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.

Emotion prediction errors guide socially adaptive behaviour

Nature Human Behaviour volume 5, pages 1391–1401 (2021)Cite this article

Subjects

Abstract

People make decisions based on deviations from expected outcomes, known as prediction errors. Past work has focused on reward prediction errors, largely ignoring violations of expected emotional experiences—emotion prediction errors. We leverage a method to measure real-time fluctuations in emotion as people decide to punish or forgive others. Across four studies (N = 1,016), we reveal that emotion and reward prediction errors have distinguishable contributions to choice, such that emotion prediction errors exert the strongest impact during decision-making. We additionally find that a choice to punish or forgive can be decoded in less than a second from an evolving emotional response, suggesting that emotions swiftly influence choice. Finally, individuals reporting significant levels of depression exhibit selective impairments in using emotion—but not reward—prediction errors. Evidence for emotion prediction errors potently guiding social behaviours challenge standard decision-making models that have focused solely on reward.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

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

Fig. 1: The tasks and PE calculations.
Fig. 2: Emotion PEs underpin punitive behaviour in the UG and JG.
Fig. 3: Temporal dynamics of emotional experiences during choice.
Fig. 4: Results of experiment 4.

Data availability

Experiment materials information and all experiment de-identified data are publicly available at https://github.com/jpheffne/epe. The materials used in this study are widely available.

Code availability

Data analysis script notebooks are publicly available at https://github.com/jpheffne/epe.

References

  1. Schultz, W., Dayan, P. & Montague, P. R. A neural substrate of prediction and reward. Science 275, 1593–1599 (1997).

    CAS  PubMed  Google Scholar 

  2. Schultz, W. & Dickinson, A. Neuronal coding of prediction errors. Annu. Rev. Neurosci. 23, 473–500 (2000).

    CAS  PubMed  Google Scholar 

  3. King-Casas, B. et al. Getting to know you: reputation and trust in a two-person economic exchange. Science 308, 78–83 (2005).

    CAS  PubMed  Google Scholar 

  4. Pessiglione, M., Seymour, B., Flandin, G., Dolan, R. J. & Frith, C. D. Dopamine-dependent prediction errors underpin reward-seeking behaviour in humans. Nature 442, 1042–1045 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Sutton, R. S. & Barto, A. G. Introduction to Reinforcement Learning (MIT Press, 1998).

  6. Ruff, C. C. & Fehr, E. The neurobiology of rewards and values in social decision making. Nat. Rev. Neurosci. 15, 549–562 (2014).

    CAS  PubMed  Google Scholar 

  7. Ho, M. K., MacGlashan, J., Littman, M. L. & Cushman, F. Social is special: a normative framework for teaching with and learning from evaluative feedback. Cognition 167, 91–106 (2017).

    PubMed  Google Scholar 

  8. Bechara, A., Damasio, H., Tranel, D. & Damasio, A. R. Deciding advantageously before knowing the advantageous strategy. Science 275, 1293–1295 (1997).

    CAS  PubMed  Google Scholar 

  9. Dalgleish, T. The emotional brain. Nat. Rev. Neurosci. 5, 583–589 (2004).

    PubMed  Google Scholar 

  10. Vuilleumier, P. How brains beware: neural mechanisms of emotional attention. Trends Cogn. Sci. 9, 585–594 (2005).

    PubMed  Google Scholar 

  11. Phelps, E. A., Lempert, K. M. & Sokol-Hessner, P. Emotion and decision making: multiple modulatory neural circuits. Annu. Rev. Neurosci. 37, 263–287 (2014).

    CAS  PubMed  Google Scholar 

  12. Phelps, E. A. Emotion and cognition: insights from studies of the human amygdala. Annu. Rev. Psychol. 57, 27–53 (2006).

    PubMed  Google Scholar 

  13. Richard, R., van der Pligt, J. & de Vries, N. Anticipated affect and behavioral choice. Basic Appl. Soc. Psychol. 18, 111–129 (1996).

    Google Scholar 

  14. Caplin, A. & Leahy, J. Psychological expected utility theory and anticipatory feelings. Q. J. Econ. 116, 55–79 (2001).

    Google Scholar 

  15. Knutson, B. & Greer, S. M. Anticipatory affect: neural correlates and consequences for choice. Philos. Trans. R. Soc. B 363, 3771–3786 (2008).

    Google Scholar 

  16. Nielsen, L., Knutson, B. & Carstensen, L. L. Affect dynamics, affective forecasting, and aging. Emotion 8, 318–330 (2008).

    PubMed  PubMed Central  Google Scholar 

  17. Mellers, B. A. & McGraw, A. P. Anticipated emotions as guides to choice. Curr. Dir. Psychol. Sci. 10, 210–214 (2001).

    Google Scholar 

  18. Mellers, B., Schwartz, A. & Ritov, I. Emotion-based choice. J. Exp. Psychol. Gen. 128, 332–345 (1999).

    Google Scholar 

  19. Feldmanhall, O. & Chang, L. J. in Goal-Directed Decision Making (eds Morris R., Bornstein A. & Shenhav A.) Ch. 14, 309–330 (Academic, 2018).

  20. Xiang, T., Lohrenz, T. & Montague, P. R. Computational substrates of norms and their violations during social exchange. J. Neurosci. 33, 1099 (2013).

    PubMed  PubMed Central  Google Scholar 

  21. Hétu, S., Luo, Y., D’Ardenne, K., Lohrenz, T. & Montague, P. R. Human substantia nigra and ventral tegmental area involvement in computing social error signals during the ultimatum game. Soc. Cogn. Affect. Neurosci. 12, 1972–1982 (2017).

    PubMed  PubMed Central  Google Scholar 

  22. Thornton, M. A. & Tamir, D. I. Mental models accurately predict emotion transitions. Proc. Natl Acad. Sci. USA 114, 5982 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Chang, L. & Sanfey, A. Unforgettable ultimatums? Expectation violations promote enhanced social memory following economic bargaining. Front. Behav. Neurosci. 3, 36 (2009).

    PubMed  PubMed Central  Google Scholar 

  24. Chang, L. J. & Sanfey, A. G. Great expectations: neural computations underlying the use of social norms in decision-making. Soc. Cogn. Affect. Neurosci. 8, 277–284 (2011).

    PubMed  PubMed Central  Google Scholar 

  25. Loewenstein, G. & Lerner, J. S. in Handbook of Affective Sciences. Series in Affective Science (eds Davidson, R. J., Scherer, K. R. & Hill Goldsmith H.) 619–642 (Oxford Univ. Press, 2003).

  26. Chang, L. J. & Eshin, J. in The Nature of Emotion: Fundamental Questions (eds Fox A. S., Lapate R. C., Shackman A. J. & Davidson R. J.) (Oxford Univ. Press, 2018).

  27. Hartley, C. & Sokol-Hessner, P. in The Nature of Emotion: Fundamental Questions (eds Fox A. S., Lapate R. C., Shackman A. J. & Davidson R. J.) (Oxford Univ. Press, 2017).

  28. Sanfey, A. G. Social decision-making: Insights from game theory and neuroscience. Science 318, 598–602 (2007).

    CAS  PubMed  Google Scholar 

  29. Pessoa, L. How do emotion and motivation direct executive control? Trends Cogn. Sci. 13, 160–166 (2009).

    PubMed  PubMed Central  Google Scholar 

  30. O’Doherty, J., Kringelbach, M. L., Rolls, E. T., Hornak, J. & Andrews, C. Abstract reward and punishment representations in the human orbitofrontal cortex. Nat. Neurosci. 4, 95 (2001).

    PubMed  Google Scholar 

  31. Dolan, R. J. Emotion, cognition, and behavior. Science 298, 1191–1194 (2002).

    CAS  PubMed  Google Scholar 

  32. Juechems, K. & Summerfield, C. Where does value come from? Trends Cogn. Sci. 23, 836–850 (2019).

    PubMed  Google Scholar 

  33. Kahneman, D. & Tversky, A. Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979).

    Google Scholar 

  34. Ironside, M. et al. Approach-avoidance conflict in major depression: congruent neural findings in human and non-human primates. Biol. Psychiatry https://doi.org/10.1016/j.biopsych.2019.08.022 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Treadway, M. T. & Zald, D. H. Parsing anhedonia: translational models of reward-processing deficits in psychopathology. Curr. Dir. Psychol. Sci. 22, 244–249 (2013).

    PubMed  PubMed Central  Google Scholar 

  36. Whitton, A. E., Treadway, M. T. & Pizzagalli, D. A. Reward processing dysfunction in major depression, bipolar disorder and schizophrenia. Curr. Opin. Psychiatry 28, 7–12 (2015).

    PubMed  PubMed Central  Google Scholar 

  37. Hooker, C. & Park, S. Emotion processing and its relationship to social functioning in schizophrenia patients. Psychiatry Res. 112, 41–50 (2002).

    PubMed  Google Scholar 

  38. Pessoa, L. On the relationship between emotion and cognition. Nat. Rev. Neurosci. 9, 148–158 (2008).

    CAS  PubMed  Google Scholar 

  39. Berridge, K. C. The debate over dopamine’s role in reward: the case for incentive salience. Psychopharmacology 191, 391–431 (2007).

    CAS  PubMed  Google Scholar 

  40. Berridge, K. C., Robinson, T. E. & Aldridge, J. W. Dissecting components of reward: ‘liking’, ‘wanting’, and learning. Curr. Opin. Pharmacol. 9, 65–73 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  41. Russell, J. A. Core affect and the psychological construction of emotion. Psychol. Rev. 110, 145–172 (2003).

    PubMed  Google Scholar 

  42. Russell, J. A. & Barrett, L. F. Core affect, prototypical emotional episodes, and other things called emotion: dissecting the elephant. J. Pers. Soc. Psychol. 76, 805–819 (1999).

    CAS  PubMed  Google Scholar 

  43. Russell, J. A., Weiss, A. & Mendelsohn, G. A. Affect grid: a single-item scale of pleasure and arousal. J. Pers. Soc. Psychol. 57, 493–502 (1989).

    Google Scholar 

  44. Dayan, P. & Daw, N. D. Decision theory, reinforcement learning, and the brain. Cogn. Affect. Behav. Neurosci. 8, 429–453 (2008).

    PubMed  Google Scholar 

  45. Berridge, K. C. From prediction error to incentive salience: mesolimbic computation of reward motivation. Eur. J. Neurosci. 35, 1124–1143 (2012).

    PubMed  PubMed Central  Google Scholar 

  46. Kaelbling, L. P., Littman, M. L. & Moore, A. W. Reinforcement learning: a survey. J. Artif. Int. Res. 4, 237–285 (1996).

    Google Scholar 

  47. Montague, P. R., Dayan, P. & Sejnowski, T. J. A framework for mesencephalic dopamine systems based on predictive Hebbian learning. J. Neurosci. 16, 1936 (1996).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. Daw, N. D., Niv, Y. & Dayan, P. Uncertainty-based competition between prefrontal and dorsolateral striatal systems for behavioral control. Nat. Neurosci. 8, 1704–1711 (2005).

    CAS  PubMed  Google Scholar 

  49. Levy, D. J. & Glimcher, P. W. The root of all value: a neural common currency for choice. Curr. Opin. Neurobiol. 22, 1027–1038 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. Güth, W., Schmittberger, R. & Schwarze, B. An experimental analysis of ultimatum bargaining. J. Econ. Behav. Organ. 3, 367–388 (1982).

    Google Scholar 

  51. FeldmanHall, O., Sokol-Hessner, P., Van Bavel, J. J. & Phelps, E. A. Fairness violations elicit greater punishment on behalf of another than for oneself. Nat. Commun. 5, 5306 (2014).

    CAS  PubMed  Google Scholar 

  52. Rutledge, R. B., Skandali, N., Dayan, P. & Dolan, R. J. A computational and neural model of momentary subjective well-being. Proc. Natl Acad. Sci. USA 111, 12252 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  53. Aiken, L. S. & West, S. G. in Multiple Regression: Testing and Interpreting Interactions (eds Aiken, L. S. & West, S. G.) Ch. XI, 212 (Sage, 1991).

  54. Iacobucci, D., Schneider, M. J., Popovich, D. L. & Bakamitsos, G. A. Mean centering helps alleviate “micro” but not “macro” multicollinearity. Behav. Res. Methods 48, 1308–1317 (2016).

    PubMed  Google Scholar 

  55. Delgado, M. R., Locke, H. M., Stenger, V. A. & Fiez, J. A. Dorsal striatum responses to reward and punishment: effects of valence and magnitude manipulations. Cogn. Affect. Behav. Neurosci. 3, 27–38 (2003).

    CAS  PubMed  Google Scholar 

  56. Murray, E. A. The amygdala, reward and emotion. Trends Cogn. Sci. 11, 489–497 (2007).

    PubMed  Google Scholar 

  57. Lang, P. J. & Bradley, M. M. in Handbook of Approach and Avoidance Motivation (ed. Elliot A. J.) 51–65 (Psychology, 2008).

  58. Clogg, C. C., Petkova, E. & Haritou, A. Statistical methods for comparing regression coefficients between models. Am. J. Sociol. 100, 1261–1293 (1995).

    Google Scholar 

  59. Sokol-Hessner, P. et al. Thinking like a trader selectively reduces individuals’ loss aversion. Proc. Natl Acad. Sci. USA 106, 5035 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  60. Montague, P. R. & Lohrenz, T. To detect and correct: norm violations and their enforcement. Neuron 56, 14–18 (2007).

    CAS  PubMed  Google Scholar 

  61. Sanfey, A. G., Rilling, J. K., Aronson, J. A., Nystrom, L. E. & Cohen, J. D. The neural basis of economic decision-making in the Ultimatum Game. Science 300, 1755–1758 (2003).

    CAS  PubMed  Google Scholar 

  62. Scherer, K. R. Emotions are emergent processes: they require a dynamic computational architecture. Philos. Trans. R. Soc. B 364, 3459–3474 (2009).

    Google Scholar 

  63. Diener, E., Larsen, R. J., Levine, S. & Emmons, R. A. Intensity and frequency: dimensions underlying positive and negative affect. J. Pers. Soc. Psychol. 48, 1253–1265 (1985).

    CAS  PubMed  Google Scholar 

  64. Kuppens, P., Oravecz, Z. & Tuerlinckx, F. Feelings change: accounting for individual differences in the temporal dynamics of affect. J. Pers. Soc. Psychol. 99, 1042–1060 (2010).

    PubMed  Google Scholar 

  65. Freeman, J. B. & Ambady, N. MouseTracker: software for studying real-time mental processing using a computer mouse-tracking method. Behav. Res. Methods 42, 226–241 (2010).

    PubMed  Google Scholar 

  66. Admon, R. & Pizzagalli, D. A. Dysfunctional reward processing in depression. Curr. Opin. Psychol. 4, 114–118 (2015).

    PubMed  Google Scholar 

  67. Keren, H. et al. Reward processing in depression: a conceptual and meta-analytic review across fMRI and EEG studies. Am. J. Psychiatry 175, 1111–1120 (2018).

    PubMed  PubMed Central  Google Scholar 

  68. Dowd, E. C., Frank, M. J., Collins, A., Gold, J. M. & Barch, D. M. Probabilistic reinforcement learning in patients with schizophrenia: relationships to anhedonia and avolition. Biol. Psychiatry. Cogn. Neurosci. Neuroimaging 1, 460–473 (2016).

    PubMed  PubMed Central  Google Scholar 

  69. Radloff, L. S. The CES-D Scale: A self-report depression scale for research in the general population. Appl. Psychol. Measure. 1, 385–401 (1977).

    Google Scholar 

  70. Moutoussis, M. et al. Neural activity and fundamental learning, motivated by monetary loss and reward, are intact in mild to moderate major depressive disorder. PLoS ONE 13, e0201451 (2018).

    PubMed  PubMed Central  Google Scholar 

  71. Demiralp, E. et al. Feeling blue or turquoise? Emotional differentiation in major depressive disorder. Psychol. Sci. 23, 1410–1416 (2012).

    PubMed  Google Scholar 

  72. Lindquist, K. A. & Barrett, L. F. in Handbook of Emotions (ed. Lewis M., Haviland-Jones, J. M. & Barrett L. F.) 513–530 (Guilford Press, 2008).

  73. Chang, L. J., Smith, A., Dufwenberg, M. & Sanfey, A. G. Triangulating the neural, psychological, and economic bases of guilt aversion. Neuron 70, 560–572 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  74. Hutchinson, J. B. & Barrett, L. F. The power of predictions: an emerging paradigm for psychological research. Curr. Dir. Psychol. Sci. 28, 280–291 (2019).

    PubMed  PubMed Central  Google Scholar 

  75. Glimcher, P. W. in Neuroeconomics 2nd edn (eds Paul W. Glimcher & Fehr E.) 373–391 (Academic, 2014).

  76. Chib, V. S., Rangel, A., Shimojo, S. & Doherty, J. P. Evidence for a common representation of decision values for dissimilar goods in human ventromedial prefrontal cortex. J. Neurosci. 29, 12315 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  77. Smith, D. V. et al. Distinct value signals in anterior and posterior ventromedial prefrontal cortex. J. Neurosci. 30, 2490 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  78. Rutledge, R. B. et al. Association of neural and emotional impacts of reward prediction errors with major depression. JAMA Psychiatry 74, 790–797 (2017).

    PubMed  PubMed Central  Google Scholar 

  79. Gradin, V. B. et al. Expected value and prediction error abnormalities in depression and schizophrenia. Brain J. Neurol. 134, 1751–1764 (2011).

    Google Scholar 

  80. Kumar, P. et al. Abnormal temporal difference reward-learning signals in major depression. Brain J. Neurol. 131, 2084–2093 (2008).

    CAS  Google Scholar 

  81. Kumar, P. et al. Impaired reward prediction error encoding and striatal–midbrain connectivity in depression. Neuropsychopharmacology 43, 1581–1588 (2018).

    PubMed  PubMed Central  Google Scholar 

  82. Ehring, T., Tuschen-Caffier, B., Schnulle, J., Fischer, S. & Gross, J. J. Emotion regulation and vulnerability to depression: spontaneous versus instructed use of emotion suppression and reappraisal. Emotion 10, 563–572 (2010).

    PubMed  Google Scholar 

  83. Chmielewski, M. & Kucker, S. C. An MTurk Crisis? Shifts in data quality and the impact on study results. Soc. Psychol. Pers. Sci. https://doi.org/10.1177/1948550619875149 (2019).

  84. Posner, J., Russell, J. A. & Peterson, B. S. The circumplex model of affect: an integrative approach to affective neuroscience, cognitive development, and psychopathology. Dev. Psychopathol. 17, 715–734 (2005).

    PubMed  PubMed Central  Google Scholar 

  85. Gross, J. J. & John, O. P. Individual differences in two emotion regulation processes: implications for affect, relationships, and well-being. J. Pers. Soc. Psychol. 85, 348–362 (2003).

    PubMed  Google Scholar 

  86. Bagby, R. M., Parker, J. D. A. & Taylor, G. J. The twenty-item Toronto Alexithymia Scale—I. Item selection and cross-validation of the factor structure. J. Psychosom. Res. 38, 23–32 (1994).

    CAS  PubMed  Google Scholar 

  87. Gard, D. E., Gard, M. G., Kring, A. M. & John, O. P. Anticipatory and consummatory components of the experience of pleasure: a scale development study. J. Res. Pers. 40, 1086–1102 (2006).

    Google Scholar 

  88. Carver, C. S. & White, T. L. Behavioral inhibition, behavioral activation, and affective responses to impending reward and punishment: the BIS/BAS Scales. J. Pers. Soc. Psychol. 67, 319–333 (1994).

    Google Scholar 

  89. Snaith, R. P. et al. A scale for the assessment of hedonic tone the Snaith–Hamilton Pleasure Scale. Br. J. Psychiatry. J. Ment. Sci. 167, 99–103 (1995).

    CAS  Google Scholar 

  90. Marin, R. S., Biedrzycki, R. C. & Firinciogullari, S. Reliability and validity of the Apathy Evaluation Scale. Psychiatry Res. 38, 143–162 (1991).

    CAS  PubMed  Google Scholar 

  91. Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effect models using lme4. J. Stat. Softw. 2015, 48 (2015).

    Google Scholar 

  92. Freeman, J., Dale, R. & Farmer, T. Hand in motion reveals mind in motion. Front Psychol. https://doi.org/10.3389/fpsyg.2011.00059 (2011).

  93. Wulff, D. U., Haslbeck, J. M. B., Kieslich, P. J., Henninger, F. & Schulte-Mecklenbeck, M. in A Handbook of Process Tracing Methods (eds M. Schulte_Mecklenbeck, A. Kughberger & J. G. Johnson) (2019).

  94. Maris, E. & Oostenveld, R. Nonparametric statistical testing of EEG- and MEG-data. J. Neurosci. Methods 164, 177–190 (2007).

    Google Scholar 

  95. Barr, D. clusterperm. Github https://github.com/dalejbarr/clusterperm (2019).

  96. Frömer, R., Maier, M. & Abdel Rahman, R. Group-Level EEG-processing pipeline for flexible single trial-based analyses including linear mixed models. Front. Neurosci. 12, 48 (2018).

    PubMed  PubMed Central  Google Scholar 

  97. Maris, E. Statistical testing in electrophysiological studies. Psychophysiology 49, 549–565 (2012).

    PubMed  Google Scholar 

Download references

Acknowledgements

The authors thank H. Fan for assistance in running participants for experiment 3, and M. Frank, V. Murty, A. Shenhav and M. Nassar for insightful feedback and comments on early manuscript drafts. The research was funded by a Center of Biological Research Excellence grant P20GM103645 from the National Institute of General Medical Sciences awarded to O.F.H. The funders had no role in the study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations

  1. Department of Cognitive, Linguistic, Psychological Sciences, Brown University, Providence, RI, USA

    Joseph Heffner, Jae-Young Son & Oriel FeldmanHall

  2. Carney Institute for Brain Science, Brown University, Providence, RI, USA

    Oriel FeldmanHall

Authors
  1. Joseph Heffner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jae-Young Son
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Oriel FeldmanHall
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.H., J.-Y.S. and O.F.H. contributed to designing the research and writing the paper. J.H. analysed the data.

Corresponding author

Correspondence to Oriel FeldmanHall.

Ethics declarations

Competing interests

The authors declare no competing interests

Additional information

Peer review information Nature Human Behaviour thanks Bernard Balleine and the other, anonymous, reviewer(s) 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.

Supplementary information

Supplementary Information

Supplementary Methods, Results, Tables 1–23, Figs. 1–18 and References.

Reporting summary

Peer review information.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Heffner, J., Son, JY. & FeldmanHall, O. Emotion prediction errors guide socially adaptive behaviour. Nat Hum Behav 5, 1391–1401 (2021). https://doi.org/10.1038/s41562-021-01213-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41562-021-01213-6

This article is cited by

Search

Advanced 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