Genealogy and genetic differentiation of populations evolving in heterogeneous environments

• Applicant: Professor Dr. Oskar Hallatschek
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2006 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 19370331

Understanding the occurrence and maintenance of genetic diversity in populations that are spread over a large territory is a fundamental goal of population genetics. In theoretical models [1], genetic differentiation is usually analyzed within a prescribed spatial population structure in equilibrium, such as a homogeneously populated continuous [2, 3], or fragmented [4, 5] habitat. However, population dynamics and genetic differentiation often happen simultaneously. Our proposal therefore aims at investigating the patterns of genetic diversity arising in a continuous population whose dynamic structure is generated by its population dynamics. Specifically, we trace back the spatial patching of a multi-species population to growth under the presence of different types of unstructured environmental randomness (e.g., in the available resources, carrying capacity, etc.) using concepts of non-equilibrium statistical physics [6, 7]. Upon including genetic drift and mutations, we plan to develop a neutral \isolation by distance [2] model that relates geographical and evolutionary distance based on a few and simple assumptions. Such a null model would help us to understand the natural process of parapatric speciation as well as to infer the demographic histories of populations from present-day patterns of genetic diversity. The validation of our theory by comparison of its predictions with real genomic data is an integral part of the proposal. Owing to the universality of the underlying statistical physics problems, we hope to explain genetic patterns found in various natural systems. Our long term goal is to extend the model by non-linear forces, such as mutations that feedback onto the population dynamics and natural selection, in order to infer topology and branching statistics of real phylogenetic trees from the predicted spatio-temporal fluctuations in the population structure. The main part of research proposal is organized as follows. In Sec. 3, we introduce the problems, questions and goals of population genetics that are relevant to the proposed research project. Our statistical physics approach and preliminary work is outlined in Sec. 4 and will guide us in advising an explicit work plan (Sec. 5) for the aspired two-years postdoctoral research period in the group of Professor Nelson at Harvard. Finally, the proposed project is related to the previous work by the applicant (Sec. 6) and we give detailed reasons for the choice of the host institution (Sec. 7).

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor David R. Nelson