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

项目重点研究在随机遗传漂变、突变、选择、重组和迁移等进化力量作用下空间种群随机进化的定性特征。本项目重点研究(1)相互作用（空间）弗莱明-维奥扩散，(2)相互作用（空间）广义（块重采样）Cannings过程，(3)外部空间结构巨灾下的无限粒子系统的长期行为，包括描述类型和地理种群组成的测量值版本，以及它们向前进化的谱系结构和血统。空间聚聚和广义分支聚聚在双过程中起关键作用。所处理的家谱的主要特征是：(1)罕见突变体的选择性扫描；停滞，间断平衡，适应性景观(2)突变，选择，重组和迁移的相对强度对大规模行为的影响，(3)模型参数的普适性问题，空间连续极限，鞅问题表征，(4)外部噪声（随机环境）对谱系结构的影响，(5)重组对大规模行为的影响，重点关注一般框架和具体例子。延续向重组、随机环境和连续空间转变。

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.