Entropic structure of chickadee calls
Jack P. Hailman · The Journal of the Acoustical Society of America · 2001
Language-like ‘‘chick-a-dee’’ calls of the black-capped chickadee are combinations of four note types with repetitions but no permutations. Written English has higher values of entropy (bits/letter) than calls (bits/note) at all orders of a Markov chain because it has 26 elements compared with only four. More importantly, the values of bits/letter falls evenly with increasing orders of Markov chain, reflecting long-range dependencies, whereas values of bits/note drop noticeably from entropy based on probability of occurrence to that based on probability of transition to the next note. This latter structure has been called ‘‘semi-Markovian’’ and reflects the lack of permutation in this chickadee’s calls. The ‘‘entropic structure’’ of calls also differs from that of English words, which have a theoretically immense channel capacity. Nevertheless, constraints on English are so severe that actual words on the average have less than twice the source entropy of calls (11.8 bits/word vs 6.7 bits/call). English is far more informative than chick-a-dee calls, though, because words are themselves combined into meaningful sentences whereas successive chick-a-dee calls appear to be merely repetitive.