Humpback whales produce songs consisting of more than a dozen sounds repeated in a complicated pattern. Many researchers have analyzed this song structure using manual classification and visual inspection of the sequence of sounds. Payne and McVay (1971) proposed a hierarchical syntax, which is currently most commonly accepted, but which also raises a linguistic question: do the songs really have a hierarchical syntax, or is this structure a result of human bias?

We applied information theoretic techniques to these songs to analyze the structure in an objective, quantitative manner. This talk will first present a short tutorial on information theory techniques used in this research. We then apply these techniques to analyze humpback whale songs classified by both neural nets and human observers. The entropy of the songs is estimated using an independent identically distributed model, a first-order Markov model and the nonparametric sliding window match length (SWML) estimator (Kontoyiannis et. al. 1998). This SWML estimator is universal, asymptotically unbiased, robust and converging quickly.

This sequence of entropy estimates indicate that the production of the songs are governed by strong structural or syntactic constraints. Also, the estimates from parametric models were significantly higher than that from the non-parametric estimator, indicating that both memoryless and first order Markov models are too simple to model the syntax of humpback whale songs. Correlation functions of units in the songs demonstrate repetitive structure with two different periods, approximately 8 and 200 units. Such a phenomenon can be simply described by assuming a hierarchy in syntax. Any model consistent with this behavior without hierarchy must manage a huge number of parameters. This result is consistent with the Payne and McVay (1971) proposed syntax.

This material is based upon work supported by the National Science Foundation under Grant No. 9733391.