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Mathematical Structure of Evolutionary Theory | | P. Ao
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15 Mar 2004 | | Subject: | Quantitative Methods; Populations and Evolution; Adaptation and Self-Organizing Systems; Statistical Mechanics; Dynamical Systems | q-bio.QM cond-mat.stat-mech math.DS nlin.AO q-bio.PE | | 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. | | Source: | arXiv, q-bio.QM/0403020 | | Services: | Forum | Review | PDF | Favorites | |
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