scholarly journals THE VARIANCE OF THE NUMBER OF LOCI HAVING A GIVEN GENE FREQUENCY

Genetics ◽  
1973 ◽  
Vol 73 (2) ◽  
pp. 361-366
Author(s):  
Takeo Maruyama
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Random Mating ◽  
Finite Size ◽  
Selection Coefficient ◽  
Average Heterozygosity ◽  
Random Mating Population ◽  
Mating Population

ABSTRACT Considering a random mating population of finite size, the variance of the number of loci having a given gene frequency was derived under the assumption of a steady flux of mutations. The variance of average heterozygosity among populations was also derived under the same assumption. It was shown that these variances are proportional to the population size if the mutants are selectively neutral, and they are inversely proportional to the selection coefficient if the mutants are selectively advantageous and additive in their fitness.

scholarly journals Detecting Linkage between a Trait and a Marker in a Random Mating Population without Pedigree Record

PLoS ONE ◽  
2009 ◽  
Vol 4 (3) ◽  
pp. e4956
Author(s):  
Shuhei Mano ◽  
Takaho A. Endo ◽  
Akira Oka ◽  
Akira Ozawa ◽  
Takashi Gojobori ◽  
...  
Keyword(s):  
Random Mating ◽  
Random Mating Population ◽  
Mating Population

A general theory of the distribution of gene frequencies - I. Overlapping generations

1958 ◽  
Vol 149 (934) ◽  
pp. 102-112 ◽  
Keyword(s):  
General Theory ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Random Mating ◽  
Phenotypic Selection ◽  
Single Locus ◽  
Heuristic Methods ◽  
Gene Frequencies ◽  
Mating Population

The distribution of gene frequency at a single locus in a population of diploid individuals, with two sexes, subject to mutation, non-random mating and phenotypic selection, is obtained in the case where the generations are overlapping so that individuals die one by one. This distribution is of the same form as that obtained by heuristic methods by S. Wright in a randomly mating population but the coefficients are altered both by the non-randomness of the mating and the overlapping of the generations.

scholarly journals On the theory of artificial selection in finite populations

1969 ◽  
Vol 13 (2) ◽  
pp. 143-163 ◽  
Author(s):  
W. G. Hill
Keyword(s):  
Diffusion Equation ◽  
Artificial Selection ◽  
Quantitative Trait ◽  
Gene Frequency ◽  
Transition Probability ◽  
Random Mating ◽  
Finite Size ◽  
Individual Performance ◽  
Exact Method ◽  
Approximate Methods

The effect of selection on individual performance for a quantitative trait is studied theoretically for populations of finite size. The trait is assumed to be affected by environmental error and by segregation at a single locus. Exact formulae are derived to predict the change in gene frequency at this locus, initially by finding the probability distribution of the numbers of each genotype selected from a finite population of specified genotypic composition. Assuming that there is random mating and no natural selection the results are extended to describe repeated cycles of artificial selection for a monecious population. The formulae are evaluated numerically for the case of normally distributed environmental errors.Using numerical examples comparisons are made between the exact values for the predicted change in gene frequency with values obtained using approximate, but simpler, methods. Unless the gene has a large effect (α) on the quantitative trait, relative to the standard deviation of the environmental errors, the agreement between exact and approximate methods is satisfactory for most predictive purposes. The chance of fixation after repeated generations of selection is also evaluated using the exact method, and by means of a diffusion approximation and simple transition probability matrix methods. Except for very small values of population size (N) and large α the results from the diffusion equation agree closely with those from the exact method. Similar results are found from tests made of the prediction from the diffusion equation that the limit is only a function of Nα for a given intensity of selection and initial frequency, and that the rate of advance in gene frequency is proportional to 1/N for the same set of parameters.

scholarly journals The effect of repeated cycles of selection and regeneration in populations of finite size

1968 ◽  
Vol 11 (1) ◽  
pp. 105-112 ◽  
Author(s):  
R. N. Curnow ◽  
L. H. Baker
Keyword(s):  
Gene Frequency ◽  
Random Mating ◽  
Finite Size ◽  
Transition Matrices ◽  
Gene Frequencies ◽  
Multiple Alleles ◽  
Expected Gain ◽  
Approximate Form ◽  
Breeding Programmes ◽  
Selection Intensities

Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population are used to develop an iterative method for studying the effects of repeated cycles of selection and random mating. This is done by assuming a particular, but flexible and probably realistic, approximate form for the distribution of gene frequencies at each generation.The method gives for each generation the first two moments of the gene frequency distribution, the expected gain from selection, the probabilities of fixation and also the variability of gain. The variability of gain is of considerable importance in evolution, selection experiments and in plant and animal breeding programmes.Kojima's (1961) formulae have been extended to allow for differentiation between males and females. Hence different selection intensities and population sizes for the two sexes can be studied. Selfing with selection is considered separately. Extensions to cover simple examples of multiple alleles, linkage and epistasis are possible. Reference is made to previous work using transition matrices.

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