Aperiodic processes explaining rhythms in behavior: A matter of false detection or definition?

Abstract

Behavioral studies suggest attention-related performancefluctuates at a 3-8Hz rhythm (Landau and Fries, 2012;Fiebelkorn et al., 2013). Brookshire (2022) argues that theseprevious studies failed to distinguish periodic from aperiodicprocesses, which led to the spurious detection of rhythms. Theargument is based on simulations of accuracy time courses(ATCs) by autoregressive models of order 1 (AR(1)), which is aknown aperiodic process. Brookshire shows that for this aperi-odic process, conventional methods often detect spurious peaksin the 3-8Hz range. Here, we argue that stationary stochasticAR(1) processes are invalid models of ATCs in general as ATCsare deterministic, non-stationary signals. When AR(1) realiza-tions are taken as models for deterministic signals, they do notconstitute per definition aperiodic processes. It is therefore notclear whether previous methods indeed detected rhythms spuri-ously. Furthermore, we show that because Brookshire’s methodrelies on AR(1) model fits, it can have very low sensitivity whennon-rhythmic signals are superimposed onto rhythmic signals.Here, we argue that an appropriate model of an ATCs is a de-terministic signal (akin to an impulse response or event-relatedpotential) with additive white noise due to random sampling ofhits and misses. Such a deterministic ATC can be either peri-odic or aperiodic. We show that when the deterministic ATC istruly aperiodic, detrending and random sampling lead to spu-rious rhythm detection. This supports the general point thatprevious studies did not adequately distinguish periodic fromaperiodic processes. Our analysis naturally suggests an effec-tive alternative method based on cross-validation which avoidsthe use of AR(1) models.

Perplexity about periodicity repeats perpetually: A response to Brookshire

“…The second method proposed, the robust estimation method, is presented as having an acceptable detection ratio. However, the true-positive rate of this methodology is unacceptably low (Figure 3; as pointed out by several commentaries on this work, e.g., Fiebelkorn, 2022; Vinck et al, 2022). This fact is masked in the detection ratios by false-positive rates approaching zero.…”

“…When periodicity has been established, the evidence can be further strengthened by replication, e.g. across different conditions within one study (for a similar approach, see Vinck et al, 2022). Indeed, several studies have found that different experimental conditions produce phase locking to the reset event at very similar frequencies (Landau and Fries, 2012; Zhang et al, 2019).…”

Performance modulations phase-locked to action depend on internal state

“…Here we recorded a larger sample size compared to previous experiments, and we performed both fixed-effects and random-effects statistical testing, using for the analysis the methods that, to our knowledge, provide the best trade-off between sensitivity and specificity (Tosato et al, 2022). We stress the need in the field for studies with higher statistical power (Button et al, 2013) random-effects statistics (Fries and Maris, 2021), and a careful consideration in the choice of the analysis methods (Kienitz et al, 2021; Tosato et al, 2022; Vinck et al, 2022).…”

“…Recently, there was a debate about reproducibility of psychophysics studies reporting such modulations (Lin et al, 2021; Morrow and Samaha; van der Werf et al, 2021) and about the correct use of analysis methods in the field (Brookshire, 2022; Re et al, 2022; Tosato et al, 2022; Vinck et al, 2022). The fact that different studies applied different analysis methods and statistical tests makes the comparison difficult.…”

Periodic neglect after frontoparietal lesions provides causal evidence for rhythmic attention sampling

“…Specifically, electrophysiological recordings in non-human primates 11,41 and humans 13,42 demonstrated that theta oscillations shape neural excitability in a phase-specific manner and periodically reweight functional connections between different nodes in the frontoparietal attention network 11,42,43 . Recently, the rhythmic nature of attention has been called into question based on behavioral modeling 44 and is now actively debated 45 . These controversial findings are a direct consequence of the lack of causal data linking rhythmic fluctuations in behavior to oscillatory brain activity.…”