Behavior needs neural variability

Human and non-human animal behavior is highly malleable adapts successfully to internal external demands. Such behavioral success stands in striking contrast the apparent instability neural activity (i.e., variability) from which it arises. Here, we summon considerable evidence across scales, species, imaging modalities that variability represents a key, undervalued dimension for understanding brain-behavior relationships at inter- intra-individual levels. We believe only by incorporating specific focus on will foundation of be comprehensively understood. The ability adapt our multitude ever-changing demands (despite limited toolset) forms basis extraordinary cognitive capability efficiency human animals. For example, consider cyclist their daily commute work as upcoming traffic light suddenly switches green yellow. If streets are empty feels fit, then they may speed up clear crossing just before turns red. However, if crowded cyclist's legs tired, instead choose stop wait next light. How does brain enable flexible adaptation these different contexts task allow choosing optimal alternative? formation execution such complex, adaptive relate processing integration information brain? propose processes emerges through capacity dynamically adjust moment moment—that is, (Figure 1). From single-cell spiking order milliseconds (Harris Thiele, 2011Harris K.D. Thiele A. Cortical state attention.Nat. Rev. Neurosci. 2011; 12: 509-523Crossref PubMed Scopus (443) Google Scholar) ensemble measured blood oxygenation level-dependent (BOLD) fMRI over seconds (Garrett et al., 2013aGarrett D.D. Samanez-Larkin G.R. MacDonald S.W.S. Lindenberger U. McIntosh A.R. Grady C.L. Moment-to-moment signal variability: frontier mapping?.Neurosci. Biobehav. 2013; 37: 610-624Crossref (259) Scholar), variable time variety (perhaps all) temporal spatial scales (Fox Raichle, 2007Fox M.D. Raichle M.E. 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USA. 2015; 112: 7593-7598Crossref (39) Waschke 2019Waschke Tune Obleser Local desynchronization pupil-linked arousal differentially shape states sensory performance.eLife. 2019; e51501Crossref (9) It no longer debated likely present every level nervous system function (Faisal 2008Faisal A.A. Selen L.P.J. Wolpert D.M. Noise system.Nat. 2008; 9: 292-303Crossref (1390) argue how why aspects behaviorally relevant. first outline recently developed methodologies define quantify specifically recordings (from single-unit BOLD fMRI). show not captures inter-individual (even “trait-like”) differences overall but also tracks available resources, information, within an individual (“states”). Despite strong initial relevance variability, its precise role remains unclear present. Hence, experimental designs probe distinct sources aim maximizing sensitivity intra- behavior. By summarizing communalities variability-based between invasive non-invasive neuroscience, bridge methodological conceptual gaps fields. To foster into various approximations highlight three primary complementary “families” measures typically used field: variance-based, frequency-based, theory-based (see Figure 2). facilitate implementation families measures, point key publications provide details examples methods, well online resources commonly software packages Table Of note, depending design used, all highlighted below theoretically capable detecting both strictly task-related task-unrelated probing associations behavior.Table 1Overview common variabilityMeasure familyExample measureNeural signalOverviewResourcesVariance-based measurestime series varianceall typesvariance (or SD) Scholar)VarTbX (https://github.com/LNDG/vartbx); in-built functions most programming analyses platforms (R, Python, MATLAB)Fano factorspikingvariance divided mean “mean-matched”) conditions variance estimation (Churchland 2010Churchland M.M. Yu B.M. Cunningham J.P. Sugrue L.P. Cohen Corrado G.S. Newsome W.T. Clark A.M. Hosseini P. Scott B.B. al.Stimulus onset quenches widespread phenomenon.Nat. 2010; 13: 369-378Crossref (530) Scholar)In-built analysis platformsFrequency-based measuresspectral powerLFP, MEG/EEG, BOLD(time-resolved) estimates oscillatory power, more low frequencies (e.g., 2–10 Hz), computed using Fourier-based (Pachitariu 2015Pachitariu M. Lyamzin D.R. Sahani Lesica N.A. State-dependent population coding auditory cortex.J. 35: 2058-2073Crossref Scholar)Fieldtrip (Oostenveld 2011Oostenveld R. Fries Maris E. Schoffelen J.-M. FieldTrip: open source advanced MEG, EEG, electrophysiological data.Comput. Intell. 2011: 156869Crossref (3663) Scholar): https://www.fieldtriptoolbox.org/; Python MNE (Gramfort 2013Gramfort Luessi Larson Engemann D.A. Strohmeier D. Brodbeck Goj Jas Brooks T. Parkkonen Hämäläinen MEG EEG data MNE-Python.Front. 7: 267Crossref (472) https://mne.tools/stable/index.html; BrainStorm (Tadel 2011Tadel F. Baillet Mosher J.C. Pantazis Leahy R.M. Brainstorm: user-friendly application MEG/EEG analysis.Comput. 879716Crossref (1202) https://neuroimage.usc.edu/brainstorm/1/f exponentLFP, MEG/EEGseparation aperiodic analyzing peaks steepness power spectra; resolved, estimated sections single trials)FOOOF (Donoghue 2020Donoghue Haller Peterson E.J. Varma Sebastian Gao Noto Lara A.H. Wallis J.D. Knight R.T. al.Parameterizing spectra periodic components.Nat. 2020; 23: 1655-1665Crossref (5) https://github.com/fooof-tools/fooof; eBOSC (Kosciessa 2020aKosciessa J.Q. Grandy T.H. Werkle-Bergner Single-trial characterization rhythms: potential challenges.Neuroimage. 206: 116331Crossref (6) https://github.com/jkosciessa/eBOSC; IRASA (Wen Liu, 2016Wen H. Liu Z. Separating Fractal Oscillatory Components Power Spectrum Neurophysiological Signal.Brain Topogr. 2016; 29: 13-26Crossref (47) https://github.com/raphaelvallat/yasa/Information-theoretic measuresMSELFP, BOLDirregularity scales; based recurring patterns (Costa 2002Costa Goldberger A.L. Peng C.K. Multiscale entropy complex physiologic series.Phys. Lett. 2002; 89: 068102Crossref Kosciessa 2020bKosciessa Kloosterman Standard multiscale reflects dynamics mismatched scales: what’s irregularity got do it?.PLoS Comput. Biol. 16: e1007885Crossref (3) Scholar); also, resolved sparse (Grandy 2016Grandy Schmiedek On neuroimaging data.Sci. Rep. 6: 23073Crossref (0) Scholar)mMSE (Kloosterman 2020Kloosterman Fahrenfort J.J. Boosts track liberal shifts decision bias.eLife. e54201Crossref modification original MSE, controlling power-related, scale-specific biases (https://github.com/LNDG/mMSE; https://www.fieldtriptoolbox.org/example/entropy_analysis/)WPELFP, MEG/EEGtime-resolved symbolic patterns; amplitude re-introduced weighting (Bandt Pompe, 2002Bandt Pompe B. Permutation entropy: natural complexity measure 88: 174102Crossref Fadlallah 2013Fadlallah Chen Keil Príncipe Weighted-permutation information.Phys. E Stat. Nonlin. 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Bandettini P.A. Calhoun V.D. Corbetta Penna S.D. Duyn J.H. Glover G.H. Gonzalez-Castillo al.Dynamic connectivity: Promise, issues, interpretations.Neuroimage. 80: 360-378Crossref (1223) Scholar)GIFT: https://trendscenter.org/software/gift/; DynaConn (Sakoğlu 2010Sakoğlu Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A method evaluating dynamic network task-modulation: schizophrenia.MAGMA. 351-366Crossref CONN (Whitfield-Gabrieli Nieto-Castanon, 2012Whitfield-Gabrieli Nieto-Castanon Conn: correlated anticorrelated networks.Brain Connect. 2012; 2: 125-141Crossref Scholar)BOLD, dependent; dFC, connectivity; electroencephalography; LFP, local field potential; magnetoencephalography; multi-scale entropy; SD, standard deviation; WPE, weighted permutation entropy. Open table new tab BOLD, simplest deviation (square root variance), representing distributional width 2B). Variance applied ways neuroscience/neuroimaging disciplines, including single- multi-unit estimate Fano factor), electrophysiology electro- magnetoencephalography (EEG, MEG), fMRI-BOLD (SDBOLD) squared successive (the derivative series; von Neumann 1941von Kent R.H. Bellinson H.R. Hart B.I. Mean Square Successive Difference.Ann. Math. 1941; 153-162Crossref analyzed frequency domain calculating spectral wide range frequencies. As transformation domains lossless via Fourier transform, mathematically nothing than frequency-specific (with total equivalent variance). Importantly, assumes signals consist sinusoidal waveforms. Under (still contentious) assumption oscillations primary, “filter” understand function, types field. typical calculate time-resolved Low-frequency (∼2–10 Hz) widely approximation (LFP) Pachitariu Reimer 2014Reimer Froudarakis Cadwell C.R. Yatsenko Denfield Tolias A.S. 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