**Project Heads**

Jochen Blath (until 03/22), Maite Wilke Berenguer

**Project Members**

Tobias Paul (HU)

**Project Duration**

01.04.2021 − 31.03.2024

**Located at**

HU Berlin

Dormancy is an ubiquitous trait in microbial communities. It describes the ability of an organism to switch into a metabolically inactive and protected state, for example in response to environmental stress. Dormancy has important implications for the evolutionary, ecological and pathogenic character of microbial systems. This project derives and analyses new stochastic individual based models for the dynamics of dormancy-exhibiting biological systems.

We pursue two larger goals: On one hand, we aim to understand the influence of dormany on patterns of genetic diversity through the tools of population genetics, deriving as scaling limits from individual based models dual pairs of processes of diffusions and coalescents that incorporate feaures such as varying population size.

On the other hand we study invasion, fixation and coexistence regimes withing the framework of adaptive dynamics, again, based on individual based models and their many particle limits.

**Results**

In our article [6] we investigate an individual-based model with rare mutations. There, we found numerous effects of introducing a competition-induced dormancy mechanism into a preexisting model. For example, dormancy may favour the emergence of evolutionary branching, it may increase (or decrease) the speed of adaptation, dormancy increases the width of niches occupied by subspecies and dormancy may enable alternative mutational pathways in the trait space.

In the preprint [7] we considered a general individual-based model with power law mutations for which we derived the canonical equation of adaptive dynamics. This equation was previously only proven for rare mutations. The canonical equation in this setting is only piecewise continuously differentiable and has a slower speed of adaptation through the trait space.

The preprint [8] is concerned with an adaptive dynamics model for the impact of cellular dormancy on the outcome of different treatment strategies under variable measures of treatment success. We consider the strategy to wake-up dormant cancer cells, to retain dormant cancer cells in their dormant state and to directly kill dormant cells. We measure success by considering the total number of cancer cells at the end of the treatment period and by conisdering the area under the curve which corresponds (up to a factor of mutation rates) to the number of resistance mutations that we may observe over the course of treatment.

**Current work in progress**

Current working points are

- developing Moran-type models from which we obtain the Kingman coalescent, the weak seed bank coalescent and the strong seed bank coalescent by scaling to have comparable models for these three coalescents. In this context we study the Species Abundance Distribution (SAD) as a measure of biodiversity and we aim to understand the impact of the different seed bank effects on the SAD.
- investigating the effect of dormancy on cancer and in particular on the effectiveness of various treatment plans for chemotherapy.

**External Website**

**Related Publications
**

**Principles of seed banks and the complexity emerging from dormancy**,**Nature Communications****12**, 4807, (2021)

J. T. Lennon, F. den Hollander, M. Wilke Berenguer, J. Blath**The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes, Theoretical Population Biology 139,**18-49, (2021)

J. Blath, A. Tóbiás**Virus dynamics in the presence of contact-mediated host-dormancy**,**ESAIM: Probability and Statistics 27,**174-220, (2023)

J. Blath, A. Tóbiás**A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy and transfer**,**Latin American Journal of Probability and Mathematical Statistics 20,**313-357 (2023)

J. Blath, T. Paul, A. Tóbiás.**Lambda-coalescents arising in populations with dormancy**,**Electronic Journal of Probability 27,**(2022)**The impact of dormancy on evolutionary branching**,**Theoretical Population Biology 156**, 66-76**(2024)****The canonical equation of adaptive dynamics in individual-based models with power law mutation rates**,**preprint,**(2023)**A stochastic population model for the impact of cancer cell dormancy on therapy success**,**preprint,**(2023)

**Related Pictures
**

Simulation of the model in [6] exhibiting a “tunneling” effect as mechanism for branching

An example path of the canonical equation of adaptive dynamics with power law mutation rates.