Hierarchical network structure as the source of hierarchical dynamics (power law frequency spectra) in living and non-living systems: how state-trait continua (body plans, personalities) emerge from first principles in biophysics

TL;DR

This paper proposes that the hierarchical network structure of living systems underpins their fractal-like dynamics and power-law frequency spectra, explaining how physical and behavioral traits emerge from first principles in biophysics.

Contribution

It introduces a theory linking hierarchical network structures to power-law dynamics in living and non-living systems, providing a unified explanation for state-trait continua from first principles.

Findings

Hierarchical structures produce power-law frequency spectra.

Nested modularity embeds high frequencies within lower frequencies.

System development and collapse leave detectable dynamic traces.

Abstract

Living systems are hierarchical control systems that display a small world network structure, in which many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a power-law cluster size distribution (a mereology). Apart from their structure, the dynamics of living systems also shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or states (treble) that are nested within lower frequencies or traits (bass), producing a power-law frequency spectrum that is known as a state-trait continuum in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms vertically encode the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies produce physical as well as behavioral traits (i.e. body plans and personalities). Nested-modular structure then causes higher frequencies to be embedded within lower frequencies, producing a power law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.g. earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g. during maturation and disease) should leave specific traces in the dynamics of nested modular systems that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.