that it is worthwhile to investigate the use of more aggregated, simplified models to
provide qualitative “back-of-the-envelope” estimates of system response. Developing
valid yet simplified models is an inherently mathematical question. It is possible that the
forms of feedback inherent in certain component agricultural system models may be
amenable to simplification that produces results sufficient for general policy and
management comparisons.
- Mathematical themes
Several consistent themes arise within the above examples. All these cases
involve crossing scales and crossing domains. Consider the case of forest management:
information on forest components presents itself at different scales such as insect
dynamics operating at localized within-tree scale, dispersal over many kilometers, and
weather, which is known at a much coarser resolution. Human management of forests
operates at intermediate scales between individual trees and broad scale weather
patterns. Similarly, different temporal responses are intertwined with spatial
heterogeneity. In such cases, defining models at an appropriate level of aggregation
across and within scales is a challenging mathematical modeling question.
Issues of uncertainty arise when dealing with how to estimate parameters from
variable and often sparse data sets. For example in agricultural systems, economic
aspects of production are poorly characterized for some regions relative to others.
Uncertainty in process and parameterization are common in sustainability examples
including climate variability and human system responses arising from different political
and policy decisions. In addition to the difficulty of taking into account effects of model
uncertainty, a significant challenge remains in solving large scale stochastic problems.
Recovery of overexploited fisheries is a dynamical transients problem that is
poorly understood. The dynamics of climate systems in general have not been well
incorporated into human system response and management for many components of
sustainability. The estimation of uncertain population levels is a substantial problem in
fisheries management and in the management of forest insect pests. Many components
of sustainability involve linkages between dynamical systems operating on differing
temporal and spatial scales and connecting these requires new approaches for
multiscale modeling, a challenge for the study of such dynamical systems. - Connecting with the communities
4.1. Education
Every student is exposed to mathematics throughout their education. A critical
challenge in mathematics education is to draw the link between the abstractions of
mathematics and its utility across many areas of science. Sustainability issues are
therefore an excellent focal point around which to demonstrate the power of
mathematics to students; sustainability-related topics provide pedagogically useful
examples that can engage K-12 students. In addition, the use of sustainability examples
in mathematics courses provides the further benefit of engaging youth to become more
involved in helping to address the sustainability issues existing in the world today.
Colleges and universities across North America have instituted a vast array of
new courses, degrees and certificate programs involving sustainability. These programs
could benefit from an explicit course on the mathematics of sustainability that may be