Fish swim in schools by stacking like ladder rungs

For 50 years, scientists believed that fish schools saved energy by swimming in diamond formations. This view, rooted in models by Weihs and Lighthill from the 1970s, shaped decades of research and robotic design.

However, new research from Princeton and Harvard scientists turns that theory on its head. Fish don’t move in neat, flat diamonds. Instead, they prefer dynamic, three-dimensional ladders.

A new look at fish schooling patterns

The researchers tracked six giant danios swimming continuously for ten hours in a recirculating flow tank. They used synchronized side and bottom cameras, along with deep learning software, to collect detailed 3D data on fish positions.

This advanced setup allowed the team to record over 260,000 frames where at least four fish were clearly visible and trackable from both views.

The findings challenged long-held assumptions about fish schooling patterns. Only 0.1% of the frames showed fish in the classical diamond formation, long thought to be the most energy efficient.

Fish mostly swim in ladders

Instead, the fish predominantly adopted a new three-dimensional arrangement termed the ladder formation. In this pattern, fish were staggered vertically, with some swimming slightly above or below others, rather than maintaining a flat side-by-side structure.

The ladder pattern appeared in 79% of fish pairings, making it by far the most common. Additionally, only 25.2% of all fish pairs swam in the same horizontal plane. This indicates that vertical positioning is a key feature of natural fish school behavior, something that earlier two-dimensional studies overlooked.

The study reveals that fish prefer dynamic 3D arrangements that likely reduce drag without requiring precise alignment.

Why the fish ladder works

“When swimming, fish on average generate a jet going backward, like the jet engine of a plane,” said Hungtang Ko, lead author of the study. Staying out of that jet reduces drag.

The ladder formation allows this. A fish swims slightly above or below the one in front, avoiding the jet while still staying close. This creates energy savings similar to the diamond model but with less need for perfect timing or alignment.

The diamond model assumes fish must synchronize tail beats and stay level. But in real schools, coordination varies. Fish rarely beat tails in exact anti-phase, a condition the diamond pattern needs to be effective.

Even in controlled experiments, fish constantly rearranged positions. The average pattern changed every 48 seconds for individuals and 32 seconds for the whole school.

Ko’s team observed that fish ladder formations shift based on flow rate. As speed increased from 1.6 to 5.6 body-lengths per second, the fish ladder stretched longer. This adaptation resembled behavior in other biological collectives, like fire ant rafts.

Tracking fish in three dimensions

Older studies limited fish to shallow tanks or still water, forcing unnatural formations. This experiment used deeper tanks and steady flow, removing boundary effects.

The researchers trained AI to detect nose and tail positions in 3D space using SLEAP.ai and a custom MATLAB pipeline.

According to the heatmaps, fish were most likely to swim either above and behind, or below and ahead, of a partner – never directly inline.

This ladder structure formed naturally, not by training or conditioning. It shows how real-world conditions reshape what we think of as “efficient.”

Why this matters beyond biology

The Nagpal lab is designing robot fish swarms inspired by these new insights. By mimicking ladder formations, underwater robots might conserve energy, move more smoothly, and navigate better in tasks like reef monitoring.

“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?”

Fish schools conserve energy

This study shows that energy savings don’t come from holding a perfect formation. Instead, savings come from many temporary, varied arrangements.

Even fish that constantly shift positions still gain benefits by staying out of each other’s wake.

The study also raises new questions. Can robot fish switch positions while still conserving energy? Do vertical ladders work better in turbulent water? Future experiments, especially using robotic models, may find answers.

For now, one thing is certain. Nature prefers complexity over perfection. Fish don’t swim in flat diamonds. They climb invisible ladders, one body length at a time.

The study is published in the journal Scientific Reports.

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