Fig 1.
Stimulus paradigm and two possible percepts.
A: Repeating ABA- triplet sequences (two triplets shown) consist of higher frequency pure tones A interleaved with lower frequency pure tones B of duration TD separated by a frequency difference Δf. The time between tone onsets (dashed vertical lines) is inverse of the presentation rate 1/PR (the “-” in “ABA-” represents a silence of duration 1/PR). Throughout this paper tone duration will be set to TD = 1/PR such that offset of an A tone abuts the onset of the next B tone. B: The stimulus is perceived as either integrated into a single stream ABA-ABA- or as two separate streams A-A-A-A- and -B---B--. C: Subject reports of integrated and segregated from a single 4-minute trial (480 triplets) at Δf = 5 st and PR = 8 Hz.
Fig 2.
A: The tone frequency difference between A and B is Δf. The spread of inputs IA and IB across A1 is governed by the decaying input gain function w(Δf). Example A1 response patterns to the ABA- stimulus are shown (see Fig 3 and associated text for more details); these form the inputs to three neuronal populations rA, rB and rAB at the competition stage. Lateral inhibition strength can depend on Δf (ilcl case) or be independent of Δf (igbl case) as governed by Ci(Δf). B: Each population has a slow adaptation ak on a timescale τa with strength g, recurrent excitation ek on an intermediate timescale τe with strength βe and an independent noise source χk with strength γ. Slow synaptic depression dk on the recurrent excitation ek is not shown. Recurrent inhibition ik with strength Ci(0) is instantaneous allowing for the simplification ik = rk. See Eq (1) for an illustrative single-unit equation and Model equations and details for the full model (Eq (4)). C: The Δf-dependent profiles for the input spread w(Δf) (exponential decay (Eq (7))) and lateral inhibition Ci(Δf) (Gaussian decay (Eq (6)) for ilcl or constant βi for igbl). D: Sigmoidal firing rate function F(u) (Eq (5)) with maximal slope kF/4 at the threshold θF.
Fig 3.
A: Input time courses are represented by double alpha functions (see Model equations and details and Eq (8)) that capture the onset and plateau characteristics of A1-responses from [28]. For a single 125 ms tone of frequency A less input will arrive at locations AB and B than at A as described by Eq (7) and plotted here for Δf = 4 [26]. B: Inputs (see legend in C) to the respective populations rA, rB and rAB for an ABA- triplet of 0.5 s (tone duration and post-triplet silence “-” of 125 ms, i.e. PR = 8 Hz). Tone onsets: black circle for A-tone, gray diamond for B-tone. C: As B with curves distributed across the model’s tonotopy. The A-tone input is full amplitude at the A location, less at the AB location and further less at the B location, correspondingly for the B-tone input.
Table 1.
Model parameters as defined in Neuromechanistic model of auditory bistability and forming part of the general model equations given in Eq (4).
Fig 4.
Time courses of model responses (A–C), predicted percepts (D–E), and an example of perceptual reports from our psychoacoustic experiments (F).
A: Population firing rate time courses with Δf = 5 st and PR = 8 Hz. The firing rate function threshold θF is a horizontal dashed black line. Abrupt perceptual switches are seen when AB firing decreases/increases drastically (vertical black lines); see text for the exact criterion for a switch. B: As in A, here for the synaptic excitation variables. C: As in A for the adaptation variables. D: Percept as encoded from A, see text. E: Encoded percept for the full 240 s simulation; panels A–D show only first 20 s. F: Time course of continuous percept reporting in psychoacoustic experimental for a 240 s trial at Δf = 5 st.
Fig 5.
Statistics of dominance durations.
A: Histogram of 1000 durations from model simulations at Δf = 5 combined across perceptual type after normalising by the mean, see text. Curves show best-fit by gamma and log-normal distributions, P-values from one-way KS test are shown (in gray if the distribution can be rejected at the 0.05 significant level). B: As in A, here for the experimental condition Δf = 5; normalized data combined across subjects.
Fig 6.
Perceptual organization for stimulus parameters.
A: Schematic diagram of the perceptual regions in terms of presentation rate and frequency difference, redrawn after [2]. B: Grayscale map of proportion (of time) integrated Uint (see Eq (2)), segregated region is above red contour at Uint = 0.05, integrated region is below blue contour at Uint = 0.95, ambiguous region lies in between with equidominance at Uint = 0.5 along the dashed green contour. Vertical dashed line at PR = 8 corresponds to the frequency difference sweep used later in Figs 8 and 9.
Fig 7.
Scenarios for parametric dependence of perceptual dominance.
Schematic diagrams illustrate how the mean percept durations may change as a stimulus parameter S is varied and dominance shifts gradually from percept 1 to percept 2. The upper row illustrates the weaker percept being affected more and the lower row the stronger percept being affected more. A,D: Proportion of time when percept 1 is dominant decreases monotonically through equidominance (0.5) (dashed lines) in both scenarios. When S < Seq percept 1 is stronger, when S > Seq percept 2 is stronger. B,E: Percept durations are equal (T1 = T2 = Teq) at equidominance (S = Seq) in both scenarios. When the weaker percept is affected more the lower branches decrease more on either side of equidominance (B). When the stronger percept is affected more the upper branches increase more on either side of equidominance (E). C,F: The measure η (defined by Eq (3)) is zero at equidominance (S = Seq) for both scenarios. It decreases on either side of equidominance when the weaker percept is affected more (C) and increases on either side of equidominance when the stronger percept is affected more (F).
Fig 8.
Parametric dependence of perceptual dominance: model prediction with (efix, ilcl).
A: Proportion integrated computed across 50 simulations of 240 s at each of 15 values of Δf ∈ [1, 15] with fixed PR = 8 (this parameter range corresponds to the dashed vertical black line in Fig 6A). There is a shift from integrated being stronger to segregated being stronger with equidominance (indicated by dashed lines) at Δf ≈ 5. B: Normalized durations integrated and durations segregated with a crossover at Δf ≈ 5 where Tint = Tseg. C: The measure η given by Eq (3), which equals 0 at equidominance. The results are consistent with Δf affecting the stronger percept more (Fig 7D–7F).
Fig 9.
Parametric dependence of perceptual dominance: experiment.
Comparison of experimental and computational results. A–C: Proportion integrated, durations integrated and segregated, and the measure η plotted against Δf. Experimental data are solid curves with data points at the Δf-values indicated on the x-axis, error bars show standard error of the mean with N = 15 subjects except at Δf = 1 (N = 13) and Δf = 15 (N = 14). Model data with dynamic recurrent excitation and global inhibition (edyn, igbl) plotted for comparison. D–F: Model data with (edyn, igbl) plotted with model data for fixed recurrent excitation and spatially localized inhibition (efix, ilcl) for comparison.
Fig 10.
Perceptual organization for stimulus parameters in model (edyn, igbl).
A: Proportion integrated Uint varying Δf and PR plotted as a grayscale map. Solid are contours at Uint = 0.05 (red) and Uint = 0.95 (blue) demarcating regions where segregated and integrated are considered dominant, respectively. A dashed green contour in the ambiguous region indicates equidominance Uint = 0.5. Vertical dashed line at PR = 8 corresponds to the frequency difference sweep used in Figs 8 and 9. B: Surface plots of mean duration integrated and mean duration segregated (not normalized) across the same range as A. Black curve is the intersection of the two surfaces (equidominance). Dashed and solid curves indicate the cross sections plotted in C at PR = 5 and PR = 15, respectively. C: Durations integrated and segregated varying Δf for fixed PR as indicated; in each case the equidominance point is a black dot.
Table 2.
Frequency conditions used.
Fig 11.
First and subsequent durations, summary statistics of the subject’s grand mean durations.
A: Mean first percept duration and mean subsequent percept duration for all durations combined across both percept types, N = 16 subjects and R = 3 repetitions. Error bars show standard error of the mean. B: Standard Tukey box plot of Tglob for N = 16 subjects (box shows quartiles, whiskers are most extreme data points within 1.5 × iqr of the upper and lower quartiles, “+” are individual outliers).
Fig 12.
Non-normalized percept durations.
Durations integrated and segregated without normalization plotted against Δf for experiment and model with (edyn, igbl), as Fig 9B.
Table 3.
One-way repeated measures ANOVA of proportion integrated for the factor Δf (eight conditions, see Fig 9A).
Analysis shows a significant effect of Δf on proportion integrated. Data for N = 12 subjects, see text. Mauchly test for sphericity reaches significance, Greenhouse-Geisser correct P-value reported in the text.
Table 4.
Two-way repeated measures ANOVA of log noramlized durations for Percept type (integrated or segregated), Δf (eight conditions) and their interaction, see Fig 9B.
Analysis shows a significant interaction for Percept * Δf. Data for N = 12 subjects, see text. Mauchly test for sphericity reaches significance for the Percept * Δf interaction, Greenhouse-Geisser corrected P-value reported in the text.
Table 5.
One-way repeated measures ANOVA for the measure η with Δf as a factor (eight conditions) see Fig 9C.
Analysis shows that effect of Δf on η does not reach significance. Mauchly test for sphericity reaches significance, Greenhouse-Geisser corrected P-value reported in the text. Data for N = 12 subjects, see text.