P2-11 Stochastic processes and applications in ecology and genetics

PhD Student: Tibor Mach
Thesis Committee: Anja Sturm, Tatyana Krivobokova, Henner Simianer

Currently, my work consists of generalizing some of the results from a paper 'Coalescence in a random background' by Barton et al. The authors consider a fixed population size model with a single genetic locus with two alleles and an attached neutral locus, i.e. one with no influence on the reproduction chances.

The aim of the project is to study the genealogy of a sample at the neutral locus if we allow for mutation and recombination. For this purpose, a backwards in time process (p,n1,n2)t is derived, where p is the proportion of the first allele at the selective locus in the whole population and n1 and n2 are numbers of individuals from the sample at the neutral locus associated with the first and the second allele at the selective locus, respectively. Afterwards, a diffusion limit of that process is derived - a process which is obtained by fast forwarding time by the factor of population size N, rescaling the mutation, recombination and selection rates accordingly and sending N to infinity. Such a process is then useful in applications as a good approximation if we have a large population and since it is generally easier to work with the distribution of that process, it can be used for statistical inference.

There are possible extensions of this model such as allowing the selection to be in a sense time dependent, which might be eventually developed during the project as well.

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