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 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 A MIXED MODEL OF MUTATION FOR ELECTROPHORETIC IDENTITY OF PROTEINS WITHIN AND BETWEEN POPULATIONS

Genetics ◽  
1976 ◽  
Vol 83 (2) ◽  
pp. 423-432
Author(s):  
Wen-Hsiung Li
Keyword(s):  
Genetic Distance ◽  
Mixed Model ◽  
Present Model ◽  
Natural Populations ◽  
The Other ◽  
Effective Number ◽  
Infinite Allele Model ◽  
Stepwise Mutation ◽  
Allele Model ◽  
Nei's Genetic Distance

ABSTRACT A model which is a mixture of the model of infinite alleles and the Ohta-Kimura model of stepwise mutation has been proposed for the study of eletcrophoretic variants in natural populations. Mutations which alter the mobility of a protein are divided into two classes: stepwise mutations and nonstepwise mutations. It is assumed that stepwise mutations follow the Ohta-Kimura model while nonstepwise mutations follow the infinite allele model. It is then shown that even if the proportion of nonstepwise mutations is only 5%, with the other 95% stepwise mutations, the effective number of alleles given by the present model is considerably larger than that given by the Ohta-Kimura model of stepwise mutation. The result has also been applied to study Nei's genetic distance.

Signatures of Population Expansion in Microsatellite Repeat Data

Genetics ◽  
1998 ◽  
Vol 148 (4) ◽  
pp. 1921-1930 ◽  
Author(s):  
Marek Kimmel ◽  
Ranajit Chakraborty ◽  
J Patrick King ◽  
Michael Bamshad ◽  
W Scott Watkins ◽  
...  
Keyword(s):  
Population Expansion ◽  
Logistic Growth ◽  
Racial Groups ◽  
Equilibrium Conditions ◽  
Allele Size ◽  
Infinite Allele Model ◽  
Moran Model ◽  
Tetranucleotide Repeats ◽  
Stepwise Mutation ◽  
Allele Model

Abstract To examine the signature of population expansion on genetic variability at microsatellite loci, we consider a population that evolves according to the time-continuous Moran model, with growing population size and mutations that follow a general asymmetric stepwise mutation model. We present calculations of expected allele-size variance and homozygosity at a locus in such a model for several variants of growth, including stepwise, exponential, and logistic growth. These calculations in particular prove that population bottleneck followed by growth in size causes an imbalance between allele size variance and heterozygosity, characterized by the variance being transiently higher than expected under equilibrium conditions. This effect is, in a sense, analogous to that demonstrated before for the infinite allele model, where the number of alleles transiently increases after a stepwise growth of population. We analyze a set of data on tetranucleotide repeats that reveals the imbalance expected under the assumption of bottleneck followed by population growth in two out of three major racial groups. The imbalance is strongest in Asians, intermediate in Europeans, and absent in Africans. This finding is consistent with previous findings by others concerning the population expansion of modern humans, with the bottleneck event being most ancient in Africans, most recent in Asians, and intermediate in Europeans. Nevertheless, the imbalance index alone cannot reliably estimate the time of initiation of population expansion.

scholarly journals Estimating the Total Number of Alleles Using a Sample Coverage Method

Genetics ◽  
2001 ◽  
Vol 159 (3) ◽  
pp. 1365-1373 ◽  
Author(s):  
Shu-Pang Huang ◽  
B S Weir
Keyword(s):  
Recurrent Mutation ◽  
Allele Frequencies ◽  
Simulation Studies ◽  
Infinite Allele Model ◽  
Mutation Model ◽  
True Number ◽  
Stepwise Mutation ◽  
Microsatellite Alleles ◽  
Allele Model

Abstract Previously reported methods for estimating the number of different alleles at a single locus in a population have not described a useful general result. Using the number of alleles observed in a sample gives an underestimate for the true number of alleles. The similar problem of estimating the number of species in a population was first investigated in 1943. In this article we use the sample coverage method proposed by Chao and Lee in 1992 to estimate the number of alleles in a population when there are unequal allele frequencies. Simulation studies under the recurrent mutation model show that, for reasonable sample sizes, a significantly better estimate of the true number can be obtained than that using only the observed alleles. Results under the stepwise mutation model and infinite-allele model are presented. Possible applications include improving the characterization of the prior distribution for the allele frequencies, adjusting the estimates of genetic diversity, and estimating the range of microsatellite alleles.

scholarly journals Variance and limiting distribution of coalescence times in a diploid model of a consanguineous population

2020 ◽  
Author(s):  
Alissa L. Severson ◽  
Shai Carmi ◽  
Noah A. Rosenberg
Keyword(s):  
Population Size ◽  
Kinship Coefficient ◽  
Demographic Parameters ◽  
Mating Pair ◽  
Runs Of Homozygosity ◽  
Identity By Descent ◽  
Coalescence Time ◽  
Diploid Populations ◽  
Diploid Model ◽  
Coalescence Times

AbstractRecent modeling studies interested in runs of homozygosity (ROH) and identity by descent (IBD) have sought to connect these properties of genomic sharing to pairwise coalescence times. Here, we examine a variety of features of pairwise coalescence times in models that consider consanguinity. In particular, we extend a recent diploid analysis of mean coalescence times for lineage pairs within and between individuals in a consanguineous population to derive the variance of coalescence times, studying its dependence on the frequency of consanguinity and the kinship coefficient of consanguineous relationships. We also introduce a separation-of-time-scales approach that treats consanguinity models analogously to mathematically similar phenomena such as partial selfing, using this approach to obtain coalescence-time distributions. This approach shows that the consanguinity model behaves similarly to a standard coalescent, scaling population size by a factor 1 − 3c, where c represents the kinship coefficient of a randomly chosen mating pair. It provides the explanation for an earlier result describing mean coalescence time in the consanguinity model in terms of c. The results extend the potential to make predictions about ROH and IBD in relation to demographic parameters of diploid populations.

scholarly journals A Genealogical Interpretation of Linkage Disequilibrium

Genetics ◽  
2002 ◽  
Vol 162 (2) ◽  
pp. 987-991 ◽  
Author(s):  
Gilean A T McVean
Keyword(s):  
Monte Carlo Simulation ◽  
Population Structure ◽  
Linkage Disequilibrium ◽  
Population Bottlenecks ◽  
Neutral Model ◽  
Demographic Models ◽  
Degree Of Association ◽  
Different Parts ◽  
Direct Correspondence ◽  
Coalescence Times

Abstract The degree of association between alleles at different loci, or linkage disequilibrium, is widely used to infer details of evolutionary processes. Here I explore how associations between alleles relate to properties of the underlying genealogy of sequences. Under the neutral, infinite-sites assumption I show that there is a direct correspondence between the covariance in coalescence times at different parts of the genome and the degree of linkage disequilibrium. These covariances can be calculated exactly under the standard neutral model and by Monte Carlo simulation under different demographic models. I show that the effects of population growth, population bottlenecks, and population structure on linkage disequilibrium can be described through their effects on the covariance in coalescence times.

scholarly journals Average Number of Nucleotide Differences in a Sample From a Single Subpopulation: A Test for Population Subdivision

Genetics ◽  
1987 ◽  
Vol 117 (1) ◽  
pp. 149-153
Author(s):  
Curtis Strobeck
Keyword(s):  
Monte Carlo Simulation ◽  
Population Structure ◽  
Random Mating ◽  
Population Subdivision ◽  
Expected Number ◽  
Migration Rates ◽  
Mating Population ◽  
Unbiased Estimates ◽  
Increasing Function ◽  
Stepping Stone Model

ABSTRACT Unbiased estimates of θ = 4Nµ in a random mating population can be based on either the number of alleles or the average number of nucleotide differences in a sample. However, if there is population structure and the sample is drawn from a single subpopulation, these two estimates of θ behave differently. The expected number of alleles in a sample is an increasing function of the migration rates, whereas the expected average number of nucleotide differences is shown to be independent of the migration rates and equal to 4N  Tµ for a general model of population structure which includes both the island model and the circular stepping-stone model. This contrast in the behavior of these two estimates of θ is used as the basis of a test for population subdivision. Using a Monte-Carlo simulation developed so that independent samples from a single subpopulation could be obtained quickly, this test is shown to be a useful method to determine if there is population subdivision.

A Phenomenological Theory of Socioeconomic Systems with Spatial Interactions

1982 ◽  
Vol 14 (7) ◽  
pp. 869-888 ◽  
Author(s):  
P F Lesse
Keyword(s):  
Lagrange Multipliers ◽  
Average Cost ◽  
Phenomenological Theory ◽  
Traffic Flows ◽  
Spatial Interactions ◽  
Practical Application ◽  
Density Distributions ◽  
Expected Values ◽  
Probability Density Distributions ◽  
The Relationship

This paper deals with a class of models which describe spatial interactions and are based on Jaynes's principle. The variables entering these models can be partitioned in four groups: (a) probability density distributions (for example, relative traffic flows), (b) expected values (average cost of travel), (c) their duals (Lagrange multipliers, traffic impedance coefficient), and (d) operators transforming probabilities into expected values. The paper presents several dual formulations replacing the problem of maximizing entropy in terms of the group of variables (a) by equivalent extreme problems involving groups (b)-(d). These problems form the basis of a phenomenological theory. The theory makes it possible to derive useful relationships among groups (b) and (c). There are two topics discussed: (1) practical application of the theory (with examples), (2) the relationship between socioeconomic modelling and statistical mechanics.

scholarly journals Selection, Load and Inbreeding Depression in a Large Metapopulation

Genetics ◽  
2002 ◽  
Vol 160 (3) ◽  
pp. 1191-1202 ◽  
Author(s):  
Michael C Whitlock
Keyword(s):  
Population Structure ◽  
Inbreeding Depression ◽  
Population Subdivision ◽  
Response To Selection ◽  
Mutation Load ◽  
Deleterious Alleles ◽  
Subdivided Population ◽  
Soft Selection ◽  
Mean Fitness ◽  
The Mean

Abstract The subdivision of a species into local populations causes its response to selection to change, even if selection is uniform across space. Population structure increases the frequency of homozygotes and therefore makes selection on homozygous effects more effective. However, population subdivision can increase the probability of competition among relatives, which may reduce the efficacy of selection. As a result, the response to selection can be either increased or decreased in a subdivided population relative to an undivided one, depending on the dominance coefficient FST and whether selection is hard or soft. Realistic levels of population structure tend to reduce the mean frequency of deleterious alleles. The mutation load tends to be decreased in a subdivided population for recessive alleles, as does the expected inbreeding depression. The magnitude of the effects of population subdivision tends to be greatest in species with hard selection rather than soft selection. Population structure can play an important role in determining the mean fitness of populations at equilibrium between mutation and selection.

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