Lines of descent under selection

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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.