Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spontaneous travelling cortical waves gate perception in behaving primates


Perceptual sensitivity varies from moment to moment. One potential source of this variability is spontaneous fluctuations in cortical activity that can travel as waves1. Spontaneous travelling waves have been reported during anaesthesia2,3,4,5,6,7, but it is not known whether they have a role during waking perception. Here, using newly developed analytic techniques to characterize the moment-to-moment dynamics of noisy multielectrode data, we identify spontaneous waves of activity in the extrastriate visual cortex of awake, behaving marmosets (Callithrix jacchus). In monkeys trained to detect faint visual targets, the timing and position of spontaneous travelling waves before target onset predicted the magnitude of target-evoked activity and the likelihood of target detection. By contrast, spatially disorganized fluctuations of neural activity were much less predictive. These results reveal an important role for spontaneous travelling waves in sensory processing through the modulation of neural and perceptual sensitivity.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Spontaneous LFP fluctuations often travel as waves across the cortex.
Fig. 2: Spontaneous travelling waves modulate ongoing spiking probability.
Fig. 3: Waves facilitate detection when aligned with the retinotopic location of visual targets.
Fig. 4: Wave state predicts target-evoked response magnitude and perceptual sensitivity.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

An open-source code repository for all methods is available on GitHub:


  1. 1.

    Engel, T. A. & Steinmetz, N. A. New perspectives on dimensionality and variability from large-scale cortical dynamics. Curr. Opin. Neurobiol. 58, 181–190 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. 2.

    Roland, P. E. et al. Cortical feedback depolarization waves: a mechanism of top-down influence on early visual areas. Proc. Natl Acad. Sci. USA 103, 12586–12591 (2006).

    ADS  CAS  PubMed  Google Scholar 

  3. 3.

    Ferezou, I., Bolea, S. & Petersen, C. C. H. Visualizing the cortical representation of whisker touch: voltage-sensitive dye imaging in freely moving mice. Neuron 50, 617–629 (2006).

    CAS  PubMed  Google Scholar 

  4. 4.

    Xu, W., Huang, X., Takagaki, K. & Wu, J.-Y. Compression and reflection of visually evoked cortical waves. Neuron 55, 119–129 (2007).

    PubMed  PubMed Central  Google Scholar 

  5. 5.

    Nauhaus, I., Busse, L., Carandini, M. & Ringach, D. L. Stimulus contrast modulates functional connectivity in visual cortex. Nat. Neurosci. 12, 70–76 (2009).

    CAS  PubMed  Google Scholar 

  6. 6.

    Reimer, A., Hubka, P., Engel, A. K. & Kral, A. Fast propagating waves within the rodent auditory cortex. Cereb. Cortex 21, 166–177 (2011).

    PubMed  Google Scholar 

  7. 7.

    Townsend, R. G. et al. Emergence of complex wave patterns in primate cerebral cortex. J. Neurosci. 35, 4657–4662 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Tomko, G. J. & Crapper, D. R. Neuronal variability: non-stationary responses to identical visual stimuli. Brain Res. 79, 405–418 (1974).

    CAS  PubMed  Google Scholar 

  9. 9.

    Shadlen, M. N. & Newsome, W. T. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18, 3870–3896 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

  10. 10.

    Okun, M., Naim, A. & Lampl, I. The subthreshold relation between cortical local field potential and neuronal firing unveiled by intracellular recordings in awake rats. J. Neurosci. 30, 4440–4448 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Luczak, A., Bartho, P. & Harris, K. D. Gating of sensory input by spontaneous cortical activity. J. Neurosci. 33, 1684–1695 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  12. 12.

    Tan, A. Y. Y., Chen, Y., Scholl, B., Seidemann, E. & Priebe, N. J. Sensory stimulation shifts visual cortex from synchronous to asynchronous states. Nature 509, 226–229 (2014).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  13. 13.

    Katzner, S. et al. Local origin of field potentials in visual cortex. Neuron 61, 35–41 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Buzsáki, G., Anastassiou, C. A. & Koch, C. The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nat. Rev. Neurosci. 13, 407–420 (2012).

    PubMed  PubMed Central  Google Scholar 

  15. 15.

    Ray, S. & Maunsell, J. H. R. Network rhythms influence the relationship between spike-triggered local field potential and functional connectivity. J. Neurosci. 31, 12674–12682 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Rubino, D., Robbins, K. A. & Hatsopoulos, N. G. Propagating waves mediate information transfer in the motor cortex. Nat. Neurosci. 9, 1549–1557 (2006).

    CAS  PubMed  Google Scholar 

  17. 17.

    Benucci, A., Frazor, R. A. & Carandini, M. Standing waves and traveling waves distinguish two circuits in visual cortex. Neuron 55, 103–117 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. 18.

    Muller, L., Reynaud, A., Chavane, F. & Destexhe, A. The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave. Nat. Commun. 5, 3675 (2014).

    ADS  PubMed  PubMed Central  Google Scholar 

  19. 19.

    Zanos, T. P., Mineault, P. J., Nasiotis, K. T., Guitton, D. & Pack, C. C. A sensorimotor role for traveling waves in primate visual cortex. Neuron 85, 615–627 (2015).

    CAS  PubMed  Google Scholar 

  20. 20.

    Bullock, T. H., Mcclune, M. C. & Enright, J. T. Are the electroencephalograms mainly rhythmic? Assessment of periodicity in wide-band time series. Neuroscience 121, 233–252 (2003).

    CAS  PubMed  Google Scholar 

  21. 21.

    Zhang, H., Watrous, A. J., Patel, A. & Jacobs, J. Theta and alpha oscillations are traveling waves in the human neocortex. Neuron 98, 1269–1281 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Steriade, M., Nuñez, A. & Amzica, F. A novel slow (<1 Hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components. J. Neurosci. 13, 3252–3265 (1993).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

    Steriade, M., Timofeev, I. & Grenier, F. Natural waking and sleep states: a view from inside neocortical neurons. J. Neurophysiol. 85, 1969–1985 (2001).

    CAS  PubMed  Google Scholar 

  24. 24.

    Muller, L. et al. Rotating waves during human sleep spindles organize global patterns of activity that repeat precisely through the night. eLife 5, e17267 (2016).

    PubMed  PubMed Central  Google Scholar 

  25. 25.

    Buzsáki, G. & Draguhn, A. Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004).

    ADS  PubMed  Google Scholar 

  26. 26.

    Kayser, C., Montemurro, M. A., Logothetis, N. K. & Panzeri, S. Spike-phase coding boosts and stabilizes information carried by spatial and temporal spike patterns. Neuron 61, 597–608 (2009).

    CAS  PubMed  Google Scholar 

  27. 27.

    Lopour, B. A., Tavassoli, A., Fried, I. & Ringach, D. L. Coding of information in the phase of local field potentials within human medial temporal lobe. Neuron 79, 594–606 (2013).

    CAS  PubMed  Google Scholar 

  28. 28.

    McGinley, M. J., David, S. V. & McCormick, D. A. Cortical membrane potential signature of optimal states for sensory signal detection. Neuron 87, 179–192 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Zanos, T. P., Mineault, P. J. & Pack, C. C. Removal of spurious correlations between spikes and local field potentials. J. Neurophysiol. 105, 474–486 (2011).

    PubMed  Google Scholar 

  30. 30.

    Xing, D., Yeh, C.-I. & Shapley, R. M. Spatial spread of the local field potential and its laminar variation in visual cortex. J. Neurosci. 29, 11540–11549 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Bringuier, V., Chavane, F., Glaeser, L. & Frégnac, Y. Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons. Science 283, 695–699 (1999).

    ADS  CAS  PubMed  Google Scholar 

  32. 32.

    Lewis, D. A. Horizontal synaptic connections in monkey prefrontal cortex: an in vitro electrophysiological study. Cereb. Cortex 10, 82–92 (2000).

    PubMed  Google Scholar 

  33. 33.

    Girard, P., Hupé, J. M. & Bullier, J. Feedforward and feedback connections between areas V1 and V2 of the monkey have similar rapid conduction velocities. J. Neurophysiol. 85, 1328–1331 (2001).

    CAS  PubMed  Google Scholar 

  34. 34.

    Alexander, D. M., Ball, T., Schulze-Bonhage, A. & van Leeuwen, C. Large-scale cortical travelling waves predict localized future cortical signals. PLOS Comput. Biol. 15, e1007316 (2019).

    PubMed  PubMed Central  Google Scholar 

  35. 35.

    van Vugt, B. et al. The threshold for conscious report: Signal loss and response bias in visual and frontal cortex. Science 360, 537–542 (2018).

    ADS  PubMed  Google Scholar 

  36. 36.

    Palmer, C., Cheng, S.-Y. & Seidemann, E. Linking neuronal and behavioral performance in a reaction-time visual detection task. J. Neurosci. 27, 8122–8137 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Luck, S. J., Chelazzi, L., Hillyard, S. A. & Desimone, R. Neural mechanisms of spatial selective attention in areas V1, V2, and V4 of macaque visual cortex. J. Neurophysiol. 77, 24–42 (1997).

    CAS  PubMed  Google Scholar 

  38. 38.

    Niell, C. M. & Stryker, M. P. Modulation of visual responses by behavioral state in mouse visual cortex. Neuron 65, 472–479 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. 39.

    Stringer, C. et al. Spontaneous behaviors drive multidimensional, brainwide activity. Science 364, eaav7893 (2019).

    CAS  Google Scholar 

  40. 40.

    Brüers, S. & VanRullen, R. Alpha power modulates perception independently of endogenous factors. Front. Neurosci. 12, 279 (2018).

    PubMed  PubMed Central  Google Scholar 

  41. 41.

    Petersen, C. C. H., Hahn, T. T. G., Mehta, M., Grinvald, A. & Sakmann, B. Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex. Proc. Natl Acad. Sci. USA 100, 13638–13643 (2003).

    ADS  CAS  PubMed  Google Scholar 

  42. 42.

    Poulet, J. F. A. & Petersen, C. C. H. Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice. Nature 454, 881–885 (2008).

    ADS  CAS  PubMed  Google Scholar 

  43. 43.

    Busch, N. A., Dubois, J. & VanRullen, R. The phase of ongoing EEG oscillations predicts visual perception. J. Neurosci. 29, 7869–7876 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Mathewson, K. E., Gratton, G., Fabiani, M., Beck, D. M. & Ro, T. To see or not to see: prestimulus α phase predicts visual awareness. J. Neurosci. 29, 2725–2732 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  45. 45.

    Samaha, J., Gosseries, O. & Postle, B. R. Distinct oscillatory frequencies underlie excitability of human occipital and parietal cortex. J. Neurosci. 37, 2824–2833 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  46. 46.

    Helfrich, R. F. et al. Neural mechanisms of sustained attention are rhythmic. Neuron 99, 854–865 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Fiebelkorn, I. C., Pinsk, M. A. & Kastner, S. A dynamic interplay within the frontoparietal network underlies rhythmic spatial attention. Neuron 99, 842–853 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. 48.

    Gabor, D. Theory of communication. Part 1: The analysis of information. J. Inst. Electr. Eng. 3 93, 429–441 (1946).

    Google Scholar 

  49. 49.

    Le Van Quyen, M. et al. Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. J. Neurosci. Methods 111, 83–98 (2001).

    Google Scholar 

  50. 50.

    Oppenheim, A. V., Schafer, R. W. & Buck, J. R. Discrete-Time Signal Processing. (Prentice Hall, 1999).

  51. 51.

    Marple, L. Computing the discrete-time analytic signal via FFT. IEEE Trans. Signal Process. 47, 2600–2603 (1999).

    ADS  MATH  Google Scholar 

  52. 52.

    Johansson, M. The Hilbert transform. Masters Thesis. Växjö University (1999);

  53. 53.

    Feldman, M. Hilbert transform in vibration analysis. Mech. Syst. Signal Process. 25, 735–802 (2011).

    ADS  Google Scholar 

  54. 54.

    Pereda, E., Gamundi, A., Rial, R. & González, J. Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages. Neurosci. Lett. 250, 91–94 (1998).

    CAS  PubMed  Google Scholar 

  55. 55.

    Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M. & Ilmoniemi, R. J. Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. 21, 1370–1377 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  56. 56.

    Milstein, J., Mormann, F., Fried, I. & Koch, C. Neuronal shot noise and Brownian 1/f2 behavior in the local field potential. PLoS ONE 4, e4338 (2009).

    ADS  PubMed  PubMed Central  Google Scholar 

  57. 57.

    Rao Jammalamadaka, S. & Sengupta, A. Topics in Circular Statistics (World Scientific, 2001).

  58. 58.

    Rosa, M. G. P. & Elston, G. N. Visuotopic organisation and neuronal response selectivity for direction of motion in visual areas of the caudal temporal lobe of the marmoset monkey (Callithrix jacchus): middle temporal area, middle temporal crescent, and surrounding cortex. J. Comp. Neurol. 393, 505–527 (1998).

    CAS  PubMed  Google Scholar 

  59. 59.

    Frank, T. D. & Richardson, M. J. On a test statistic for the Kuramoto order parameter of synchronization: An illustration for group synchronization during rocking chairs. Physica D 239, 2084–2092 (2010).

    ADS  MathSciNet  CAS  MATH  Google Scholar 

  60. 60.

    Menard, S. Applied Logistic Regression Analysis (Sage, 2002).

  61. 61.

    Menard, S. Six approaches to calculating standardized logistic regression coefficients. Am. Stat. 58, 218–223 (2004).

    MathSciNet  Google Scholar 

  62. 62.

    Tehovnik, E. J., Slocum, W. M., Carvey, C. E. & Schiller, P. H. Phosphene induction and the generation of saccadic eye movements by striate cortex. J. Neurophysiol. 93, 1–19 (2005).

    CAS  PubMed  Google Scholar 

  63. 63.

    Bremmer, F., Kubischik, M., Hoffmann, K.-P. & Krekelberg, B. Neural dynamics of saccadic suppression. J. Neurosci. 29, 12374–12383 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

Download references


We thank M. Avery, K. Williams, S. Adams and M. LeBlanc for their contributions to this project and T. Movshon for his feedback in the early stages of this project. This work received funding from The Dan and Martina Lewis Biophotonics Fellowship, Gatsby Charitable Foundation, the Fiona and Sanjay Jha Chair in Neuroscience, the Canadian Institute for Health Research, the Swartz Foundation, BrainsCAN at Western University through the Canada First Research Excellence Fund (CFREF), the Office of Naval Research N00014-16-1-2829, and NIH grants R01-EY028723, U01-NS108683, P30-EY0190005, T32 EY020503-06 and T32 MH020002-16A.

Author information




Conceptualization: Z.W.D., L.M., J.H.R.; data curation: Z.W.D., L.M.; formal analysis: Z.W.D., L.M.; funding acquisition: Z.W.D., L.M., T.S., J.H.R.; investigation: Z.W.D., L.M.; methodology: Z.W.D., L.M., T.S., J.M.-T., J.H.R.; supervision: T.S., J.M.-T., J.H.R.; visualization: Z.W.D., L.M.; writing original draft: Z.W.D., L.M., J.H.R.; and writing, review and editing: Z.W.D., L.M., T.S., J.M.-T. and J.H.R.

Corresponding authors

Correspondence to Zachary W. Davis or John H. Reynolds.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Retinotopic mapping and motion direction tuning is consistent with the anatomical organization and tuning preferences of marmoset MT.

a, Receptive fields for recorded units were measured by reverse correlation. Monkeys held fixation on a marmoset face while visual probes (drifting Gabor) appeared at random locations in the visual hemifield contralateral to the recording array. Each probe would appear, drift for 200 ms, and disappear after which a new probe would appear in a new random location and the process would repeat until the monkey broke fixation. b, The estimated position and orientation of Utah arrays in area MT based on retinotopy and histological examination for monkey W (blue) and monkey T (red). c, Example receptive fields and their preference for motion direction were consistent with previous reports of marmoset MT58.

Extended Data Fig. 2 Detection of spontaneous travelling waves.

a, The method for detecting spontaneous waves from the Generalized Phase. First, the detection algorithm found the most likely starting point for a putative wave as the point that maximizes the divergence of the phase gradient (step 1). b, With this source point found, the algorithm then quantified the spatiotemporal organization about this point from the circular-linear correlation of phase with distance across the whole array (step 2). With this approach, the algorithm can robustly detect arbitrarily shaped wavefronts in the array data. c, The average power spectrum for waves (N = 215) had significantly less power in low frequencies (<12 Hz) as compared to non-wave fluctuations (N = 524). Dotted bounds represent s.e.m. Asterisk: P < 1 × 10−5, two-tailed Wilcoxon rank-sum test. d, Detected waves in both monkeys predominantly travelled at speeds consistent with the conduction velocity of unmyelinated horizontal axons (0.1–0.6 m/s, red dashed lines; monkey W, 5571 waves, blue line; monkey T, 9285 waves, red line). e, There was no difference in the amplitude of fluctuations that were detected as waves (blue line; N = 696 waves) or rejected (non-wave, grey line; N = 565 non-wave fluctuations; example monkey T session).

Extended Data Fig. 3 Wideband GP is better coupled to spike timing than narrowband alpha or theta filters.

a, The phase and amplitude of the raw (5–100 Hz) LFP was poorly captured by narrow-band theta (4–8 Hz, blue dotted line) or alpha (8–13 Hz, red dotted line) filters. b, Scatter plot showing spontaneous spike-phase coupling was greater for GP (5–40 Hz) than alpha or theta narrowband filtered phases. Coupling averaged across electrodes for individual recording sessions is plotted as black dots and each red dot represents the average value across sessions. c, Spontaneous spike-phase coupling remained stronger for GP than the narrow frequency bands even when the spontaneous LFP epochs were restricted to periods where there is large alpha (12.06% of recorded time) or theta (7.24%) LFP power during fixation (5 dB SNR, narrow- to broad-band power ratio). Results are presented from monkey W.

Extended Data Fig. 4 Spike coupling to GP is spatially dependent.

a, Scatter plot showing the average spike–GP coupling across the distances of the array. Each point was averaged across a given spike-phase distance for a single recording session in monkey W (N = 22 sessions). The red dashed line shows the average null distribution for shuffled phases ± 2 s.d. (shaded region). b, Same as a, but for monkey T (N = 18 sessions). c, Scatter plot showing the cross-channel GP correlation for 200 ms of LFP during fixation across the electrode distances of the recording array. Each dot is the average circular correlation within an individual recording session across that channel distance. Shaded region represents the mean (±2 s.d.) correlation after shuffling the spatial position of the electrodes. d, Same as c, but for monkey T.

Extended Data Fig. 5 Spontaneous travelling waves are present during normal viewing of naturalistic visual scenes.

Marmosets freely viewed static natural images for 10 s while head-fixed. a, An example high-contrast image with the gaze of the marmoset over the 10 s viewing interval shown in red. b, An example of a spontaneous travelling wave detected during a period of fixation while monkey T was freely viewing a high-contrast image. c, Across 86 trials, 593 spontaneous travelling waves were detected during spontaneous fixations while the monkey freely viewed the images (−50 to +100 ms perisaccadic activity excluded). d, The density of observed wave speeds was consistent with the conduction velocity of unmyelinated axons (0.1–0.6 m s−1).

Extended Data Fig. 6 False alarms are not predicted by the phase of travelling waves.

To test whether the alignment of waves with the target location produces a bias towards saccading to that location, we examined the spontaneous activity before false alarms, time locked to the eye movement. This is distinct from our analysis of hits, which was time locked to the onset of the target, and is a limitation in our design for comparing hits to false alarms. However, we did find a significant modulation of spontaneous spiking activity that was possibly the sensory signal generating the false alarm, giving us a window to explore their potential relationship with waves62. If waves increase the likelihood of false alarms, they should show some phase-dependent relationship similar to what we observe in hits, but time-locked to the spiking activity predictive of a false alarm. a, Multi-unit spiking activity (normalized to the baseline, shaded regions ± s.e.m.) for monkey W (blue) and monkey T (red) was significantly increased in the interval before a false alarm (grey shaded box, −120 ms to −60 ms, P < 0.001, two-sided Wilcoxon rank-sum test). b, Scatter plot showing the average firing rate before the false alarm (y axis, shaded interval in a) was significantly greater than the spontaneous background firing rate (x axis, −400 ms to −200 ms) for monkey W (blue dots; N = 62 multi-units, P < 0.0001, Wilcoxon signed rank test) and monkey T (red dots; N = 70 multi-units). c, Cross-trial phase alignments for waves aligned to the location of false alarm for the interval preceding the occurrence of a false alarm. There was no strong phase alignment during the period of significant spiking activity (shaded region) for either monkey W (blue line) or monkey T (red line) that would show a wave state is predictive of a false alarm. However, there was a strong phase alignment just before (monkey T −40 ms) and during the eye movement (monkey W, 0 ms). Given their close proximity to the onset of the eye movement we suspect the observed alignment may reflect an efference signal related to the pending saccade63. d, The distribution of observed wave phases was uniform during the period of significantly increased spiking activity (−90 ms before false alarm), indicating there was no relationship between the phase of spontaneous waves and the spontaneous spiking fluctuation associated with false alarms. Data collapsed across both monkeys as there was no difference in their distributions.

Extended Data Fig. 7 Target-evoked response magnitude is correlated with detection performance.

a, Detection performance of different target contrasts for monkey W (blue) and monkey T (red) across training days where those contrasts were presented. Both monkeys had similar psychophysical thresholds, defined as the contrast where the monkey detected the target 50 percent of the time on average (c50) as estimated from a sigmoid fit (grey dashed line). b, c, Distributions of reaction times for monkey W (b) and monkey T (c) during the detection task at their c50 value. The median reaction time for each monkey is shown by a red line. d, Spike rasters for an example neuron with trials sorted into hits (bottom rasters) and misses (top rasters). e, Scatter plot showing the distribution of mean hit (x axis) and miss (y axis) evoked responses (80–200 ms) for all single- (x) and multi-units (dot) recorded across all sessions for monkey W (blue) and monkey T (red). The circled x is the example neuron from d. Target-evoked responses were significantly stronger for detected targets in both monkeys. (monkey W, N = 25 single- and 83 multi-units, P < 0.01; monkey T, N = 27 single and 110 multi-units, P < 1 × 10−5; two-sided Wilcoxon signed-rank test).

Extended Data Fig. 8 Narrowband filters fail to detect any significant wave phase alignment before target onset.

a, The cross-trial phase alignment computed as in Fig. 3, but using a narrowband alpha (8–13 Hz) filter, did not show any significant alignment (grey dashed line) for hits (blue) or misses (grey) before target onset (grey region) for either monkey T (top) or monkey W (bottom). b, The same as in a, but for a beta (15–30 Hz) narrowband filter.

Extended Data Fig. 9 Instantaneous voltage is less predictive of spike timing and perception than GP.

a, Scatter plot showing the relationship between instantaneous LFP amplitude in voltage, and GP. The same voltage value occurred across a broad range of phases. b, While we found wave phase to be predictive of detection, the average LFP voltage was not different preceding a hit (blue) or a miss (red). Shaded area indicates s.e.m. across 18 sessions in monkey T. c, Scatter plot showing the coupling of spike probability to GP. Each point is the probability of a spike occurring in that phase bin within a recording session (N = 18). There was a strong circular-linear correlation of GP with spike probability (r = 0.87). d, Scatter plot showing weaker spike-amplitude coupling. Each point is the relative probability of a spike occurring in each voltage bin, normalized by the amount of time that instantaneous voltage occurs. Spike probability was less correlated with LFP amplitude (Spearman’s rank correlation, r = −0.48).

Supplementary information

Supplementary Information

Table S1. GLM analysis for predictors of network state.

Reporting Summary

Video 1

Example of multiple detected traveling waves. Video with 205 ms of spontaneous LFP data while monkey T is fixating a white dot on a gray screen. The wave examples in Figure 1b begin at 24 ms and 168 ms in this video. Color axis scales from 80 µV (blue) to -80 µV (red).

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Davis, Z.W., Muller, L., Martinez-Trujillo, J. et al. Spontaneous travelling cortical waves gate perception in behaving primates. Nature 587, 432–436 (2020).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing