A mathematical look at frog choruses

A further attempt to understand croaking:

Spatio-Temporal Dynamics in Collective Frog Choruses Examined by Mathematical Modeling and Field Observations,” Ikkyu Aihara, Takeshi Mizumoto, Takuma Otsuka, Hiromitsu Awano, Kohei Nagira, Hiroshi G. Okuno and Kazuyuki Aihara, Scientific Reports, vol. 4, Article 3891, January 27, 1014. The authors, at Brain Science Institute, RIKEN and Kyoto University, and the The University of Tokyo, explain:

“This paper reports theoretical and experimental studies on spatio-temporal dynamics in the choruses of male Japanese tree frogs. First, we theoretically model their calling times and positions as a system of coupled mobile oscillators. Numerical simulation of the model as well as calculation of the order parameters show that the spatio-temporal dynamics exhibits bistability between two-cluster antisynchronization and wavy antisynchronization, by assuming that the frogs are attracted to the edge of a simple circular breeding site. Second, we change the shape of the breeding site from the circle to rectangles including a straight line, and evaluate the stability of two-cluster and wavy antisynchronization. Numerical simulation shows that two-cluster antisynchronization is more frequently observed than wavy antisynchronization. Finally, we recorded frog choruses at an actual paddy field using our sound-imaging method.”

Here’s detail from the study:


Figure 6 | Field research on frog choruses, by using our sound-imaging method14. (A) A photograph of a male Japanese tree frog (Hyla japonica). (B)A photograph of our sound-imaging device Firefly. The Firefly unit consists of a microphone and a light emitting diode (LED) that is illuminated when capturing nearby sounds14. (C) A photograph of a paddy field in Japan. Along one edge of this paddy field, we deployed 85 or 86 sound-imaging devices at intervals of 40 cm. As shown here, an index was attached to each device from one end of the edge, which was closer to the camera, to the other end. The spatio-temporal light pattern of these devices was recorded by a video camera. Note that the lights of some devices were not detected, when those devices were deployed far from the camera and were not illuminated by frog calls.We carefully checked all the data, and confirmed that the lights of at least 40 devices close to the camera were stably captured even when those were not strongly illuminated by frog calls. Hence, we used the light patterns of 40 devices close to the camera for data analysis of all the observations. These photographs were taken by I.A. and H.G.O.