Information theory analysis of Australian humpback whale song

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 [( 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 ( 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 ( 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.