First, the frog,I wish they had a recording of the mating calls for Japanese tree frogs since they were the inspiration for mathematicians at Cornell University (New York state, US) according to a November 17, 2017 news item on ScienceDaily,
How does the Japanese tree frog figure into the latest work of noted mathematician Steven Strogatz? As it turns out, quite prominently.
“We had read about these funny frogs that hop around and croak,” said Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics. “They form patterns in space and time. Usually it’s about reproduction. And based on how the other guy or guys are croaking, they don’t want to be around another one that’s croaking at the same time as they are, because they’ll jam each other.”
A November 15, 2017 Cornell University news release (also on EurekAlert but dated November 17, 2017) by Tom Fleischman, which originated the news item, details how the calls led to ‘swarmalators’ (Note: Links have been removed),
Strogatz and Kevin O’Keeffe, Ph.D. ’17, used the curious mating ritual of male Japanese tree frogs as inspiration for their exploration of “swarmalators” – their term for systems in which both synchronization and swarming occur together.
Specifically, they considered oscillators whose phase dynamics and spatial dynamics are coupled. In the instance of the male tree frogs, they attempt to croak in exact anti-phase (one croaks while the other is silent) while moving away from a rival so as to be heard by females.
This opens up “a new class of math problems,” said Strogatz, a Stephen H. Weiss Presidential Fellow. “The question is, what do we expect to see when people start building systems like this or observing them in biology?”
Their paper, “Oscillators That Sync and Swarm,” was published Nov. 13  in Nature Communications. Strogatz and O’Keeffe – now a postdoctoral researcher with the Senseable City Lab at the Massachusetts Institute of Technology – collaborated with Hyunsuk Hong from Chonbuk National University in Jeonju, South Korea.
Swarming and synchronization both involve large, self-organizing groups of individuals interacting according to simple rules, but rarely have they been studied together, O’Keeffe said.
“No one had connected these two areas, in spite of the fact that there were all these parallels,” he said. “That was the theoretical idea that sort of seduced us, I suppose. And there were also a couple of concrete examples, which we liked – including the tree frogs.”
Studies of swarms focus on how animals move – think of birds flocking or fish schooling – while neglecting the dynamics of their internal states. Studies of synchronization do the opposite: They focus on oscillators’ internal dynamics. Strogatz long has been fascinated by fireflies’ synchrony and other similar phenomena, giving a TED Talk on the topic in 2004, but not on their motion.
“[Swarming and synchronization] are so similar, and yet they were never connected together, and it seems so obvious,” O’Keeffe said. “It’s a whole new landscape of possible behaviors that hadn’t been explored before.”
Using a pair of governing equations that assume swarmalators are free to move about, along with numerical simulations, the group found that a swarmalator system settles into one of five states:
- Static synchrony – featuring circular symmetry, crystal-like distribution, fully synchronized in phase;
- Static asynchrony – featuring uniform distribution, meaning that every phase occurs everywhere;
- Static phase wave – swarmalators settle near others in a phase similar to their own, and phases are frozen at their initial values;
- Splintered phase wave – nonstationary, disconnected clusters of distinct phases; and
- Active phase wave – similar to bidirectional states found in biological swarms, where populations split into counter-rotating subgroups; also similar to vortex arrays formed by groups of sperm.
Through the study of simple models, the group found that the coupling of “sync” and “swarm” leads to rich patterns in both time and space, and could lead to further study of systems that exhibit this dual behavior.
“This opens up a lot of questions for many parts of science – there are a lot of things to try that people hadn’t thought of trying,” Strogatz said. “It’s science that opens doors for science. It’s inaugurating science, rather than culminating science.”
Here’s a link to and a citation for the paper,
Oscillators that sync and swarm by Kevin P. O’Keeffe, Hyunsuk Hong, & Steven H. Strogatz. Nature Communications 8, Article number: 1504 (2017) doi:10.1038/s41467-017-01190-3 Published online: 15 November 2017
This paper is open access.
One last thing, these frogs have also inspired WiFi improvements (from the Japanese tree frog Wikipedia entry; Note: Links have been removed),
Journalist Toyohiro Akiyama carried some Japanese tree frogs with him during his trip to the Mir space station in December 1990. Calling behavior of the species was used to create an algorithm for optimizing Wi-Fi networks.
While it’s not clear in the Wikipedia entry, the frogs were part of an experiment. Here’s a link to and a citation for the paper about the experiment, along with an abstract,
The Frog in Space (FRIS) experiment onboard Space Station Mir: final report and follow-on studies by Yamashita, M.; Izumi-Kurotani, A.; Mogami, Y.; Okuno,k M.; Naitoh, T.; Wassersug, R. J. Biol Sci Space. 1997 Dec 11(4):313-20.
The “Frog in Space” (FRIS) experiment marked a major step for Japanese space life science, on the occasion of the first space flight of a Japanese cosmonaut. At the core of FRIS were six Japanese tree frogs, Hyla japonica, flown on Space Station Mir for 8 days in 1990. The behavior of these frogs was observed and recorded under microgravity. The frogs took up a “parachuting” posture when drifting in a free volume on Mir. When perched on surfaces, they typically sat with their heads bent backward. Such a peculiar posture, after long exposure to microgravity, is discussed in light of motion sickness in amphibians. Histological examinations and other studies were made on the specimens upon recovery. Some organs, such as the liver and the vertebra, showed changes as a result of space flight; others were unaffected. Studies that followed FRIS have been conducted to prepare for a second FRIS on the International Space Station. Interspecific diversity in the behavioral reactions of anurans to changes in acceleration is the major focus of these investigations. The ultimate goal of this research is to better understand how organisms have adapted to gravity through their evolution on earth.
The paper is open access.