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… 
Solving the selection-recombination equation: Ancestral lines under selection and recombination
TLDR
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.
Solving the migration–recombination equation from a genealogical point of view
TLDR
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.
Fragmentation process, pruning poset for rooted forests, and M̈obius inversion
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
Chromosome Painting: how recombination mixes ancestral colors.
TLDR
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.
Chromosome painting: How recombination mixes ancestral colors
TLDR
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.
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
Natural selection promotes the evolution of recombination 2: during the process of natural selection*
TLDR
It is shown that natural selection acting on standing heritable variation always creates conditions favoring the evolution of recombination, in expectation, and that sex and recombination may have evolved more as a byproduct than as a catalyst of natural selection.
Ancestral lines under recombination
TLDR
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.
A probabilistic analysis of a continuous-time evolution in recombination
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
...
...

References

SHOWING 1-10 OF 53 REFERENCES
Asymptotic behavior of a Moran model with mutations, drift and recombination among multiple loci
TLDR
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.
TRACTABLE STOCHASTIC MODELS OF EVOLUTION FOR LOOSELY LINKED LOCI
TLDR
This paper derives two new stochastic population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates.
TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI.
TLDR
Two new multilocus population genetic models are derived, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates.
Approximating the coalescent with recombination
TLDR
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.
Single-crossover recombination and ancestral recombination trees
TLDR
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.
AN ASYMPTOTIC SAMPLING FORMULA FOR THE COALESCENT WITH RECOMBINATION.
  • P. Jenkins, Yun S. Song
  • Mathematics
    The annals of applied probability : an official journal of the Institute of Mathematical Statistics
  • 2010
TLDR
It is shown that it is possible to obtain useful closed-form results in the case the population-scaled recombination rate ρ is large but not necessarily infinite, and an asymptotic expansion of the two-locus sampling formula is considered in inverse powers of ρ and results are obtained.
Single-Crossover Dynamics: Finite versus Infinite Populations
TLDR
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.
Moment closure in a Moran model with recombination
TLDR
The Moran model is extended to include general recombination and mutation and shows that, in the case without resampling, the expectations of products of marginal processes defined via partitions of sites form a closed hierarchy, which is exhaustively described by a finite system of differential equations.
A random evolution related to a Fisher–Wright–Moran model with mutation, recombination and drift
The paper deals with a model of the genetic process of recombination, one of the basis mechanisms of generating genetic variability. Mathematically, the model can be represented by the so‐called
...
...