Lines of descent under selection

理解（随机）繁殖、突变和选择的相互作用是群体遗传学研究的一个主要课题。与进化研究的历史观点相一致，现代方法的目的是追溯从当前人口中提取的个体样本的祖先。一般来说，在以时间静止的方式进化的种群中（比如基因或没有重组的基因组），在一个长时间跨度内，种群规模受到控制（理想情况下是恒定的），祖先的血统最终会在时间上向后合并成一个单一的血统。从时间上看（并投射到未来），这会产生一条不朽的线。在第一个资助期间，我们已经使用的概念的平衡祖先选择图，并开发了一个新的建设，“修剪向下看祖先选择图”，研究的不朽线的属性。这个延续项目的中心目标是进一步发展这些方法，使它们适用于更广泛的问题，如在有限的时间范围内的样本谱系，更一般的类型空间，适应度函数和突变方案，以及包括地理和遗传结构的模型。

Understanding the interplay of (random) reproduction, mutation, and selection is a major topic of population genetics research. In line with the historical perspective of evolutionary research, modern approaches aim at tracing back the ancestry of a sample of individuals taken from a present population. Generically, in populations (of genes, or genomes without recombination, say) that evolve in a time stationary manner with a controlled (ideally constant) population size over a long time span, the ancestral lines will eventually coalesce backwards in time into a single line of descent. Viewed forwards in time (and projected into the future) this gives rise to an immortal line. In the first funding period, we have used the concept of the equilibrium ancestral selection graph and developed a new construction, the ` pruned lookdown ancestral selection graph', to study the properties of the immortal line. The central objective of this continuation project is to develop these approaches further and make them available for a broader spectrum of problems, such as the genealogies of samples in a finite time horizon, more general type spaces, fitness functions and mutation schemes, and models including geographic and genetic structure.