ESR5 – Critical Transitions in Evolutionary Games

ESR5: Critical Transitions in Evolutionary Games

Recruiting beneficiary: University College Cork, Ireland


Internal supervisors: Prof. Sebastian Wieczorek, Dr. Kieran Mulchrone


Brief project description: In this project, we will identify key questions in the area of stability analysis in evolutionary games and build on the existing techniques from bifurcation theory, critical transitions theory, and network science to develop a new mathematical framework to study instabilities in evolutionary games. The focus will be on stability criteria for Nash and Stackelberg equilibria, and on critical transitions (tipping points) that are triggered by changing external conditions. The methods developed will be applied to identify:

  • Optimal strategies in cancer treatment
  • Critical factors for “failure to adapt” to changing environment (e.g. climate) in ecosystems


Updates: The first half of the project focused on carcinogenesis, i.e. the onset of cancer respectively the transition from a healthy state to non-health one. Frank built a deterministic non-autonomous base model and combined it with a stochastic process. By choosing breast cancer as a case study and tuning the parameters of the model, the cumulative risk of breast cancer was replicated accordingly. The next step is to expand the deterministic base model with treatment and evolving resistance to investigate optimal treatment strategies against breast cancer.


Selected contributions:

Bastian, F. (2023, May 14-18). Cancer growth and evolutionary games; choosing the right mode [Poster]. SIAM Conference on Applications of Dynamical Systems (DS23). Portland, USA.