scholarly journals Detrimental genes with partial selfing and effects on a neutral locus

1974 ◽  
Vol 23 (2) ◽  
pp. 191-200 ◽  
Author(s):  
Tomoko Ohta ◽  
C. Clark Cockerham
Keyword(s):  
Linkage Disequilibrium ◽  
Mutational Load ◽  
Complete Linkage ◽  
Single Mutant ◽  
Infinite Population ◽  
Neutral Locus ◽  
Dominant Mutant ◽  
Self Fertilization ◽  
Recessive Mutant ◽  
Mutant Genes

SUMMARYGene and genotypic frequencies for a deleterious mutant in mutation selection balance are derived for an infinite population undergoing partial self-fertilization. These provide formulations of mean survival and the mutational load. Obtained also are the average number of mutant genes and affected individuals stemming from a single mutant.As a concomitant effect on frequencies at a neutral locus the mutational load is distributed disproportionately among the neutral genotypes. For partially recessive mutant genes on the 1, 1-sh, 1-s scale, the effect is to increase the frequency of the heterozygote and to decrease the frequencies of homozygotes at the neutral locus relative to the frequencies expected with complete neutrality. This apparent overdominance at the neutral locus has been shown to be connected with identity disequilibrium rather than linkage disequilibrium. It increases generally as s and h decrease, and as the proportion of self-fertilization and the degree of linkage increase. The apparent overdominance with complete linkage is generally less than double that for free recombination. For partially dominant mutant genes, h ≥ ½, the effects on the frequencies of heterozygote and homozygotes at the neutral locus are reversed.

scholarly journals An Inbreeding Model of Associative Overdominance During a Population Bottleneck

Genetics ◽  
2000 ◽  
Vol 155 (4) ◽  
pp. 1981-1990 ◽  
Author(s):  
Nicolas Bierne ◽  
Anne Tsitrone ◽  
Patrice David
Keyword(s):  
Linkage Disequilibrium ◽  
Mating System ◽  
Gene Diversity ◽  
Marker Gene ◽  
Marine Species ◽  
Population Bottleneck ◽  
Small Populations ◽  
Infinite Population ◽  
Neutral Locus ◽  
Physical Linkage

AbstractAssociative overdominance, the fitness difference between heterozygotes and homozygotes at a neutral locus, is classically described using two categories of models: linkage disequilibrium in small populations or identity disequilibrium in infinite, partially selfing populations. In both cases, only equilibrium situations have been considered. In the present study, associative overdominance is related to the distribution of individual inbreeding levels (i.e., genomic autozygosity). Our model integrates the effects of physical linkage and variation in inbreeding history among individual pedigrees. Hence, linkage and identity disequilibrium, traditionally presented as alternatives, are summarized within a single framework. This allows studying nonequilibrium situations in which both occur simultaneously. The model is applied to the case of an infinite population undergoing a sustained population bottleneck. The effects of bottleneck size, mating system, marker gene diversity, deleterious genomic mutation parameters, and physical linkage are evaluated. Bottlenecks transiently generate much larger associative overdominance than observed in equilibrium finite populations and represent a plausible explanation of empirical results obtained, for instance, in marine species. Moreover, the main origin of associative overdominance is random variation in individual inbreeding whereas physical linkage has little effect.

scholarly journals Unusual behaviour of linkage disequilibrium in two-locus gene conversion models

1988 ◽  
Vol 51 (1) ◽  
pp. 55-58 ◽  
Author(s):  
J. Bruce Walsh
Keyword(s):  
Linkage Disequilibrium ◽  
Gene Conversion ◽  
Recombination Rate ◽  
Conversion Rate ◽  
Population Model ◽  
Complete Linkage ◽  
Conversion Event ◽  
Infinite Population ◽  
Unusual Behaviour

SummaryThe amount of linkage of disequilibrium maintained in a two-locus infinite population model by gene conversion and recombination is examined. Intrachromosomal conversion (conversion between different loci on the same chromosome) generates positive linkage disequilibrium. Specifically, = p(1 − p) [1 − r/(γ + r − γr)], where p is the frequency of allele A at both loci, r is the recombination rate between loci and γ is the per-gamete conversion rate. Somewhat unexpectedly, interchromosomal conversion (conversion between loci on different chromosomes) also generates positive disequilibrium, albeit very small. More interestingly, the behaviour of this disequilibrium as a function of recombination is unusual. If β is the interchromosomal conversion rate between a pair of loci, then = p(1 − p) [rβ/(β+r − βr)]. increases with increasing recombination, being zero for the case of complete linkage (r = 0), and maximized at r = 1/2. This unusual behaviour can be accounted for by the generation of excess coupling gametes when an interchromosomal conversion event is followed by recombination.

Genetic Drift in an Infinite Population: The Pseudohitchhiking Model

Genetics ◽  
2000 ◽  
Vol 155 (2) ◽  
pp. 909-919 ◽  
Author(s):  
John H Gillespie
Keyword(s):  
Genetic Drift ◽  
Stochastic Dynamics ◽  
Diffusion Theory ◽  
Stochastic Effects ◽  
Stochastic Force ◽  
Infinite Population ◽  
Sample Paths ◽  
Neutral Locus ◽  
Linked Selection ◽  
Number Of Branches

Abstract Selected substitutions at one locus can induce stochastic dynamics that resemble genetic drift at a closely linked neutral locus. The pseudohitchhiking model is a one-locus model that approximates these effects and can be used to describe the major consequences of linked selection. As the changes in neutral allele frequencies when hitchhiking are rapid, diffusion theory is not appropriate for studying neutral dynamics. A stationary distribution and some results on substitution processes are presented that use the theory of continuous-time Markov processes with discontinuous sample paths. The coalescent of the pseudohitchhiking model is shown to have a random number of branches at each node, which leads to a frequency spectrum that is different from that of the equilibrium neutral model. If genetic draft, the name given to these induced stochastic effects, is a more important stochastic force than genetic drift, then a number of paradoxes that have plagued population genetics disappear.

Linkage disequilibrium between neutral genes in finite populations

1974 ◽  
Vol 6 (01) ◽  
pp. 13-15
Author(s):  
William G. Hill
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linkage Disequilibrium ◽  
Finite Populations ◽  
Gene Frequencies ◽  
Infinite Population ◽  
Asymptotic Values

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

scholarly journals Selection for recombination in a polygenic model – the mechanism

1988 ◽  
Vol 51 (1) ◽  
pp. 59-63 ◽  
Author(s):  
J. Maynard Smith
Keyword(s):  
Linkage Disequilibrium ◽  
Recombination Rate ◽  
Phenotypic Variability ◽  
Directional Selection ◽  
Polygenic Model ◽  
Infinite Population ◽  
Selection For ◽  
Repulsion Linkage

SummaryA polygenic model has been simulated in order to reveal the process whereby selection in an infinite population can lead to an increase in the frequency of alleles causing higher rates of recombination (CH alleles). Directional selection generates repulsion linkage disequilibrium (+ − + −), which is less strong in CH gametes (gametes carrying CH alleles). In consequence, CH gametes contribute greater phenotypic variability, and therefore respond more to directional selection: that is, they accumulate more selectively favoured alleles. CH alleles then increase in frequency by hitch-hiking. In contrast, normalizing selection, or frequent changes in the direction of selection, favour alleles for a low recombination rate.

scholarly journals SELECTION IN COMPLEX GENETIC SYSTEMS I. THE SYMMETRIC EQUILIBRIA OF THE THREE-LOCUS SYMMETRIC VIABILITY MODEL

Genetics ◽  
1974 ◽  
Vol 76 (1) ◽  
pp. 135-162
Author(s):  
Marcus W Feldman ◽  
Ian Franklin ◽  
Glenys J Thomson
Keyword(s):  
Linkage Disequilibrium ◽  
Linkage Equilibrium ◽  
Symmetric Equilibrium ◽  
Third Order ◽  
Complete Linkage ◽  
High Frequencies ◽  
New Class ◽  
Linkage Disequilibria ◽  
Tight Linkage ◽  
Stable Equilibria

ABSTRACT The symmetric equilibria of the three-locus symmetric viability model are determined and their stability analyzed. For tight linkage there may be four stable equilibria, each characterized by having one pair of complementary chromosomes in high frequencies, with all others low. For looser linkage the only stable symmetric equilibrium is that with complete linkage equilibrium. For intermediate recombination values both types of equilibria may be stable. A new class of equilibria with all pairwise linkage disequilibria zero, but with third order linkage disequilibrium, has been discovered. It may be stable for tight linkage.

Recessive mutant genes predisposing to human cancer

1986 ◽  
Vol 168 (1) ◽  
pp. 3-14 ◽  
Author(s):  
Webster K. Cavenee ◽  
Alex Koufos ◽  
Marc F. Hansen
Keyword(s):  
Human Cancer ◽  
Recessive Mutant ◽  
Mutant Genes
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