Information-Theoretic Origins of Metabolic Scaling

Abstract

Universal scaling laws are a signature of complex biological systems, yet the mechanisms by which microscopic stochastic processes generate robust macroscopic behaviour remain debated. Here we develop an information-theoretic approach to identify robust biological scaling using a stochastic ontogenetic growth model, in which correlated cellular bursts propagate from microscopic noise to organism-level metabolic fluctuations. We show that an information-neutral regime, defined as the minimum Kullback-Leibler divergence between fluctuation distributions generated under different microscopic correlation structures, identifies stochastic regimes for which macroscopic observables become maximally insensitive to microscopic details. Within this regime, metabolic scaling exponents converge across species sizes to a narrow range close to linear scaling relationship. The information-theoretic optimum is robust to temporal coarse-graining, indicating non-critical scale robustness without requiring proximity to a phase transition. Our results suggest that information neutrality provides a general principle for identifying robust stochastic mechanisms underlying biological scaling and illustrate how universal macroscopic behaviour can emerge from noisy microscopic dynamics.