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Spatio-Temporal Dynamics in Collective Frog Choruses Examined by Mathematical Modeling and Field Observations

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ABSTRACT

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. Analysis of the video demonstrated a consistent result with the aforementioned simulation: namely, two-cluster antisynchronization was more frequently realized.

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Wavy antisynchronization obtained from our numerical simulation with the same parameter values as those in Figure 2 but with a different initial condition.(A) Spatial structure in a frog chorus. Frogs are positioned along the edge of the circular field at the same interval. (B) Wavy antisynchronization in a frog chorus. Neighboring frogs synchronize in almost anti-phase π, and then a wavy state is generated in each cluster. (C) Time series data of the order parameters Rcluster, Rwavy and Rin. Red, blue, green, and black lines represent the time series data of Rcluster, Rwavy for k = 1 and k = −1, and Rin, respectively. When wavy antisynchronization is realized as shown in Figure 3B, only Rwavy for k = 1 takes a high value around 1.
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f3: Wavy antisynchronization obtained from our numerical simulation with the same parameter values as those in Figure 2 but with a different initial condition.(A) Spatial structure in a frog chorus. Frogs are positioned along the edge of the circular field at the same interval. (B) Wavy antisynchronization in a frog chorus. Neighboring frogs synchronize in almost anti-phase π, and then a wavy state is generated in each cluster. (C) Time series data of the order parameters Rcluster, Rwavy and Rin. Red, blue, green, and black lines represent the time series data of Rcluster, Rwavy for k = 1 and k = −1, and Rin, respectively. When wavy antisynchronization is realized as shown in Figure 3B, only Rwavy for k = 1 takes a high value around 1.

Mentions: Figures 2 and 3 show the results of numerical simulation, which are obtained by assuming different initial conditions but the same parameter values ωn = 8π rad/s, L = 20 m, N = 20, and Knm = 1. Frogs are indexed from 1 to N along the edge of the circular field in the counterclockwise direction (Fig. 2A). Our simulation demonstrates that two kinds of spatio-temporal dynamics are bistable depending on the initial conditions (Figs. 2 and 3). The first dynamical structure is shown in Figure 2A and B; whereas the male frogs are positioned along the edge of the field at the same interval (Fig. 2A), each neighboring pair of male frogs synchronize in anti-phase, forming two clusters (Fig. 2B). The second structure is shown in Figure 3A and B; whereas the male frogs are positioned along the edge of the field as well (Fig. 3A), each neighboring pair of male frogs synchronize in almost anti-phase with a spatial phase shift (Fig. 3B); consequently, a wavy state is realized in each cluster, which can be described as by using a nonzero integer k describing the wave number of this state. We name the spatio-temporal dynamics in Figure 2 as two-cluster antisynchronization, and that in Figure 3 as wavy antisynchronization.


Spatio-Temporal Dynamics in Collective Frog Choruses Examined by Mathematical Modeling and Field Observations
Wavy antisynchronization obtained from our numerical simulation with the same parameter values as those in Figure 2 but with a different initial condition.(A) Spatial structure in a frog chorus. Frogs are positioned along the edge of the circular field at the same interval. (B) Wavy antisynchronization in a frog chorus. Neighboring frogs synchronize in almost anti-phase π, and then a wavy state is generated in each cluster. (C) Time series data of the order parameters Rcluster, Rwavy and Rin. Red, blue, green, and black lines represent the time series data of Rcluster, Rwavy for k = 1 and k = −1, and Rin, respectively. When wavy antisynchronization is realized as shown in Figure 3B, only Rwavy for k = 1 takes a high value around 1.
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Related In: Results  -  Collection

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f3: Wavy antisynchronization obtained from our numerical simulation with the same parameter values as those in Figure 2 but with a different initial condition.(A) Spatial structure in a frog chorus. Frogs are positioned along the edge of the circular field at the same interval. (B) Wavy antisynchronization in a frog chorus. Neighboring frogs synchronize in almost anti-phase π, and then a wavy state is generated in each cluster. (C) Time series data of the order parameters Rcluster, Rwavy and Rin. Red, blue, green, and black lines represent the time series data of Rcluster, Rwavy for k = 1 and k = −1, and Rin, respectively. When wavy antisynchronization is realized as shown in Figure 3B, only Rwavy for k = 1 takes a high value around 1.
Mentions: Figures 2 and 3 show the results of numerical simulation, which are obtained by assuming different initial conditions but the same parameter values ωn = 8π rad/s, L = 20 m, N = 20, and Knm = 1. Frogs are indexed from 1 to N along the edge of the circular field in the counterclockwise direction (Fig. 2A). Our simulation demonstrates that two kinds of spatio-temporal dynamics are bistable depending on the initial conditions (Figs. 2 and 3). The first dynamical structure is shown in Figure 2A and B; whereas the male frogs are positioned along the edge of the field at the same interval (Fig. 2A), each neighboring pair of male frogs synchronize in anti-phase, forming two clusters (Fig. 2B). The second structure is shown in Figure 3A and B; whereas the male frogs are positioned along the edge of the field as well (Fig. 3A), each neighboring pair of male frogs synchronize in almost anti-phase with a spatial phase shift (Fig. 3B); consequently, a wavy state is realized in each cluster, which can be described as by using a nonzero integer k describing the wave number of this state. We name the spatio-temporal dynamics in Figure 2 as two-cluster antisynchronization, and that in Figure 3 as wavy antisynchronization.

View Article: PubMed Central - PubMed

ABSTRACT

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. Analysis of the video demonstrated a consistent result with the aforementioned simulation: namely, two-cluster antisynchronization was more frequently realized.

No MeSH data available.