Scaling and Scale Symmetries in Biological Systems

Abstract

This chapter reviews experimental results showing scaling, as a fundamental form of “theoretical symmetry” in biology. Allometry and scaling are the transformations of quantitative biological observables engendered by considering organisms of different sizes and at different scales, respectively. We then analyze anatomical fractal-like structures, the latter being ubiquitous in organs’ shape, yet with a fair amount of variability. We also discuss some observed temporal fractal like structures in biological time series. In the final part, we will provide some examples of space-time and of network configurations and dynamics.

The few concepts and mathematics needed to understand allometry and scaling are progressively introduced, always accompanied by a discussion of the main experimental findings, either through special cases or more general results. We focus in particular on the robustness of these empirical observations and the corresponding variability.