Comprehensive scaling laws across animals, microorganisms and plants

TL;DR

This paper develops a comprehensive set of biological scaling laws applicable across animals, microorganisms, and plants, supported by extensive data, revealing fundamental principles of biological form and function.

Contribution

It introduces a unified framework of scaling laws based on invariance principles for complex biological systems, integrating fluid dynamics and elasticity.

Findings

Scaling laws accurately predict biological dynamics across diverse species.

Extensive data supports the universality of the proposed scaling laws.

Predictions made for prehistoric organisms where data is unavailable.

Abstract

Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e., invariant) under a change of units. A more general framework is a change of variables for the governing laws that takes all equations, boundary, and interaction conditions into themselves. We consider an accepted macroscale system of partial differential equations including coupled fluid dynamics, nonlinear elasticity, and rigid body mechanics for a complex organism. We show that there is a set of scaling laws where length, time, density, elastic modulus, viscosity, and gravitational constant undergo nontrivial scaling (Table 1). We compare these results to extensive data sets mined from the literature on beating frequency of flying, swimming, and running animals, speed of bacteria, insects, fish, mammals and reptiles, leg stiffness of mammals, and modulus of elasticity of plants. The uniform agreement of the scaling laws with the dynamics of fauna, flora, and microorganisms supports the dominating role of coupled nonlinear elasticity and fluid dynamics in evolutionary development. We conclude with predictions for some prehistoric cases for which observations are unavailable.