Higher-order Markov chains can also be represented through first-order statistics in a hidden Markov model (HMM). Formally, this implies that song syntax must be modeled with a second-order or higher order Markov chain. However, analysis of the Bengalese finch song also reveals non-adjacent dependencies where transition probabilities between syllables depend not only on the current active syllable, but also one or more prior syllables sung –. between adjacent syllables in the zebra finch or syllable chunks, in the nightingale and Bengalese finch. Birdsong has often been described in terms of first-order transition statistics, e.g. However, quantitative information about the statistical complexity of song is available only for a few species, –. Among the 4500+ species of songbirds, simple and complex songs can be found, and a rich history of detailed song descriptions can be found across a wide variety of literature –. Songbirds, in their own ways, build complex vocal forms from elementary units known as syllables. So too, the complex performances of a musician or swordfighter are composed of discrete motor gestures that may be composed of more elementary motor modules or muscle synergies. The ultimate example is speech where sequences of phonemes form words that in turn are rearranged to form sentences. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Ĭompeting interests: The authors have declared that no competing interests exist.īrains build complex behaviors from simple modules. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.įunding: This work is supported by the NSF Science of Learning Center CELEST (SBE-0354378) and by a Career Award at the Scientific Interface to TJG from the Burroughs Wellcome Fund and a Smith family award to TJG. Received: SeptemAccepted: MaPublished: May 2, 2013Ĭopyright: © 2013 Markowitz et al. PLoS Comput Biol 9(5):Įditor: Dezhe Jin, The Pennsylvania State University, United States of America This vocal complexity provides a valuable model to examine how ordered behaviors are assembled from more elementary neural components in a relatively simple neural circuit.Ĭitation: Markowitz JE, Ivie E, Kligler L, Gardner TJ (2013) Long-range Order in Canary Song. Like most forms of human music, the songs of canaries contain patterns expressed over long timescales, governed by rules that apply to multiple levels of a temporal hierarchy. The choice of how long to repeat a given note or which note to choose next depends on the history of the song, and these dependencies span intervals of time much longer than previously assumed for birdsong. Here we show that one complex singer-the domesticated canary-produces a song that is strongly influenced by long-range rules. However, the complexity of these rules has not been examined statistically for the most elaborate avian singers. Recent studies suggest that bird songs may contain non-adjacent dependencies where the choice of what to sing next depends on the history of what has already been produced. The neural basis of these long-range correlations may provide insight into how complex behaviors are assembled from more elementary, stereotyped modules.īird songs range in form from the simple notes of a Chipping Sparrow to the complex repertoire of the nightingale. We show that the ordering of phrases is governed by long-range rules: the choice of what phrase to sing next in a given context depends on the history of the song, and for some syllables, highly specific rules produce correlations in song over timescales of up to ten seconds. Phrases are defined by a fundamental time-scale that is independent of the underlying syllable duration. Here we examine the song of the domesticated canary, a complex singer whose song consists of syllables, grouped into phrases that are arranged in flexible sequences. Non-adjacent correlations can be found in the syntax of some birdsongs, indicating that the choice of what to sing next is determined not only by the current syllable, but also by previous syllables sung. Bird songs range in form from the simple notes of a Chipping Sparrow to the rich performance of the nightingale.
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