Ancestral lines under recombination

  title={Ancestral lines under recombination},
  author={Ellen Baake and Michael Baake},
  journal={Probabilistic Structures in Evolution},
  • E. Baake, M. Baake
  • Published 20 February 2020
  • Biology
  • Probabilistic Structures in Evolution
Solving the recombination equation has been a long-standing challenge of \emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of \emph{stochastic} models of population genetics, into the deterministic setting. 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, we… 

Figures from this paper

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.
Natural selection and the advantage of recombination
It is shown that on average: 1) natural selection amplifies poorly-matched gene combinations and 2) creates time-averaged negative associations in the process.
Solving the migration–recombination equation from a genealogical point of view
The discrete-time migration–recombination equation is considered, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of large numbers setting, and the limiting and quasi-limiting behaviour of the Markov chain are investigated.
Selection, recombination, and the ancestral initiation graph.
The general labelled partitioning process in action: recombination, selection, mutation, and more
This work aims to unify and generalise a recursive construction of the solution of the selectionrecombination equation by introducing a new labelled partitioning process with general Markovian labels.


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
Single-crossover recombination and ancestral recombination trees
The ancestry of single individuals from the present population is traced back by a random tree, whose branching events correspond to the splitting of the sequence due to recombination, and the probabilities of the topologies of the ancestral trees are calculated.
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.
Partitioning, duality, and linkage disequilibria in the Moran model with recombination
It is proved that the partitioning process (backward in time) is dual to the Moran population process (forward in time), where the sampling function plays the role of the duality function.
The general recombination equation in continuous time and its solution
The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an
Asymptotic behavior of a Moran model with mutations, drift and recombination among multiple loci
The theoretical treatment of the Moran model of genetic drift with recombination and mutation is extended to the case of n loci and it is found that asymptotically the effects of recombination become indistinguishable, at least as characterized by the set of distributions the authors consider, from the effect of mutation and drift.
The Mathematical Theory of Selection, Recombination, and Mutation
The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics and applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail.
Single-Crossover Dynamics: Finite versus Infinite Populations
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated and the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.
Probability models for DNA sequence evolution
This small book has five chapters, the first four of which cover theoretical population genetics, and the author did an admirable job in providing a concise and up-to-date summary of modern molecular population genetics.