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Songs of many songbird species consist of variable sequences of a finitenumber of syllables. A common approach for characterizing the syntax of thesecomplex syllable sequences is to use transition probabilities between thesyllables. This is equivalent to the Markov model, in which each syllable isassociated with one state, and the transition probabilities between the statesdo not depend on the state transition history. Here we analyze the song syntaxin a Bengalese finch. We show that the Markov model fails to capture thestatistical properties of the syllable sequences. Instead, a state transitionmodel that accurately describes the statistics of the syllable sequencesincludes adaptation of the self-transition probabilities when states arerepeatedly revisited, and allows associations of more than one state to thesame syllable. Such a model does not increase the model complexitysignificantly. Mathematically, the model is a partially observable Markov modelwith adaptation (POMMA). The success of the POMMA supports the branching chainnetwork hypothesis of how syntax is controlled within the premotor song nucleusHVC, and suggests that adaptation and many-to-one mapping from neuralsubstrates to syllables are important features of the neural control of complexsong syntax.

A compact statistical model of the song syntax in Bengalese finch