Biosonar Responsivity Sets the Stage for the Terminal Buzz

AO_SCPLOWBSTRACTC_SCPLOWEcholocating bats dynamically adjust their sonar signals during prey pursuit, yet the mechanistic limits that govern these rapid transitions have remained unclear. Here, we introduce the responsivity framework, a predictive model that formalises the scaling between echo delay, call rate, and relative velocity through a single parameter-the responsivity coefficient kr. From this relation, we derive biologically interpretable quantities such as the reaction window Tb and the buzz-readiness threshold, marking the onset of a high-gain sensorimotor regime preceding the terminal buzz. Simulations of bat-prey interactions, incorporating both stationary and motile targets, reproduced systematic velocity-call-rate trade-offs and realistic behavioural profiles, from which distances, velocities, and reaction times could be inferred using call timing alone. Internal consistency checks confirmed that the frameworks analytical identities for distance and velocity hold across sequences, while spatio-temporal maps revealed how Tb contracts with increasing kr and velocity, defining the biophysical limit of temporal control. Comparisons with high-resolution field recordings showed that observed call-rate dynamics followed the predicted trends, with variability arising from environmental context and localisation uncertainty. By linking simple acoustic observables to a broad set of derived parameters, the responsivity framework provides a mechanistic and predictive tool for interpreting echolocation behaviour. It explains variable buzz lengths and reaction limits consistent with experimental observations. It establishes a general principle: sequential adaptive behaviours unfold under constraints set by the speed of regulatory feedback. While demonstrated in bat biosonar, this principle offers broader relevance to understanding adaptive control and sensory-motor integration across biological systems.