Some Exact Results from a Coarse Grained Formulation of Genetic Dynamics

C. R. Stephens

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arXiv · nlin/0105029

Some Exact Results from a Coarse Grained Formulation of Genetic Dynamics

C. R. Stephens

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Abstract

We extend a recently developed exact schema based, or coarse grained, formulation of genetic dynamics \cite{stewael,stewael1,stewael2} and its associated exact Schema theorem to an arbitrary selection scheme and a general crossover operator. We show that the intuitive``building block'' interpretation of the former is preserved leading to hierarchical formal solutions of the equations that upon iteration lead to new results for the limiting distribution of a population in the case of 1-point crossover and ``weak'' selection, where we define quantitatively ``weak''. We also derive an exact, analytic form for the population distribution as a function of time for a flat landscape and 1-point crossover.

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C. R. Stephens. 2001-05-17. Some Exact Results from a Coarse Grained Formulation of Genetic Dynamics. https://arxiv.org/abs/nlin/0105029

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