Ikkyu Aihara

Mathematical modeling of frogs’ calling behavior and its possible application to artificial life and robotics

This paper theoretically and qualitatively describes the calling behavior of the Japanese tree frog Hyla japonica with a simple model of phase oscillators. Experimental analysis showed that while an isolated single male frog called nearly periodically, two interacting male frogs called periodically but alternately, with little overlap. We model these phenomena as a system of coupled phase oscillators, where each isolated oscillator behaves periodically as a model of the calling of a single frog, and two coupled oscillators show antiphase synchronization, reflecting the alternately calling behavior of two interacting frogs. Then, we extend the model to a system of three coupled oscillators virtually corresponding to three interacting male frogs, and analyse the nonlinear dynamics and the bifurcation. We also discuss the biological meaning of the calling behavior and its possible application to artificial life and robotics.

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

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.

Echolocating bats use future-target information for optimal foraging

Significance This study shows how an animal dynamically and rationally controls its sensing and navigates to capture multiple prey items. To perform this study, we extracted sonar attention and flight attention of foraging wild bats from both empirical data and mathematical modeling. We show that the bats directed their sonar and flight attention toward not only an immediate prey but also the next prey. In addition, numerical simulation shows a possibility that the bats select suitable flight paths for the consecutive capture. Hence, wild echolocating bats plan their flight paths by distributing their attention among multiple prey items, which means that the bats do not forage in a hit-or-miss fashion but rather spatially anticipate their future targets for optimum routing. When seeing or listening to an object, we aim our attention toward it. While capturing prey, many animal species focus their visual or acoustic attention toward the prey. However, for multiple prey items, the direction and timing of attention for effective foraging remain unknown. In this study, we adopted both experimental and mathematical methodology with microphone-array measurements and mathematical modeling analysis to quantify the attention of echolocating bats that were repeatedly capturing airborne insects in the field. Here we show that bats select rational flight paths to consecutively capture multiple prey items. Microphone-array measurements showed that bats direct their sonar attention not only to the immediate prey but also to the next prey. In addition, we found that a bat’s attention in terms of its flight also aims toward the next prey even when approaching the immediate prey. Numerical simulations revealed a possibility that bats shift their flight attention to control suitable flight paths for consecutive capture. When a bat only aims its flight attention toward its immediate prey, it rarely succeeds in capturing the next prey. These findings indicate that bats gain increased benefit by distributing their attention among multiple targets and planning the future flight path based on additional information of the next prey. These experimental and mathematical studies allowed us to observe the process of decision making by bats during their natural flight dynamics.

Sound imaging of nocturnal animal calls in their natural habitat

We present a novel method for imaging acoustic communication between nocturnal animals. Investigating the spatio-temporal calling behavior of nocturnal animals, e.g., frogs and crickets, has been difficult because of the need to distinguish many animals’ calls in noisy environments without being able to see them. Our method visualizes the spatial and temporal dynamics using dozens of sound-to-light conversion devices (called “Firefly”) and an off-the-shelf video camera. The Firefly, which consists of a microphone and a light emitting diode, emits light when it captures nearby sound. Deploying dozens of Fireflies in a target area, we record calls of multiple individuals through the video camera. We conduct two experiments, one indoors and the other in the field, using Japanese tree frogs (Hyla japonica). The indoor experiment demonstrates that our method correctly visualizes Japanese tree frogs’ calling behavior. It has confirmed the known behavior; two frogs call synchronously or in anti-phase synchronization. The field experiment (in a rice paddy where Japanese tree frogs live) also visualizes the same calling behavior to confirm anti-phase synchronization in the field. Experimental results confirm that our method can visualize the calling behavior of nocturnal animals in their natural habitat.

Dynamical Calling Behavior Experimentally Observed in Japanese Tree Frogs (Hyla japonica)

We recorded time series data of calls of Japanese tree frogs (Hyla japonica; Nihon-Ama-Gaeru) and examined the dynamics of the experimentally observed data not only through linear time series analysis such as power spectra but also through nonlinear time series analysis such as reconstruction of orbits with delay coordinates and different kinds of recurrence plots, namely the conventional recurrence plot (RP), the iso-directional recurrence plot (IDRP), and the iso-directional neighbors plot (IDNP). The results show that a single frog called nearly periodically, and a pair of frogs called nearly periodically but alternately in almost anti-phase synchronization with little overlap through mutual interaction. The fundamental frequency of the calls of a single frog during the interactive calling between two frogs was smaller than when the same frog first called alone. We also used the recurrence plots to study nonlinear and nonstationary determinism in the transition of the calling behavior. Moreover, we quantified the determinism of the nonlinear and nonstationary dynamics with indices of the ratio R of the number of points in IDNP to that in RP and the percentage PD of contiguous points forming diagonal lines in RP by the recurrence quantification analysis (RQA). Finally, we discuss a possibility of mathematical modeling of the calling behavior and a possible biological meaning of the call alternation.

Qualitative and quantitative analyses of the echolocation strategies of bats on the basis of mathematical modelling and laboratory experiments.

Prey pursuit by an echolocating bat was studied theoretically and experimentally. First, a mathematical model was proposed to describe the flight dynamics of a bat and a single prey. In this model, the flight angle of the bat was affected by angles related to the flight path of the single moving prey, that is, the angle from the bat to the prey and the flight angle of the prey. Numerical simulation showed that the success rate of prey capture was high, when the bat mainly used the angle to the prey to minimize the distance to the prey, and also used the flight angle of the prey to minimize the difference in flight directions of itself and the prey. Second, parameters in the model were estimated according to experimental data obtained from video recordings taken while a Japanese horseshoe bat (Rhinolphus derrumequinum nippon) pursued a moving moth (Goniocraspidum pryeri) in a flight chamber. One of the estimated parameter values, which represents the ratio in the use of the angles, was consistent with the optimal value of the numerical simulation. This agreement between the numerical simulation and parameter estimation suggests that a bat chooses an effective flight path for successful prey capture by using the angles. Finally, the mathematical model was extended to include a bat and prey. Parameter estimation of the extended model based on laboratory experiments revealed the existence of bat’s dynamical attention towards prey, that is, simultaneous pursuit of prey and selective pursuit of respective prey. Thus, our mathematical model contributes not only to quantitative analysis of effective foraging, but also to qualitative evaluation of a bat’s dynamical flight strategy during multiple prey pursuit.

Call alternation between specific pairs of male frogs revealed by a sound-imaging method in their natural habitat

Male frogs vocalize calls to attract conspecific females as well as to announce their own territories to other male frogs. In the choruses, acoustic interaction allows the male frogs to alternate their calls with each other. Such call alternation is reported in various species of frogs including Japanese tree frogs (Hyla japonica). During call alternation, both male and female frogs are likely to discriminate calls of the male frogs because of small amount of call overlaps. Here, we show that call alternation is observed in natural choruses of male Japanese tree frogs especially between neighboring pairs. First, we demonstrate that caller positions and call timings can be estimated by a sound-imaging method. Second, the occurrence of call alternation is detected on the basis of statistical tests on phase differences of calls between respective pairs. Although our previous study revealed a global synchronization pattern in natural choruses of the male frogs, local chorus structures were not examined well. Through the observation of call alternation between specific pairs, this study suggests the existence of selective attention in the frog choruses.

Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica)

Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.

Visualizing Phonotactic Behavior of Female Frogs in Darkness

Many animals use sounds produced by conspecifics for mate identification. Female insects and anuran amphibians, for instance, use acoustic cues to localize, orient toward and approach conspecific males prior to mating. Here we present a novel technique that utilizes multiple, distributed sound-indication devices and a miniature LED backpack to visualize and record the nocturnal phonotactic approach of females of the Australian orange-eyed tree frog (Litoria chloris) both in a laboratory arena and in the animal’s natural habitat. Continuous high-definition digital recording of the LED coordinates provides automatic tracking of the female’s position, and the illumination patterns of the sound-indication devices allow us to discriminate multiple sound sources including loudspeakers broadcasting calls as well as calls emitted by individual male frogs. This innovative methodology is widely applicable for the study of phonotaxis and spatial structures of acoustically communicating nocturnal animals.

Prey pursuit strategy of Japanese horseshoe bats, Rhinolophus ferrumequinum Nippon, during target selection task

We investigated prey pursuit behavior of Japanese horseshoe bats, while they were tasked to make a choice between two tethered fluttering moths during flight. Echolocation pulses were recorded by a telemetry microphone mounted on the bat, combined with a 17-ch horizontal microphone array to measure pulse directions. Flight paths of the bat and moths were monitored by using two high-speed video cameras. Acoustical measurements of CF echoes from fluttering moths (67 kHz : CF2 frequency) was conducted using an ultrasonic loudspeaker, turning the head direction of the moth to the loudspeaker from 0deg. to 180deg. in the horizontal plane. Amount of acoustical glints caused by moth fluttering varied with the sound direction, showing the maximum between 70deg. and 100deg.. In the flight experiment, moths chosen by the bat fluttered within or moved across these angles to the bats pulse direction, which would cause dynamic changes in frequency and amplitude of acoustical glints during flight. This result suggests that dynamic changes in acoustical glints appear to attract the bats for prey selection. Furthermore, mathematical modeling implied that the bats possibly took the optimum flight path for capturing a target which the bat selected based on the acoustical cues in the echoes.