Modeling Coral Reef Health

Coral Reef

Julie Blackwood is using math to solve ecological problems.

Assistant professor of mathematics Julie Blackwood is using mathematical modeling to uncover the mechanisms that will limit algae overgrowth and promote reef health 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.

“Sea urchins had been the dominant grazer of Caribbean reefs, and, when they were gone, much of the reef became overgrown by algae,” Blackwood says. “It’s also possible that fishing removes other grazers from the ecosystem and that climate change affects the rate of algae growth in ways we don’t yet understand.”

Blackwood has studied ecology for almost as long as she’s studied math. Her adviser at University of California, Davis, where she earned her Ph.D. in applied mathematics, was an ecologist. Blackwood recently joined forces with a biologist and a mathematician from Bennington College; her role is to better understand the dynamical consequences of scenarios designed to free the reefs of algae overgrowth.

“One of the models I’m working on aims to determine the population densities of different herbivores that will most effectively lead to a reduction in algae,” Blackwood says.

To build that model, she starts by constructing two non-linear differential equations that show how coral and algae change with respect to time. The coral equation captures coral growth when algae are grazed and coral mortality when it’s covered  by algae. The algae equation considers what happens if humans fish too heavily, thus potentially removing important grazers.

“The trick is to find the right level of complexity in the model,” says Blackwood. “If I consider too many different factors, it’s difficult to parameterize and analyze the interactions between them. If I make the model too simple, I might not get meaningful results.”

Blackwood then turns to a computer program called MATLAB that can make predictions based on her model. “I input differential equations, and it numerically solves the equations, outputting what the variables do over time,” she says. This information can be graphed to display how the density of coral, as it competes for space with algae, changes over time in the presence of different grazing fish.

Blackwood also uses statistical inference to estimate parameters, based on data from the field, to ensure that her models accurately reflect the past. “If I can prove that my model is accurate in hindsight, I am better able to trust its predictions for the future,” she says.

The project—still in its early stages—is ever-evolving and deeply cyclical. Says Blackwood, “As my biologist colleague collects data from the field, we use it to create and refine models. The information from the models can then guide her fieldwork, and she comes back with more data for our models.”

Using math to solve ecological problems dates back several centuries, but Blackwood says there has been an exponential increase in this work in the last 20 years. “Much of it is thanks to advances in computer science and statistics, as well as the high-powered computers I use to run my models,” she says. “It’s opened doors for interactions between very different fields and helped to blur the boundaries between disciplines.”

-Julia Munemo