Exploring the directivities of whistle in the Indo-Pacific humpback dolphin (<i>Sousa chinensis</i>) and their dependency on the whistles' frequency contour

Directional communication plays a pivotal role in enabling odontocetes to maintain group coordination and social interactions. The fundamental frequency, number of harmonics, and their relative energy distribution in whistles exhibit temporal variation. This study investigated the whistles produced by the Indo-Pacific humpback dolphins (Sousa chinensis) in Xiamen Bay, China. Using computed tomography scanning data, we developed a numerical model of the species and used finite element modeling to examine the beam patterns at both fundamental and harmonic frequencies of whistles, ranging from 3.9 to 64.9 kHz, which corresponds to directivity indices (DIs) between 2.2 and 16.2 dB. We weighted the beams at the fundamental frequencies and harmonics based on their energy distribution to derive composite beam patterns at specific time stamps, allowing us to investigate temporal variations in the corresponding DI within individual whistles. The time-varying properties of DIs were analyzed for various whistle types, including constant, upsweep, downsweep, convex, and sine. Given that harmonics are integer multiples of the fundamental frequency, their contours exhibit similar shapes, whereas the composite DI showed more complexity. These findings indicate that the proportion of energy between the fundamental frequency and harmonics is a key determinant of whistle directivity in Indo-Pacific humpback dolphins.