Genealogies of populations with competition and large variation in the offspring distribution in multi locus and spatially structured settings

• Applicant: Professorin Dr. Anja Sturm
• Subject Area: Mathematics
• Term: from 2012 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221951386

We propose to analyse the genealogies of single genes and gene sequences obtained from a sample of individuals from the present day population. For the underlying stochastic population models we consider a variety of settings: models with selection and competition, large variation in their offspring distribution as well as with spatial structure. More precisely, we propose to investigate population models with constant total population size and various genetic types, in which one type is selectively favoured. We study both the case of a selective sweep, where the beneficial type fixes in the population, as well as balancing selection, where we have an equilibrium situation. We also consider logistic branching processes in which the individuals compete for limited resources and the total population size fluctuates randomly as a result. Another focus lies on population models of constant total size with large variation in their offspring distribution such that the offspring of single individuals may be of the order of the total population size. This can, for example, be due to competition or selection, in particular due to recurring selective sweeps. Spatially structured settings for some of the aforementioned models will be studied as well. The ultimate aim of the proposed research is to provide a basis for the analysis of genetic data by assessing the impact of the different underlying populations scenarios on the joint ancestral relationships of various genes and hence also on quantities that can be read off from the gene sequences in the sample, such as measures of genetic variability.

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