The span of correlations in dolphin whistle sequences

Abstract

Long-range correlations are found in symbolic sequences from human language, music andDNA. Determining the span of correlations in dolphin whistle sequences is crucial for sheddinglight on their communicative complexity. Dolphin whistles share various statistical propertieswith human words, i.e. Zipf’s law for word frequencies (namely that the probability of theith most frequent wordof a text is about i−α) and a parallel of the tendency of more frequent words to have more meanings. The findingof Zipf’s law for word frequencies in dolphin whistles has been the topic of an intensedebate on its implications. One of the major arguments against the relevance of Zipf’s lawin dolphin whistles is that it is not possible to distinguish the outcome of a die-rollingexperiment from that of a linguistic or communicative source producing Zipf’s law for wordfrequencies. Here we show that statistically significant whistle–whistle correlations extendback to the second previous whistle in the sequence, using a global randomization test, andto the fourth previous whistle, using a local randomization test. None of these correlationsare expected by a die-rolling experiment and other simple explanations of Zipf’s law forword frequencies, such as Simon’s model, that produce sequences of unpredictableelements.