Math in Coral Reef Growth

The Cities of the Sea

The multicolored coral reefs that hold fish, protect shorelines, and delight local swimmers are often mistake for simply rocks and plants. However, these organisms are made up of millions of micro animals called polyps. The cylindrical bodies of these creatures are only millimeters in size, yet they do so much for the ecosystem of the ocean floor. With a mouth at one end surrounded by tentacles, polyps absorb calcium in the seawater to create a skeleton around themselves.

It is these colonies of skeletons that represent the beauty of coral reefs. Often times the polyps of coral reefs are referred to as "cities of the sea" because they provide a habitat for thousands of other species. Interestingly enough, coral reefs cover up less than one percent of the ocean floor, yet they hold nearly twenty-five percent of all marine life.

Decline in the Deep

Unfortunately, the plentiful biodiversity coral reefs provide are under serious attack from climate change. All over the world, from the Great Barrier Reef to the Caribbean Sea, coral is rapidly declining.

Researchers have found that temperature is the most important determinant in coral reef growth and that only a modest temperature can lead to a rise in production of CaCO3, which is the calcium carbonate secreted by tiny animals that coral is engineered from. If the temperatures of the ocean rises too high, corals will be bleached and lose the symbiotic algae that live in their tissues and give them their color. Along with being expelled, high water temperatures can allow hostile pathogens to infect the reefs with diseases and ultimately destroy them.

But their is hope! Biologists have conducted a mathematical model that could help protect these coral cities.

Keeping Our Coral Colorful

The underwater model consists of two different equations that include all factors of coral growth and decline. To understand how these pathogens diseases take hold in coral, biologists at Cornell University created this mathematical model to describe how the population of microbes change over time. In the equation, b stands for the number of beneficial microbes, whereas p stands for the number of pathogens in the mucus layer. The two functions contain information about factors such as the microbes' growth rates at different temperatures and the efficiency of the antibiotics fighting the pathogens.

Although writing out these systems of equations looks extremely difficult, one can easily conclude some general concepts from them. For instance, both functions increase when s increases because microbes spread into free space within the mucus. Also, p decreases when b increases because of the greater amount of beneficial microbes being produced from the increase of antibiotics.

Finally, the model shows that even a gradual rise in temperature can lead to a sudden change in which microbes are dominant, allowing pesky pathogens to invade and kill coral. Preventing this increase of pathogens is key in preserving coral reefs, especially in a heating world. More detailed mathematical research could lead to other solutions, and help keep the extremely important coral reefs alive.

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This page by Halie F. ('18)

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