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 Prediction of rates of inbreeding in selected populations

1990 ◽  
Vol 55 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Naomi R. Wray ◽  
Robin Thompson
Keyword(s):  
Selective Advantage ◽  
Mass Selection ◽  
Effective Population ◽  
The Matrix ◽  
Mean And Variance ◽  
Unselected Population ◽  
The Mean ◽  
Number Of Individuals ◽  
The Relationship

SummaryA method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into ‘contribution’ matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, where N is the number of individuals per generation and μr and are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing ‘competitiveness’ of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.

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 Some sampling properties of selectively neutral alleles

1979 ◽  
Vol 34 (3) ◽  
pp. 253-267 ◽  
Author(s):  
Ranajit Chakraborty ◽  
Paul A. Fuerst
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Genetic Variability ◽  
Mutation Rate ◽  
Natural Populations ◽  
Single Locus ◽  
Population Parameter ◽  
Mean And Variance ◽  
The Mean

SUMMARYSome sampling properties related with the mean and variance of the number of alleles and single locus heterozygosity are derived to study the effect of variations in mutation rate of selectively neutral alleles. The correlation between single locus heterozygosity and the number of alleles is also derived. Monte Carlo simulation is conducted to examine the effect of stepwise mutations. The relevance of these results in estimating the population parameter, 4Neν, is discussed in connexion with neutralist-selectionist controversy over the maintenance of genetic variability in natural populations.

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 Models of long-term artificial selection in finite population with recurrent mutation

1986 ◽  
Vol 48 (2) ◽  
pp. 125-131 ◽  
Author(s):  
William G. Hill ◽  
Jonathan Rasbash
Keyword(s):  
Population Size ◽  
First Generation ◽  
Finite Population ◽  
Effective Population ◽  
Term Selection ◽  
Cumulative Response ◽  
Mean And Variance ◽  
The Mean ◽  
Selection For

SummaryThe effects of mutation on mean and variance of response to selection for quantitative traits are investigated. The mutants are assumed to be unlinked, to be additive, and to have their effects symmetrically distributed about zero, with absolute values of effects having a gamma distribution. It is shown that the ratio of expected cumulative response to generation t from mutants, , and expected response over one generation from one generation of mutants, , is a function of t/N, where t is generations and N is effective population size. Similarly, , is a function of t/N, where is the increment in genetic variance from one generation of mutants. The mean and standard deviation of response from mutations relative to that from initial variation in the population, in the first generation, are functions of . Evaluation of these formulae for a range of parameters quantifies the important role that population size can play in response to long-term selection.

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.

Research on the Grading Theory of Thick and Thin Defects in the Electronic Testing for Raw Silk

2011 ◽  
Vol 175-176 ◽  
pp. 439-444 ◽  
Author(s):  
Jian Tao Niu ◽  
Qi Hu ◽  
Jian Mei Xu ◽  
Suo Zhuai Dong ◽  
Lun Bai
Keyword(s):  
Negative Binomial ◽  
Mean And Variance ◽  
The Mean ◽  
Spot Tests ◽  
The Difference ◽  
Grading Standards ◽  
The Right ◽  
Power Law Equation ◽  
The Relationship ◽  
Electronic Detector

Based on the sampling and grading theory of raw silk test, this paper studied the grading theory method of thick and thin defects of the raw silk in the electronic testing. By means of analyzing the data obtained from the raw silk electronic detector, the fact that the thick and thin defects of the raw silk appropriately take negative binomial distribution in the electronic testing has been confirmed. Under such circumstance, the distribution of the average of the sampling samples of the thick and thin defects was given, and fitting on the relationship between the mean and variance of the thick and thin defects were carried out by introducing Taylor’s power law equation, thus the right grading rate and probability of the difference between two spot tests about the thick and thin defects of the raw silk in the electronic testing was deduced. Moreover, the conclusion of the theoretical analysis was confirmed by simulation tests. The results might provide a basis for establishing the grading standards of the thick and thin defects in the electronic testing for raw silk.

scholarly journals Variance-effective population number: the effects of sex ratio and density on the mean and variance of offspring numbers in the flour beetle, Tribolium castaneum

1984 ◽  
Vol 43 (3) ◽  
pp. 249-256 ◽  
Author(s):  
Michael J. Wade
Keyword(s):  
Experimental Study ◽  
Sex Ratio ◽  
Tribolium Castaneum ◽  
Sex Ratios ◽  
Effective Number ◽  
Effective Population ◽  
Population Number ◽  
Flour Beetle ◽  
Mean And Variance ◽  
The Mean

SUMMARYI report the results of an experimental study of the effects of sex ratio and density on the mean and variance in offspring numbers in both sexes of the flour beetle, Tribolium castaneum. The variance-effective number is estimated from the observed variance in offspring numbers using the methods of Crow & Morton (1955).Both the mean and the variance in offspring numbers were found to vary with sex ratio and density; as was found in previous studies (Wade, 1980), males were generally more variable in offspring numbers than females. The ratio of variance to mean progeny numbers in each sex was approximately unity at all sex ratios.

FREQUENCY- AND DENSITY-DEPENDENT SELECTION ON A QUANTITATIVE CHARACTER

Genetics ◽  
1979 ◽  
Vol 93 (3) ◽  
pp. 755-771
Author(s):  
Montgomery Slatkin
Keyword(s):  
Genetic Model ◽  
Quantitative Character ◽  
Density Dependent ◽  
Correlation Models ◽  
Mean And Variance ◽  
The Mean ◽  
The Relationship ◽  
Range Of Values ◽  
Density Dependent Selection ◽  
Infinite Range

ABSTRACT The equilibrium distribution of a quantitative character subject to frequency- and density-dependent selection is found under different assumptions about the genetical basis of the character that lead to a normal distribution in a population. Three types of models are considered: (1) one-locus models, in which a single locus has an additive effect on the character, (2) continuous genotype models, in which one locus o r several loci contribute additively to a character, and there is an effectively infinite range of values of the genotypic contributions from each locus, and (3) correlation models, in which the mean and variance of the character can change only through selection at modifier loci. I t is shown that the second and third models lead to the same equilibrium values of the total population size and the mean and variance of the character. One-locus models lead to different equilibrium values because of constraints on the relationship between the mean and variance imposed by the assumptions of those models.—The main conclusion is that, at the equilibrium reached under frequency- and density-dependent selection, the distribution of a normally distributed quantitative character does not depend on the underlying genetic model as long as the model imposes no constraints on the mean and variance.

scholarly journals Nearly Neutral Evolution Across the Drosophila melanogaster Genome

2017 ◽  
Author(s):  
David Castellano ◽  
Jennifer James ◽  
Adam Eyre-Walker
Keyword(s):  
Drosophila Melanogaster ◽  
Neutral Theory ◽  
Neutral Evolution ◽  
Effective Population ◽  
Synonymous Mutations ◽  
Fitness Effects ◽  
Independent Estimate ◽  
Polymorphism Data ◽  
Neutral Mutations ◽  
The Relationship

AbstractUnder the nearly neutral theory of molecular evolution the proportion of effectively neutral mutations is expected to depend upon the effective population size (Ne). Here we investigate whether this is the case across the genome of Drosophila melanogaster using polymorphism data from North American and African lines. We show that the ratio of the number of non-synonymous and synonymous polymorphisms is negatively correlated to the number of synonymous polymorphisms, even when the non-independence is accounted for. The relationship is such that the proportion of effectively neutral non-synonymous mutations increases by ~45% as Ne is halved. However, we also show that this relationship is steeper than expected from an independent estimate of the distribution of fitness effects from the site frequency spectrum. We investigate a number of potential explanations for this and show, using simulation, that this is consistent with a model of genetic hitch-hiking: genetic hitch-hiking depresses diversity at neutral and weakly selected sites, but has little effect on the diversity of strongly selected sites.

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