projecting the impacts of human management actions and policies on sustainable
development. The multiple scales and variability inherent in the diversity of human and
natural systems potentially affected by management actions imply that mathematical
scientists offer a uniquely useful skill set and conceptual foundation upon which to build
the science of sustainability.
- Examples
The problem of managing for sustainability is broad, and many of the topics that
must be addressed demand mathematical understanding to be managed effectively. In
most of these cases, mathematical techniques are already being applied. Our focus is
on examples not just where mathematical understanding is required for management,
but where new mathematical perspectives or approaches hold at least potential promise
to improve management. The world of sustainability is complex, and our examples are
not intended to be exhaustive.
The sustainability problems that confront us are almost all deeply inter-related,
and one important challenge is dealing with these interactions. Most of the important
problems are international in scope, and require international co-operation in order to to
be handled effectively. Pollution does not recognize borders, nor do greenhouse gases
or fish or sea water.
An important component of managing for sustainability will be understanding how
human systems work, and how policy initiatives may play out through human social and
economic networks to lead to results in natural and human-run systems. Many
sustainability issues, including pollution abatement, climate change, the harvesting of
living resources, and so on, involve “public goods” whose utility to individuals is affected
by the actions of others. It is well known that individual users of public goods often
behave in ways that are inimical to sustainable use. Game-theoretic models are useful in
understanding such behavior, and in predicting the response of users to various
management initiatives.
Managing for sustainability implies both trying to limit damage to the Earth’s
natural capital, and finding ways to provide for human well-being once damage has
occurred. For example, one goal is to limit deforestation, and another related goal is to
use remaining forests efficiently. Similarly, the goal of limiting the extent of human-
induced climate change should be modeled and addressed in conjunction with the study
of ways to maintain society in the face of an already-changing climate.
As we think about how to manage for sustainability, we should ask both what our
objectives are, and how our progress towards these objectives should be evaluated.
2.1. Fisheries
Fisheries are an important source of healthy and delicious protein. But many
marine fish populations have been severely overfished. In addition, ocean pollution
negatively impacts fish stocks, reducing their food source, and harming marine habitats.
For example, ocean acidification destroys coral reefs and reduces zooplankton
communities worldwide.
Mathematical models have been central to fisheries management for over 50
years. The initial, logistic-type models were very simple, and management for many
years was based on a “maximum sustainable yield” (MSY) paradigm. Later, bio-
economic models, starting with the so-called Gordon-Shaefer model, combined the MSY