An interesting story from Howard Hughes Medical Institute (via Science Blog) about the information content of whale song. They don't know what the whales are communicating, but they can assess the number of bits transmitted:
[HHMI predoctoral fellow Ryuji] Suzuki said that information theory also enabled the researchers to determine how much information can be conveyed in a whale song. Despite the "human-like" use of hierarchical syntax to communicate, Suzuki and his colleagues found that whale songs convey less than one bit of information per second. By comparison, humans speaking English generate 10 bits of information for each word spoken. "Although whale song is nothing like human language, I wouldn't be surprised if some marine mammals have the ability to communicate in a complex way," said Suzuki. "Given that the underwater environment is very different from our world, it is not surprising that they would communicate in rather a different way from land mammals."
There seems to be much emphasis on the "hierarchical" aspect of the songs, and this is important -- a single call is made up of many smaller subunits, each of which may carry information content and the arrangement of them may itself carry information content.
Suzuki, who began the project as an electrical engineering undergraduate at the University of Massachusetts, Dartmouth, worked with Buck and Tyack to develop a computer program to break down the elements of the whale's song and assign an abstract symbol to each of those elements. Suzuki wanted to see if he could design a computer program that enabled scientists to classify the structure of the whales' songs.
He used the program to analyze structural characteristics of the humpback songs recorded in Hawaii. To measure a song's complexity, Suzuki analyzed the average amount of information conveyed per symbol. He then asked human observers who had no previous knowledge of the structure of the whale songs to classify them in terms of complexity, redundancy, and predictability. The computer-generated model and the human observers agreed that the songs are hierarchical, confirming a theory first proposed by biologists Roger Payne and Scott McVay in 1971.
The structure of the humpback whale song is repetitive and rigid. The whales repeat unique phrases made up of short and long segments to craft a song. There are multiple layers, or scales, of repetition, denoted as periodicities. One scale is made up of six units, while a longer one consists of 180-400 units. The combined periodicities give the song its hierarchical structure.
A hierarchical format is vastly more learnable than any nonhierarchical alternative capable of encoding an equivalent amount of information, so it should not be surprising that this structure would have arisen in another highly communicative species. It emphasizes that limits on information transfer are just as fundamental to the evolution of social intelligence as limits on optics are to visual perception.