Constrained branching random walks as a minimal stochastic model of asexual adaptation

• Applicant: Professor Dr. Oskar Hallatschek
• Subject Area: Mathematics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221580509

An important challenge of theoretical population genetics is the joint mathematical description of natural selection and genetic drift. While approximations neglecting either natural selection or genetic drift are readily available for many evolutionary scenarios, analytical progress has been sparse when both of these forces matter. The difficulties are due to the fact that models combining genetic drift and selection are non-linear and stochastic, and therefore plagued by an infinite hierarchy of moment equations that can only be dealt with using uncontrolled truncations. We have recently described a promising new route to combining natural selection and genetic drift, based on branching processes under constraints, which generates analytical tractable models closed at the first moment equation. We plan to apply our theoretical framework to the dynamics of asexual adaptation with the goal to quantify the transient dynamics, the impact of deleterious mutations and adaptation in two-dimensional fitness landscapes as a first step towards epistatic models. As we argue, these research efforts will be helpful for interpreting microbial evolution experiments. On a more general level, we plan to advance our theoretical framework to capture fluctuations in addition to the first moment, which will establish constrained branching processes as a versatile tool for predicting evolutionary dynamics quantitatively in regimes where natural selection and genetic drift matter.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1590: Probabilistic Structures in Evolution