New model for gain control of signal intensity to object distance in echolocating bats

Echolocating bats emit ultrasonic calls and listen for the returning echoes to orient and localize prey in darkness. The emitted source level, SL (estimated signal intensity 10 cm from the mouth), is adjusted dynamically from call to call in response to sensory feedback as bats approach objects. A logarithmic relationship of SL=20 log(10)(x), i.e. 6 dB output reduction per halving of distance, x, has been proposed as a model for the relationship between emitted intensity and object distance, not only for bats but also for echolocating toothed whales. This logarithmic model suggests that the approaching echolocator maintains a constant intensity impinging upon the object, but it also implies ever-increasing source levels with distance, a physical and biological impossibility. We developed a new model for intensity compensation with an exponential rise to the maximum source level: SL=SL(max)-ae(-)(bx). In addition to providing a method for estimating maximum output, the new model also offers a tool for estimating a minimum detection distance where intensity compensation starts. We tested the new exponential model against the 'conventional' logarithmic model on data from five bat species. The new model performed better in 77% of the trials and as good as the conventional model in the rest (23%). We found much steeper rates of compensation when fitting the model to individual rather than pooled data, with slopes often steeper than -20 dB per halving of distance. This emphasizes the importance of analyzing individual events. The results are discussed in light of habitat constraints and the interaction between bats and their eared prey.