Research
Mathematical modelling in biology abstracts complex systems to a level which allows analytical or numerical results. The goal is to support or falsify assumptions or mechanisms made in the real world. For this we use population genetic models and Evolutionary Game Theory. Typical tools are deterministic differential equations, stochastic differntial equations to stochastic simulations of individual interactions. The time-discrete or time-continuous models are often inspired by statistical physics.
Red Queen dynamics
Parasites are a major player in evolution and especially in co-evolution. They can be found everywhere and have developed the most intriguing mechanisms to exploit and manipulate their host organisms. Lewis Carroll already pointed out that
"It takes all the running you can do, to keep in the same place" in Through the Looking-Glass, and What Alice Found There.
This race is a nice metaphor for the competition within and between two species and the subsequent oscillation of relative abundances of host and parasite strains is now known as Red Queen dynamics. Whether Red Queen dynamics persist when more types are present (standing genetic variation) is analysed using deterministic but higher dimensional models. The image shows how different initial conditions (by colour) lead to different shapes in the Poincaré section. The more scattered the more irregular the dynamics.
Red Queen oscillations and the diversity within populations can decline when genetic drift (stochastic diffusion) is included, especially when population size fluctuations are permitted in the model. We study what happens to host-parasite Evolutionary dynamics when Ecology is involved in this way (ongoing work).
Virus-bacteria interactions
Bacteria-infecting viruses (Bacteriophage) can be used against bacterial infections as an alternative to antibiotics. This requires fundamental knowlede of the system and the population dynamics and evolutionary possibilities. Since phage are replicated in the bacterial cell, their fate depends on the physiology of the bacterium. We have included this dependency in a well known mathematical model (ongoing work).
Bacterial infections and persister formation
Most antibiotics attack the proliferation cycle of bacteria. Dormant stages that do not or hardly grow are thus less affected by the medication. We analyse how persisters are formed in macrophage immune cells, which usually digest and destroy unwanted bacteria.
Publication list
Abou Chakra M, Bumann S, Schenk H, Oschlies A, Traulsen A. Immediate action is the best strategy when facing uncertain climate change Nature communications 2018
Schenk H, Traulsen A, Gokhale CS. Chaotic provinces in the kingdom of the Red Queen JTB. 2017