Universiteit Leiden

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Research project

Adaptive Semi-Strong Ecosystem Dynamics

Developing methodes to understand the evolution of patches in natural ecosystems

Arjen Doelman
Mathematics of Planet Earth (MPE) grant Mathematics of Planet Earth (MPE) grant

In 2013 more than 120 mathematical institutions have been involved in the international initiative under the UNESCO flag  Mathematics of Planet Earth 2013.

This worldwide initiative shows how math can contribute to the challenges we face regarding climate change, sustainability, natural disasters, ecology, biodiversity, epidemiology.

Following this initiative NWO-physical sciences developed a research program named  Mathematics of Planet Earth within the Netherlands. This program aims to stimulate mathematical research that contributes to a better understanding of essential dynamics and uncertainties regarding "earth systems".


Ecosystems with competing feedback mechanisms at distinct spatial scales - such as drylands, peatlands and coral reefs - exhibit large scale spatial 'patchiness' - like the large systems of vegetation patterns observed in arid regions. The main theme of the proposed research is developing methods by which the evolution of these patches can be understood, with a special focus on how patches adapt to changing environmental conditions - induced by climate change or human exploitation. In the proposed approach, the dynamics of a full model of the ecosystem (of reaction-diffusion type) is reduced to an explicit N-dimensional dynamical system that governs the interactions of N localized patches. By the nature of the ecosystem, these interaction are 'semi-strong', it is therefore possible to explicitly trace the position of the patches, as well as their spatial extend and their biomass. Spatially extended ecosystems may degenerate in various ways: a vegetated dryland may suddenly collapse into a desert state by a catastrophe at which all vegetation patches die out simultaneously, it may also degrade more gradually by a scenario of subsequent local regime shifts at which only one or two patches disappear. Moreover, it may also recover by a similar gradual process. The proposed research provides an analytical method by which the nature of possible destabilizations of an N-patch pattern can be determined and predicted, and thus makes it possible to predict whether an ecosystem may undergo a full desertification catastrophe or a local regime shift.

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