The role of dormancy in population genetics

• Applicants: Professor Dr. Jochen Blath; Professorin Dr. Noemi Kurt
• Subject Area: Mathematics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 285659567

Dormancy is a well-documented trait in many taxa, including microorganisms, and generates a seedbank that is considered to play an important role in the population genetics of a species. Very recently, a new universal coalescent structure, the seedbank coalescent, has been introduced, arising in a natural way as the backward in time scaling limit of the genealogy of a new Wright-Fisher model that includes dormancy. A first mathematical inspection of this model exhibits qualitative differences to standard coalescent models such as the Kingman coalescent. While some preliminary results have already been obtained, this new objects opens up many new lines of research in population genetics. In the proposed project, we plan a thorough mathematical and statistical investigation of the seedbank model and the seedbank coalescent and related models, following three main lines of research: First, we will carry out a detailed mathematical analysis of the model concerning in particular its longterm behaviour, the corresponding genealogical tree properties, limit theorems, generated partition structures, and universality properties. Second, we will incorporate further evolutionary forces into the model, in particular general mutation spaces, different types of selection, fluctuating population size, or variable environments, and also extend the model to accommodate different mechanisms of initiating and terminating dormancy. This will lead to a better understanding of the role of dormancy as an evolutionary force, and its interplay with other forces in population genetics. Third, we will undertake a statistical analysis of the model, investigate classical quantities such as the site frequency spectrum, under the seedbank coalescent. We will also aim to obtain (approximate) sampling formulae to derive explicit sample likelihoods. We aim to estimate model parameters, in particular for the seedbank size, the dormancy rate, and the mutation rates, and also to develop tests for the presence of (weak or strong) seed banks, or the presence of mutation in dormant forms. These inference methods should then be assessed using simulations, and ultimately lead to a toolbox that can be used by biologists to investigate real DNA sequence data.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1590: Probabilistic Structures in Evolution