# Partitioning, duality, and linkage disequilibria in the Moran model with recombination

@article{Esser2016PartitioningDA, title={Partitioning, duality, and linkage disequilibria in the Moran model with recombination}, author={Mareike Esser and Sebastian Probst and Ellen Baake}, journal={Journal of Mathematical Biology}, year={2016}, volume={73}, pages={161-197} }

The multilocus Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. We investigate a marginal ancestral recombination process, where each site is sampled only in one individual and we do not make any scaling assumptions in the first place. Following the ancestry of these loci backward in time yields a partition-valued Markov process, which experiences splitting and coalescence. In the diffusion…

## 13 Citations

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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.

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The distribution of the length of the leftmost block of the partition of the chromosome that carries the same color as 0 converges to an exponential distribution and the geometry of this block can be described in terms of a Poisson point process with an explicit intensity measure.

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The distribution of the length of the leftmost block of the partition of the chromosome that carries the same color as 0 converges to an exponential distribution and the geometry of this block can be described in terms of a Poisson point process with an explicit intensity measure.

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The process of recombination in population genetics, in its
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- 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.

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- 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…

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