The effects of finite population size and selection on the correlation between gene frequency changes at two different loci and on the amount of linkage disequilibrium

1972 ◽  
Vol 42 (8) ◽  
pp. 335-345 ◽  
Author(s):  
Susan J. Galley ◽  
R. N. Curnow
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Gene Frequency ◽  
Finite Population ◽  
Frequency Changes

scholarly journals PROBABILITY OF FIXATION AND MEAN FIXATION TIME OF AN OVERDOMINANT MUTATION

Genetics ◽  
1973 ◽  
Vol 74 (2) ◽  
pp. 371-380
Author(s):  
Masatoshi Nei ◽  
A K Roychoudhury
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Finite Population ◽  
Retardation Factor ◽  
Fixation Time ◽  
Selection Intensity ◽  
Infinite Population ◽  
Probability Of Fixation

ABSTRACT The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.

scholarly journals LINKAGE DISEQUILIBRIUM IN A FINITE POPULATION THAT IS PARTIALLY SELFING

Genetics ◽  
1980 ◽  
Vol 94 (3) ◽  
pp. 777-789 ◽  
Author(s):  
G B Golding ◽  
C Strobeck
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Random Mating ◽  
Effective Population ◽  
Infinite Allele Model ◽  
Inbreeding Coefficients ◽  
Linkage Disequilibria ◽  
Recombination Value ◽  
Allele Model

ABSTRACT The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size Ne = (l—½S)N and the effective recombination value re = (l-S)r/(l-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value, Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1 — ½S and the recombination value by a factor (l-S)/(l—½S).

scholarly journals Distribution of linkage disequilibrium with selection and finite population size

1979 ◽  
Vol 33 (1) ◽  
pp. 29-48 ◽  
Author(s):  
P. J. Avery ◽  
W. G. Hill
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Finite Population ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Large Expansion ◽  
Large Populations ◽  
The Difference ◽  
Successive Generations ◽  
Stable Points

SUMMARYThe effects of finite population size, occurring either as a bottleneck in a single generation followed by a large expansion or in all generations, are considered for models of two linked heterotic loci. Linkage is assumed to be tight because it is required if there is to be stable linkage disequilibrium, D ǂ 0, in infinitely large populations. (D is the difference between gamete frequencies and the product of the gene frequencies.)If a substantial perturbation of frequencies occurs as a result of a bottleneck but the population is subsequently very large, D may take hundreds of generations to return to its stable point. In finite populations, the distribution of D can be ⋃-shaped, unimodal or bimodal. The correlation of D in successive generations is higher with tight linkage and is little affected by selection or the size of the population.The utility of infinite population studies of linkage disequilibrium and its stable points is questioned, and considerable pessimism is expressed about the possibilities of distinguishing selection and sampling effects at linked loci.

scholarly journals The effect of finite population size on models of linked overdominant loci

1978 ◽  
Vol 31 (3) ◽  
pp. 239-254 ◽  
Author(s):  
P. J. Avery
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Genetic Drift ◽  
High Probability ◽  
Finite Population ◽  
Equilibrium Points ◽  
Gene Frequencies ◽  
Wide Range ◽  
Stable Equilibria ◽  
Range Of Values

SUMMARYModels of two linked overdominant loci in moderately large, but finite, populations are examined by looking at the variance-covariance matrix of the two gene frequencies and the linkage disequilibrium around stable deterministic equilibrium points. In particular, the effect of genetic drift is examined in cases where, in infinite populations, two stable equilibria with non-zero linkage disequilibrium, D, are maintained. Theoretical formulae are produced and checked by computer simulation. In general, the results show that unless the population size is very large indeed, genetic drift causes the values of D to vary considerably about the equilibrium values and that for many models, where stable equilibria exist at non-zero D values, a wide range of values of D have a high probability. Thus it is very difficult to draw conclusions about the selection regime by measuring Linkage disequilibrium in a finite population.

Genetic and Nongenetic Bases for the L-Shaped Distribution of Quantitative Trait Loci Effects

Genetics ◽  
2001 ◽  
Vol 157 (4) ◽  
pp. 1773-1787 ◽  
Author(s):  
Bruno Bost ◽  
Dominique de Vienne ◽  
Frédéric Hospital ◽  
Laurence Moreau ◽  
Christine Dillmann
Keyword(s):  
Linkage Disequilibrium ◽  
Quantitative Trait Loci ◽  
Population Size ◽  
Quantitative Trait ◽  
Metabolic Flux ◽  
Genetic Model ◽  
Small Population ◽  
Additive Genetic Model ◽  
Metabolic Mechanism ◽  
Qtl Effects

Abstract The L-Shaped distribution of estimated QTL effects (R2) has long been reported. We recently showed that a metabolic mechanism could account for this phenomenon. But other nonexclusive genetic or nongenetic causes may contribute to generate such a distribution. Using analysis and simulations of an additive genetic model, we show that linkage disequilibrium between QTL, low heritability, and small population size may also be involved, regardless of the gene effect distribution. In addition, a comparison of the additive and metabolic genetic models revealed that estimates of the QTL effects for traits proportional to metabolic flux are far less robust than for additive traits. However, in both models the highest R2's repeatedly correspond to the same set of QTL.

The variance of linkage disequilibrium between three loci in a finite population

1983 ◽  
Vol 25 (2) ◽  
pp. 139-145 ◽  
Author(s):  
C. Strobeck ◽  
G. B. Golding
Keyword(s):  
Linkage Disequilibrium ◽  
Finite Population ◽  
Intragenic Recombination ◽  
Random Drift ◽  
Third Order ◽  
Linkage Disequilibria ◽  
Order Of Magnitude ◽  
Infinite Alleles Model

The variance of three-locus linkage disequilibria for an equilibrium infinite alleles model is solved numerically on a computer, using identity coefficients. It is shown that the variance of three-locus linkage disequilibrium created by random drift, although smaller than the variance of two-locus linkage disequilibrium, is of the same order of magnitude. Hence third-order disequilibria are not necessarily good indications of selection. The formula for the variance of linkage disequilibrium is given when there is no recombination between the genes. This model can also be interpreted as intragenic recombination between three sites within a gene.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used 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 to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

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