Skip to main content

Thank you for visiting nature.com. 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.

  • Article
  • Published:

History-dependent variability in population dynamics during evidence accumulation in cortex

Abstract

We studied how the posterior parietal cortex combines new information with ongoing activity dynamics as mice accumulate evidence during a virtual navigation task. Using new methods to analyze population activity on single trials, we found that activity transitioned rapidly between different sets of active neurons. Each event in a trial, whether an evidence cue or a behavioral choice, caused seconds-long modifications to the probabilities that govern how one activity pattern transitions to the next, forming a short-term memory. A sequence of evidence cues triggered a chain of these modifications resulting in a signal for accumulated evidence. Multiple distinguishable activity patterns were possible for the same accumulated evidence because representations of ongoing events were influenced by previous within- and across-trial events. Therefore, evidence accumulation need not require the explicit competition between groups of neurons, as in winner-take-all models, but could instead emerge implicitly from general dynamical properties that instantiate short-term memory.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: A navigation-based evidence accumulation task in virtual reality.
Figure 2: Distributed representation of task-relevant information across PPC neurons.
Figure 3: Clustering neuronal activity across trials reveals trial-to-trial variability.
Figure 4: Long-timescale temporal structure in PPC activity.
Figure 5: Neuronal population activity in the current trial reflects the previous trial's choice and outcome.
Figure 6: Analysis of neuronal activity related to evidence accumulation.

Similar content being viewed by others

References

  1. Gold, J.I. & Shadlen, M.N. The neural basis of decision making. Annu. Rev. Neurosci. 30, 535–574 (2007).

    Article  CAS  PubMed  Google Scholar 

  2. Wang, X.-J. Neural dynamics and circuit mechanisms of decision-making. Curr. Opin. Neurobiol. 22, 1039–1046 (2012).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  3. Shadlen, M.N. & Newsome, W.T. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001).

    Article  CAS  PubMed  Google Scholar 

  4. Hanks, T.D. et al. Distinct relationships of parietal and prefrontal cortices to evidence accumulation. Nature 520, 220–223 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Raposo, D., Kaufman, M.T. & Churchland, A.K. A category-free neural population supports evolving demands during decision-making. Nat. Neurosci. 17, 1784–1792 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Licata, A.M. et al. Posterior parietal cortex guides visual decisions in rats. Preprint at bioRxiv http://dx.doi.org/10.1101/066639 (2016).

  7. Goard, M.J., Pho, G.N., Woodson, J. & Sur, M. Distinct roles of visual, parietal, and frontal motor cortices in memory-guided sensorimotor decisions. Elife 5, 471 (2016).

    Article  Google Scholar 

  8. Harvey, C.D., Coen, P. & Tank, D.W. Choice-specific sequences in parietal cortex during a virtual-navigation decision task. Nature 484, 62–68 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Wong, K.-F. & Wang, X.-J. A recurrent network mechanism of time integration in perceptual decisions. J. Neurosci. 26, 1314–1328 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Machens, C.K., Romo, R. & Brody, C.D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307, 1121–1124 (2005).

    Article  CAS  PubMed  Google Scholar 

  11. Horwitz, G.D. & Newsome, W.T. Separate signals for target selection and movement specification in the superior colliculus. Science 284, 1158–1161 (1999).

    Article  CAS  PubMed  Google Scholar 

  12. Fujisawa, S., Amarasingham, A., Harrison, M.T. & Buzsáki, G. Behavior-dependent short-term assembly dynamics in the medial prefrontal cortex. Nat. Neurosci. 11, 823–833 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Baeg, E.H. et al. Dynamics of population code for working memory in the prefrontal cortex. Neuron 40, 177–188 (2003).

    Article  CAS  PubMed  Google Scholar 

  14. Crowe, D.A., Averbeck, B.B. & Chafee, M.V. Rapid sequences of population activity patterns dynamically encode task-critical spatial information in parietal cortex. J. Neurosci. 30, 11640–11653 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Rajan, K., Harvey, C.D. & Tank, D.W. Recurrent network models of sequence generation and memory. Neuron 90, 128–142 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Vogelstein, J.T. et al. Fast nonnegative deconvolution for spike train inference from population calcium imaging. J. Neurophysiol. 104, 3691–3704 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  17. Meister, M.L.R., Hennig, J.A. & Huk, A.C. Signal multiplexing and single-neuron computations in lateral intraparietal area during decision-making. J. Neurosci. 33, 2254–2267 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Jun, J.K. et al. Heterogenous population coding of a short-term memory and decision task. J. Neurosci. 30, 916–929 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Mante, V., Sussillo, D., Shenoy, K.V. & Newsome, W.T. Context-dependent computation by recurrent dynamics in prefrontal cortex. Nature 503, 78–84 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Rigotti, M. et al. The importance of mixed selectivity in complex cognitive tasks. Nature 497, 585–590 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Maimon, G. & Assad, J.A. Beyond Poisson: increased spike-time regularity across primate parietal cortex. Neuron 62, 426–440 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Churchland, M.M. et al. Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci. 13, 369–378 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Frey, B.J. & Dueck, D. Clustering by passing messages between data points. Science 315, 972–976 (2007).

    Article  CAS  PubMed  Google Scholar 

  24. Churchland, M.M. et al. Neural population dynamics during reaching. Nature 487, 51–56 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Mazor, O. & Laurent, G. Transient dynamics versus fixed points in odor representations by locust antennal lobe projection neurons. Neuron 48, 661–673 (2005).

    Article  CAS  PubMed  Google Scholar 

  26. Briggman, K.L., Abarbanel, H.D. & Kristan, W.B. Jr. Optical imaging of neuronal populations during decision-making. Science 307, 896–901 (2005).

    Article  CAS  PubMed  Google Scholar 

  27. Renart, A. & Machens, C.K. Variability in neural activity and behavior. Curr. Opin. Neurobiol. 25, 211–220 (2014).

    Article  CAS  PubMed  Google Scholar 

  28. Marcos, E. et al. Neural variability in premotor cortex is modulated by trial history and predicts behavioral performance. Neuron 78, 249–255 (2013).

    Article  CAS  PubMed  Google Scholar 

  29. Churchland, A.K. et al. Variance as a signature of neural computations during decision making. Neuron 69, 818–831 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Bernacchia, A., Seo, H., Lee, D. & Wang, X.-J. A reservoir of time constants for memory traces in cortical neurons. Nat. Neurosci. 14, 366–372 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Donahue, C.H. & Lee, D. Dynamic routing of task-relevant signals for decision making in dorsolateral prefrontal cortex. Nat. Neurosci. 18, 295–301 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Seo, H., Barraclough, D.J. & Lee, D. Dynamic signals related to choices and outcomes in the dorsolateral prefrontal cortex. Cereb. Cortex 17 (Suppl. 1), i110–i117 (2007).

    Article  PubMed  Google Scholar 

  33. Seo, H. & Lee, D. Temporal filtering of reward signals in the dorsal anterior cingulate cortex during a mixed-strategy game. J. Neurosci. 27, 8366–8377 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Busse, L. et al. The detection of visual contrast in the behaving mouse. J. Neurosci. 31, 11351–11361 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Safaai, H., Neves, R., Eschenko, O., Logothetis, N.K. & Panzeri, S. Modeling the effect of locus coeruleus firing on cortical state dynamics and single-trial sensory processing. Proc. Natl. Acad. Sci. USA 112, 12834–12839 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Curto, C., Sakata, S., Marguet, S., Itskov, V. & Harris, K.D. A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex. J. Neurosci. 29, 10600–10612 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Nikolić, D., Husler, S., Singer, W. & Maass, W. Distributed fading memory for stimulus properties in the primary visual cortex. PLoS Biol. 7, e1000260 (2009).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  38. Klampfl, S., David, S.V., Yin, P., Shamma, S.A. & Maass, W. A quantitative analysis of information about past and present stimuli encoded by spikes of A1 neurons. J. Neurophysiol. 108, 1366–1380 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  39. Seo, H., Barraclough, D.J. & Lee, D. Lateral intraparietal cortex and reinforcement learning during a mixed-strategy game. J. Neurosci. 29, 7278–7289 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Sugrue, L.P., Corrado, G.S. & Newsome, W.T. Matching behavior and the representation of value in the parietal cortex. Science 304, 1782–1787 (2004).

    Article  CAS  PubMed  Google Scholar 

  41. Chaudhuri, R., Knoblauch, K., Gariel, M.-A., Kennedy, H. & Wang, X.-J. A large-scale circuit mechanism for hierarchical dynamical processing in the primate cortex. Neuron 88, 419–431 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Murray, J.D. et al. A hierarchy of intrinsic timescales across primate cortex. Nat. Neurosci. 17, 1661–1663 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Yang, Y. & Zador, A.M. Differences in sensitivity to neural timing among cortical areas. J. Neurosci. 32, 15142–15147 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Klampfl, S. & Maass, W. Emergence of dynamic memory traces in cortical microcircuit models through STDP. J. Neurosci. 33, 11515–11529 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Buonomano, D.V. & Maass, W. State-dependent computations: spatiotemporal processing in cortical networks. Nat. Rev. Neurosci. 10, 113–125 (2009).

    Article  CAS  PubMed  Google Scholar 

  46. Hoerzer, G.M., Legenstein, R. & Maass, W. Emergence of complex computational structures from chaotic neural networks through reward-modulated Hebbian learning. Cereb. Cortex 24, 677–690 (2014).

    Article  PubMed  Google Scholar 

  47. Murakami, M., Vicente, M.I., Costa, G.M. & Mainen, Z.F. Neural antecedents of self-initiated actions in secondary motor cortex. Nat. Neurosci. 17, 1574–1582 (2014).

    Article  CAS  PubMed  Google Scholar 

  48. Jaeger, H. & Haas, H. Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004).

    Article  CAS  PubMed  Google Scholar 

  49. Maass, W., Natschläger, T. & Markram, H. Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput. 14, 2531–2560 (2002).

    Article  PubMed  Google Scholar 

  50. Sussillo, D. & Abbott, L.F. Generating coherent patterns of activity from chaotic neural networks. Neuron 63, 544–557 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Harvey, C.D., Collman, F., Dombeck, D.A. & Tank, D.W. Intracellular dynamics of hippocampal place cells during virtual navigation. Nature 461, 941–946 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Aronov, D. & Tank, D.W. Engagement of neural circuits underlying 2D spatial navigation in a rodent virtual reality system. Neuron 84, 442–456 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Dombeck, D.A., Harvey, C.D., Tian, L., Looger, L.L. & Tank, D.W. Functional imaging of hippocampal place cells at cellular resolution during virtual navigation. Nat. Neurosci. 13, 1433–1440 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Pologruto, T.A., Sabatini, B.L. & Svoboda, K. ScanImage: flexible software for operating laser scanning microscopes. Biomed. Eng. Online 2, 13 (2003).

    Article  PubMed  PubMed Central  Google Scholar 

  55. Greenberg, D.S. & Kerr, J.N.D. Automated correction of fast motion artifacts for two-photon imaging of awake animals. J. Neurosci. Methods 176, 1–15 (2009).

    Article  PubMed  Google Scholar 

  56. Shi, J. & Malik, J. Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22, 888–905 (2000).

    Article  Google Scholar 

  57. Murphy, K.P. Machine Learning: A Probabilistic Perspective (MIT Press, 2012).

  58. Smola, A. & Vapnik, V. Support vector regression machines. Adv. Neural Inf. Process. Syst. 281–287 (1997).

  59. Chang, C.C. & Lin, C.J. LIBSVM: A library for support vector machines. ACM Trans. Intell. Syst. Technol. 2.3, 27 (2011).

    Google Scholar 

  60. Chang, C.-C. & Lin, C.-J. Training v-support vector regression: theory and algorithms. Neural Comput. 14.8, 1959–1977 (2002).

    Article  Google Scholar 

Download references

Acknowledgements

We thank S. Chettih and M. Minderer for developing the cell selection software; M. Andermann, J. Assad, W. Maass, O. Mazor, S. Panzeri, and A. Trott for discussions; and B. Datta, D. Dombeck, J. Drugowitsch, C. Gu, and members of the Harvey laboratory for comments on the manuscript. We also thank the Research Instrumentation Core at Harvard Medical School. This work was supported by a Burroughs-Wellcome Fund Career Award at the Scientific Interface, the Searle Scholars Program, the New York Stem Cell Foundation, the Alfred P. Sloan Research Foundation, a NARSAD Brain and Behavior Research Young Investigator Award, NIH grants from the NIMH BRAINS program (R01MH107620) and NINDS (R01NS089521), and a Stuart H.Q. & Victoria Quan Fellowship (A.S.M.). C.D.H. is a New York Stem Cell Foundation Robertson Neuroscience Investigator. Portions of this research were conducted on the Orchestra High Performance Compute Cluster at Harvard Medical School (supported by grant NCRR 1S10RR028832-01).

Author information

Authors and Affiliations

Authors

Contributions

A.S.M. and C.D.H. conceived of the project, designed the experiments and analyses, and wrote the paper. A.S.M. collected and analyzed the data.

Corresponding author

Correspondence to Christopher D Harvey.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Behavioral training.

a, Mazes used for behavioral training. Asterisks indicate reward location. Only some example mazes are shown (for example, right choice and not left choice maze in maze 1). b, Distribution of net evidence corresponding to different difficulties used in training the final task (maze 8; see d). c, Screen captures of the virtual environment at cue 1, cue 6, and the turn in maze 8. d, Behavioral performance across sessions for three example mice. Colors correspond to the maze colors indicated in a. Shapes correspond to the net evidence probabilities in b.

Supplementary Figure 2 Behavioral analysis of evidence accumulation.

a, Behavioral performance on each of the 11 imaging sessions, fit with a logistic function. b, Example performance from a single mouse across seven behavioral sessions fit by a linear (green) and logistic (purple) model (Methods). c, Across mice, the logistic model fit the data significantly better than the linear model (p < 0.05 for all mice, two-sample Student’s t-test), suggesting that mice used more than one piece of evidence per trial to make a choice. Error bars represent mean ± s.e.m. across datasets. Mice are colored the same as in Fig. 1c. d, Multivariate linear regression in which the mouse’s choice was the response variable and the six cue identities were separate explanatory variables. Regression coefficients for five mice (7-12 sessions each) are shown. Four of the five mice weighted early cues more than late cues. Error bars indicate confidence intervals. e-f, Fraction of correct (black) and error (gray) trials containing a minority cue (a cue indicating the incorrect choice) at each cue position, for a single mouse (e) and as the difference of the error and correct points (f) for five mice. g, Relationship between net evidence and view angle for each mouse combined across all cue positions.

Supplementary Figure 3 Example imaging field of view and activity traces.

a, Example histology image of GCaMP6m-expressing neurons in the PPC. b, Example two-photon image of GCaMP6m-expressing neurons in layer 2/3 of the PPC. c, Example ∆F/F traces (black) and deconvolved estimated spike counts (green) (Methods).

Supplementary Figure 4 Mean population activity patterns in PPC for all cells and selective cells.

a, Normalized mean activity across correct left 6-0 (left) and correct right 0-6 (right) trials for all neurons pooled across all datasets (n = 3840 cells from 11 datasets, 5 mice). Traces were normalized to the peak of each cell’s activity on either correct left 6-0 (top) or correct right 0-6 (bottom) trials, averaged, and sorted by the peak’s maze position. b, Same as in a, except for on preferred (top) or non-preferred (bottom) correct 6-0 trials. Cells were sorted according to each cell’s activity in its preferred condition. Preferred trial type was determined for each cell individually based on which trial type had higher mean activity. c-d, Same as a-b, but only for selective cells. Selective cells were defined as all cells with choice classification accuracy above 70%.

Supplementary Figure 5 Analyses of single-neuron- and population-level representations of task-relevant features.

a-b, Histogram of the fraction of the entire trial (a) and cue period (cues 1-6) (b) neurons were active (n = 3840 neurons from 5 mice). c, SVM classification accuracy (mean ± s.e.m., n = 11 datasets) for choice based on population activity on correct and error trials. Independent classifiers were trained and tested at each maze position. d, Same as Fig. 6a except for a mouse with equal cue weightings. Cumulative distribution of the pairwise trial-trial population activity correlation coefficients for epochs with the same (black) or different (green) previous cues, keeping net evidence and epoch constant (e.g. LRLXXX vs. RLLXXX trials at cue 3) (p < 1.4 x 10-4, two-sample KS test, n = 2 datasets; mouse colored as red in Fig. 1c, Supplementary Fig. 2b, d). This analysis tested if neuronal activity at a given epoch contained information about the previous epoch’s cue, independent of maze epoch and net evidence. e-f, SVR classifiers for net evidence performed on trials with nearly identical (±2.5°) view angles on left choice (e) and right choice (f) trials. g, Actual net evidence vs. net evidence predicted by an SVR classifier trained on behavioral parameters only (gray) or both behavioral parameters and neuronal population activity (black) (Methods). Error bars represent mean ± s.e.m. across datasets (n = 11). Across mice the predicted vs. actual net evidence correlation coefficient was significantly higher for the model with behavioral parameters and neuronal activity than for the model with behavioral parameters only (p < 0.001 relative to shuffled net evidence labels). Net evidence therefore appeared decodable beyond information provided by view angle. h, Data from (g) shown for individual datasets. Green crosses represent means across datasets (n = 11; p = 3.7 x 10-5, two-sample Student’s t-test). i, Peak classifier accuracy for choice for classifiers constructed with increasing numbers of neurons, added from least to most selective (based on histograms from Fig. 2c). Real data are shown in black and a simulated pseudo-population is shown in green. To create the pseudo-population, trial identities were shuffled (within a trial-type category) independently for each neuron to break neuron-neuron correlation structure but to preserve each neuron’s activity within the trial (Methods). Shaded error bars represent mean ± s.e.m. across datasets, and max individual neuron classification accuracies/correlations were the mean across datasets. j, Individual neurons’ choice classification accuracy as a function of the magnitude of the weight placed on each neuron by a linear SVM choice classifier trained on all neurons. The population classifier reached a peak accuracy of 100%. While neurons with higher individual classification accuracy were weighted more strongly, the SVM still weighted some neurons with low individual accuracy. Single trial activity on left 6-0 and right 0-6 trials for two example neurons with relatively high weight are also shown. These two neurons illustrate two ways that neurons with low individual selectivity can contribute to a population code. The left neuron (green) is active on both trial types with high variability, but slightly more so on right trials. The right neuron (purple) is primarily active on left trials, but is only active on a small subset of trials (see Methods). Top panels: each row is an individual trial. Bottom panels: mean ± s.e.m. For each net evidence condition (e.g. 2L), the mean spike count was calculated by combining the activity at all cue epochs matching the given net evidence.

Supplementary Figure 6 Characterization of behavioral and neuronal patterns across clusters.

a, Fraction of trials in each cluster in the turn epoch that were left choice trials for an example dataset. Clustering revealed neuronal activity patterns related to behavioral choices. Gray area indicates the median and 99% confidence intervals of the shuffled distribution of trial assignments to clusters. b, Comparison of the total difference from a uniform distribution for the real data (circles) to the 99% confidence intervals of the corresponding shuffle for each dataset (lines). The total difference was calculated as the summed absolute difference from the shuffle median across clusters. c-d, Same as in a-b, but for net evidence during the fifth cue. e, Distribution of trials per cluster across all epochs and datasets (n = 2457 clusters). f, Cluster self-transition probabilities for clustering performed using all epochs together. Transition probabilities were considered from one epoch to the next epoch. Low self-transition probabilities suggested that activity patterns changed over the time of consecutive epochs. Error bars represent mean ± s.e.m across datasets. g, Cumulative distribution of the number of neurons active in each cluster for different z-score activity thresholds. h, Cumulative distribution of the number of maze epochs in which a neuron was active in at least one cluster for different z-score activity thresholds. i, Cumulative distribution of the number of clusters in which a neuron was active within a single epoch for different z-score activity thresholds. j, For a given trial based on the current cluster identity, the accuracy of predicting the clusters occupied by that trial in the past and future epochs did not depend greatly on the clustering preference parameters (percentile of the distance matrix used for clustering; 1st, 10th, 30th, 50th, 70th from left to right) and, hence, numbers of clusters. Cluster numbers are the mean number of clusters for each preference parameter across datasets. Error bars represent mean ± s.e.m. across datasets.

Supplementary Figure 7 Visualizations of neuronal activity across clusters.

a-e, Mean z-scored spike count for individual neurons across clusters comprised only of correct left 6-0 trials at two adjacent epochs (Cues 4 and 5) from a single dataset. These plots demonstrate that the activity across clusters and epochs featured largely different patterns of active neurons. Neurons were either unsorted (a) or sorted according to their activity in clusters 1, 3, 7, or 9 (b-e). Neurons whose mean z-scored activity was less than 0.001 in all of the displayed clusters were excluded for display purposes (these neurons were active during a different trial epoch). Clusters were generated from correct left 6-0 trials. f-h, Left panels: Matrix of population activity correlations between each pair of cluster centers sorted according to the cluster’s left choice probability at three different maze epochs. For each cluster, the population activity was calculated as the mean activity vector across trials for each cluster. Right panels: Population activity correlation between each pair of clusters as a function of their difference in left choice probability. i-k, Same as in f-h, but for net evidence.

Supplementary Figure 8 Contribution of behavioral variability to trial–trial variability and classification of the previous trial’s outcome.

a-c, Our ability to predict the past and future population activity pattern based on the current population activity pattern could not be explained by behavioral variability. We performed a multivariate logistic regression to predict a trial’s cluster identity at a given epoch based on only the behavioral parameters at another epoch (gray) or both the behavioral parameters and the cluster identity at another epoch (black). To allow for a binary classifier, we only included those trials whose cluster identity contained either the most or second most trials during the prediction epoch (Methods). Consistently, the model based on both behavioral parameters and the previous cluster identity outperformed the model based on only behavioral parameters. This analysis was performed on left 6-0 trials (b) and right 0-6 trials (c) separately, and pooled together for all 6-0 trials (a). The behavioral parameters used were x/y position, x/y treadmill velocity, and view angle. Separate models were fit for each combination of previous and future cluster identities and combined based on the number of maze epochs between them (∆maze epochs). Adjusted R2 values were used to compare the predictive power of models with different numbers of explanatory variables. *P < 0.05, **P < 0.01, ***P < 0.001, two-sample Student’s t-test. d, Comparison of a neuronal activity-based SVM (black), behavioral parameter-based SVM (green), and the 99% confidence interval of a neuronal activity-based SVM with shuffled labels (gray) for the previous trial’s choice for a single dataset. The behavioral parameter-based SVM could not discriminate the previous trial’s choice. Classifiers were trained to distinguish the mouse’s choice on the previous trial independently at each bin in the current trial. e, Difference between the classification accuracy of the neuronal activity-based SVM and the behavioral parameter-based SVM for the previous trial’s choice. Error bars represent mean ± s.e.m. across datasets. f-g, Same as in (d-e), but with classifiers for whether or not the previous trial was rewarded.

Supplementary Figure 9 Visualizations of trial trajectories.

a-c, Trajectories of correct trials colored by the current trial type (a), the current trial’s choice (b), and the previous trial’s choice (c). Trials with the same choice but different trial types were highly overlapping (a), while trials with different choices were highly different (b). Much of the variance within a choice could be explained by the outcome of the previous trial (c). Green and black circles mark the trial start and trial end, respectively. For visualization purposes, the dimensionality of the data was reduced using factor analysis.

Supplementary Figure 10 Main results reanalyzed using ∆F/F values.

a, Classification accuracy for choice as a function of maze position (SVM, radial basis function kernel). Independent classifiers were trained and tested at each maze position. Error bars represent mean ± s.e.m. across datasets. Compare to Fig. 2e. b, Actual net evidence vs. net evidence predicted by a SVR classifier. Error bars represent mean ± s.e.m. across datasets. Compare to Fig. 2f. c, For a given trial based on the current epoch’s cluster identity, the accuracy of predicting the clusters occupied by that trial in the past and future epochs, compared to shuffled assignments of trials to clusters. Error bars represent mean ± s.e.m. across datasets. Compare to Fig. 4e. d-e, Classification accuracy as in (a), but for previous trial’s choice and for whether the previous trial was rewarded (e). Compare to Fig. 5b-c. f, Cumulative distribution of the pairwise trial-trial population activity correlation coefficients for trials with the same (black) or different (green) previous cues given the same maze epoch and same net evidence (p < 4 x 10-7, two-sample KS test). Compare to Fig. 6a. g, Relationship between classification accuracy of the previous cue and the classification accuracy of net evidence across datasets (r = 0.76, p < 0.001). Compare to Fig. 6b.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–10 and Supplementary Table 1 (PDF 2623 kb)

Supplementary Methods Checklist (PDF 434 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morcos, A., Harvey, C. History-dependent variability in population dynamics during evidence accumulation in cortex. Nat Neurosci 19, 1672–1681 (2016). https://doi.org/10.1038/nn.4403

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn.4403

This article is cited by

Search

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