Bats time their echolocation calls according to a proportional rule that ties each call to the distance of the target, the animal’s speed, and the slice of the returning echo the animal chooses to listen to, according to a new theoretical framework published in BMC Biology. The work, by Ravi Umadi and Uwe Firzlaff, addresses a long-standing gap: the temporal patterning of bat echolocation has been extensively characterised, but a general mathematical account linking call timing to acoustic propagation, relative motion, and behaviourally selected information has remained incomplete.
The framework, called the responsivity framework, represents each call event as a delayed active-sensing cycle made up of two parts: an acoustic acquisition interval, the time the bat spends producing a call and receiving echoes, and a behavioural interval that follows. The proportional relation between these two intervals is captured by a single quantity, the responsivity coefficient, written as k_r. This coefficient connects call timing to four factors: the effective anchor distance, the relative velocity between bat and target, the duration of the call itself, and the selected echo window, meaning the portion of the returning echoes the animal actually uses.
From this single relationship, the authors derive several familiar features of bat echolocation as consequences of one timing process. Analytical derivation, call-by-call simulation, internal validation, and comparison with field recordings show that the framework generates hyperbolic call-rate–distance relationships, in which call rate rises steeply as a bat closes in on a target. It also shows how approach timing shifts when the animal selects a different echo window, and it places the terminal buzz, the rapid burst of calls at the end of an attack, at the near-target limit of the same timing process rather than treating it as a separate behaviour.
The theory separates two influences on the final phase of an attack. Responsivity and kinematics have separable terminal effects: the coefficient k_r constrains terminal update density and the attainable call rate, whereas the closing velocity determines how much time is available within the terminal region. In other words, how fast a bat can update its acoustic picture of a target is governed by one factor, while how long that final close-range phase lasts is governed by another.
The framework also introduces a behavioural precursor to the buzz. A buzz-readiness state precedes the complete expression of buzz, suggesting that the transition into the terminal phase is staged rather than instantaneous. In addition, transient sonar strobe groups, brief clustered patterns of calls, emerge under multi-target anchor allocation without any explicit grouping rule being built into the model, indicating that apparent grouping in call sequences can arise as a by-product of how a bat allocates its acoustic attention across several targets.
Field recordings provide the empirical side of the study. The authors report broad correspondence between the simulations and real recordings in the organisation of movement, call timing, and call duration. The recordings also illustrate conditional evaluation of acquisition-window and anchor assumptions, meaning that the assumptions a bat appears to make about where its acoustic anchor lies and which echo window it uses can be assessed call by call against the data.
The authors position the work as a process-based descriptor of echolocation timing rather than a mere curve-fitting exercise. Responsivity theory provides a diagnostic framework for hypothesis generation and empirical testing, and identifies the measurements needed to test how selected acoustic information governs subsequent call timing. The article was published open access on 31 October 2026 as an early-share version that is citable and carries a permanent DOI, subject to further edits before the final Version of Record.
Subject of Research: A mathematical theory of how bats time echolocation calls based on acoustic propagation, motion and selected echo information
Article Title: A responsivity theory of call timing patterns in bat echolocation
Article References: Umadi, R., & Firzlaff, U. (2026). A responsivity theory of call timing patterns in bat echolocation. BMC Biology. https://doi.org/10.1186/s12915-026-02774-6
Image Credits: AI Generated
DOI: 10.1186/s12915-026-02774-6
Keywords: bat echolocation, responsivity framework, call timing, terminal buzz, echo window, active sensing, call rate, sonar strobe groups, acoustic acquisition, BMC Biology, responsivity, theory
News Source: Drew Townsend. (November 5, 2026). New theory links bat echolocation call timing to motion and echo windows. Scienmag.
