A new study done by researchers at UC Davis and Hokkaido University in Japan seeks to understand collective behavior through leader-follower information exchanges
By SONORA SLATER — email@example.com
Have you ever seen a flock of birds flying in formation or watched a school of fish swim in perfect sync and wondered how it was possible?
Researchers at UC Davis and Hokkaido University in Japan have suggested a new way to look at information and how it flows between individuals to influence a group’s behavior, which has many potential applications in understanding collective behavior in various fields of study. This research was published on Feb. 9 in the journal Science Advances.
James Crutchfield, a distinguished professor in the Department of Physics at UC Davis, described how collective behavior came to be studied through the framework of “information theory,” or the scientific and mathematical study of information.
“It really comes out of much more basic questions,” Crutchfield said. “In physics, energy comes in different forms: kinetic, potential and chemical. […] We are trying to put this concept of information into a physical basis.”
Just as there are different types of energy, Crutchfield said that the researchers found different types of information, as well as different modes of information flow.
“So we ask, what kinds of information are there, and how are they transformed into each other?” Crutchfield said. “This is new in the sense that it refines previous notions of information that treated information as this kind of one, unitary thing.”
Ryan James, a previous postdoc researcher at UC Davis and one of the co-authors of the paper, elaborated on how their ideas challenge previous concepts of information theory.
“The oldest information theory quantity used is something called time-delayed mutual information,” James said. “Which is the idea that you look at one time series at Time A, and you look at another at Time B and you ask, how much information do they share?”
He offered an analogy, comparing Davis’ time zone to where he is an hour ahead in Mountain Time.
“If we looked at the clock in my room here, it says 3:06,” James said. “A clock in Davis, it’ll say 3:06 an hour later. But my clock isn’t influencing your clock in any way, even though my clock perfectly predicts yours — the issue is that they’re both synchronized from a common source. So even though our clocks share information in that sense, it’s meaningless to say that my clock is influencing your clock.”
A theory called “transfer entropy” tries to solve this by removing the information that two time series share based on the fact that they might have some sort of common history, according to James. However, this method has other problems.
“Just relying on transfer entropy numbers can be misleading,” James said. “Two time series could be deeply intertwined synergistically, and not just one giving information to the other. In [a paper I wrote], I suggested an alternative, using intrinsic mutual information. [Sulimon Sattari] saw this, and was interested in looking at collective behavior.”
Sattari, an assistant professor at Hokkaido University and the first author on the paper, was studying a type of amoeba called ‘Dictyostelium discoideum.’ During its lifetime, it transitions from a collection of unicellular organisms into a multicellular slug; a small percentage of cells spontaneously become leaders and the others become followers.
When Sattari heard about James and Crutchfield’s theory, he reached out to see if they might be able to use the intrinsic mutual information framework to understand how a collective functions by using a leader-follower framework.
“We cannot ask each cell, how do you feel?” said Tamiki Komatsuzaki, one of the co-authors of the paper and a researcher at Hokkaido University. “Do you feel that you are a leader? So we have to look at the motion to see what information they are using.”
He went on to explain the three different types of information that the researchers identified — intrinsic, synergistic and shared/redundant — using an ice cream metaphor.
“Suppose we’re looking at whether or not you and I get ice cream,” Sattari said. “With intrinsic, we can only predict whether or not I’ll get ice cream today if we know whether or not you got ice cream yesterday. For synergistic, we need to know if you got ice cream yesterday and if I got ice cream yesterday in order to predict if I’ll get ice cream today. And with shared information, we can predict if I’ll get ice cream today if we know if you got ice cream yesterday or if we know if I got ice cream yesterday.”
Udoy Basak, another co-author on the paper, explained that transfer entropy is the combination of intrinsic and synergistic information. Their research found that when they recognized and separated these different types of information flow, the distribution of the elements “shed light on the influences that drive leader-follower relationships,” according to Basak.
In the paper, the team looked at a few very simplified examples, mostly focusing on situations where there was one leader and one follower, according to James.
“The leader kind of moves around randomly, and the follower also moves around randomly, but it also takes into account what the leader’s doing,” James said. “We looked at how the amount of information flow went from leader to follower and follower to leader.”
Sulimon used this framework to begin to understand how the collective communicates and coordinates their motion.
“Using just simplified rules where you only look at your immediate neighbors, you get things like bird flocks and fish schools, where a whole group coherently moves as a whole wave,” James said.
Crutchfield explained how this new research could be used in the field of animal behavior. He is currently working on a project studying humpback whales near Alaska, where he is applying information theory to understand their auditory communication.
“The tools that we’ve developed are desperately needed in the field of animal behavior,” Crutchfield said.
James talked about another application: stock markets.
“We looked at how individual stocks are influenced by and how they influence the market index,” James said. “Oil companies, for example, the value of their stocks was effectively independent of what the overall market was doing. But then consumer products, like Pepsi, for example, were highly influenced by how the overall index was doing. […] I do know a few people who have taken this work and have used it for investing purposes and have done well.”
From understanding disease processes, to traffic issues, to observing human behavior, Komatsuzaki said that one of the things the researchers find so exciting about this new theoretical framework is that the potential applications are not limited to one field.
“It’s almost infinite,” Komatsuzaki said.
Written by: Sonora Slater — firstname.lastname@example.org