Research published in Proceedings of the National Academy of Sciences
Everyone knows that birds flock and fish school, and that a number of different biological reasons, such as protection, are at play. What is relatively unknown is how they do these things.
Now, a StFX mathematics professor is shining light on the issue.
Dr. Ryan Lukeman’s research, which combines field observations he made of ducks in Vancouver, BC with mathematical modeling, appears this month in the widely-read and multi-disciplinary journal, Proceedings of the National Academy of Sciences (PNAS)
“The novel thing about this paper is the quality of the data, and the comparison to mathematical models that it allows,” says Dr. Lukeman, who has been able to study flocking behavior in ducks, including the individual rules that govern groups and how individuals interact.
"These ducks were swimming in very regular array formations, and because they were in two dimensions, we were able to mathematically reconstruct both positions and velocities.”
Dr. Lukeman began the research while a PhD student at the University of British Columbia. His advisor had been walking around the waterfront boardwalk at Canada Place convention centre when she noticed a large group of ducks that dove and foraged, in synchrony, for mussels in the harbour.
Dr. Lukeman photographed a timed series of images of the flock on the surface of the water, and used this observed behavior to infer what rules of interaction were at play in the flock.
Determining how individuals form cohesive, self-organized group motion in nature is challenging, he says, as models tend to be hypothetical, and lack comparison with real data.
“Here, we bridge the gap by gathering and analyzing a high quality dataset of flocking surf scoters, forming well-spaced groups of hundreds of individuals on the water surface,” he writes in the paper entitled Inferring individual rules from collective behavior.
“By reconstructing each individual’s position, velocity and trajectory, we generate spatial and angular neighbor-distribution plots, revealing distinct concentric structure in positioning.”
Dr. Lukeman, a 2003 StFX alumnus, who just completed his first year teaching in the Department of Mathematics, Statistics and Computer Science, says he’s pleased the paper appears in PNAS.
The journal has a large, diverse readership, and gets as many as 12 million hits a month on its website, which should bring good exposure to his research program, he says.
And Dr. Lukeman’s results?
Flocking birds interact with their neighbours in a number of ways, he says. They repel at close distances, attract at longer distances, and align with nearby neighbors, enabling the group to move cohesively.
Additionally, these ducks have a preference to position themselves directly behind a neighbor. "With our model, we found that repulsion among ducks was much stronger than other interactions," he says.