ponderosas slowly fill in and displace the aspens. By characterizing this process
mathematically, it’s fairly straightforward to predict the percentage of aspen and
ponderosa pine some number of years after a fire. Such predictions can guide
foresters in managing timber resources or biologists in understanding
biodiversity.
In the Amazon rainforest, however, a similar interaction might criticallyinvolve the interactions of 300 species rather than just two. While a model can be
built to describe such a complicated set of interactions, it would be so complex
that it would be impossible to analyze or use to generate predictions. So, new
mathematical techniques are needed to handle these complex interactions – for
example, statistical methods that can characterize the interaction of many
species without having to trace the impact on each individual species.
A similar difficult question is to understand the interactions betweenindividual trees, rather than species of trees. Since trees compete with one
another for water, light and minerals, they affect one another’s growth – more if
they’re closer, less if they’re further away. Mathematical scientists can
model such interactions effectively for a pair of trees, but with even three trees,
the problem gets extremely difficult, because the pairwise interactions end up
affecting one another in an infinite sequence.
Figure 14: In southern Brazil, the forest was cleared for grassland, but it is now protected and is
coming back. Mathematical modeling helps estimate the rate of forest expansion and understand
the different stable states of the system. Credit: Madhur Anand.