Research

I am a theoretical probabilist by training (and by heart) but through my collaboration with Adrián González Casanova, Noemi Kurt and Jochen Blath I was introduced into the world of probabilistic population genetics that has since moved into the center of my research.

It is an area where math is inspired and motivated by biological phenomena. This can on one hand lead to exciting theoretical mathematical observations and objects (that no biologist will care much about, but that are fascinating to us mathematicians) and on the other hand to „applied“ results that can help shed some light on questions in theoretical biology.

Currently my main two aspects I am studying are dormancy and coordination. Dormancy refers to the capacity of individuals in a population to enter (and exit) a „protected“ state during wich reproduction is halted – think of seeds for plants or rather cysts for some amoeba. By coordination we very generally refer to the effect of evolutionary events being driven by a random environment rather than independently – an example of this is rare selection (as opposed to the classical weak selection) when selection events occur rarely, but then are of the order of magnitude of the population size. Like what might have happened to these lizards.

As part of my PhD I also had the privilege of working on percolation and random dynamical systems under the supervision of Michael Scheutzow.

Preprints and publications

The effective strength of selection in random environment,
A. González Casanova, D. Spanò and M. Wilke-Berenguer
Accepted in AAP (2024) arXiv:1903.12121 arXiv

Stationary distribution approximation of two-island Wright-Fisher and seed-bank models under weak and strong migration using Stein's method.
H.L. Gan, and M. Wilke-Berenguer
arXiv:2405.18763 arXiv

The impact of dormancy on evolutionary branching,
J. Blath, T. Paul, A. Tobias, and M. Wilke-Berenguer
Theoretical Population Biology, 156:66-76, (2024) arXiv TPB

Lambda-coalescents arising in populations with dormancy,
F. Cordero, A. González Casanova, J. Schweinsberg, and M. Wilke-Berenguer
Electronic Journal of Probability, 27, paper no 9, 1-34, (2022) arXiv, EJP

Principles of seed banks and the emergence of complexity from dormancy,
J.T. Lennon, F. Den Hollander, M. Wilke-Berenguer, and J. Blath
Nature Communications, 12, 4807 arXiv, NatCom (open access)

Separation of time-scales in the seed bank diffusion and its jump-diffusion limit,
J. Blath, E. Buzzoni und A. González Casanova and M. Wilke-Berenguer
Journal of Mathematical Biology, 82(6):53 (2021) arXiv, JOMB (open access)

Statistical tools for seed bank detection.
J. Blath, E. Buzzoni, J. Koskela, and M. Wilke-Berenguer
Theoretical Population Biology, 132:1-15, (2020) arXiv, TPB

The seed bank coalescent with simultaneous switching.
J. Blath, A. González Casanova, N. Kurt, and M. Wilke-Berenguer
Electronic Journal of Probability 25, paper no 27, 21pp, (2020) arXiv, EJP

Structural properties of the seed bank and the two-island diffusion.
J. Blath, E. Buzzoni, A. González Casanova, and M. Wilke-Berenguer
Journal of Mathematical Biology, 79:269-392, (2019) arXiv, JOMB

Robust model selection between population growth and multiple merger coalescents.
J. Blath, E. Buzzoni, A. González Casanova, and M. Wilke-Berenguer
Mathematical Biosciences, 311:1-12, (2019) arXiv, MBS

Random Delta-Hausdorff-attractors.
M. Scheutzow and M. Wilke-Berenguer
Discrete and Continuous Dynamical Systems, Series B, 23(3):1199-1217, (2018) arXiv, DCDS

A new coalescent for seed-bank models.
J. Blath, A. González Casanova, N. Kurt and M. Wilke-Berenguer
Annals of Applied Probability 26(2):857-891, (2016) arXiv, AAP

On the random dynamics of Volterra quadratic operators.
U.U. Jamilov, M. Scheutzow and M. Wilke-Berenguer,
Ergodic Theory and Dynamical Systems , 16:1-16, (2016) arXiv , ETDS

Asymptotics for Lipschitz percolation above tilted planes.
A. Drewitz, M. Scheutzow, and M. Wilke-Berenguer
Electronic Journal of Probability 20, 23 pp., (2015) arXiv , EJP

Genetic variability under the seed bank coalescent,
J. Blath, B. Eldon, A. González Casanova, N. Kurt, and M. Wilke-Berenguer
Genetics 200:921-934, (2015) Genetics

Collaborative Research projects

I am a PI in the IRTG2544 Berlin-Oxford “Stochastic Analysis in Interaction” where I have the pleasure of supervising a PhD Student – Marta dai Pra – jointly with Alison Etheridge from the University of Oxford.

I have a project within the Berlin Mathematics Research Center MATH+ titled EF 4-7 „The impact of dormancy on the evolutionary, ecological and pathogenic properties of microbial populations“. This is jointly with Jochen Blath from Goethe- University Frankfurt (formerly TU Berlin) for the position of our PhD student Tobias Paul.

I was a PI in the RTG 2131 „High dimensional phenomena in probability – fluctuations and discontinuity“ when I was at the Ruhr-university Bochum (joint RTG with University Duisburg-Essen and TU Dortmund) where I supervised my PhD student Nils Hansen.