Allometric Laws in Modular Dynamics: The Bauplan of Ontogenesis

Abstract

In recent decades, a resurgence of allometry in ecology and its associated scaling laws has been observed, going under the name macroecology. It is reasonable to think that the plethora of current works on experimental physiology using allometry is a continuation of the tradition of searching for the “Holy Grail” or Bauplan, the foundation of organic form and metabolic function. The project our group focused on over several decades is the development of a corpus of geometric techniques, especially Finsler differential geometry, for the study of systems of second order ordinary differential equations called Analytical Modular Dynamics, which seeks to describe interactions between cell populations of various organs. Thus, the Huxley/Needham Law in allometry becomes a consequence of metabolism and physiological interactions. The models obtained contrast strongly with Riemannian theory. The geodesic coefficients for our example depend only on the x-variables, as in all Riemannian geometries, but, is true in Finsler theory only for Berwald spaces.