Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe

Abstract

An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the genetic sequence is large. Applying the equation to the mutation-selection model by Eigen provides the critical mutation rate for the error catastrophe. Phenotypic fluctuation of clones (individuals sharing the same gene) is introduced into this evolution equation. With this formalism, it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations, i.e., noise can enhance robustness of a fitted state to mutation. Our formalism is systematic and general, while approximations to derive more tractable evolution equations are also discussed.

22 pages, 2 figures

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• The intermediate evolution phase in case of truncated selection
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• Robustness and epistasis in mutation-selection models
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• The Baldwin effect under multi-peaked fitness landscapes: Phenotypic fluctuation accelerates evolutionary rate
• Biological Evolution in a Multidimensional Fitness Landscape
• Dynamics of the Chemical Master Equation, a strip of chains of equations in d-dimensional space
• Evolution of Genetic Redundancy : The Relevance of Complexity in Genotype-Phenotype Mapping
• Exact results in the large system size limit for the dynamics of the Chemical Master Equation, a one dimensional chain of equations