Stepping stone models of finite length

1970 ◽  
Vol 2 (02) ◽  
pp. 229-258 ◽  
Author(s):  
Takeo Maruyama
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Finite Length ◽  
Correlation Coefficients ◽  
Gene Frequencies ◽  
Explicit Formulas ◽  
Stepping Stone ◽  
Monte Carlo Experiments ◽  
Stepping Stone Models ◽  
Stepping Stone Model

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

Stepping stone models of finite length

1970 ◽  
Vol 2 (2) ◽  
pp. 229-258 ◽  
Author(s):  
Takeo Maruyama
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Finite Length ◽  
Correlation Coefficients ◽  
Gene Frequencies ◽  
Explicit Formulas ◽  
Stepping Stone ◽  
Monte Carlo Experiments ◽  
Stepping Stone Models ◽  
Stepping Stone Model

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

scholarly journals Isolation-By-Distance-and-Time in a stepping-stone model

2015 ◽  
Author(s):  
Nicolas Duforet-Frebourg ◽  
Montgomery Slatkin
Keyword(s):  
Principal Component Analysis ◽  
Population Genetics ◽  
Population Structure ◽  
Isolation By Distance ◽  
Principal Component ◽  
Joint Effect ◽  
Stepping Stone ◽  
Ancient Times ◽  
The Impact ◽  
Stepping Stone Model

With the great advances in ancient DNA extraction, population genetics data are now made of geographically separated individuals from both present and ancient times. However, population genetics theory about the joint effect of space and time has not been thoroughly studied. Based on the classical stepping--stone model, we develop the theory of Isolation by Distance and Time. We derive the correlation of allele frequencies between demes in the case where ancient samples are present in the data, and investigate the impact of edge effects with forward-in-time simulations. We also derive results about coalescent times in circular/toroidal models. As one of the most common way to investigate population structure is to apply principal component analysis, we evaluate the impact of this theory on plots of principal components. Our results demonstrate that time between samples is a non-negligible factor that requires new attention in population genetics.

GENETIC DRIFT IN CLINES WHICH ARE MAINTAINED BY MIGRATION AND NATURAL SELECTION

Genetics ◽  
1975 ◽  
Vol 81 (1) ◽  
pp. 191-207 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Genetic Drift ◽  
Gene Frequency ◽  
Local Behavior ◽  
Lateral Variation ◽  
Gene Frequencies ◽  
Stepping Stone ◽  
Expected Values ◽  
Pathological Behavior ◽  
Expected Position ◽  
Stepping Stone Model

ABSTRACT Genetic drift will cause a migration-selection cline to wobble about its expected position. A rough linear approximation is developed, valid when local populations are large. This is used to calculate effects of genetic drift on clines in a stepping-stone model with abrupt and with gradual changes of selection coefficients at a single haploid locus. Among the quantities calculated are measures of slope, standardized variation of gene frequencies around their expected values, and correlation among neighboring populations with respect to deviations from the expected gene frequencies. These quantities appear to be primarily functions of Ns and Nm for a given pattern of selection. Computer simulation gives rough confirmation of these results. Standardized variances of gene frequencies and correlation of neighbors differ along the cline in the case of smooth changes in selection. In no case is pathological behavior of gene frequency deviations found near the boundaries of selective regions. Local behavior of gene frequencies of nearby colonies is approximately predicted by a simple adaptation of the stepping-stone theory of Kimura and Weiss. Approximate measures of the lateral variation of the midpoint of a cline and the probability of non-monotonicity are also calculated and discussed.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

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.

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