The Mathematics of Coral Reef Health

Photo by Elizabeth Sherman

By Julia Munemo

A group of undergraduate researchers in Williams’ SMALL Program—which brings to campus students from colleges across the country for a residential summer program in mathematics—is helping to improve the health of coral reefs.

They worked with Assistant Professor of Mathematics Julie Blackwood, who is collaborating with a biologist and an applied mathematician from Bennington College, to determine what contributes to the deterioration of coral reefs in the Cayman Islands.

Coral reefs host thousands of species of fish and other animals and contribute to the biodiversity and health of marine ecosystems in the tropics and around the world. In 1983, a disease wiped out the sea urchin population throughout the Caribbean—and coral reefs were badly affected.

“Because sea urchins grazed on the algae that grows on top of coral reefs, when they were gone the reefs became overgrown,” Blackwood says. An applied mathematician who uses math to further research in ecology and biology, Blackwood’s role on the team is to better understand the dynamical consequences of scenarios designed to free the reefs of this overgrowth of macroalgae. She does so through mathematical modeling.

One of the questions Blackwood and her Bennington colleagues are asking is about the right conditions in which to reintroduce sea urchins. That’s where the SMALL students came in. Williams student Eliza Matt ’18 helped develop spatial models that capture sea urchin’s reproductive patterns and movement as a first step in designing sea urchin reintroductions to the region. Another question asks what other potential grazers might make a difference and under what circumstances.

In each scenario, there are interactions and processes that Blackwood’s models help illuminate. “As new information comes in from the field, we adjust and refine the models,” Blackwood says. “In turn, model analysis helps inform field research decisions. It’s a continuous cycle.”

Another of Blackwood’s SMALL students—Colin Okasaki, a senior at Harvey Mudd College—uncovered a possibility that the team hadn’t considered: “Sea sponges,” Blackwood says, “which have long been overlooked as important grazers.”

Based on the literature Okasaki reviewed, Blackwood and a group of SMALL students spent the summer learning everything they could about sponges: how they behave, what they eat, and what role they might play in the preservation of coral reefs. They started to build models—work that Blackwood will continue in the coming academic year—that help inform the work going on in the field.

Another team of SMALL students worked with Blackwood to build and analyze mathematical models of the Zika virus. Their goal was to understand the differences between sexual and vector-borne transmission of the virus.

“As an applied mathematician whose work is very interdisciplinary, I have worked with researchers in a variety of fields,” says Blackwood. “SMALL allows me to introduce undergraduates to that research, and together we draw ideas and methods from different fields to help create new approaches to complex problems.”