Sigmoidal adaptation model of repeats and model predictions.

<p>a: Six example repeat count histograms (black bars) from the neural network simulations with adapting auditory feedback and the best fit distributions from the sigmoidal adaptation model (red lines). The decay constants of the auditory feedback and the syllable lengths are varied to produce different repeat number distributions. Syllable lengths are changed by altering the number of groups per chain. All fit errors are smaller than benchmark errors. b: Best fit geometric adaptation models for the first histogram in a. With geometric adaptation, the probably of a state repeating is decreased by a constant factor with each consecutive repeat (Materials and Methods): (i) single state; (ii) two-states, both repeating; (iii) multiple-states, only final state repeating. In all cases, numbers on arrows are initial transition probabilities while the number in parenthesis is the constant adaptation factor. c: Comparison of model fits. Red is the best fit of the sigmoidal adaptation model with one state. Other colors are best fits of the corresponding models in b. The sigmoidal adaptation model provides a superior fit while only requiring a single state. d: Peak repeat number as a function of the initial auditory feedback strength and the adaptation strength generated using the sigmoidal adaptation model. The peak repeat number increases for increasing initial feedback strength and decreases for increasing adaptation strength. For a given adaptation strength, there is a threshold feedback strength at which repeat distributions become non-Markovian (i.e. peak repeat number > 1).