Related papers: Rethinking tipping points in spatial ecosystems
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
Assessing and managing risks in a changing climate requires projections that account for decision-relevant uncertainties. These deep uncertainties are often approximated by ensembles of Earth-system model runs that sample only a subset of…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Social ecological systems are often difficult to investigate and manage because of their inherent complexity1. Small variations in external drivers can lead to abrupt changes associated with instabilities and bifurcations in the underlying…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…
Using an intermediate complexity climate model (Planet Simulator), we investigate the so-called Snowball Earth transition. For certain values of the solar constant, the climate system allows two different stable states: one of them is the…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…
The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential…
Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…
System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems' spatial dependencies, most applications have been…
The relationship between inequality and the biosphere has been hypothesized to mutual dependecies and feedbacks. If that is true, such feedbacks may give rise to inequality regimes and potential tipping points between them. Here we explore…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…
Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes often modify their environments so strongly that they are forced out of the exponential state into…
We explore the potential multistability of the climate for a planet around the habitable zone. We focus on conditions reminiscent to those of the Earth system, but our investigation aims at presenting a general methodology for dealing with…
Network structures in a wide array of systems such as social networks, transportation, power and water distribution infrastructures, and biological and ecological systems can exhibit critical thresholds or tipping points beyond which there…