A generalized scaling law reveals synchrony-driven reorganization of brain dynamics across human lifespan

Ecological systems obey universal scaling laws such as Taylor’s law, which links population variance to the sample mean. Whether other complex systems with integrated and segregated network topology, the human brain, in particular, follow analogous scaling laws, and how these laws behave under synchronized neural activity, remains unknown. To address this question, our initial attempt to implement the Taylor’s law, has been hindered because neural signals at all measurement scales contain both positive and negative values, whereas Taylor’s law was restricted to non-negative ecological data [1]. To circumvent this limitation, we extend spatial Taylor’s law by replacing the sample mean with the root-mean-square (RMS) of the measurements, and apply this generalized law to detrended multivariate neural time series. The detrending operation has been performed as a necessary step to remove the trends and temporal mean from the data. Within this framework, we address our next question how synchronous or coordinated activity of the brain network influences the scaling law. We quantify synchrony using a dedicated metric of functional coordination and show analytically, and via numerical simulations using multivariate Poisson, negative binomial, uniform and gamma distributions, that the scaling exponent is inversely related to synchrony. Applying this approach to human fMRI data from three large cohorts (N = 840, ages 18–88 years) reveals distinct age-related trajectories of the scaling exponent, with healthy aging characterized by a substantial synchrony-induced reduction in this exponent. The synchrony–scaling relationship remains stable during resting-state activity but progressively shifts during naturalistic tasks across the lifespan, and is pronounced in limbic, subcortical, and cerebellar subnetworks, indicating preservation at subnetwork levels. Finally, individuals with ADHD exhibit altered synchrony–scaling coupling, highlighting the potential clinical and translational utility of this generalized scaling metric.Author summary: The human brain constantly reorganizes the way its regions coordinate with one another, yet a general, quantitative way to link this coordination to the brain’s variability has been missing. Classical scaling laws from ecology, such as Taylor’s law, connect the variance of a population to its mean, but they only work for non-negative data distributions and therefore could not be applied directly to brain signals, which fluctuate above and below zero once slow trends are removed. Here we generalize this scaling law by replacing the mean with the root-mean-square of detrended brain activity, which lets us apply it to the blood-oxygen-level-dependent activity (BOLD). Using analytical, simulations, and functional Magnetic Resonance Imaging (fMRI) data from 840 participants aged 18–88 years, we show that the strength of coordinated activity between brain regions, captured by average synchrony, systematically changes how the variance of brain activity scales in space. The average synchrony-scaling law association is stable in the resting state but changes during naturalistic tasks, such as movie watching or sensorimotor tasks, becomes weaker with healthy brain aging, and is disrupted in people with Attention-Deficit/Hyperactivity Disorder (ADHD). Our findings introduce a compact, interpretable, and broadly applicable metric that links long-term coordination to the variability of neural activity, with potential use as a marker of healthy aging and neurological or psychiatric disorders.