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Mathematics and Statistics

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Dr Bert Wuyts

Postdoctoral Research Fellow

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I am a Postdoctoral Research Fellow specialising in analysis and modelling of ecosystems via complex systems approaches. My BSc/MSc were an interdisciplinary mix of environmental sciences and physics (physical geograpy and physics at KULeuven, Belgium; environmental systems science at ETH Zuerich, Switzerland). I obtained my PhD at the University of Bristol (Centre for Complexity Sciences), focusing on alternative stable vegetation states in Amazonia and Africa (with Alan Champneys and Joanna House). 

Research interests

The motto of the complexity sciences is that complicated dynamics can emerge from simple rules. Yet, for the study of real ecosystems, idealised models of complex systems do not suffice. In my work, I use models of idealised complex systems and relax their idealisations. The assumptions I have so far been working on have to do with spatial homogeneity and the nature of spatial interaction. The application I have mostly worked on is catastrophic transitions between rainforest and tropical savanna in the Amazon rainforest.

In my PhD, I used ad-hoc partial differential equation descriptions of a locally bistable model of the Amazon rainforest and showed that relaxing the assumption of spatial homogeneity can lead to complete elimination of bistability in practical settings, which was confirmed by our analysis of geospatial data of the Amazon region. The PDE description relies implicitly on a mean-field assumption.

In my current work with Jan Sieber, I mainly focus on micro-scale stochastic spatial models of tropical vegetation dynamics, modelling the spread of vegetation and fire via simple interaction rules. Applying feedback control to the stochastic simulations allowed us to derive bifurcation diagrams of the stochastic model and assess the validity of mean field models. Relying on insights from percolation and phase transitions theory, we derived concrete indicators of tropical forest change consistent with the assumed spatio-temporal dynamics, providing testable predictions of the bistability hypothesis.

As a general way to learn about mean-field models, I also developed a Mathematica package of moment closure for discrete-state dynamics on networks along with a Gillespie algorithm in Matlab to simulate the stochastic dynamics.

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