Probabilistic Structures in EvolutionThis programme was approved by the Senate of the DFG on April the 19/20th, 2011.
Biological evolution is a complex phenomenon driven by various underlying processes, such as mutation and recombination of genetic material, reproduction of individuals, competition, and selection of favourable types. Studying the interplay of these processes requires a substantial use of mathematical models and methods. Over the past decades, much of this modelling and analysis took place on a deterministic level, using dynamical systems and differential equations, and this has led to an elaborate theory. However, the processes of evolution have intrinsically random elements, such as random reproduction, which leads to stochastic fluctuations of gene frequencies and the emergence of random genealogies. The underlying stochastic processes are receiving increased attention, not least because they have shaped present-day genomes. Indeed, the study of these processes is crucial for understanding observations and interpreting data that arise in modern empirical evolutionary biology. From the point of view of mathematics, challenging new structures emerge, such as Fleming-Viot and ancestral processes with high offspring variation, coalescents with spatial and genetic structure, and individual-based models of adaptive dynamics. The main objective of the Priority Programme is the in-depth theoretical study of
Retrospective genealogical aspects are an inherent part of population genetics theory, but should also be developed for game theory and adaptive dynamics. Therefore, random genealogies and trees form a conceptual anchor to all themes in the Priority Programme. In this context, structures such as evolving genealogies, coalescents with highly-variable offspring distribution, and genealogies with genetic and geographic structure will be targeted. The programme thus aims at the further development of the mathematical theory of biological evolution. In addition, projects involving the analysis of related experimental data will be targeted; here, approaches will be model driven rather than purely statistical.