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Mathematical models for population genetics

Prof. Dr. Frank den Hollander, Prof. Dr. Hans-Christian Pape
Prof. Dr. Hans-Christian Pape, Präsident der Alexander von Humboldt-Stiftung, überreicht die Urkunde an den neuen FAU-Humboldt-Preisträger Prof. Dr. Frank den Hollander (links).BARTHEL-BAMBERG

The winner of the Alexander von Humboldt Research Award Prof. Dr. Frank den Hollander in conversation

On March 29th 2019, Prof. Dr. Frank den Hollander of the Mathematical Institute of Leiden University was presented with the Humboldt Research Award at a ceremony. The Alexander von Humboldt Foundation honoured the mathematician for his work on probability theory and his commitment to initiating research networks and research groups in the field of stochastics.

As part of the research award, Frank den Hollander will work more intensively with Andreas Greven (FAU Erlangen) and Anton Bovier (University of Bonn) in Germany from September 2019 to August 2021. For this purpose, he will spend two years in Erlangen and Bonn during the winter semesters 19/20 and 20/21 and make short visits to these places during the summer semesters 2020 and 2021. At the same time, the hosts for their part will visit Leiden during this period in order to advance and expand the cooperation.

Prof. Dr. den Hollander’s research areas include the theory of stochastic processes and their applications in physics, biology and computer science. In particular, he deals with the theory of large deviations, processes in random media, metastable behaviour and potential theory, models of mathematical biology and on random graphs. For his work he has already been elected Fellow of the Institute of Mathematical Statistics (IMS) and the American Mathematical Society.

With his host at FAU, Prof. Dr. Andreas Greven from the Chair of Mathematical Stochastics, Prof. Dr. Hollander has already connected and combined various research projects. They are currently investigating the evolution of genetic populations using a seed database, on the one hand, and the evolution of genetic populations exposed to drastic events, on the other.

The research group in the field of probability theory of Prof. Dr. Greven is an international leader at the interface of statistical physics and population genetics.

Prof. Dr. den Hollander, in your research you are mainly concerned with stochastics. What exactly has sparked your interest in this field of research?

Probability theory is a very complex field of research. It has many connections to other areas of mathematics and other scientific fields, including statistical physics, population genetics, life sciences and complex networks. It is this combination of range and profundity that has always fascinated me.

In September 2019 you came to FAU to work with Prof. Dr. Greven at the Chair of Mathematical Stochastics. Could you please describe your joint research project?

We worked on two projects. One of the projects is a joint project with Margriet Oomen from Leiden University, which deals with the evolution of genetic populations with the help of a seed database. The database serves as a reservoir in which individual seeds can retreat for short or long periods of time to become inactive and thus temporarily not participate in the evolutionary process. The effect of the seed bank is to increase the genetic diversity of the population. This property is very important for the survival of genetic traits.

The other project is a collaboration with Rongfeng Sun of the University of Singapore and deals with the evolution of genetic populations that are exposed to drastic events, where a single individual can transfer its genetic traits to a very large number of other individuals. This high inconsistency is contrary to the effect of the seed bank: It has a tendency to reduce genetic diversity.

What do you and Prof. Dr. Greven hope to achieve with your research?

A better understanding of how evolutionary forces such as resampling, migration and instability interact to determine the long-term behaviour of genetic populations.

I have been working with Prof. Dr. Greven for many years, and the collaboration has been long, continuous and fruitful. It is a pleasure to spend a long time with him and his research group in Erlangen.

What have been the most important findings from your research to date?

We have succeeded in identifying sharp thresholds for evolutionary parameters at which transitions occur between the prevalence of populations with monotonous traits and the prevalence of populations with multiple traits. In other words, we have found the boundaries between the loss of genetic diversity and the survival of genetic diversity.

How could society benefit from your research?

There is much debate these days about climate change and sustainability. We need mathematical models to measure the transition between diversity and non-diversity. Furthermore, population genetic models can be applied to scenarios where there is a struggle for resources. Mathematics has the power of abstraction.

Why did you choose FAU as your host university?

I have been working with Prof. Dr. Greven for many years, and the collaboration has been continuous and fruitful. It is a pleasure to spend a long time with him and his research group in Erlangen. I am pleased that Prof. Dr. Greven will spend February 2020 as Kloosterman Professor at my chair in Leiden.

What do you like most about FAU?

The hospitality. The pleasant working atmosphere. The high quality office rooms. The friendly support. And the perfect accommodation in the guest house.

How internationally visible is FAU in your research area?

Prof. Dr. Greven’s research group in the field of probability theory is an international leader at the interface of statistical physics and population genetics. It was one of the most important nodes in various Priority Programmes and Research Units of the German Research Foundation (DFG). A high-profile workshop on population genetics took place on December 12th and 13th 2019, attracting leading researchers from around the world.

Would you like to add anything else?

I will come back to Erlangen in November and December 2020.

Thank you very much for the interview, Prof. Dr. den Hollander.