Is the between-population variance negligible in the total variance of heterozygosity? Case of a finite number of loci subject to the infinite-allele model in finite monoecious populations

1981 ◽  
Vol 20 (3) ◽  
pp. 394-410 ◽  
Author(s):  
S. Lessard
Keyword(s):  
Finite Number ◽  
Total Variance ◽  
Population Variance ◽  
Infinite Allele Model ◽  
Allele Model

scholarly journals Equilibrium Values of Measures of Population Subdivision for Stepwise Mutation Processes

Genetics ◽  
1996 ◽  
Vol 142 (4) ◽  
pp. 1357-1362
Author(s):  
François Rousset
Keyword(s):  
Population Structure ◽  
Population Subdivision ◽  
Identity By Descent ◽  
Infinite Allele Model ◽  
Coalescence Time ◽  
Stepwise Mutation ◽  
Expected Values ◽  
The Relationship ◽  
Allele Model ◽  
Coalescence Times

Abstract Expected values of Wright'sF-statistics are functions of probabilities of identity in state. These values may be quite different under an infinite allele model and under stepwise mutation processes such as those occurring at microsatellite loci. However, a relationship between the probability of identity in state in stepwise mutation models and the distribution of coalescence times can be deduced from the relationship between probabilities of identity by descent and the distribution of coalescence times. The values of FIS and FST can be computed using this property. Examination of the conditional probability of identity in state given some coalescence time and of the distribution of coalescence times are also useful for explaining the properties of FIS and FST at high mutation rate loci, as shown here in an island model of population structure.

scholarly journals Infinite allele model with varying mutation rate.

1976 ◽  
Vol 73 (11) ◽  
pp. 4164-4168 ◽  
Author(s):  
M. Nei ◽  
R. Chakraborty ◽  
P. A. Fuerst
Keyword(s):  
Mutation Rate ◽  
Infinite Allele Model ◽  
Allele Model

scholarly journals Microsatellite variation in honey bee (Apis mellifera L.) populations: hierarchical genetic structure and test of the infinite allele and stepwise mutation models.

Genetics ◽  
1995 ◽  
Vol 140 (2) ◽  
pp. 679-695 ◽  
Author(s):  
A Estoup ◽  
L Garnery ◽  
M Solignac ◽  
J M Cornuet
Keyword(s):  
Apis Mellifera ◽  
Phylogenetic Trees ◽  
Microsatellite Data ◽  
Effective Population ◽  
Average Heterozygosity ◽  
Microsatellite Variation ◽  
Infinite Allele Model ◽  
Population Sizes ◽  
Stepwise Mutation ◽  
Allele Model

Abstract Samples from nine populations belonging to three African (intermissa, scutellata and capensis) and four European (mellifera, ligustica, carnica and cecropia) Apis mellifera subspecies were scored for seven microsatellite loci. A large amount of genetic variation (between seven and 30 alleles per locus) was detected. Average heterozygosity and average number of alleles were significantly higher in African than in European subspecies, in agreement with larger effective population sizes in Africa. Microsatellite analyses confirmed that A. mellifera evolved in three distinct and deeply differentiated lineages previously detected by morphological and mitochondrial DNA studies. Dendrogram analysis of workers from a given population indicated that super-sisters cluster together when using a sufficient number of microsatellite data whereas half-sisters do not. An index of classification was derived to summarize the clustering of different taxonomic levels in large phylogenetic trees based on individual genotypes. Finally, individual population x loci data were used to test the adequacy of the two alternative mutation models, the infinite allele model (IAM) and the stepwise mutation models. The better fit overall of the IAM probably results from the majority of the microsatellites used including repeats of two or three different length motifs (compound microsatellites).

scholarly journals THE SAMPLING DISTRIBUTION OF LINKAGE DISEQUILIBRIUM

Genetics ◽  
1984 ◽  
Vol 108 (1) ◽  
pp. 257-274 ◽  
Author(s):  
G B Golding
Keyword(s):  
Linkage Disequilibrium ◽  
Population Size ◽  
Effective Population Size ◽  
Correlation Coefficient ◽  
Bimodal Distribution ◽  
Test Statistic ◽  
Effective Population ◽  
Chi Square ◽  
Infinite Allele Model ◽  
Allele Model

ABSTRACT The probabilities of obtaining particular samples of gametes with two completely linked loci are derived. It is assumed that the population consists of N diploid, randomly mating individuals, that each of the two loci mutate according to the infinite allele model at a rate µ and that the population is at equilibrium. When 4Nµ is small, the most probable samples of gametes are those that segregate only two alleles at either locus. The probabilities of various samples of gametes are discussed. The results show that most samples with completely linked loci have either a very small or a very large association between the alleles of each locus. This causes the distribution of linkage disequilibrium to be skewed and the distribution of the correlation coefficient to be bimodal. The correlation coefficient is commonly used as a test statistic with a chi square distribution and yet has a bimodal distribution when the loci are completely linked. Thus, such a test is not likely to be accurate unless the rate of recombination between the loci and/or the effective population size are sufficiently large enough so that the loci can be treated as unlinked.

Correct and incorrect estimation of within-day and between-day variation.

1986 ◽  
Vol 32 (9) ◽  
pp. 1734-1737 ◽  
Author(s):  
M J Bookbinder ◽  
K J Panosian
Keyword(s):  
Statistical Theory ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Total Population ◽  
Total Variance ◽  
Population Variance ◽  
Biased Estimators ◽  
The Impact ◽  
Estimation Of Variance

Abstract Between-day variance is an ambiguous term representing either total variance or pure between-day variance. In either case, it is often incorrectly calculated even though analysis of variance (ANOVA) and other excellent methods of estimation are available. We used statistical theory to predict the magnitude of error expected from using several intuitive approaches to estimation of variance components. We also evaluated the impact of estimating the total population variance instead of pure between-day variance and the impact of using biased estimators. We found that estimates of variance components could be systematically biased by several hundred percent. On the basis of these results, we make recommendations to remove these biases and to standardize precision estimates.

scholarly journals Molecular basis of polymorphism at the esterase-5B locus in Drosophila pseudoobscura.

Genetics ◽  
1995 ◽  
Vol 141 (1) ◽  
pp. 255-262 ◽  
Author(s):  
M Veuille ◽  
L M King
Keyword(s):  
Amino Acid ◽  
Sequence Variation ◽  
Random Distribution ◽  
Amino Acid Level ◽  
Drosophila Pseudoobscura ◽  
Nucleotide Polymorphisms ◽  
Nucleotide Level ◽  
Infinite Allele Model ◽  
Major Class ◽  
Allele Model

Abstract Sequence variation was studied in a 2.2-kb region encompassing the esterase-5B locus in Drosophila pseudoobscura from two California populations. In these populations, two common electrophoretic classes and many less frequent variants occur, and it was formerly shown by KEITH (1983) that allele frequencies differed from random distribution under an infinite allele model. Nucleotide polymorphisms were determined in 16 sequences representing 14 electrophoretic classes. There was no significant sequence differentiation between populations, and both synonymous and nonsynonymous polymorphisms are distributed homogeneously along the sequence. The data show that the two major electrophoretic classes are heterogeneous at the amino acid level with no diagnostic amino acid(s) distinguishing them. At the nucleotide level, members of one major class are more similar to members of other electrophoretic classes than they are to each other. It appears that random combinations of the neutral amino acid polymorphisms and other undefined physical properties of the proteins generate the different electrophoretic classes and maintain considerable variation at Est-5B.

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 Description and Power Analysis of Two Tests for Detecting Recent Population Bottlenecks From Allele Frequency Data

Genetics ◽  
1996 ◽  
Vol 144 (4) ◽  
pp. 2001-2014 ◽  
Author(s):  
Jean Marie Cornuet ◽  
Gordon Luikart
Keyword(s):  
Power Analysis ◽  
Statistical Tests ◽  
Population Sample ◽  
Type I ◽  
Population Bottlenecks ◽  
Infinite Allele Model ◽  
Bottleneck Detection ◽  
Size Number ◽  
Heterozygosity Excess ◽  
Allele Model

When a population experiences a reduction of its effective size, it generally develops a heterozygosity excess at selectively neutral loci, i.e., the heterozygosity computed from a sample of genes is larger than the heterozygosity expected from the number of alleles found in the sample if the population were at mutation drift equilibrium. The heterozygosity excess persists only a certain number of generations until a new equilibrium is established. Two statistical tests for detecting a heterozygosity excess are described. They require measurements of the number of alleles and heterozygosity at each of several loci from a population sample. The first test determines if the proportion of loci with heterozygosity excess is significantly larger than expected at equilibrium. The second test establishes if the average of standardized differences between observed and expected heterozygosities is significantly different from zero. Type I and II errors have been evaluated by computer simulations, varying sample size, number of loci, bottleneck size, time elapsed since the beginning of the bottleneck and level of variability of loci. These analyses show that the most useful markers for bottleneck detection are those evolving under the infinite allele model (IAM) and they provide guidelines for selecting sample sizes of individuals and loci. The usefulness of these tests for conservation biology is discussed.

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