# Lines of Descent Under Selection

@article{Baake2017LinesOD, title={Lines of Descent Under Selection}, author={Ellen Baake and A. Wakolbinger}, journal={Journal of Statistical Physics}, year={2017}, volume={172}, pages={156-174} }

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 ancestral selection graph and the pruned lookdown ancestral selection graph. The killed ancestral selection graph gives a representation of the type of a random individual from a stationary population, based upon the individual’s potential ancestry back until the mutations that define the individual’s type…

## 8 Citations

Lines of descent in a Moran model with frequency-dependent selection and mutation

- Mathematics
- 2020

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…

On the stationary distribution of the block counting process for population models with mutation and selection

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

Moran model and Wright-Fisher diffusion with selection and mutation in a one-sided random environment

- Mathematics
- 2019

Consider a two-type Moran population of size $N$ subject to selection and mutation, which is immersed in a varying environment. The population is susceptible to exceptional changes in the…

Microbial populations under selection

- Biology
- 2020

A model of a host-pathogen system where the population of pathogenes experiences balancing selection, migration, and mutation, as motivated by observations of the genetic diversity of HCMV (the human cytomegalovirus) across hosts is described.

Solving the selection-recombination equation: Ancestral lines under selection and recombination

- Biology
- 2020

This contribution uses a probabilistic, genealogical approach for the case of an \emph{arbitrary} number of neutral sites that are linked to one selected site to obtain a stochastic representation of the deterministic solution, along with the Markov semigroup in closed form.

Lines of descent in the deterministic mutation-selection model with pairwise interaction

- Mathematics
- 2018

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

- BiologyProbabilistic Structures in Evolution
- 2020

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.

Wright-Fisher processes with selection and mutation in a random environment

- Mathematics
- 2019

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…

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