Bird and Whale Songs Follow the Same Mathematical Laws As Human Language

Researchers have found that the vocal sequences of Bengalese finches and humpback whales obey the same statistical patterns long observed in human languages. Two related studies by an international team show that learned, culturally transmitted songs across these species display Zipfian structure — including Zipf's law of abbreviation, where frequently used units tend to be shorter.

What the Studies Did

The team analyzed recordings of Bengalese finches, a species noted for complex learned melodies, and used analytical tools originally developed to study how human infants segment speech. Those infant-focused methods track which sounds tend to occur together, helping identify candidate 'word-like' units. Applied to birdsong, the methods revealed statistically consistent sequences of notes that behave much like words in human speech.

Key Findings

Across both birdsong and previously analyzed humpback whale song, a small number of sequences appeared very frequently while most sequences were rare — matching the characteristic Zipfian frequency distribution found in human vocabularies. The researchers also observed Zipf's law of abbreviation: commonly used chunks tended to be shorter than rare ones. In birds, these patterns were visible even in juveniles' earliest singing attempts, suggesting the structure emerges from the learning process rather than from a fixed genetic template.

Professor Kazuo Okanoya of Teikyo University summarized the result: 'Frequently used chunks of syllables tend to be shorter, while less frequently used chunks tend to be longer — a pattern known as Zipf's law.'

Why It Matters

The studies strengthen the idea that deep mathematical properties of language can arise wherever complex vocal systems are learned and transmitted across generations. The researchers emphasize that this shared structure is not evidence of recent common ancestry but of a common cultural-learning process: individuals listen, learn, and pass on vocal patterns that then evolve socially. Professor Simon Kirby of the University of Edinburgh described the cross-species commonality as surprising, while Professor Inbal Arnon of the Hebrew University of Jerusalem noted the findings do not diminish what is unique about human language.

The bird study and the team’s earlier whale study together suggest that Zipfian organization may be a general outcome of any communication system that is (1) complex, (2) learned, and (3) transmitted across generations. The new bird research is published in Science Advances and builds on the team’s prior humpback whale results published in Science.