Managing a complex human environment system involving forests would require
balancing the positive and negative effects of humans on forests. This is important for
sustainable use of resources of any kind. These ecology-human models should
ultimately be linked to climate models creating tripartite models.
Challenges for the mathematical sciences include:
- Models with high diversity (e.g., some tropical forests have over 300 tree
species, not to mention within species variation); how to deal with redundancy
and high dimensionality that are implied - Predicting spatial and temporal strategies for deforestation and afforestation; for
example, do we need to reforest twice the amount we deforest? Do we need to
introduce time intervals between harvesting? Which areas should we prioritize for
deforestation or afforestation (decision trees – no pun intended)? - How to deal with imperfect human behavior (e.g., individual, political, and
corporate priorities not aligning with socially optimal outcomes). - How to deal with changing state space (e.g., the forest is always evolving in time
due to climate change; value of wood fluctuates due to availability/scarcity and
fashion).
3.3. Economic Systems (Rivas)
Within the spectrum of social systems, it is clear that economic activities and
processes are central to the relationship between sustainability and modeling Human-
Environmental Systems (HES). Modeling economic systems is therefore essential to
coupled HES. This is especially true if one of our goals is to develop tools to aid
decision-makers in addressing the issue of sustainability. When economics, in its
current “neoclassical” form, developed starting in the 1870s, it relied primarily on linear
relationships, comparative static methods, and the assumption of stable equilibria.
Despite tremendous advancements in mathematical methods since then, economics
continues, to a large extent, to be theorized and modeled in this way. However, human
systems in general, and economic systems in particular, are clearly not limited to linear
relationships and stable equilibria. Human systems are complex adaptive systems
which exhibit non-linear and chaotic dynamics, with instabilities produced by positive
feedback loops, thresholds, emergent properties, unpredictable behaviors and persistent
uncertainties.
Are there compelling reasons to bring more advanced mathematical methods to
the theorization and modeling of economic systems? If our economic theories and
models are limited to linear relationships and stable systems and feedbacks are
modeled only as negative (thus always moving the solution back to an equilibrium), they
are likely to miss the reciprocal dynamics and positive feedbacks that lead to economic
bubbles, economic crises and economic collapses. Bubbles are by definition
unsustainable dynamic processes with positive feedbacks. The collapses occur when
these processes pass some unsustainable threshold causing a downward spiral itself
composed of positive feedbacks. As a result, in the vast majority of the economics
literature, bubbles and crises are still seen as aberrations or problems with the system
rather than inherent outcomes of the properties and structure of the system. The
general failure to predict the current economic crises is indicative of these gaps in
current modeling methods.