Computational and mathematical methods for population genetics analysis of multi-locus data under selection and strong recombination

• Applicant: Dr. Matthias Steinrücken
• Subject Area: Mathematics
• Term: from 2010 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 191584514

Markov diffusion processes are used to model the dynamics of genetic information in a population. The neutral one-locus case has been extended to include selection and recombination. This is complemented by coalescent processes describing the ancestry of individuals. The probability of sampling a certain genetic configuration from a population can be estimated via importance sampling on coalescent histories. A central object in this approach is the conditional sampling distribution of an additionally sampled individual, having already observed a given genetic configuration.I will apply the conditional sampling distribution introduced by Paul and Song (2010) to impute missing sequence data and to infer local ancestry in admixed populations using established algorithms that update individual genetic information based on known data for related individuals using the conditional sampling distribution. I will also develop an approach to impute missing data via importance sampling on incomplete histories.Since it has been argued that detection of selection has to account for epistatic interaction between loci to explain the inheritance of certain diseases, I will investigate the influence of epistatic and epistasis-free selection on statistical measures of correlation among loci to develop a test for epistasis. To foster this, I will also introduce epistatic selection into the asymptotic expansion of the sampling probability given by Jenkins and Song (2010).Genome-wide association studies detecting genetic markers that influence diseases rely on the linkage structure of genetic sequences. Linkage disequilibrium plays an important role and understanding its dynamics is essential. The hosts postdoc has shown that for large recombination probabilities the linkage disequilibrium can be approximated by an amenable diffusion process. I want to derive a process that approximates the ancestry for large recombination probabilities and analyse its duality to this diffusion.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Yun Song