The Common Ancestor Process Revisited

@article{Kluth2013TheCA,
  title={The Common Ancestor Process Revisited},
  author={Sandra Kluth and Thiemo Hustedt and Ellen Baake},
  journal={Bulletin of Mathematical Biology},
  year={2013},
  volume={75},
  pages={2003-2027}
}
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Probab. 39 (2002), 38–54) and Taylor (Electron. J. Probab. 12 (2007), 808–847), we characterise this distribution via the fixation probability of the offspring of all individuals of favourable type (regardless of the offspring’s types). We concentrate on a finite population and stay with the… 
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The Moran model with selection (and mutation) : fixation probabilities, ancestral lines, and an alternative particle representation
This thesis is devoted to a classical model of population genetics, namely, the Moran model in continuous time with two allelic types, (fertility) selection, and mutation. We concentrate on the…
The historical Moran model
TLDR
The limit theorem has two applications and it is obtained that the conditioned genealogical distance of two individuals given the types of the two individuals is distributed as a certain stopping time of a further functional of the backward process which is a new approach towards a proof that genealogyical distances are stochastically smaller under selection.
The Moran model with selection: fixation probabilities, ancestral lines, and an alternative particle representation.
Common ancestor type distribution: a Moran model and its deterministic limit
Lines of descent in a Moran model with frequency-dependent selection and mutation
We consider the two-type Moran model with frequency-dependent selection and two-way mutation, where selection follows either the nonlinear dominance or the fittest-type-wins scheme, which will turn…
The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation
TLDR
A strong pathwise Siegmund dual is identified of the ancestor in a two-type Wright-Fisher population with mutation and selection, conditional on the overall type frequency in the old population, and the equilibrium tail probabilities of $L$ are characterised in terms of hitting probabilities of the dual process.
On the stationary distribution of the block counting process for population models with mutation and selection
Dualities and genealogies in stochastic population models
In the thesis, population processes are studied in two different settings. In Part I, which arose in collaboration with Dr. Jan Swart, a so-called cooperative branching process is considered. We…
Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution.

References

SHOWING 1-10 OF 26 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.
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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We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r . If r…
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TLDR
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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.
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