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 The transient distribution of allele frequencies under mutation pressure

1976 ◽  
Vol 28 (3) ◽  
pp. 205-214 ◽  
Author(s):  
Masatoshi Nei ◽  
Wen-Hsiung Li
Keyword(s):  
Steady State ◽  
Population Size ◽  
Finite Population ◽  
Allele Frequencies ◽  
Effective Population ◽  
Expected Number ◽  
Steady State Distribution ◽  
Mutation Pressure ◽  
Transient Distribution ◽  
Expected Heterozygosity

SUMMARYThe transient distribution of allele frequencies in a finite population is derived under the assumption that there are k possible alleic states at a locus and mutation occurs in all directions. At steady state this distribution becomes identical with the distribution obtained by Wright, Kimura and Crow when k = ∞. The rate of approach to the steady state distribution is generally very slow, the asymptotic rate being 2v + 1/(2N), where v and N are the mutation rate and effective population size, respectively. Using this distribution it is shown that when population size is suddenly increased, the expected number of alleles increases more rapidly than the expected heterozygosity. Implications of the present study on testing hypotheses for the maintenance of genetic variability in populations are discussed.

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 Effective population size: the effects of sex, genotype, and density on the mean and variance of offspring numbers in the flour beetle, Tribolium castaneum

1980 ◽  
Vol 36 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Michael J. Wade
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Tribolium Castaneum ◽  
Black Body ◽  
Body Colour ◽  
Effective Population ◽  
Flour Beetle ◽  
Colour Mutant ◽  
Mean And Variance ◽  
The Mean

SUMMARYIn this paper I present the results of an experimental study of the effects of genotype and density on the mean and variance of offspring numbers in both sexes of the flour beetle, Tribolium castaneum. From the observed variance in offspring numbers the effective population size at several different densities is estimated using the methods of Crow & Morton (1955).I found that both the mean and variance of offspring numbers varied with genotype and density. In general, males were more variable in offspring numbers than females and this variability increased with density. Individuals homozygous for the black body colour mutant, b/b, were less variable in offspring numbers than + / + individuals, but the latter produced more offspring at most densities. As density increased, + / + individuals became more variable in offspring numbers whereas b/b individuals were less sensitive in this regard. These findings are discussed in relation to the ecology of selection at the black and closely linked loci.

scholarly journals IDENTITY COEFFICIENTS IN FINITE POPULATIONS. I. EVOLUTION OF IDENTITY COEFFICIENTS IN A RANDOM MATING DIPLOID DIOECIOUS POPULATION

Genetics ◽  
1977 ◽  
Vol 86 (3) ◽  
pp. 697-713
Author(s):  
C Chevalet ◽  
M Gillois ◽  
R F Nassar
Keyword(s):  
Genetic Variability ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Matrix Multiplication ◽  
Inbred Lines ◽  
Inbreeding Coefficient ◽  
Effective Population ◽  
The Mean ◽  
Over Time

ABSTRACT Properties of identity relation between genes are discussed, and a derivation of recurrent equations of identity coefficients in a random mating, diploid dioecious population is presented. Computations are run by repeated matrix multiplication. Results show that for effective population size (Ne) larger than 16 and no mutation, a given identity coefficient at any time t can be expressed approximately as a function of (1—f), (1—f)3 and (1—f)6, where f is the mean inbreeding coefficient at time t. Tables are presented, for small Ne values and extreme sex ratios, showing the pattern of change in the identity coefficients over time. The pattern of evolution of identity coefficients is also presented and discussed with respect to N eu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.

Population structure of the Sahiwal breed in Pakistan

1995 ◽  
Vol 60 (2) ◽  
pp. 163-168 ◽  
Author(s):  
A. Dahlin ◽  
U. N. Khan ◽  
A. H. Zafar ◽  
M. Saleem ◽  
M. A. Chaudhry ◽  
...  
Keyword(s):  
Population Structure ◽  
Population Size ◽  
Effective Population Size ◽  
Breeding Population ◽  
Effective Population ◽  
Data Set ◽  
Inbreeding Coefficients ◽  
Sahiwal Cows ◽  
The Mean ◽  
Average Population Size

AbstractThe present study was undertaken to assist conservation and improvement schemes in the Sahiwal breed of cattle in Pakistan. A data set, consisting of records of 244 pure Sahiwal breeding bulls and 5247 cows, the latter representing about 80% of all recorded Sahiwal cows in Pakistan born during a period covering about 20 years, was analysed with regard to inbreeding, additive relationships, effective population size and generation intervals. Average inbreeding coefficients of 1224 cows and 49 bulls, for which at least the grandparents and great-grandsires were known, were 0·043 and 0·046, respectively. About two-thirds of the inbreeding was due to matings between animals with parents or grandparents in common. The mean additive relationship among the cows was 0·062, with within-herd averages ranging from 0·087 to 0·358. The average population size in a subdata set of recorded Sahiwal cattle from 1980 to 1984 was 1612, whereas the most likely estimate of the effective population size was about 30 animals for the same active breeding population. The study indicated the immediate need for an active conservation programme whereby the Sahiwal subpopulations of India and Kenya also should be involved.

Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution

1985 ◽  
Vol 22 (3) ◽  
pp. 611-618 ◽  
Author(s):  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
First Passage ◽  
The Mean

The asymptotic behavior of the first-passage-time p.d.f. through a constant boundary is studied when the boundary approaches the endpoints of the diffusion interval. We show that for a class of diffusion processes possessing a steady-state distribution this p.d.f. is approximately exponential, the mean being the average first-passage time to the boundary. The proof is based on suitable recursive expressions for the moments of the first-passage time.

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.

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