A Compact Statistical Model of the Song Syntax in Bengalese Finch

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. Author Summary: Complex action sequences in many animals are organized according to syntactical rules that specify how individual actions are strung together. A critical problem for understanding the neural basis of action sequences is how to derive the syntax that captures the statistics of the sequences. Here we solve this problem for the songs of Bengalese finch, which consist of variable sequences of several stereotypical syllables. The Markov model is widely used for describing variable birdsongs, where each syllable is associated with one state, and the transitions between the states are stochastic and depend only on the state pairs. However, such a model fails to describe the syntax of Bengalese finch songs. We show that two modifications are needed. The first is adaptation. Syllable repetitions are common in the Bengalese finch songs. Allowing the probability of repeating a syllable to decrease with the number of repetitions leads to better fits to the observed repeat number distributions. The second is many-to-one mapping from the states to the syllables. A given syllable can be generated by more than one state. With these modifications, the model successfully describes the statistics of the observed syllable sequences.