scholarly journals PERSISTENCE OF COMMON ALLELES IN TWO RELATED POPULATIONS OR SPECIES

Genetics ◽  
1977 ◽  
Vol 86 (4) ◽  
pp. 901-914
Author(s):  
Wen-Hsiung Li ◽  
Masatoshi Nei
Keyword(s):  
Mutation Rate ◽  
Extinction Time ◽  
Effective Population ◽  
Expected Number ◽  
Single Population ◽  
Molecular Population Genetics ◽  
The Common ◽  
The Mean ◽  
Time Required ◽  
Two Populations

ABSTRACT Mathematical studies are conducted on three problems that arise in molecular population genetics. (1) The time required for a particular allele to become extinct in a population under the effects of mutation, selection, and random genetic drift is studied. In the absence of selection, the mean extinction time of an allele with an initial frequency close to 1 is of the order of the reciprocal of the mutation rate when 4Nv << 1, where N is the effective population size and v is the mutation rate per generation. Advantageous mutations reduce the extinction time considerably, whereas deleterious mutations increase it tremendously even if the effect on fitness is very slight. (2) Mathematical formulae are derived for the distribution and the moments of extinction time of a particular allele from one or both of two related populations or species under the assumption of no selection. When 4Nv << 1, the mean extinction time is about half that for a single population, if the two populations are descended from a common original stock. (3) The expected number as well as the proportion of common neutral alleles shared by two related species at the tth generation after their separation are studied. It is shown that if 4Nv is small, the two species are expected to share a high proportion of common alleles even 4N generations after separation. In addition to the above mathematical studies, the implications of our results for the common alleles at protein loci in related Drosophila species and for the degeneration of unused characters in cave animals are discussed.

scholarly journals GENETIC VARIABILITY MAINTAINED BY MUTATION AND OVERDOMINANT SELECTION IN FINITE POPULATIONS

Genetics ◽  
1981 ◽  
Vol 98 (2) ◽  
pp. 441-459 ◽  
Author(s):  
Takeo Maruyama ◽  
Masatoshi Nei
Keyword(s):  
Mutation Rate ◽  
Allozyme Polymorphism ◽  
Random Genetic Drift ◽  
Effective Population ◽  
Mathematical Properties ◽  
Overdominant Selection ◽  
Mean And Variance ◽  
The Mean ◽  
Neutral Mutations ◽  
The Relationship

ABSTRACT Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Itô and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2Ns (N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient (s) to mutation rate (ν) is large and the mean heterozygosity (h) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.

scholarly journals HIDDEN GENETIC VARIABILITY WITHIN ELECTROMORPHS IN FINITE POPULATIONS

Genetics ◽  
1976 ◽  
Vol 84 (2) ◽  
pp. 385-393
Author(s):  
Ranajit Chakraborty ◽  
Masatoshi Nei
Keyword(s):  
Genetic Variability ◽  
Probability Generating Function ◽  
Effective Population ◽  
Finite Populations ◽  
Site Model ◽  
Stepwise Mutation ◽  
Mean And Variance ◽  
The Mean ◽  
Bivariate Probability ◽  
Two Populations

ABSTRACT The amount of hidden genetic variability within electromorphs in finite populations is studied by using the infinite site model and stepwise mutation model simultaneously. A formula is developed for the bivariate probability generating function for the number of codon differences and the number of electromorph state differences between two randomly chosen cistrons. Using this formula, the distribution as well as the mean and variance of the number of codon differences between two identical or nonidentical electromorphs are studied. The distribution of the number of codon differences between two randomly chosen identical electromorphs is similar to the geometric distribution but more leptokurtic. Studies are also made on the number of codon differences between two electromorphs chosen at random one from each of two populations which have been separated for an arbitrary number of generations. It is shown that the amount of hidden genetic variability is very large if the product of effective population size and mutation rate is large.

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.

scholarly journals RATE OF GENE SILENCING AT DUPLICATE LOCI: A THEORETICAL STUDY AND INTERPRETATION OF DATA FROM TETRAPLOID FISHES

Genetics ◽  
1980 ◽  
Vol 95 (1) ◽  
pp. 237-258 ◽  
Author(s):  
Wen-Hsiung Li
Keyword(s):  
Large Scale ◽  
Null Allele ◽  
Gene Loss ◽  
Extinction Time ◽  
Effective Population ◽  
Tight Linkage ◽  
Order Of Magnitude ◽  
The Mean ◽  
Duplicate Loci ◽  
Sheltering Effect

ABSTRACT A large-scale simulation has been conducted on the rate of gene loss at duplicate loci under irreversible mutation. It is found that tight linkage does not provide a strong sheltering effect, as thought by previous authors; indeed, the mean loss time for the case of tight linkage is of the same order of magnitude as that for no linkage, as long as Nu is not much larger than 1, where N is the effective population size and u the mutation rate. When Nu is 0.01 or less, the two loci behave almost as neutral loci, regardless of linkage, and the mean loss time is about only half the mean extinction time for a neutral allele under irreversible mutation. However, the former becomes two or more times larger than the latter when Nu ≥ 1.—In the simulation, the sojourn times in the frequency intervals (0, 001) and (0.99, 1) and the time for the frequency of the null allele to reach 0.99 at one of the two loci have also been recorded. The results show that the populatian is monomorphic for the normal allele most of the time if Nu ≤ 0.01, but polymorphic for the null and the normal alleles most of the time if Nu ≥ 0.1.—The distribution of the frequency of the null allele in an equilibrium tetraploid population has been studied analytically. The present results have been applied to interpret data from some fish groups that are of tetraploid origin, and a model for explaining the slow rate of gene loss in these fishes is proposed.

scholarly journals GENE GENEALOGY AND VARIANCE OF INTERPOPULATIONAL NUCLEOTIDE DIFFERENCES

Genetics ◽  
1985 ◽  
Vol 110 (2) ◽  
pp. 325-344
Author(s):  
Naoyuki Takahata ◽  
Masatoshi Nei
Keyword(s):  
Sample Size ◽  
Standard Error ◽  
Mathematical Theory ◽  
Effective Population ◽  
Approximate Estimate ◽  
Expected Time ◽  
Different Populations ◽  
The Mean ◽  
Time Of Divergence ◽  
Two Populations

ABSTRACT A mathematical theory is developed for computing the probability that m genes sampled from one population (species) and n genes sampled from another are derived from l genes that existed at the time of population splitting. The expected time of divergence between the two most closely related genes sampled from two different populations and the time of divergence (coalescence) of all genes sampled are studied by using this theory. It is shown that the time of divergence between the two most closely related genes can be used as an approximate estimate of the time of population splitting (T) only when T ≡ t/(2 N) is small, where t and N are the number of generations and the effective population size, respectively. The variance of Nei and Li's estimate (d) of the number of net nucleotide differences between two populations is also studied. It is shown that the standard error (sd) of d is larger than the mean when T is small (T << 1). In this case, sd is reduced considerably by increasing sample size. When T is large (T > 1), however, a large proportion of the variance of d is caused by stochastic factors, and increase in the sample size does not help to reduce sd. To reduce the stochastic variance of d, one must use data from many independent unlinked gene loci.

scholarly journals Maximum-Likelihood Estimation of Migration Rates and Effective Population Numbers in Two Populations Using a Coalescent Approach

Genetics ◽  
1999 ◽  
Vol 152 (2) ◽  
pp. 763-773 ◽  
Author(s):  
Peter Beerli ◽  
Joseph Felsenstein
Keyword(s):  
Maximum Likelihood ◽  
Mutation Rate ◽  
Likelihood Estimation ◽  
Effective Population ◽  
Migration Rates ◽  
Coalescent Approach ◽  
Population Sizes ◽  
Two Populations ◽  
Better Than ◽  
Population Numbers

Abstract A new method for the estimation of migration rates and effective population sizes is described. It uses a maximum-likelihood framework based on coalescence theory. The parameters are estimated by Metropolis-Hastings importance sampling. In a two-population model this method estimates four parameters: the effective population size and the immigration rate for each population relative to the mutation rate. Summarizing over loci can be done by assuming either that the mutation rate is the same for all loci or that the mutation rates are gamma distributed among loci but the same for all sites of a locus. The estimates are as good as or better than those from an optimized FST-based measure. The program is available on the World Wide Web at http://evolution.genetics.washington.edu/lamarc.html/.

Comparison of Heffner Criteria and Light Criteria in Differentiating Exudative and Transudative Pleural Effusion

2020 ◽  
Vol 22 (3) ◽  
pp. 141-145
Author(s):  
Krishna Chandra Devkota ◽  
S Hamal ◽  
PP Panta
Keyword(s):  
Pleural Effusion ◽  
Cross Sectional Study ◽  
Pleural Space ◽  
Sectional Study ◽  
Inclusion Criteria ◽  
Cross Sectional ◽  
Medical College ◽  
The Common ◽  
The Mean ◽  
Exudative Pleural Effusion

Pleural effusion is present when there is >15ml of fluid is accumulated in the pleural space. It can be divided into two types; exudative and transudative pleural effusion. Tuberculosis and parapneumonic effusion are the common cause of exudative pleural effusion whereas heart failure accounts for most of the cases of transudative pleural effusion. This study was a hospital based cross sectional study performed at Nepal Medical College during the period of January 2016-December 2016. A total of 50 patients who fulfilled the inclusion criteria were enrolled. Pleural effusion was confirmed by clinical examination and radiology. After confirmation of pleural effusion, pleural fluid was aspirated and was analysed for protein, LDH, cholesterol. The Heffner criteria was compared with Light criteria to classify exudative or transudative pleural effusion. Among 50 patients, 30 were male and 20 were female. The mean age of patient was 45.4±21.85 years. The sensitivity and specificity of using Light criteria to detect the two type of pleural effusion was 100% and 90.9%, whereas using Heffner criteria was 94.87%, 100% respectively(P<0.01). There are variety of causes for development of pleural effusion and no one criteria is definite to differentiate between exudative or transudative effusion. In this study Light criteria was more sensitive whereas Heffner criteria was more specific to classify exudative pleural effusion. Hence a combination of criteria might be useful in case where there is difficulty to identify the cause of pleural effusion.

Of Reformed Versifying

2018 ◽  
Author(s):  
Neil Rhodes
Keyword(s):  
Sixteenth Century ◽  
Faerie Queene ◽  
Classical Literature ◽  
Native Form ◽  
Christian Doctrine ◽  
English Verse ◽  
The Common ◽  
The Mean ◽  
The Faerie Queene ◽  
Stylistic Ideal

This chapter examines how the development of English poetry in the second half of the sixteenth century is characterized by the search for an appropriate style. In this context, ‘reformed versifying’ may be understood as a reconciliation of high and low in which the common is reconfigured as a stylistic ideal of the mean. That development can be traced in debates about prosody where an alternative sense of ‘reformed versifying’ as adapting classical metres to English verse is rejected in favour of native form. At the same time Sidney recuperates poetry by reforming it as an agent of virtue. Reformation and Renaissance finally come together in Spenser, who realizes Erasmus’ aim of harmonizing the values of classical literature with Christian doctrine, and reconciles the foreign and the ‘homewrought’. The Faerie Queene of 1590 represents the triumph of the mean in both style and, through its celebration of marriage, in substance.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document