Recent Results for the Stepping Stone Model

1987 ◽  
pp. 73-83 ◽  
Author(s):  
J. Theodore Cox ◽  
David Griffeath
Keyword(s):  
Stepping Stone ◽  
Stepping Stone Model

scholarly journals Geographical variation in a quantitative character.

Genetics ◽  
1994 ◽  
Vol 136 (1) ◽  
pp. 361-381
Author(s):  
T Nagylaki
Keyword(s):  
Local Population ◽  
Weighted Average ◽  
Two Dimensions ◽  
Quantitative Character ◽  
Stabilizing Selection ◽  
Convergence To Equilibrium ◽  
Stepping Stone ◽  
Evolutionary Forces ◽  
Local Averages ◽  
Stepping Stone Model

Abstract A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.

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.

The expected probabilities of identity for the circular stepping-stone model

1986 ◽  
Vol 28 (6) ◽  
pp. 1048-1050
Author(s):  
Curtis Strobeck
Keyword(s):  
Population Ecology ◽  
Identity By Descent ◽  
Model Population ◽  
Stepping Stone ◽  
Expected Values ◽  
Stepping Stone Model

The expected values of the probabilities of identity by descent are derived for the circular stepping-stone model. The results are more easily interpreted than those derived previously.Key words: model, population, ecology.

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 Reevaluating human colonization of the Caribbean using chronometric hygiene and Bayesian modeling

2019 ◽  
Vol 5 (12) ◽  
pp. eaar7806 ◽  
Author(s):  
Matthew F. Napolitano ◽  
Robert J. DiNapoli ◽  
Jessica H. Stone ◽  
Maureece J. Levin ◽  
Nicholas P. Jew ◽  
...  
Keyword(s):  
South America ◽  
Bayesian Modeling ◽  
Human Settlement ◽  
Stepping Stone ◽  
Critical Information ◽  
Initial Settlement ◽  
Human Colonization ◽  
The Caribbean ◽  
Stepping Stone Model

Human settlement of the Caribbean represents the only example in the Americas of peoples colonizing islands that were not visible from surrounding mainland areas or other islands. Unfortunately, many interpretive models have relied on radiocarbon determinations that do not meet standard criteria for reporting because they lack critical information or sufficient provenience, often leading to specious interpretations. We have collated 2484 radiocarbon determinations, assigned them to classes based on chronometric hygiene criteria, and constructed Bayesian colonization models of the acceptable determinations to examine patterns of initial settlement. Colonization estimates for 26 islands indicate that (i) the region was settled in two major population dispersals that likely originated from South America; (ii) colonists reached islands in the northern Antilles before the southern islands; and (iii) the results support the southward route hypothesis and refute the “stepping-stone model.”

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.

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.

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