Mathematical modeling of evolution. Solved and open problems |
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Authors: | Peter Schuster |
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Institution: | 1.Institut für Theoretische Chemmie,Universit?t Wien,Wien,Austria |
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Abstract: | Evolution is a highly complex multilevel process and mathematical modeling of evolutionary phenomenon requires proper abstraction
and radical reduction to essential features. Examples are natural selection, Mendel’s laws of inheritance, optimization by
mutation and selection, and neutral evolution. An attempt is made to describe the roots of evolutionary theory in mathematical
terms. Evolution can be studied in vitro outside cells with polynucleotide molecules. Replication and mutation are visualized
as chemical reactions that can be resolved, analyzed, and modeled at the molecular level, and straightforward extension eventually
results in a theory of evolution based upon biochemical kinetics. Error propagation in replication commonly results in an
error threshold that provides an upper bound for mutation rates. Appearance and sharpness of the error threshold depend on
the fitness landscape, being the distribution of fitness values in genotype or sequence space. In molecular terms, fitness landscapes are the results of two consecutive mappings from sequences into structures and from
structures into the (nonnegative) real numbers. Some properties of genotype–phenotype maps are illustrated well by means of
sequence–structure relations of RNA molecules. Neutrality in the sense that many RNA sequences form the same (coarse grained)
structure is one of these properties, and characteristic for such mappings. Evolution cannot be fully understood without considering
fluctuations—each mutant originates form a single copy, after all. The existence of neutral sets of genotypes called neutral networks, in particular, necessitates stochastic modeling, which is introduced here by simulation of molecular evolution in a kind
of flowreactor. |
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