Leiden University

Are you self-motivated, with a strong scientific background in the field of mathematics, ecology, environmental sciences or physics, preferably spanning two of the disciplines, and with excellent English language skills? And looking for a PhD position?

For our ERC-Synergy project Pathways of resilience and evasion of tipping in ecosystems (RESILIENCE) we are offering two PhD positions at Leiden University.

In the PhD project Unified spatial ecosystem models – the mathematical angle at Leiden University, you will study classes of multi-component spatial ecosystem models, i.e. reaction-diffusion type models that typically have a singularly perturbed nature. Central issues to be addressed are: Which kinds of mechanisms may initiate the onset of patterns? What are the regions in parameter space within which stable patterns exist and what is the (bifurcational) nature of their boundaries? How does the system respond to slowly varying parameters (induced by external, climatological, effects)? Which paths may the system take through the region of stable patterns? Under which conditions may tipping be evaded? What is the impact of spatial heterogeneities and/or sudden ‘extreme events’ (localized in time and space)? The research within this project will be done in collaboration with other PhD’s, postdocs and senior researchers from the different involved universities and especially in direct interaction with those involved in the closely related twin project Unified spatial ecosystem models – the ecological angle.

In the PhD project Turing before tipping at Leiden University, you will study and develop fundamental mechanisms by which an ecosystem may evade tipping by the formation of patterns. Ecosystems are usually modeled by reaction-diffusion systems in which patterns are typically generated by a Turing bifurcation. However, the onset of Turing patterns by itself is insufficient to enable the ecosystem to avoid collapse, it is also crucial that a family of Turing patterns extends beyond the tipping point. Essential research questions will be: Can we determine general conditions for which Turing patterns extend beyond the tipping point? What will be the nature of such patterns? (Stripes? Spots? Labyrinths?) What will be the impact of spatial heterogeneities? May other non-Turing pattern forming mechanisms play a similar role? The research will have a focus on mathematical analysis, but numerical methods – simulations and continuation – will also be central to this project. Moreover, by collaboration with other PhD’s, postdocs and senior researchers from the various involved universities, there will be a strong cross-fertilization between the mathematical approach and insights from ecology and physics. 

If you are our ideal candidate, you have a background and proven interest in mathematics, physics, environmental sciences or ecology, preferably bridging two of those disciplines, programming skills (e.g. Matlab, Python) and a relevant Master’s degree. The project is interdisciplinary, excellent English language skills are required, and affinity with or interest in working in an interdisciplinary environment is important.

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