Nicole Althermeler (started October 2014)

Ancestral processes are driven by biological forces such as mutation, recombination, natural selection and random transmission of genetic material.
These forces are largely of random nature, thus statistical models support inferring and predicting genetic patterns created by them.
A collection of statistical models is offered by coalescent theory, which describe the demographic history of species.
The *n-coalescent* by Kingman (1982) marks a milestone in the field (Reference). It is a tree-structure that describes the history of a sample of individuals from one species. The corresponding mathematical process describes the neutral case, in which no selection is present. A graph structure that does take selection into account is the *ancestral selection graph* [@ASG]. Here, one individual and all its potential ancestors are described in one graph. This graph can be constructed by random poisson processes
and models not only different reproduction and mutation rates, but also the effects of selection.

Several important question arise in this field of research, for instance: Given an initial frequency *x* of a beneficial type in a population in the distance past, what is the probability that the ancestor of today's population had the beneficial type?

It is possible to analytically derive these probabilities for simpler, restricted cases (Reference). However, as studied scenarios become more complicated, analytical results become nearly impossible. Here, a solution are simulations of ancestral processes via Markov chains. These should result to close approximations of the underlying probabilities.

The project is devoted to the simulation and thorough understanding of random genealogies and ancestral lineages under various models of mutation and selection. Particular emphasis will be on the single ancestral line that leads back into the distant past and also connects with other species, thus building the bridge to phylogenetics, the evolutionary relationship of species. This may, for example, help to understand the large discrepancy between mutation rates estimated from species trees and those estimated from population samples.

*Supervisors: Ellen Baake (Bielefeld University), Cedric Chauve (Simon Fraser University), Leonid Chindelevitch (Simon Fraser University)*

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