Some of the major mathematical sciences challenges in the area of
human-environment systems as complex adaptive systems are:
- New mathematical models need to be built that can describe complex
adaptive systems. Such models need to operate at a variety of scales:
for example, on a small scale, an individual subsistence farmer
interacts with the land he’s cleared from the Amazon forest, while on a
large scale, the clearing of the rainforest has an impact on the global
climate. An individual farmer and his land would be described by one
model, while the rainforest’s relationship with global climate would be
captured by another. These models need to be designed so that they
can be put together into a super-model capturing both levels of
interaction. The output of the model needs to shed light on the
behavior of the system at all its different scales, both describing how
the farmers and their land will act differently over time and how the
rainforest and climate will develop. - These models need to be powerful enough to deal with the
complexities of messy, real-world data, which has the mathematically
unpleasant characteristics of being “discrete” and “non-smooth.” - Once such multi-scale, composable models have been developed,
they need to be understood theoretically. In particular, what happens
when two models that are designed in very different ways – for
example, a network model and a traditional differential equation model- are put together?
- Modern techniques in network models allow us to understand and
utilize huge and complex networks. These are especially important,
and the practical and theoretical basis for utilizing such massive
network models needs to be developed. In particular, new techniques
are needed to understand how the shape of these networks changes
over time. - An expanded mathematical toolkit is needed to couple model of the
environment with models of human activity. A particular challenge is
that the cycles of human activity are often at odds with the cycles of