Information theory analysis of Australian humpback whale song

Abstract

Songs produced by migrating whales were recorded off the coast of Queensland, Australia, over six consecutive weeks in 2003. Forty-eight independent song sessions were analyzed using information theory techniques. The average length of the songs estimated by correlation analysis was approximately 100 units, with song sessions lasting from 300 to over 3100 units. Song entropy, a measure of structural constraints, was estimated using three different methodologies: (1) the independently identically distributed model, (2) a first-order Markov model, and (3) the nonparametric sliding window match length (SWML) method, as described by Suzuki et al. [(2006). "Information entropy of humpback whale song," J. Acoust. Soc. Am. 119, 1849-1866]. The analysis finds that the song sequences of migrating Australian whales are consistent with the hierarchical structure proposed by Payne and McVay [(1971). "Songs of humpback whales," Science 173, 587-597], and recently supported mathematically by Suzuki et al. (2006) for singers on the Hawaiian breeding grounds. Both the SWML entropy estimates and the song lengths for the Australian singers in 2003 were lower than that reported by Suzuki et al. (2006) for Hawaiian whales in 1976-1978; however, song redundancy did not differ between these two populations separated spatially and temporally. The average total information in the sequence of units in Australian song was approximately 35 bits/song. Aberrant songs (8%) yielded entropies similar to the typical songs.