Mathematical Structure of Evolutionary Theory

Abstract

Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential equation. A precise definition of Wright's adaptive landscape is given and a new and consistent interpretation of Fisher's fundamental theorem of natural selection is provided. Based on a recently discovered theorem the generality of the proposed laws is illustrated by an explicit demonstration of their equivalence to a general conventional non-equilibrium dynamics formulation. The proposed laws provide a coherence framework to discuss several current evolutionary problems, such as speciation and stability, and gives a firm base for the application of statistical physics tools in Darwinian dynamics.