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 nonequilibrium 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:qbio/0403020
 Bibcode:
 2004q.bio.....3020A
 Keywords:

 Quantitative Biology  Quantitative Methods;
 Quantitative Biology  Populations and Evolution;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems
 EPrint:
 10 pages