Master Thesis Defense by Cilie Feldager Hansen – Niels Bohr Institute - University of Copenhagen

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Master Thesis Defense by Cilie Feldager Hansen

The Effect of Mixing on Cyclic Competition in One Dimension

Cyclic competition is found in a great variety of biological systems. Often such systems are investigated using the cyclic Lotka-Volterra model. The deterministic version predicts oscillations in the size of the populations which allow the interacting species to coexist. On the other hand, studies of stochastic Lotka-Volterra models, that accounts for fluctuating population sizes, show that at least one species go extinct. Motivated by this contrast, we study cyclically competing species on a one-dimensional lattice with random mixing at finite rate. The cyclic competition has been well studied but only few studies investigates mixing in this context.

We study both coexistence and extinction through a perturbation approach from the infinite limit of mixing rate. By linear stability analysis of the coexistence fixed point, we characterize the rich behavior induced by finite mixing speed such as growing oscillations and extinction for different numbers of interacting species. We also explore extinction for cyclic competition with three and four species and find that finite mixing drive the system to different types of extinction which is supported by Monte Carlo simulations. As our main result, we show that for large, finite mixing rates, a system with any number of interacting species is deterministically driven to extinction. 

Supervisor: Namiko Mitarai & Hiroki Ohta