*3.2. Tracking Evasive Prey*

When targets move in linear trajectories, many different organisms, including falcons [54], dogs [3], and fish [55], track moving targets by approaching along a straight trajectory, while keeping constant the angle between the animal's heading and the selected target, as the distance between the two decreases. This strategy is known as a constant bearing (CB) strategy, which is effective for intercepting a target moving along a straight and predictable path. However, the pursuer of an erratically moving target would never converge to the optimum bearing by using the CB strategy.

Many insectivorous bats must contend with prey that can actively maneuver to avoid capture and even jam echolocation. The predator–prey dynamics between bats and insects have revealed an evolutionary arms race that produces extremely specialized behaviors through selective pressures. Many different insects have evolved hearing sensitivities in the ultrasound frequency ranges of the echolocation signals used by predatory bats [56–59]. Some insects have also evolved various evasive flight maneuvers in response to bat signals, from highly stereotyped linear movement away from the bat, demonstrated by Coleopterans (beetles) [56,60,61], to erratic flight trajectories in Lepidopterans (butterflies and moths). Praying mantids have a cyclopean ear to detect bat ultrasound and drop to the ground in response to sonar signals [56]; lacewing moths also cease flying and suddenly plummet downward when they detect the hunting echolocation calls of their main predator, *Pipistrellus pipistrellus*, [57]. This plummeting strategy significantly decreases capture success by the bats [62–64]. Additionally, some insects, such as the tiger moth *Bertholdia trigona,* have developed ultrasonic clicks, which disrupt the bat's ability to successfully track prey by using echolocation [65]. When bats hear tiger moth ultrasonic clicks, they reverse their insect-capture-sequence pattern by elongating call durations and pulse intervals, likely to contend with multiple sound streams [66]. Bats must not only

employ their own tracking strategies for capturing moving targets in midair, but also contend with counter strategies that insects have developed specifically to evade capture.

**Figure 2.** Classic insect-pursuit sequence of an FM bat. The top panel shows a depiction of a bat pursuing an insect. The grayscale fans illustrate the directional aim of the bat's sonar beam, with the darkest regions illustrating the beam axis containing greatest sound energy. In the search phase, bats orient their beam aim to scan the environment in different directions and emit narrowband, long-duration sonar calls. The approach phase commences when echo information about a target returns to the bat; it is characterized by an increase in FM bandwidth, the bat locking its sonar beam aim onto the selected target, and the bat increasing its rate of sonar calls. Finally, when the bat moves to capture the insect, it emits a quick succession of calls, further decreasing the inter-pulse interval, until it intercepts the target. The center panel depicts spectrograms (time frequency representations) of natural echolocation calls from a target tracking sequence of a big brown bat, *Eptesicus fuscus*, in the lab, and shows the approach and capture phases of insect pursuit (low signal-to-noise ratio may have affected the quality of the spectrograms of some signals). The lower panel shows the waveform of the above sequence. Increases in signal amplitude with decreasing target distance are an artifact of the recording conditions. These panels illustrate the change in sonar-call repetition rate in a bat approaching and intercepting a target.

The challenges echolocating bats face in capturing erratically flying insect prey means that a CB strategy would not incorporate the flexibility needed for successful capture. By extension, it has been proposed that bats maintain an optimal bearing by minimizing changes in the absolute direction relative to the target, termed a constant absolute target direction (CATD) strategy [67]. The CATD model posits that an animal generates and updates internal estimations of the distance and direction of the target relative to itself (in the bat through echolocation), to compute a time-optimal strategy for intercepting erratically moving targets (Figure 3). The CATD strategy, analogous to parallel navigation [68], has been demonstrated in predatory robber flies [69] and interpreted as a strategy for motion camouflage in dragonflies [70]. It has also been implemented in models with a sensorimotor feedback system that relies on delays, which may have application for unmanned vehicle control [71].

**Figure 3.** Modified from Ghose et al. 2006 [67]. (**a**) Constant bearing strategy (CB). Target (insect) moves in a straight line, at a constant velocity (blue line), and is pursued by bat that holds a fixed target bearing (green line), aiming where it will intercept the target (interception point Z). An alternative nonlinear path (pink) can be adopted by the bat when pursuing a target with constant linear velocity, resulting in a shorter intercept time at point Y (see Ghose et al. 2006 for further description). (**b**) Constant Absolute Target Direction strategy (CATD). Target (insect) moves erratically, by changing both direction and speed along path (blue). True erratic target motion cannot have a global time-minimum intercept, but can be approximated by infinite constant velocity segments. The bat's path (green) can follow a locally time-optimal path by adjusting its flight trajectory to minimize changes in the absolute direction of the target. This strategy relies on the target position update acquired from returning echoes.

Although the CATD strategy suggests that bats build an internal model of target motion, the echolocating bat's implementation of predictive strategies for target tracking has been a controversial topic. Masters and colleagues previously reported that the big brown bat *Eptesicus fuscus* uses a non-predictive strategy when tracking a moving target, orienting head aim to the location of the last returning echo, rather than the target's actual location [72]. Further studies in bats, however, indicate that a non-predictive model cannot account for the success of bats tracking occluded or evasive targets. Behavioral studies of the fishing bat *Noctilio leporinus* demonstrated that this species could use the movement of an artificial fish before it disappeared under water from the acoustic view of the bat, to accurately plan target interception [73]. Computational modeling of the trajectories of foraging bats have shown that anticipatory motor planning reflects realistic capture performance [74], and that bats attend to the future location of prey items in a sequence, to guide flight-path selection and improve capture rates [75]. Recently, we conclusively demonstrated that *E. fuscus* relies on predictive models of

target trajectories when tracking moving targets [76]. Specifically, we have empirical evidence to refute the Masters et al. [72] claim of non-predictive tracking, and show that bats rely on a predictive model to track moving objects and even continue to track targets when echoes are blocked by an occluder during a portion of the target's trajectory. This suggests a strategy bats may employ to contend with insect prey that disappear momentarily behind clutter in the environment. Furthermore, we found that when internal models of target motion were violated by unpredictable changes in velocity, bats quickly modified echolocation behavior, to probe the environment for additional information, in order to update internal models and resume tracking the target. Our behavioral data align with a model in which bats estimate target velocity based on the echo arrival time differences between past sampled locations and further advance head aim by a fixed angle. Bats are able to track evasive or occluded targets by building predictive models of target trajectory and use this information to successfully intercept erratic prey. Future studies will investigate constraints on sonar tracking models that bats use to navigate in complex environments.
