scholarly journals Coalescent Theory for a Partially Selfing Population

Genetics ◽  
1997 ◽  
Vol 146 (4) ◽  
pp. 1489-1499 ◽  
Author(s):  
Yun-Xin Fu
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
Coalescent Theory ◽  
Selfing Rate ◽  
Effective Population ◽  
Diploid Population ◽  
Approximate Formulas ◽  
Segregating Sites

A coalescent theory for a sample of DNA sequences from a partially selfing diploid population and an algorithm for simulating such samples are developed in this article. Approximate formulas are given for the expectation and the variance of the number of segregating sites in a sample of k sequences from n individuals. Several new estimators of the important parameters θ = 4Nμ and the selfing rate s, where N and μ are, respectively, the effective population size and the mutation rate per sequence per generation, are proposed and their sampling properties are studied.

scholarly journals A phylogenetic estimator of effective population size or mutation rate.

Genetics ◽  
1994 ◽  
Vol 136 (2) ◽  
pp. 685-692 ◽  
Author(s):  
Y X Fu
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
High Efficiency ◽  
Minimum Variance ◽  
Population Subdivision ◽  
Effective Population ◽  
Fisher Model ◽  
Mitochondrial Sequences

Abstract A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators of the parameter and is substantially smaller than that of any existing estimator. The high efficiency of the new estimator is achieved by making full use of phylogenetic information in a sample of DNA sequences from a population. An example of estimating theta by the new method is presented using the mitochondrial sequences from an American Indian population.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x 1 N,…,x K N, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes x j N and x i N, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as G ij . Under minimal conditions on the first three moments of G ij for all i and j, a suitable effective population size N e is derived. Then if time is recorded in a backward direction in units of 2N e generations, it can be shown that coalescent theory holds.

A Coalescent Estimator of the Population Recombination Rate

Genetics ◽  
1997 ◽  
Vol 145 (3) ◽  
pp. 833-846 ◽  
Author(s):  
Jody Hey ◽  
John Wakeley
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Dna Sequences ◽  
Recombination Rate ◽  
Population Sample ◽  
Population Level ◽  
Effective Population ◽  
Genome Level ◽  
Population Recombination

Population genetic models often use a population recombination parameter 4Nc, where N is the effective population size and c is the recombination rate per generation. In many ways 4Nc is comparable to 4Nu, the population mutation rate. Both combine genome level and population level processes, and together they describe the rate of production of genetic variation in a population. However, 4Nc is more difficult to estimate. For a population sample of DNA sequences, historical recombination can only be detected if polymorphisms exist, and even then most recombination events are not detectable. This paper describes an estimator of 4Nc, hereafter designated γ (gamma), that was developed using a coalescent model for a sample of four DNA sequences with recombination. The reliability of γ was assessed using multiple coalescent simulations. In general γ has low to moderate bias, and the reliability of γ is comparable, though less, than that for a widely used estimator of 4Nu. If there exists an independent estimate of the recombination rate (per generation, per base pair), γ can be used to estimate the effective population size or the neutral mutation rate.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x1N,…,xKN, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes xjN and xiN, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as Gij. Under minimal conditions on the first three moments of Gij for all i and j, a suitable effective population size Ne is derived. Then if time is recorded in a backward direction in units of 2Ne generations, it can be shown that coalescent theory holds.

scholarly journals Mobile elements reveal small population size in the ancient ancestors of Homo sapiens

2010 ◽  
Vol 107 (5) ◽  
pp. 2147-2152 ◽  
Author(s):  
Chad D. Huff ◽  
Jinchuan Xing ◽  
Alan R. Rogers ◽  
David Witherspoon ◽  
Lynn B. Jorde
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Dna Sequences ◽  
Mobile Element ◽  
Small Population ◽  
Mobile Elements ◽  
Population History ◽  
Recent Common Ancestor ◽  
Demographic Model ◽  
Effective Population

The genealogies of different genetic loci vary in depth. The deeper the genealogy, the greater the chance that it will include a rare event, such as the insertion of a mobile element. Therefore, the genealogy of a region that contains a mobile element is on average older than that of the rest of the genome. In a simple demographic model, the expected time to most recent common ancestor (TMRCA) is doubled if a rare insertion is present. We test this expectation by examining single nucleotide polymorphisms around polymorphic Alu insertions from two completely sequenced human genomes. The estimated TMRCA for regions containing a polymorphic insertion is two times larger than the genomic average (P < <10−30), as predicted. Because genealogies that contain polymorphic mobile elements are old, they are shaped largely by the forces of ancient population history and are insensitive to recent demographic events, such as bottlenecks and expansions. Remarkably, the information in just two human DNA sequences provides substantial information about ancient human population size. By comparing the likelihood of various demographic models, we estimate that the effective population size of human ancestors living before 1.2 million years ago was 18,500, and we can reject all models where the ancient effective population size was larger than 26,000. This result implies an unusually small population for a species spread across the entire Old World, particularly in light of the effective population sizes of chimpanzees (21,000) and gorillas (25,000), which each inhabit only one part of a single continent.

scholarly journals DISTRIBUTION OF NUCLEOTIDE DIFFERENCES BETWEEN TWO RANDOMLY CHOSEN CISTRONS IN A FINITE POPULATION

Genetics ◽  
1977 ◽  
Vol 85 (2) ◽  
pp. 331-337
Author(s):  
Wen-Hsiung Li
Keyword(s):  
Steady State ◽  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Finite Population ◽  
Effective Population ◽  
Steady State Distribution ◽  
State Distribution ◽  
Simple Estimate ◽  
The Mean

ABSTRACT Watterson's (1975) formula for the steady-state distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population has been extended to transient states. The rate for the mean of this distribution to approach its equilibrium value is 1/2 N and independent of mutation rate, but that for the variance is dependent on mutation rate, where N denotes the effective population size. Numerical computations show that if the heterozygosity (i.e., the probability that two cistrons are different) is low, say of the order of 0.1 or less, the probability that two cistrons differ at two or more nucleotide sites is less than 10 percent of the heterozygosity, whereas this probability may be as high as 50 percent of the heterozygosity if the heterozygosity is 0.5. A simple estimate for the mean number (d) of site differences between cistrons is d = h/(1 - h) where h is the heterozygosity. At equilibrium, the probability that two cistrons differ by more than one site is equal to h  2, the square of heterozygosity.

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