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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References

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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.
Mutation, selection, and ancestry in branching models: a variational approach
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Ancestral Processes with Selection
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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.
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TLDR
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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,
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  • Biology
    Theoretical population biology
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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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