Project
EF4-7
The Impact of Dormancy on the Evolutionary, Ecological and
Pathogenic Properties of Microbial Populations
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
Description
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 features such as varying population size.
On the other hand we study invasion, fixation and coexistence regimes within 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 to understand the role of dormancy in speciation. 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 in higher dimensions has a slower speed of adaptation through the trait space due to the limited directions of mutations. In one-dimensional trait spaces we recover exactly the usual canonical equation.
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 for two states of the cancer cell (active/dormant) and two drugs targeting active and dormant cells respectively. 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. Due to the intricate dynamics, rigorous mathematical analysis is limited and we rely largely on a simulation study. We conclude that in general a dormant population comprising a small fraction of the total population can prohibit successful treatment, with regards to the final number of cells treatment is largely indifferent to the intervals between drug administrations under constant daily doses but with regards to the area under the curve longer time intervals are preferred and that for the strategy to retain dormant cancer cells it is in general best to have treatment as frequent as possible.
In addition, we have derived a Moran type model for the weak and strong seed bank coalescent from which both coalescent models emerge under different rescalings of dormancy rates. In this way, we obtain a new description of the effect of a weak seed bank on the coalescent effective population size as well as comparibility of the coalescents through the unified dormancy parameters. We apply our model to study the species abundance distribution and find that the weak seed bank has no qualitative impact but instead alters the biodiversity constant by a constant factor depending on the switching rates. Strong seed banks however show a qualitatively different total species abundance and will therefore also have a qualitatively different species abundance distribution.
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
A simulation of our model presented in [6] featuring evolutionary branching. The image shows the population size of given traits over time where the size is indicated by colour.
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.
The decay of the number of singletons (species with exactly one representative in the sample) in the SAD as the dormancy rate forwards in time increases.