The Evolving Moran Genealogy.

  title={The Evolving Moran Genealogy.},
  author={Johannes Wirtz and Thomas Wiehe},
  journal={Theoretical population biology},
4 Citations
The Moran Genealogy Process
We give a novel representation of the Moran Genealogy Process, a continuous-time Markov process on the space of size-$n$ genealogies with the demography of the classical Moran process. We derive the
Counting, grafting and evolving binary trees
Binary trees are fundamental objects in models of evolutionary biology and population genetics and they present the object of choice when studying tree structure in the framework of evolving genealogies.
Fine human genetic map based on UK10K data set
This study used a refined artificial intelligence approach to estimate the recombination rate of the human genome using the UK10K human genomic dataset and its three subsets with 200, 400 and 2,000 genomic sequences under the Out-of-Africa demography model, and obtained an accurate human genetic map.
Fine human genetic map based on UK10K data set.
This study used a refined machine learning approach to estimate the recombination rate of the human genome using the UK10K human genomic dataset and its three subsets with 200, 400 and 2,000 genomic sequences, and obtained an accurate human genetic map.


On the genealogy of nested subsamples from a haploid population
For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion
Coalescent Theory and Yule Trees in time and space
The two main focuses of this thesis are the description of the processes that shape the genealogy in time and in space, making use of the relation between Coalescent and Yule Process and the results are of mainly theoretical nature.
Genealogical processes for Fleming-Viot models with selection and recombination
Infinite population genetic models with general type space incorporating mutation, selection and recombination are considered. The Fleming– Viot measure-valued diffusion is represented in terms of a
On the Two Oldest Families for the Wright-Fisher Process
We extend some of the results of Pfaffelhuber and Wakolbinger on the process of the most recent common ancestors in evolving coalescent by taking into account the size of one of the two oldest
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.
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.
Tree-valued resampling dynamics Martingale problems and applications
The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate
Topology of genealogical trees - theory and application
A measure of topological linkage disequilibrium, which is based on clustering individuals with respect to their position in the genealogy rather than clustering alleles and haplotypes, is presented and its application to the beforehand processed human data is demonstrated.