Figure 3.

Gap durations are formed by the underlying respiratory patterns. (a) Model of the respiratory timescales that generate different modes of gap durations. Schematics illustrate all parameters of the gap duration distributions described in the text. (b) An exponential distribution (time constant τ₁) is used to model the durations of expiratory (mode-1) gaps. (c) Gap duration distribution of a subsong bird overlaid with the distribution of mode-1 gaps (red trace). The distributions overlap well at short durations. (d) Histogram of mode-1 gap timescales (τ₁), determined from exponential fits to the overall gap duration distribution at short durations (<~30ms, see Methods). Red symbols show mode-1 gap timescales directly determined from birds with air sac pressure measurements. (e) A Gaussian distribution (mean μ, standard deviation σ) is used to model the distribution of gaps whose durations are tightly coupled to IP durations (mode-2 gaps). (f) Gap duration distribution and IP duration distribution (green trace), measured in the same bird and rescaled to match peak height. (g) Histogram of peak centers identified in gap duration distributions, μ. Green symbols show average IP durations directly determined from air sac pressure measurements. (h) Mode-3 gap durations are modeled by the sum of an exponentially-distributed expiratory period duration (time constant τ₃, blue trace) and a Gaussian-distributed IP duration (green trace), forming an ex-Gaussian duration distribution (orange trace). (i) Gap duration distribution plotted with the distribution of positive-pressure periods in mode-3 gaps, shifted by the mean IP duration (blue trace). (j) Histogram of long (100–200 ms) gap timescales (τ₃). Blue symbols show timescales of the positive-pressure periods in mode-3 gaps, determined from air sac pressure measurements.