Excitatory and inhibitory interactions affect the balance of chorus activity and energy efficiency in the aggregations of male frogs: Numerical simulations using a hybrid dynamical model.

We numerically study the role of excitatory and inhibitory interactions in the aggregations of male frogs. In most frogs, males produce sounds to attract conspecific females, which activates the calling behavior of other males and results in collective choruses. While the calling behavior is effective for mate attraction, it requires high energy consumption. In contrast, satellite behavior is an alternative mating strategy in which males deliberately stay silent in the vicinity of a calling male and attempt to intercept the female attracted to the caller, allowing the satellite males to reduce their energy consumption while having a chance of mating. Here we propose a hybrid dynamical model in which male frogs autonomously switch among three behavioral states (i.e., calling state, resting state, and satellite state) due to the excitatory and inhibitory interactions. Numerical simulations of the proposed model demonstrated that (1) both collective choruses and satellite behavior can be reproduced and (2) the satellite males can prolong the energy depletion time of the whole aggregation while they split the maximum chorus activity into two levels over the whole chorusing period. This study highlights the importance of the multiple behavioral types and their transitions for the performance of the whole aggregation.

Rhythm interaction in animal groups: selective attention in communication networks.

Animals communicating interactively with conspecifics often time their broadcasts to avoid overlapping interference, to emit leading, as opposed to following, signals or to synchronize their signalling rhythms. Each of these adjustments becomes more difficult as the number of interactants increases beyond a pair. Among acoustic species, insects and anurans generally deal with the problem of group signalling by means of 'selective attention' in which they focus on several close or conspicuous neighbours and ignore the rest. In these animals, where signalling and receiving are often dictated by sex, the process of selective attention in signallers may have a parallel counterpart in receivers, which also focus on close neighbours. In birds and mammals, local groups tend to be extended families or clans, and group signalling may entail complex timing mechanisms that allow for attention to all individuals. In general, the mechanisms that allow animals to communicate in groups appear to be fully interwoven with the basic process of rhythmic signalling. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

The dual benefits of synchronized mating signals in a Japanese treefrog: attracting mates and manipulating predators.

In dense mating aggregations, such as leks and choruses, acoustic signals produced by competing male conspecifics often overlap in time. When signals overlap at a fine temporal scale the ability of females to discriminate between individual signals is reduced. Yet, despite this cost, males of some species deliberately overlap their signals with those of conspecifics, synchronizing signal production in the chorus. Here, we investigate two hypotheses of synchronized mating signals in a Japanese treefrog (Buergeria japonica): (1) increased female attraction to the chorus (the beacon effect hypothesis) and (2) reduced attraction of eavesdropping predators (the eavesdropper avoidance hypothesis). Our results from playback experiments on female frogs and eavesdropping micropredators (midges and mosquitoes) support both hypotheses. Signal transmission and female phonotaxis experiments suggest that away from the chorus, synchronized calls are more attractive to females than unsynchronized calls. At the chorus, however, eavesdroppers are less attracted to calls that closely follow an initial call, while female attraction to individual signals is not affected. Therefore, synchronized signalling likely benefits male B. japonica by both increasing attraction of females to the chorus and reducing eavesdropper attacks. These findings highlight how multiple selective pressures likely promoted the evolution and maintenance of this behaviour. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

Visualization of a chorus structure in multiple frog species by a sound discrimination device.

We developed a sound discrimination device to identify and localize the species of nocturnal animals in their natural habitat. The sound discrimination device is equipped with a microphone, a light-emitting diode, and a band-pass filter. By tuning the center frequency of the filter to include a dominant frequency of the calls of a focal species, we enable the device to be illuminated only when detecting the calls of the focal species. In experiments in a laboratory room, we tuned the sound discrimination devices to detect the calls of Hyla japonica or Rhacophorus schlegelii and broadcast the frog calls from loudspeakers. By analyzing the illumination pattern of the devices, we successfully identified and localized the two kinds of sound sources. Next, we placed the sound discrimination devices in a field site where actual male frogs (H. japonica and R. schlegelii) produced sounds. The analysis of the illumination pattern demonstrates the efficacy of the developed devices in a natural environment and also enables us to extract pairs of male frogs that significantly overlapped or alternated their calls.

Interaction mechanisms quantified from dynamical features of frog choruses.

We employ a mathematical model (a phase oscillator model) to describe the deterministic and stochastic features of frog choruses in which male frogs attempt to avoid call overlaps. The mathematical model with a general interaction term is identified using a Bayesian approach, and it qualitatively reproduces the stationary and dynamical features of the empirical data. In addition, we quantify the magnitude of attention paid among the male frogs from the identified model, and then analyse the relationship between attention and behavioural parameters using a statistical approach. Our analysis demonstrates a negative correlation between attention and inter-frog distance, and also suggests a behavioural strategy in which male frogs selectively attend to a less attractive male frog (i.e. a male producing calls at longer intervals) in order to more effectively advertise their superior relative attractiveness to females.

Mathematical modelling and application of frog choruses as an autonomous distributed communication system.

Interactions using various sensory cues produce sophisticated behaviour in animal swarms, e.g. the foraging behaviour of ants and the flocking of birds and fish. Here, we investigate the behavioural mechanisms of frog choruses from the viewpoints of mathematical modelling and its application. Empirical data on male Japanese tree frogs demonstrate that (1) neighbouring male frogs avoid call overlaps with each other over a short time scale and (2) they collectively switch between the calling state and the silent state over a long time scale. To reproduce these features, we propose a mathematical model in which separate dynamical models spontaneously switch due to a stochastic process depending on the internal dynamics of respective frogs and also the interactions among the frogs. Next, the mathematical model is applied to the control of a wireless sensor network in which multiple sensor nodes send a data packet towards their neighbours so as to deliver the packet to a gateway node by multi-hop communication. Numerical simulation demonstrates that (1) neighbouring nodes can avoid a packet collision over a short time scale by alternating the timing of data transmission and (2) all the nodes collectively switch their states over a long time scale, establishing high network connectivity while reducing network power consumption. Consequently, this study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology that is applicable to the control of a wireless sensor network.

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.

Echolocating bats use future-target information for optimal foraging.

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.

Rapid shifts of sonar attention by Pipistrellus abramus during natural hunting for multiple prey.

Flight paths of echolocating Japanese house bats, Pipistrellus abramus, were tracked during insect hunting in a natural setting using a 32-microphone array. The array surrounded the foraging area, locating each bat, and determined the directional aim of the sonar beam. Successive interceptions, indicated by feeding "buzzes" and post-buzz pauses, occurred singly at intervals from over 20 s down to multiple interceptions at 2-3 s intervals. Bats flew on looping, curved paths. Turning radius tightened as rate of interceptions increased, keeping the bat in a smaller area of higher capture density. Broadcast beams shifted direction during search, often alternating between the direction of flight and another direction where, moments later, the next interception would occur. Broadcasts also shifted direction between the current target and the next target. Bats time-share biosonar attention between objects by alternating acoustic gaze. During search, most interpulse intervals (IPIs) were 70-120 ms, but bats interspersed long IPIs up to 200 ms when the rate of interception was low and flight paths followed broad curves. Mathematical modeling of search paths demonstrated that circular flight-paths with occasional long IPIs would be more effective for target search than either random, correlated random, or linear flights.

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.

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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] angles. Finally, the mathematical model was extended to include a bat and [Formula: see text] prey. Parameter estimation of the extended model based on laboratory experiments revealed the existence of bat's dynamical attention towards [Formula: see text] prey, that is, simultaneous pursuit of [Formula: see text] 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.

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.

Complex and transitive synchronization in a frustrated system of calling frogs.

This letter reports synchronization phenomena and mathematical modeling on a frustrated system of living beings, or Japanese tree frogs (Hyla japonica). While an isolated male Japanese tree frog calls nearly periodically, he can hear sounds including calls of other males. Therefore, the spontaneous calling behavior of interacting males can be understood as a system of coupled oscillators. We construct a simple but biologically reasonable model based on the experimental results of two frogs, extend the model to a system of three frogs, and theoretically predict the occurrence of rich synchronization phenomena, such as triphase synchronization and 1:2 antiphase synchronization. In addition, we experimentally verify the theoretical prediction by ethological experiments on the calling behavior of three frogs and time series analysis on recorded sound data. Note that the calling behavior of three male Japanese tree frogs is frustrated because almost perfect antiphase synchronization is robustly observed in a system of two male frogs. Thus, nonlinear dynamics of the three-frogs system should be far from trivial.

Modeling synchronized calling behavior of Japanese tree frogs.

We experimentally observed synchronized calling behavior of male Japanese tree frogs Hyla japonica; namely, while isolated single frogs called nearly periodically, a pair of interacting frogs called synchronously almost in antiphase or inphase. In this study, we propose two types of phase-oscillator models on different degrees of approximations, which can quantitatively explain the phase and frequency properties in the experiment. Moreover, it should be noted that, although the second model is obtained by fitting to the experimental data of the two synchronized states, the model can also explain the transitory dynamics in the interactive calling behavior, namely, the shift from a transient inphase state to a stable antiphase state. We also discuss the biological relevance of the estimated parameter values to calling behavior of Japanese tree frogs and the possible biological meanings of the synchronized calling behavior.

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.