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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.

No MeSH data available.


A schematic diagram describing our mathematical model of equations (5) and (6) that are mentioned in Methods.The calling times and position of the nth frog are modeled by using the calling phase θn and the spatial position rn, respectively. The nth and mth frogs mutually interact according to the functions Γnm, Γmn, Fnm, and Fmn. The function Gn is used to explain our field observations that male Japanese tree frogs aggregate along the edges of paddy fields. The geometric shape of the field is first assumed to be a circle with the radius L and the origin 0, for simplicity. This diagram was drawn by I.A.
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f1: A schematic diagram describing our mathematical model of equations (5) and (6) that are mentioned in Methods.The calling times and position of the nth frog are modeled by using the calling phase θn and the spatial position rn, respectively. The nth and mth frogs mutually interact according to the functions Γnm, Γmn, Fnm, and Fmn. The function Gn is used to explain our field observations that male Japanese tree frogs aggregate along the edges of paddy fields. The geometric shape of the field is first assumed to be a circle with the radius L and the origin 0, for simplicity. This diagram was drawn by I.A.

Mentions: We model the spatio-temporal dynamics inherent in the calling times and positions of male Japanese tree frogs by using equations (5)–(9) that are mentioned in Methods. Based on this model, we theoretically examine organized structures in their choruses at a paddy field. Note that the geometric shape of a paddy field is first assumed to be a circle in this model, for simplicity (Fig. 1). The parameter values of the model are then fixed on the basis of laboratory experiments and field observations. Laboratory experiments have revealed that an isolated male Japanese tree frog calls about 4 times per second5, so that the intrinsic angular velocity ωn in equation (5) is fixed as ωn = 8π rad/s for all the individual frogs. Furthermore, in our field observations, the perimeter of all the edges of a paddy field was typically more than 100 m, and more than about 20 individual frogs simultaneously called in one paddy field. Therefore, the radius of the paddy field L and the total number of the male frogs N are fixed as L = 20 m and N = 20, for simplicity. However, since the parameter Knm in equations (7) and (8) is difficult to be estimated from laboratory experiments or field observations, Knm is fixed to be the unit value as Knm = 1, for simplicity.


Spatio-Temporal Dynamics in Collective Frog Choruses Examined by Mathematical Modeling and Field Observations
A schematic diagram describing our mathematical model of equations (5) and (6) that are mentioned in Methods.The calling times and position of the nth frog are modeled by using the calling phase θn and the spatial position rn, respectively. The nth and mth frogs mutually interact according to the functions Γnm, Γmn, Fnm, and Fmn. The function Gn is used to explain our field observations that male Japanese tree frogs aggregate along the edges of paddy fields. The geometric shape of the field is first assumed to be a circle with the radius L and the origin 0, for simplicity. This diagram was drawn by I.A.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5384602&req=5

f1: A schematic diagram describing our mathematical model of equations (5) and (6) that are mentioned in Methods.The calling times and position of the nth frog are modeled by using the calling phase θn and the spatial position rn, respectively. The nth and mth frogs mutually interact according to the functions Γnm, Γmn, Fnm, and Fmn. The function Gn is used to explain our field observations that male Japanese tree frogs aggregate along the edges of paddy fields. The geometric shape of the field is first assumed to be a circle with the radius L and the origin 0, for simplicity. This diagram was drawn by I.A.
Mentions: We model the spatio-temporal dynamics inherent in the calling times and positions of male Japanese tree frogs by using equations (5)–(9) that are mentioned in Methods. Based on this model, we theoretically examine organized structures in their choruses at a paddy field. Note that the geometric shape of a paddy field is first assumed to be a circle in this model, for simplicity (Fig. 1). The parameter values of the model are then fixed on the basis of laboratory experiments and field observations. Laboratory experiments have revealed that an isolated male Japanese tree frog calls about 4 times per second5, so that the intrinsic angular velocity ωn in equation (5) is fixed as ωn = 8π rad/s for all the individual frogs. Furthermore, in our field observations, the perimeter of all the edges of a paddy field was typically more than 100 m, and more than about 20 individual frogs simultaneously called in one paddy field. Therefore, the radius of the paddy field L and the total number of the male frogs N are fixed as L = 20 m and N = 20, for simplicity. However, since the parameter Knm in equations (7) and (8) is difficult to be estimated from laboratory experiments or field observations, Knm is fixed to be the unit value as Knm = 1, for simplicity.

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.