# Single-crossover recombination and ancestral recombination trees

@article{Baake2014SinglecrossoverRA,
title={Single-crossover recombination and ancestral recombination trees},
author={Ellen Baake and Ute Wangenheim},
journal={Journal of Mathematical Biology},
year={2014},
volume={68},
pages={1371-1402}
}
• Published 5 June 2012
• Mathematics
• Journal of Mathematical Biology
We consider the Wright–Fisher model for a population of $$N$$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the $$N \rightarrow \infty$$ limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help…
11 Citations
The Moran model of population genetics : case studies with recombination and selection
The Moran model is a widespread model for a finite population in the field of population genetics. In the first part of the thesis, we consider a Moran model with recombination. Models of
Solving the migration–recombination equation from a genealogical point of view
• Mathematics
Journal of mathematical biology
• 2021
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.
Partitioning, duality, and linkage disequilibria in the Moran model with recombination
• Mathematics
Journal of mathematical biology
• 2016
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.
Fragmentation process, pruning poset for rooted forests, and M̈obius inversion
• Mathematics, Computer Science
• 2017
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population
A probabilistic analysis of a continuous-time evolution in recombination
• Mathematics
• 2018
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its
Ancestral lines under recombination
• Biology
Probabilistic 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.
The general recombination equation in continuous time and its solution
• Mathematics
• 2015
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
The geometry of recombination
• Biology
Information Geometry
• 2019
This work develops a framework in the context of population genetics and uses this to interpret the famous Ohta–Kimura formula, which is simply a Riemannian manifold of constant positive curvature.

## References

SHOWING 1-10 OF 94 REFERENCES
Deterministic and stochastic aspects of single-crossover recombination
A closed solution of the deterministic continuous-time system, for the important special case of single crossovers, is presented and an analogous deterministic discrete-time dynamics is provided, in terms of its generalised eigenvalues and a simple recursion for the corresponding coefficients.
Single-Crossover Dynamics: Finite versus Infinite Populations
• Mathematics
Bulletin of mathematical biology
• 2008
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.
Single-crossover recombination in discrete time
• Mathematics
Journal of mathematical biology
• 2010
This work considers a particular case of recombination in discrete time, allowing only for single crossovers, and transforms the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation.
Mutation and recombination with tight linkage
• E. Baake
• Mathematics
Journal of mathematical biology
• 2001
Abstract. An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every
Approximating the coalescent with recombination
• Biology
Philosophical Transactions of the Royal Society B: Biological Sciences
• 2005
This work introduces a simplification of the coalescent process in which coalescence between lineages with no overlapping ancestral material is banned and the resulting process has a simple Markovian structure when generating genealogies sequentially along a sequence, yet has very similar properties to the full model.
Ancestral Inference from Samples of DNA Sequences with Recombination
• Biology, Mathematics
J. Comput. Biol.
• 1996
Ancestral inference procedures are discussed for estimating recombination and mutation rates; estimating the times to the most recent common ancestors along the sequences; estimating ages of mutations; and estimating the number of recombination events in the ancestry of the sample.