Modelling of ecological and socio-ecological systems in the context of climate change
The workshop took place on the 18th June online.
|1pm-2pm||Birgit Müller & Meike Will (Helmholtz Centre for Environmental Research, Department of Ecological Modelling, Germany)||Potential and unintended side effects of weather insurance – A socio-environmental perspective|
|2pm-3pm||Madhur Anand (Global Ecological Change & Sustainability Laboratory, School of Environmental Sciences, University of Guelph, U.S.A.)||What can we learn from (mathematical equations) of ourselves?: from climate change mitigation to invasive species spread to COVID-19|
|3.30pm-4.30pm||Mary Silber (Department of Statistics, University of Chicago, U.S.A.)||Modeling the Response, and Possible Collapse, of Dryland Vegetation Patterns to Stochastic Rain Pulses|
|4.30pm-5.30pm||Frank Hilker (Institute of Mathematics, Institute of Environmental Systems Research, Osnabrück University, Germany)||Mathematical models of lake pollution dynamics with ecological regime shifts and social tipping points|
Organisers: Viktoria Freingruber, Mariya Ptashnyk, and Toyo Vignal
Birgit Müller & Meike Will:
Potential and unintended side effects of weather insurance – A socio-environmental perspective
Weather insurance products are strongly promoted by national and international donors to support land users in coping with extreme weather events, particularly in poor and vulnerable countries. Assessment studies focus mainly on insurance uptake and short-term economic impacts. However, apart from direct positive effects, the introduction of insurance may have unintended side effects. First, households might change their land use strategies which may result in a degradation of natural resources and thus threaten the livelihood security of smallholders. Second, insured households might lower their contribution to traditional informal arrangements where risk is shared through private monetary support. A loss of informal safety nets may lead to rising social inequality if poor households get excluded but cannot afford insurance. In this talk, we want to explore this topic from a socio-environmental perspective. Using agent-based modelling and social network analysis, we investigate the effects of the introduction of weather insurance on the sustainability of resource use and on risk-sharing networks in local communities in drylands. Based on these analyses, we derive conclusions for improving insurance design to avoid unintended side effects.
What can we learn from (mathematical equations) of ourselves?: from climate change mitigation to invasive species spread to COVID-19
Humans have highly diverse identities and complex social structures that affect our decision-making. We also have the ability to modify our environments (and those of other organisms) in ways fundamentally different from what other organisms do. This can lead to shifts in norms in how humans use, abuse and/or protect ecological systems and in turn feedback on human behaviour. It is becoming increasingly clear that humans and ecosystems form a single, coupled human-environment system (HES) where humans not only cause ecosystem impacts, but also react to them. Despite this, there are still far fewer examples of coupled mathematical models of human and ecological systems than mathematical models of ecological systems themselves. I report on our research in this area and suggest areas and pathways through which mathematical models of human-environment sustainability could be enhanced in future research.
Modeling the Response, and Possible Collapse, of Dryland Vegetation Patterns to Stochastic Rain Pulses
In certain dryland ecosystems, vegetation organizes in bands that alternate with bare soil. Due to increased water infiltration in vegetated zones, compared to barren ones, a redistribution of water resource occurs that sustains biomass at an appropriate coverage fraction. The large-scale bands, spaced ~100 meters apart, are oriented transverse to a gentle elevation grade, with slow upslope colonization. This spontaneous pattern formation is often modeled on long ecological timescales, using a reaction-advection-diffusion framework, with bands represented as traveling periodic wave solutions and with mean annual precipitation serving as a bifurcation parameter. However, it is known that the critical pattern formation feedbacks between water resource and biomass density occur on fast hydrological timescales of rain events. Gandhi et al. (Physica D 2020) developed a fast-slow modeling framework that resolves these feedbacks. We modify that to a pulse-response setting, in which rain storms are instantaneous. This speeds up simulations, allowing us to investigate pattern characteristics under stochastic precipitation; rain pulses, during a rainy season, are treated as a Poisson point process, with their intensity drawn from an exponential distribution. We investigate how changes to the mean rain pulse size impacts the patterns and their possible collapse. This suggests critical ways that mean annual precipitation is not all that matters to these fragile dryland ecosystems.
Frank M. Hilker:
Mathematical models of lake pollution dynamics with ecological regime shifts and social tipping points
In nature, systems can respond to gradual changes in environmental conditions by undergoing abrupt changes in their dynamics. Such regime shifts correspond mathematically to bifurcations and are well known in ecology. For instance, in the eutrophication of shallow lakes, the gradual increase in the concentration of phosphorus and other nutrients can flip the water from a clear to a turbid state. At the same time, the release of phosphorus is a result of human activities (e.g. fertilizing agricultural fields from where the nutrients run off to water bodies). Human behaviour is also known to undergo regime shifts. This talk will introduce a structurally simple model that focuses on the case when both the human and environmental dynamics exhibit tipping points. The model consists of two nonlinear differential equations, one describing lake water pollution and the other one describing human behavior of discharging pollutants. The latter uses approaches from evolutionary game theory. Stability analysis reveals up to four alternative attractors as well as limit cycle oscillations. Numerical bifurcation analysis suggests the existence of Bogdanov-Takens and saddle-node homoclinic bifurcations. In addition, some very preliminary results will be shown to indicate potential effects of discontinuous policy instruments. (Joint work with Anthony Sun.)