Mathematics of Planet Earth

During the week of September 16-20, 2013, I attended a workshop on “Sustainability and Complex Systems” at the Mathematical Biosciences Institute at Ohio State. This was the first of three workshops on the theme “Ecosystem Dynamics and Management,” organized under the umbrella of MPE2013.

The workshop was organized by Chris Cosner (Dept of Mathematics, U Miami), Volker Grimm (Helmholtz Centre for Environmental Research, Leipzig, Germany), Alan Hastings (Department of Environmental Science and Policy, UC Davis), and Otso Ovaskainen (Dept of Biosciences, U Helsinki, Finland) and was attended by some 40 researchers from a variety of disciplines, including biology, ecology, environmental science, marine science, public policy, mathematics, and statistics.

In their abstract for the workshop, the organizers wrote: “Creating mathematical models for the sustainability of ecosystems poses many mathematical challenges. Ecosystems are complex because they involve multiple interactions among organisms and between organisms and the physical environment, at multiple scales both in time and in space, with feedback loops making connections across scales.” The workshop program reflected this wide range of challenges. The talks covered anything from conceptual dynamical-systems models to highly detailed individual- or agent-based models (IBMs). During the workshop, there was ample opportunity to discuss the issues, and a display of topical posters highlighted specific case studies in more detail.

The titles of the talks give an idea of the variety of topics covered at the workshop:

• Aquaculture and Sustainability of Coastal Ecosystems (Mark Lewis)
• Modeling socio-economic aspects of ecosystem management and biodiversity conservation (Yoh Isawa)
• Individual-based Ecology (Volker Grimm)
• Sustainability of agroecosystems: insights from the multiscale insect pest monitoring (Sergei Petrovskii)
• A network-patch modeling framework for the transmission of vector-borne infections (Mac Hyman)
• A trait-based perspective of complex systems (Priyanga Amarasekare)
• Stochasticity in complex systems (Karen Abbott)
• Tipping points beyond bifurcations (Sebastian Wieczorek)
• Challenges in Modeling Biological Invasions and Population Distributions in a Changing Climate (Chris Cosner)
• Role of time scales in sustainability of complex systems (Alan Hastings)
• Coarse-graining computations for complex systems (Yannis Kevrekidis)
• Tipping Points in Contagion Models (Carl Simon)
• Beyond the proof of concept: virtual ecologists in complex dynamic systems (Damaris Zurell)
• Models and data: from individuals to populations (Otso Ovaskainen)

Various discussion groups addressed issues of current interest in the ecology community. These groups were formed on an ad-hoc basis and met several times during the workshop. The workshop participants were encouraged to rotate among the groups, to promote diversity of viewpoints. Summaries of the discussions were presented in plenary sessions. Here are some headlines that were discussed:

• Can IBMs fill in gaps when experiments are not feasible?
• How to incorporate stochasticity in IBMs and how to assess the results?
• How to couple evolution, ecology and heterogeneity and get a tractable model?
• Mathematical methods for dimension reduction;
• Construction of ecological models in the presence of uncertainty and tools for management under uncertainty;
• Human factors;
• Established concepts for the analysis of complex systems.

Other workshops in the Fall 2013 program on “Ecosystem Dynamics and Management” are devoted to “Rapid Evolution and Sustainability” (October 7-11) and “Sustainable Management of Living Natural Resources” (November 4-8).