Concerning our ecological populations, we investigated public goods games, which are used to model the interaction between two types of species: one which produces a public good at a certain production cost to the benefit of the entire population, and another species which just makes use of this public good. These models have traditionally been used to understand the phenomenon of cooperation in ecological systems; here, we focused more specifically on what type of interactions or geometries can stabilise producers of the public good. We investigated this system on a patch structure, and found that if species interact locally and do not immediate respond to changes in the environment, producers can be stabilised. This stabilisation is due to the interplay of length and time scales (patch structure and response delay). The importance of this work is that it shows that these length and time scales can give unexpected results (in our case, a very unexpected stabilisation of producers in the high mobility limit, where they should normally die out), and thus merit more detailed investigation from both experiments and theory. Work performed in the final period of this project focused on how heterogeneity in these producers can additionally stabilse them further, and how different interaction topologies can change both producer stability and spatial spreading of producers in different ways.
Concerning microbial populations, we studied a theoretical model system for bacteria under the influence of antibiotics. Here, we investigated how the competition between one more and one less tolerant or resistant bacterial population could be exploited in order to maximally reduce the population size in an antibiotic drug gradient. We assumed that the more tolerant species only got affected by the high-stress environment of the antibiotic treatment (high drug concentration), while the less tolerant species also got affected during treatment with low concentrations. We found that there exist timescales over which the low-stress regime is as effective as the high-stress regime. We also investigated the impact of multiple antibiotic pulses on our model population, and found that depending on the low-stress and high-stress durations within an antibiotic pulse, the bacterial population can get maximally reduced during the first pulse already. This work thus highlights the need for precise microbial experiments, targeting this competition, in order to investigate to what extent the predictions of this model – and similar models also used in public health policy – are applicable to real situations, where more species or an immune system may be present.
Both projects set the stage for further research, which we have already started with the funding of this fellowship. Concerning interacting ecological populations in systems where multiple length and time scales are present, we are currently finishing work on spatial spreading, which is also important to nanoengineering research with DNA-segments, where similar dynamics can occur. Concerning microbial populations and antibiotics, we are currently investigating the extinction dynamics of these populations more closely, also in connection with experiments.