopulation, these two estimates of θ behave differently. The expected number of alleles in a sample is an increasing function of the migration rates, whereas the expected average number of nucleotide differences is shown to be independent of the migration rates and equal to 4N  Tµ for a general model of population structure which includes both the island model and the circular stepping-stone model. This contrast in the behavior of these two estimates of θ is used as the basis of a test for population subdivision. Using a Monte-Carlo simulation developed so that independent samples from a single subpopulation could be obtained quickly, this test is shown to be a useful method to determine if there is population subdivision.

scholarly journals Relationship between DNA polymorphism and fixation time.

Genetics ◽  
1990 ◽  
Vol 125 (2) ◽  
pp. 447-454 ◽  
Author(s):  
F Tajima
Keyword(s):  
Computer Simulation ◽  
Dna Sequence ◽  
Dna Sequences ◽  
Dna Polymorphism ◽  
Random Mating ◽  
Random Time ◽  
Fixation Time ◽  
Expected Number ◽  
Mating Population ◽  
The Relationship

Abstract When there is no recombination among nucleotide sites in DNA sequences, DNA polymorphism and fixation of mutants at nucleotide sites are mutually related. Using the method of gene genealogy, the relationship between the DNA polymorphism and the fixation of mutant nucleotide was quantitatively investigated under the assumption that mutants are selectively neutral, that there is no recombination among nucleotide sites, and that the population is a random mating population with N diploid individuals. The results obtained indicate that the expected number of nucleotide differences between two DNA sequences randomly sampled from the population is 42% less when a mutant at a particular nucleotide site reaches fixation than at a random time, and that heterozygosity is also expected to be less when fixation takes place than at a random time, but the amount of reduction depends on the value of 4Nv in this case, where v is the mutation rate per DNA sequence per generation. The formula for obtaining the expected number of nucleotide differences between the two DNA sequences for a given fixation time is also derived, and indicates that, even when it takes a large number of generations for a mutant to reach fixation, this number is 33% less than at a random time. The computer simulation conducted suggests that the expected number of nucleotide differences between the two DNA sequences at the time when an advantageous mutant becomes fixed is essentially the same as that of neutral mutant if the fixation time is the same. The effect of recombination on the amount of DNA polymorphism was also investigated by using computer simulation.

The Kota of the Nilgiri hills: a demographic study

1976 ◽  
Vol 8 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Aloke Kumar Ghosh
Keyword(s):  
Total Population ◽  
Random Mating ◽  
High Rate ◽  
Moderate Intensity ◽  
Biological Study ◽  
Isolated Population ◽  
Demographic Structure ◽  
Effective Population ◽  
Mating Population ◽  
The Village

A population–biological study of the Kota of the Nilgiri Hills was undertaken between May 1966 and January 1968. This paper discusses the demographic structure of the tribe and its genetic implications.The Kota is a small tribe of 1203 individuals distributed in only seven villages; it is an isolated population with a low rate of fertility and a high rate of infant mortality. The Kota is not a random mating population. The rate of consanguineous marriages is high and the coefficient of inbreeding is almost equal to the highest recorded value. Besides cousin marriages, marriage within the village is very much preferred. The admixture rate (0·29%) among the Kota is very low. The effective population size is only 28·87% of the total population. The coefficient of breeding isolation is 1·01, which indicates that genetic drift may produce important differentiation in this population. The data show that selection is acting with moderate intensity in this population.

scholarly journals n-Color partitions with weighted differences equal to minus two

1997 ◽  
Vol 20 (4) ◽  
pp. 759-768 ◽  
Author(s):  
A. K. Agarwal ◽  
R. Balasubrananian
Keyword(s):  
Explicit Expression ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Combinatorial Identities ◽  
Combinatorial Identity ◽  
Divisor Function ◽  
Open Problems

In this paper we study thosen-color partitions of Agarwal and Andrews, 1987, in which each pair of parts has weighted difference equal to−2Results obtained in this paper for these partitions include several combinatorial identities, recurrence relations, generating functions, relationships with the divisor function and computer produced tables. By using these partitions an explicit expression for the sum of the divisors of odd integers is given. It is shown how these partitions arise in the study of conjugate and self-conjugaten-color partitions. A combinatorial identity for self-conjugaten-color partitions is also obtained. We conclude by posing several open problems in the last section.

scholarly journals Detecting Linkage between a Trait and a Marker in a Random Mating Population without Pedigree Record

PLoS ONE ◽  
2009 ◽  
Vol 4 (3) ◽  
pp. e4956
Author(s):  
Shuhei Mano ◽  
Takaho A. Endo ◽  
Akira Oka ◽  
Akira Ozawa ◽  
Takashi Gojobori ◽  
...  
Keyword(s):  
Random Mating ◽  
Random Mating Population ◽  
Mating Population

scholarly journals The truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule

2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Explicit Form ◽  
Recurrence Relations ◽  
Expected Number ◽  
Special Cases ◽  
Queue Discipline ◽  
Bulk Service ◽  
General Bulk Service Rule ◽  
Steady State Probabilities

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .

Level crossings and stationary distributions for general dams

1980 ◽  
Vol 17 (1) ◽  
pp. 218-226 ◽  
Author(s):  
Michael Rubinovitch ◽  
J. W. Cohen
Keyword(s):  
Explicit Expression ◽  
Stationary Distribution ◽  
Basic Relation ◽  
Expected Number ◽  
Stationary Distributions ◽  
Level Crossings ◽  
Fixed Level

Level crossings in a stationary dam process with additive input and arbitrary release are considered and an explicit expression for the expected number of downcrossings (and also overcrossings) of a fixed level, per time unit, is obtained. This leads to a short derivation of a basic relation which the stationary distribution of a general dam must satisfy.

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