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Long-held belief about shape of fish schools overturned—fish swim in 3D 'ladder' formation, not flat diamonds

For 50 years, scientists believed that schools of fish would save the most energy by swimming in flat diamond formations. Recently, a team of researchers at Princeton and Harvard ran an experiment to check this assumption.

It turns out that, contrary to what models predicted, fish don't swim in diamonds. They swim in a dynamic pattern that the researchers call a ladder, where they're staggered in three dimensions like an echelon of fighter jets.

The research team, led by Radhika Nagpal, professor of robotics at Princeton, adapted computer vision software originally developed to track individual animal movements to collect the first 3D data on fish school formation. Working with Harvard University biologist George Lauder, the researchers analyzed a group of six giant danios swimming for 10 hours in a tank with recirculating flow. They found that the fish almost never formed a diamond, instead swimming in a ladder shape 79% of the time.

The paper is in the journal Scientific Reports.

"When swimming, fish on average generate a jet going backward, like the jet engine of a plane," said Hungtang Ko, postdoctoral researcher at Princeton and lead author on the study.

Because of this, it's beneficial to avoid being directly behind one another. Ko said the ladder formation provides similar hydrodynamic benefits as in the diamond shape, but the fish don't have to work as hard to synchronize because they can stagger in multiple planes instead of just one.

The diamond formation was first proposed as the most hydrodynamically efficient in the 1970s, and has since been reinforced by models and experiments that were limited to a 2D view. Models of fish schools have generally been limited to flat planes because it's difficult to capture accurate 3D movement from multiple camera angles. The new software adaptation solved that problem, laying a foundation for future studies to examine fish schools in 3D.

The researchers said this work has interesting applications in robotics. The Nagpal lab is working on fish-inspired underwater robot swarms that in the future could move in similar dynamic ladder formations and gain energetic benefits. Understanding fish schools will help engineers design more efficient underwater robots for tasks like monitoring reefs and kelp forests.

"The collaboration is a two-way street," said Ko. "We can use computer vision to discover how and why animal groups do things together. And then we can ask, what kind of real-world robotic system could this biological insight be applied to?"