Analytical solution of the evolution dynamics on a multiplicative-fitness landscape

In an infinite population the frequency distribution of individuals carrying a given number of mutations obeys a set of recursion equations, the equilibrium solution of which describes the mutation-selection balance. Although this solution is well-known in the case of a multiplicative-fitness landsc...

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Bibliographic Details
Published in:Journal of mathematical biology 2003-11, Vol.47 (5), p.453-456
Main Authors: Maia, Leonardo P, Botelho, Daniela F, Fontanari, José F
Format: Article
Language:English
Subjects:
Alleles
Biological Evolution
Models, Genetic
Mutation
Mutation - genetics
Population Dynamics
Reproduction, Asexual - genetics
Selection, Genetic
Statistical Distributions
Studies
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Summary:In an infinite population the frequency distribution of individuals carrying a given number of mutations obeys a set of recursion equations, the equilibrium solution of which describes the mutation-selection balance. Although this solution is well-known in the case of a multiplicative-fitness landscape, where it is assumed that all mutations are deleterious and that each new mutation reduces the fitness of the individual by the same fraction, we are not aware of the existence of an analytical solution for the full dynamics. Using the generating function approach, we present here an explicit analytical solution for the frequency distribution recursion equations valid for all generations and initial conditions.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-003-0208-8