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

点击翻译按钮获取中文摘要

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.