scholarly journals LINKAGE DISEQUILIBRIUM IN A FINITE POPULATION THAT IS PARTIALLY SELFING

Genetics ◽  
1980 ◽  
Vol 94 (3) ◽  
pp. 777-789 ◽  
Author(s):  
G B Golding ◽  
C Strobeck
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Random Mating ◽  
Effective Population ◽  
Infinite Allele Model ◽  
Inbreeding Coefficients ◽  
Linkage Disequilibria ◽  
Recombination Value ◽  
Allele Model

ABSTRACT The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size Ne = (l—½S)N and the effective recombination value re = (l-S)r/(l-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value, Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1 — ½S and the recombination value by a factor (l-S)/(l—½S).

scholarly journals THE SAMPLING DISTRIBUTION OF LINKAGE DISEQUILIBRIUM

Genetics ◽  
1984 ◽  
Vol 108 (1) ◽  
pp. 257-274 ◽  
Author(s):  
G B Golding
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Effective Population Size ◽  
Correlation Coefficient ◽  
Bimodal Distribution ◽  
Test Statistic ◽  
Effective Population ◽  
Chi Square ◽  
Infinite Allele Model ◽  
Allele Model

ABSTRACT The probabilities of obtaining particular samples of gametes with two completely linked loci are derived. It is assumed that the population consists of N diploid, randomly mating individuals, that each of the two loci mutate according to the infinite allele model at a rate µ and that the population is at equilibrium. When 4Nµ is small, the most probable samples of gametes are those that segregate only two alleles at either locus. The probabilities of various samples of gametes are discussed. The results show that most samples with completely linked loci have either a very small or a very large association between the alleles of each locus. This causes the distribution of linkage disequilibrium to be skewed and the distribution of the correlation coefficient to be bimodal. The correlation coefficient is commonly used as a test statistic with a chi square distribution and yet has a bimodal distribution when the loci are completely linked. Thus, such a test is not likely to be accurate unless the rate of recombination between the loci and/or the effective population size are sufficiently large enough so that the loci can be treated as unlinked.

scholarly journals Genome-Wide Patterns of Homozygosity and Relevant Characterizations on the Population Structure in Piétrain Pigs

Genes ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 577
Author(s):  
Huiwen Zhan ◽  
Saixian Zhang ◽  
Kaili Zhang ◽  
Xia Peng ◽  
Shengsong Xie ◽  
...  
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Effective Population Size ◽  
Average Length ◽  
The Other ◽  
Runs Of Homozygosity ◽  
Effective Population ◽  
Inbreeding Coefficients ◽  
Genome Wide ◽  
Genomic Regions

Investigating the patterns of homozygosity, linkage disequilibrium, effective population size and inbreeding coefficients in livestock contributes to our understanding of the genetic diversity and evolutionary history. Here we used Illumina PorcineSNP50 Bead Chip to identify the runs of homozygosity (ROH) and estimate the linkage disequilibrium (LD) across the whole genome, and then predict the effective population size. In addition, we calculated the inbreeding coefficients based on ROH in 305 Piétrain pigs and compared its effect with the other two types of inbreeding coefficients obtained by different calculation methods. A total of 23,434 ROHs were detected, and the average length of ROH per individual was about 507.27 Mb. There was no regularity on how those runs of homozygosity distributed in genome. The comparisons of different categories suggested that the formation of long ROH was probably related with recent inbreeding events. Although the density of genes located in ROH core regions is lower than that in the other genomic regions, most of them are related with Piétrain commercial traits like meat qualities. Overall, the results provide insight into the way in which ROH is produced and the identified ROH core regions can be used to map the genes associated with commercial traits in domestic animals.

scholarly journals Estimation of Effective Population Size and Migration Rate From One- and Two-Locus Identity Measures

Genetics ◽  
2001 ◽  
Vol 157 (2) ◽  
pp. 911-925
Author(s):  
Renaud Vitalis ◽  
Denis Couvet
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Joint Estimation ◽  
Demographic Parameters ◽  
Effective Population ◽  
Mutation Bias ◽  
Infinite Allele Model ◽  
Immigration Rate ◽  
And Migration ◽  
Allele Model

Abstract Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.

The variance of linkage disequilibrium between three loci in a finite population

1983 ◽  
Vol 25 (2) ◽  
pp. 139-145 ◽  
Author(s):  
C. Strobeck ◽  
G. B. Golding
Keyword(s):  
Linkage Disequilibrium ◽  
Finite Population ◽  
Intragenic Recombination ◽  
Random Drift ◽  
Third Order ◽  
Linkage Disequilibria ◽  
Order Of Magnitude ◽  
Infinite Alleles Model

The variance of three-locus linkage disequilibria for an equilibrium infinite alleles model is solved numerically on a computer, using identity coefficients. It is shown that the variance of three-locus linkage disequilibrium created by random drift, although smaller than the variance of two-locus linkage disequilibrium, is of the same order of magnitude. Hence third-order disequilibria are not necessarily good indications of selection. The formula for the variance of linkage disequilibrium is given when there is no recombination between the genes. This model can also be interpreted as intragenic recombination between three sites within a gene.

scholarly journals Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method

1992 ◽  
Vol 60 (3) ◽  
pp. 209-220 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Computational Effort ◽  
Monte Carlo Integration ◽  
Bootstrap Sampling ◽  
Effective Population ◽  
Full Data

SummaryWe would like to use maximum likelihood to estimate parameters such as the effective population size Ne, or, if we do not know mutation rates, the product 4Neμof mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods pproximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, Ne or of 4Neμ. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.

scholarly journals Estimation of linkage disequilibrium and effective population size in New Zealand sheep using three different methods to create genetic maps

BMC Genetics ◽  
2017 ◽  
Vol 18 (1) ◽  
Author(s):  
Vincent Prieur ◽  
Shannon M. Clarke ◽  
Luiz F. Brito ◽  
John C. McEwan ◽  
Michael A. Lee ◽  
...  
Keyword(s):  
Linkage Disequilibrium ◽  
New Zealand ◽  
Population Size ◽  
Effective Population Size ◽  
Genetic Maps ◽  
Effective Population
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