Scale-free distribution of silences

Abstract

Soundscape studies help us understand ecological processes, biodiversity distribution, anthropic influences, and even urban quality, across a wide variety of places and time periods. In this work, instead of looking for differences, we ask if there are common characteristics shared by all soundscapes. Based on our results, we propose a universal distribution of quiet-time (background noise) and sound-time (acoustic energy bursts) in audio recordings. We analyzed one continuous hour during daylight and one at night, from ten randomly selected days in each environment: urban, dry forest, savanna, rupestrian field, Atlantic forest, marine, and freshwater. We found that the histograms of the quiet-time followed a power law for all scenarios analyzed, they present fractal events or scale-free distributions. This distribution covers up to four orders of magnitude, with an exponent of 1.6≤α≤2.0 for all soundscapes. By contrast, the sound-time distribution in all environments followed a log-normal or timescale dependence, with a typical time for the duration of sounds (0.06–0.12 s). Such time duration limitation can be related to the physiology of sound emission in animals.