Convergence to genetically uniform state in stepping stone models of population genetics

1980 ◽  
Vol 10 (3) ◽  
pp. 281-294 ◽  
Author(s):  
Morihiro Notohara ◽  
Tokuzo Shiga
Keyword(s):  
Population Genetics ◽  
Stepping Stone ◽  
Uniform State ◽  
Stepping Stone Models

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.

A survey of stepping-stone models in population dynamics

1986 ◽  
Vol 18 (03) ◽  
pp. 581-627 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Population Dynamics ◽  
Final Section ◽  
Main Body ◽  
Nearest Neighbour ◽  
General Applicability ◽  
Transfer Rates ◽  
Predator Prey ◽  
Stepping Stone ◽  
Vector Process ◽  
Stepping Stone Models

A survey is presented of stochastic and deterministic developments in the study of the effects of nearest-neighbour ‘migration’ between spatially separated ‘colonies’. Such processes are of general applicability, and are relevant to any vector processX(t) = (X1(t), · ··,XN(t)) in which the arrival, departure and transfer rates for the states {X(t) = n} may be written in the formαi(ni), βi(ni) andγij(ni,nj), respectively, wheren =(n1,· ··, nN). Whilst the main body of results are described in terms of birth-death, genetic and epidemic situations, the final section examines within colony interaction in the context of spatial predator-prey processes.

Cytonuclear Theory for Haplodiploid Species and X-Linked Genes. II. Stepping-Stone Models of Gene Flow and Application to a Fire Ant Hybrid Zone

Evolution ◽  
1998 ◽  
Vol 52 (5) ◽  
pp. 1423 ◽  
Author(s):  
Michael A. D. Goodisman ◽  
D. DeWayne Shoemaker ◽  
Marjorie A. Asmussen
Keyword(s):  
Gene Flow ◽  
Hybrid Zone ◽  
Fire Ant ◽  
Stepping Stone ◽  
Stepping Stone Models

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.

scholarly journals Ergodic properties of the equilibrium measure of the stepping stone model in population genetics

1981 ◽  
Vol 83 ◽  
pp. 37-51 ◽  
Author(s):  
Seiichi Itatsu
Keyword(s):  
Population Genetics ◽  
Equilibrium Measure ◽  
Stepping Stone ◽  
Ergodic Properties ◽  
Stepping Stone Model

We shall present in this paper some ergodic properties of the stepping stone model. The model has been proposed by M. Kimura [2], to describe the evolution of a genetical population with mating and geographical structures. It has been investigated and developed by M. Kimura and G. H. Weiss [3], G. H. Weiss and M. Kimura [6], W. Fleming and C.-H. Su [1], S. Sawyer [5], and others.

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