Abstract
Vocal folds are used as sound sources in various species, but it is unknown how vocal fold morphologies are optimized for different acoustic objectives. Here we identify two main variables affecting range of vocal fold vibration frequency, namely vocal fold elongation and tissue fiber stress. A simple vibrating string model is used to predict fundamental frequency ranges across species of different vocal fold sizes. While average fundamental frequency is predominantly determined by vocal fold length (larynx size), range of fundamental frequency is facilitated by (1) laryngeal muscles that control elongation and by (2) nonlinearity in tissue fiber tension. One adaptation that would increase fundamental frequency range is greater freedom in joint rotation or gliding of two cartilages (thyroid and cricoid), so that vocal fold length change is maximized. Alternatively, tissue layers can develop to bear a disproportionate fiber tension (i.e., a ligament with high density collagen fibers), increasing the fundamental frequency range and thereby vocal versatility. The range of fundamental frequency across species is thus not simply one-dimensional, but can be conceptualized as the dependent variable in a multi-dimensional morphospace. In humans, this could allow for variations that could be clinically important for voice therapy and vocal fold repair. Alternative solutions could also have importance in vocal training for singing and other highly-skilled vocalizations.
Highlights
A biological trait is usually the result of a trade-off between different selective forces and constraints [1]
Whereas the average fundamental frequency is predictable by body size, the range of fundamental frequency depends on two different factors
The first is a freedom of movement factor–how much vocal cord length change can be produced by muscles that rotate or PLOS Computational Biology | DOI:10.1371/journal.pcbi
Summary
A biological trait is usually the result of a trade-off between different selective forces and constraints [1]. In order to understand the design of vocal organs (larynx and syrinx in vertebrates), investigators have often focused on size as the primary determining factor of fundamental frequency and acoustic power produced by a sound source. A number of size-dependent factors are responsible for the observation that species of larger body sizes tend to produce lower frequencies[2],[3], yet some observations cannot be explained by vocal fold size alone. The relation between fundamental frequency (fo) and body size appears uncoupled within some species [4],[5],[6]. Mechanical properties, a direct consequence of morphological design, show a large variation and contribute to vocal differences within and between species [10],[11],[12],[8]. We present predictions from vibrating string theory that offer an explanation for why a larger than expected range of fo can be achievable in large and small species
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