Ancestral processes in population genetics - the coalescent

Over the last 25 years, coalescent theory became more and more important for ancestral population genetics. The coalescent is a stochastic process, which approximates the ancestral tree of a sample of n individuals, provided the total population size is sufficiently large. Corresponding first convergence theorems go back to Kingman (1982). The Kingman coalescent has the particular property that only binary mergers of ancestral lineages appear with positive probability. For a huge class of population models, the Kingman coalescent arises in the limit for large total population size, similar to the normal distribution in the central limit theorem. This robustness justifies the relevance of the coalescent for the applied sciences.

This talk gives an introduction to coalescent theory and characterizes the class of population models in the domain of attraction of the Kingman coalescent. At the same time, the approaches used in the proofs yield a classification of all coalescent processes which appear in the weak limit when the population size tends to infinity. In general, these coalescent processes allow for simultaneous multiple collisions of ancestral lines. The talk closes with a summary on ongoing research in this field and emphasizes the interdisciplinary importance of the coalescent for biology, computer science, mathematics and medicine.