affect the robustness of the natural environments that we depend on, in some
ways that we understand and many that we don’t fully understand. The
mathematical sciences have a key role to play in elucidating and planning for
these impacts.
A basic but challenging need is the ability to quantify how well theecosystems we depend on are doing, so that we can see whether they’re getting
better or worse. Mathematicians are particularly attuned to this need, since
mathematics is the science of deducing the logical consequences of carefully
defined statements. So when a mathematician examines ecosystem health, the
natural first question is, how do we define it?
Biologists have come to realize that the health of ecosystems is intimatelytied up with the diversity of life within them. The more complex the web of life, the
more resilient it is – and conversely, the less complex, the more fragile. When the
potato blight arrived in Ireland in the early 1840s, for example, a third of the Irish
people depended on the potato for all of their food, only two species of potato
existed on the island, and both were susceptible to the disease. A million people
starved. By contrast, when rice grassy stunt virus struck Asia in the 1970s, more
than six thousand species of rice grew in the area. Scientists tested them all, and
just one was able to withstand the virus. By hybridizing that type of rice, rice
cultivation could be saved. Examples like these have proven that an ecosystem
that is more diverse is more robust and healthier – and the people who depend
on it are less vulnerable.
But this observation, though helpful, isn’t precise enough for mathematicalscientists. In partnership with biologists, they need to formulate more specific
questions. What do we mean by biodiversity? How do we measure it? A first cut
would be simply to use the number of species: More species imply greater
diversity. Even so simple a definition as this raises mathematical questions: How
do you effectively count the number of species, particularly when comparing
different ecosystems in which species may be easier or harder to find? How does
the length of time you explore an ecosystem affect the number of species
discovered? How does the number of new species discovered in a day decrease
over time?
Furthermore, if a forest has one area that’s all hemlocks, another that’s all pines,
and another that’s all spruces, it won’t have the interconnected web of