Common ancestor type distribution: a Moran model and its deterministic limit

@article{Cordero2015CommonAT,
  title={Common ancestor type distribution: a Moran model and its deterministic limit},
  author={Fernando Cordero},
  journal={Stochastic Processes and their Applications},
  year={2015},
  volume={127},
  pages={590-621}
}
  • F. Cordero
  • Published 25 August 2015
  • Mathematics
  • Stochastic Processes and their Applications
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11 Citations
Highly Influential Citations
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Background Citations
5
Methods Citations
8

11 Citations

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Lines of Descent Under Selection
We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed…
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We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in…
Wright-Fisher processes with selection and mutation in a random environment
Consider a bi-allelic population subject to neutral reproduction, genic selection and mutation, which is susceptible to exceptional changes in the environment. Neutral reproductions are modeled as in…
Lines of descent in the deterministic mutation-selection model with pairwise interaction
TLDR
With the help of the stratified ancestral selection graph, the mutation-selection differential equation with pairwise interaction is considered and results about the ancestral type distribution in the case of unidirectional mutation are obtained.
Ancestral lines under recombination
TLDR
With the help of an ancestral partitioning process, which is obtained by letting population size tend to infinity (without rescaling parameters or time) in an ancestral recombination graph, the solution to the recombination equation is obtained in a transparent form.
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References

SHOWING 1-10 OF 26 REFERENCES
Ancestral processes with selection: Branching and Moran models
TLDR
Analytical results of Fearnhead (2002) are used to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution inforward time.
Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution.
Mutation, selection, and ancestry in branching models: a variational approach
TLDR
The quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites is used, and the fitness of letter compositions is worked out explicitly.
Ancestral Processes with Selection
TLDR
The main goal is to analyze the ancestral selection graph and to compare it to Kingman's coalescent process; it is found that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case.
The genealogy of samples in models with selection.
TLDR
It is found that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case, and this is supported by rigorous results.
The deterministic limit of the Moran model: a uniform central limit theorem
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity,…
The ancestral selection graph under strong directional selection.
Duality, ancestral and diffusion processes in models with selection.
  • S. Mano
  • Biology
    Theoretical population biology
  • 2009
The Common Ancestor Process Revisited
TLDR
This work considers the Moran model in continuous time with two types, mutation, and selection, and characterises the ancestral line and its stationary type distribution via the fixation probability of the offspring of all individuals of favourable type.
The Common Ancestor Process for a Wright-Fisher Diffusion
TLDR
This work describes the process of substitutions to the common ancestor of each population using the structured coalescent process introduced by Kaplan et al. (1988), and shows that the theory can be formally extended to diffusion models with more than two genetic backgrounds, but that it leads to systems of singular partial differential equations which it is unable to solve.
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