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

  title={Common ancestor type distribution: a Moran model and its deterministic limit},
  author={Fernando Cordero},
  journal={Stochastic Processes and their Applications},
  • F. Cordero
  • Published 25 August 2015
  • Mathematics
  • Stochastic Processes and their Applications
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
A probabilistic view on the deterministic mutation–selection equation: dynamics, equilibria, and ancestry via individual lines of descent
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.
Moran model and Wright-Fisher diffusion with selection and mutation in a one-sided random environment
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
On the stationary distribution of the block counting process for population models with mutation and selection
Solving the selection-recombination equation: Ancestral lines under selection and recombination
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 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
Haldane’s formula in Cannings models: the case of moderately weak selection
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
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
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.


Ancestral processes with selection: Branching and Moran models
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
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
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.
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
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
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.