Abstract
Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are revisited consecutively, and allows associations of more than one state to a given syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network model of how syntax is controlled within the premotor song nucleus HVC, but also suggests that adaptation and many-to-one mapping from the syllable-encoding chain networks in HVC to syllables should be included in the network model.
Highlights
Complex action sequences in animals and humans are often organized according to syntactical rules that specify how actions are strung together into sequences [1,2]
Syllable repetitions are common in the Bengalese finch songs
Complex action sequences in many animals are organized according to syntactical rules that specify how individual actions are strung together
Summary
Complex action sequences in animals and humans are often organized according to syntactical rules that specify how actions are strung together into sequences [1,2]. Pairwise transition probabilities between syllables are widely used to characterize variable birdsong sequences [3,4,7,8]. This is equivalent to using the Markov model to capture the statistical properties of the syllable sequences. The Markov model is a generative statistical model of sequences, and consists of a set of states. A state sequence starting from the start state and ending at the end state is produced through probabilistic transitions from one state to the and the corresponding syllable sequence is generated. No detailed statistical tests of these state transition models have been performed, and their validity as quantitative descriptions of the birdsong syntax remains unclear
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