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 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.
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 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…
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…
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.
References
SHOWING 1-10 OF 71 REFERENCES
A probabilistic view on the deterministic mutation–selection equation: dynamics, equilibria, and ancestry via individual lines of descent
- MathematicsJournal of mathematical biology
- 2018
The deterministic haploid mutation–selection equation with two types is reconsidered and ancestral structures inherent in this deterministic model are established, including the pruned lookdown ancestral selection graph and an alternative characterisation in terms of a piecewise-deterministic Markov process.
Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution.
- MathematicsTheoretical population biology
- 2015
Ancestral Processes with Selection
- MathematicsTheoretical population biology
- 1997
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.
Mutation, selection, and ancestry in branching models: a variational approach
- BiologyJournal of mathematical biology
- 2007
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.
The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation
- Mathematics
- 2016
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.
The Common Ancestor Process for a Wright-Fisher Diffusion
- Biology
- 2007
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.
Mutation-selection balance: ancestry, load, and maximum principle.
- BiologyTheoretical population biology
- 2002
The results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds) and lead to a clarification of concepts, as well as criteria for the existence of error thresholds.
A maximum principle for the mutation-selection equilibrium of nucleotide sequences
- BiologyBulletin of mathematical biology
- 2004
The common ancestor at a nonneutral locus
- Biology, MathematicsJournal of Applied Probability
- 2002
The expected Fitness of any ancestor (including the most recent common ancestor of any sample) is shown to be greater than the expected fitness of a randomly chosen gene from the population.