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Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

Seminar Talk - Prof. J. C. Claussen

Wann 04.05.2018 von 11:00 bis 12:00 (Europe/Berlin / UTC200) iCal
Wo PIK A56, Konferenzraum

 


Seminar Talk


 

 

Prof. Jens Christian Claussen (Aston University, Birmingham, UK)

Title: Controlling biodiversity? Feedback control in a simple evolutionary game theory model

Abstract: From large-scale econo-ecosystems down to microbial communities, abundance distributions with a high diversity of species or strategies are often claimed to be related to robustness, evolvability and other macroproperties. However both these links, as well as the explanation of natural abundance distributions, have sparse theoretical support. Therefore it is advised to gain understanding in the stability of diversity states, and eventually, how they can be controlled by state-dependent feedback schemes (having in mind e.g. governmental control based on ecological or economic observables). Specifically, I will discuss the biodiversity or coexistence fixed point and its control in an evolutionary game theoretic model, which can display oscillatory dynamics and extinction. The infinite population limit is described by a deterministic replicator equation, here exhibiting oscillations around a neutral fixed point as in the classical Lotka-Volterra system. In reality, populations are always finite, which can be discussed in a general framework of a finite-size expansion which allows to derive stochastic differential equations of Fokker-Planck type as macroscopic evolutionary dynamics. Utilizing a diversity measure as dynamical observable, finally I introduce a feedback into the payoff matrix which stabilizes the steady state of coexistence.