dorsal/arxiv
View SchemaMathematical Structure of Evolutionary Theory
| Authors | P. Ao |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0403020 |
| URL | https://arxiv.org/abs/q-bio/0403020 |
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.
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"abstract": "Here we postulate three laws which form a mathematical framework to capture\nthe essence of Darwinian evolutionary dynamics. The second law is most\nquantitative and is explicitly expressed by a unique form of stochastic\ndifferential equation. A precise definition of Wright\u0027s adaptive landscape is\ngiven and a new and consistent interpretation of Fisher\u0027s fundamental theorem\nof natural selection is provided. Based on a recently discovered theorem the\ngenerality of the proposed laws is illustrated by an explicit demonstration of\ntheir equivalence to a general conventional non-equilibrium dynamics\nformulation. The proposed laws provide a coherence framework to discuss several\ncurrent evolutionary problems, such as speciation and stability, and gives a\nfirm base for the application of statistical physics tools in Darwinian\ndynamics.",
"arxiv_id": "q-bio/0403020",
"authors": [
"P. Ao"
],
"categories": [
"q-bio.QM",
"cond-mat.stat-mech",
"math.DS",
"nlin.AO",
"q-bio.PE"
],
"title": "Mathematical Structure of Evolutionary Theory",
"url": "https://arxiv.org/abs/q-bio/0403020"
},
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