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

Abstract:
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.