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

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

2006-11-08

arxiv.org/abs/q-bio/0611031v2

Biology

Quantitative Biology

Populations and Evolution

22 pages, 2 figures

Scientific paper

10.1103/PhysRevE.75.061909

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.

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