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 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 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 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.

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 Testing the breeding strategy of Hungarian Bronze turkey strains for maintaining genetic diversity with microsatellites

2011 ◽  
Vol 54 (4) ◽  
pp. 419-429
Author(s):  
S. Kusza ◽  
S. Mihók ◽  
L. Czeglédi ◽  
A. Jávor ◽  
M. Árnyasi
Keyword(s):  
Genetic Diversity ◽  
Genetic Variability ◽  
Mating System ◽  
Breeding Strategy ◽  
Shannon Index ◽  
Inbreeding Coefficient ◽  
Control Population ◽  
Conservation Strategies ◽  
The Mean ◽  
Two Populations

Abstract. The aim of the study was to provide information on the genetic variability of the Hungarian Bronze turkey gene reserve population and its difference from the Broad-breasted turkey, and offer guidance and proposals for its future conservation strategies. Altogether, 239 Hungarian Bronze turkeys from 10 strains and 13 Broad-breasted turkeys as a control population were genotyped for 15 microsatellites. All loci were polymorphic with the average number of alleles per locus 3.20±1.146 in the Hungarian Bronze turkey. The mean expected (Hexp) and observed heterozygosity (Hobs) were not different (0.392 and 0.376, respectively) in the overall population, and similar values were obtained for hens and bucks and among hen strains. Inbreeding coefficient (FIS) and Shannon index (I) indicated that there was low inbreeding within hens and bucks. Our results confirm that the genetic diversity in the Hungarian Bronze turkey population has been preserved by the rotational mating system. Differences between the Hungarian Bronze turkey and the Broad-breasted turkey populations were determined. Nei’s unbiased values clearly indicated that the two populations are highly genetically differentiated.

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.

SCALING PROPERTIES OF FIRST RETURN TIME ON WEIGHTED TRANSFRACTALS (1,3)-FLOWERS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850095 ◽  
Author(s):  
MEIFENG DAI ◽  
HUIJIA CHI ◽  
XIANBIN WU ◽  
YUE ZONG ◽  
WENJING FENG ◽  
...  
Keyword(s):  
Complex Networks ◽  
Real Life ◽  
Probability Generating Function ◽  
Return Time ◽  
Exact Probability ◽  
Scaling Properties ◽  
Mean And Variance ◽  
The Mean ◽  
First Return Time ◽  
The Impact

Complex networks are omnipresent in science and in our real life, and have been the focus of intense interest. It is vital to research the impact of their characters on the dynamic progress occurring on complex networks for weight-dependent walk. In this paper, we first consider the weight-dependent walk on one kind of transfractal (or fractal) which is named the weighted transfractal [Formula: see text]-flowers. And we pay attention to the first return time (FRT). We mainly calculate the mean and variance of FRT for a prescribed hub (i.e. the most concerned nodes) in virtue of exact probability generating function and its properties. Then, we obtain the mean and the secondary moment of the first return time. Finally, using the relationship among the variance, mean and the secondary moment, we obtain the variance of FRT and the scaling properties of the mean and variance of FRT on weighted transfractals [Formula: see text]-flowers.

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 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 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.

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