Some of the overarching mathematical sciences challenges in the area
of managing human-environmental systems for sustainability are:
- Management problems often involve finding the optimal solution to a
set of mathematical equations. For example, we want to know how
many fish we can catch per year to get the maximum fish harvest over
the long run, or how we minimize the spread of invasive species. Good
techniques have been developed for doing this as long as there isn’t
too much random fluctuation in the system, but when the system is
impacted by unpredictable outside influences like ocean circulation
changes or weather, those techniques break down. Methods for finding
the optimal solutions in systems with large variability are essential to
solving these management problems. - It’s usually much easier to make predictions over the short run or the
very long run. Tomorrow, the condition of the Rocky Mountain forests
is likely to be quite similar to the condition today. And in the long run,
climate change will force species northward and to higher latitudes. But
predicting the intermediate term is tough: How fast will those changes
happen? Most management problems require information about
exactly those intermediate time scales. New mathematical methods
are required to understand the evolution of dynamical systems over
these intermediate time scales. - Any large-scale mathematical model has “parameters,” single numbers
that encapsulate some complex process, for example, biotic variables
needed to understand forest health that include diameter, height,
health, and live/dead status for different trees and tree species, and
plot variables such as proportion of forest, regeneration, and
understory vegetation. Better mathematical methods are needed to
find which of these parameters are most useful and to find the best
value for these parameters. The problem is particularly complex when
models are linked together and deal with uncertainty.