While biologists usually describe octopuses as solitary, the cephalopods have shown in numerous ways that they pay close attention to the creatures around them, said Alexandra Schnell, a comparative psychologist affiliated with the University of Cambridge and a peer reviewer of the new paper.

These comments made me laugh.

Dr. Sampaio compared the octopus’s role in these groups to that of a chief executive, while the fish act more like a company’s research and development team.

“You can be a leader by pushing forward and expanding boundaries and taking the group to new places,” he said. “Or you can be the leader in terms of being the decider.” The octopus lets other animals study the marketplace and then chooses the company’s direction.

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However, Dr. Papadopoulou said, “I personally don’t like the use of the word ‘leadership’ when we talk about animals.” The word might make us imagine a boss making thoughtful decisions for everyone else, she said, but the movements of an animal group can emerge because everyone is following simple rules.

Dr. Papadopoulou said the octopus was more like an online influencer than a corporate executive.