Stochastic evolution under selection, rare mutation and recombination: From configurations to genealogical structures and back

• Applicant: Professor Dr. Andreas Greven
• Subject Area: Mathematics
• Term: from 2012 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221781496

The project focusses on qualitative features of stochastically evolving spatial populations under the following evolutionary forces: random genetic drift, mutation, selection, recombination and migration. This project focusses on the longtime behaviour of (1) interacting (spatial) Fleming-Viot diffusions, (2) interacting (spatial) generalized (with block resampling) Cannings processes,(3) infinite particle systems under external spatially structured catastrophs, both the measure-valued versions to describe type and geographic population composition, as well as their forward evolving genealogical structures and lines of descent. A key role as dual processes is played by spatial coalescents and generalized branching-coalescents.The main features for genealogies treated are: (1) selective sweeps by rare mutants: stasis, punctuated equilibria,fitness landscapes (2) the effects of relative strength of mutation, selection, recombination and migration on large-scale behaviour, (3) the question of universality in model parameters, spatial continuum limits, characterization by martingale problems, (4) effect of external noise (random environments) on genealogical structures, (5) impact of recombination on the large-scale behaviour focussing both on a general framework and concrete examples. The continuation shifts towards recombination, random environment and continuum space.

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