|Systems Biology is an interdisciplinary field that pursues data-driven, model-based studies of biological organisms and functions. The use of quantitative models is intended to be tightly coupled with biological knowledge. Within this project, we pursue the development of quantitative models for the so-called predator-prey problems to study and understand competition and cooperation among organisms interacting within a resource-constrained environment.
The theory of evolutionary games provides the basis for understanding the interaction and the dynamics between populations of such organisms. The solution of these games over sets of possible strategies is related to specific optimality conditions for the populations under study. An important question is whether such strategies are evolutionary stable, i.e. unbeatable under given initial conditions.
This project focuses on development of game-theoretical and optimal control theory models for predator-prey systems, describing the intra-seasonal (continuous) and inter-seasonal (discrete) dynamics, in collaboration with colleagues in biology. Individual models together with pre-specified metrics of optimality of the interacting species will form hybrid games of the Nash or Stackelberg type. First goal is to solve such games to find optimal strategies for the involved populations. Second goal is to investigate for which parameter domains these strategies are evolutionary stable.
Another possible aim of this project is construction of new, ad-hoc optimality conditions over the considered game-theoretical problems. The use of new metrics for optimality will allow to establish a framework to understand survival properties, competitive strategies, as well as cooperative behaviors among interacting populations of organisms.
The expected outcomes of this project are models corresponding to the data provided by biologists and new computational techniques for finding optimal (and if possible evolutionary stable) strategies for the studied populations.