Microsoft Word - SustainabilityReport_BCC.doc

which hasn’t yet been undertaken at all – is valuable both for the specific

predictions they make and for the deepened understanding they create.

Developing the models takes scientists from a general, qualitative understanding

of the dynamics driving disease to a concrete, quantitative understanding of

which forces are truly critical and why.

Models also have a role to play in elucidating water quality issues, such as

how pollutants like phosphorous runoff from farmland can affect the health of

lakes. A lake is able to accommodate runoff without significant ecological

damage as long as the levels don’t get too high. A sudden, intense rainstorm,

however, might wash enough phosphorous into the lake to kill off fish, disrupt the

ecological function of the lake, and destroy much of its economic value. It’s then

difficult for the lake to return to its previous, functional state. Mathematically,

these two states (healthy and unhealthy) can be understood as “basins of

attraction” in state space, stable states that the lake can be in. While

mathematicians have worked on the local dynamics of these basins of attraction,

the theory underlying how systems can stochastically shift from one state to

another is poorly understood.

These are just a few examples of how the mathematical sciences can help

protect human well-being as ecosystems change, among many more. Changing

migration patterns of birds affect human well-being because birds help control

insect populations that can destroy crops. As the climate changes, birds

sometimes arrive in places before or after their traditional food sources have

arrived. But the effects of climate change have not yet been included in migration

models. Similar issues affect fish migration, and understanding and predicting

fish movement is key for protecting fisheries over the long term. Fish migration is

also impacted by the increasing acidification of the oceans caused by climate

change, and mathematical questions abound in models of ocean acidification.

Some of the mathematical sciences challenges in the area of human

well-being and the natural environment are:

• Climate models strongly need new mathematical methods for
  understanding uncertainty. Additionally, better models are needed of
  extreme events like heat waves or hurricanes, or gradual events such
  as increase in sea level, at the scale of cities rather than large regions
  of the globe. And we need statistical tools for analyzing the impact