2006/04/11 by David B. Saakian, D. B. Saakian, Enrique Muñoz +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Applied mathematics #Biology #Demography #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Fitness approximation #Fitness function #Fitness landscape #Genetics #Lagrange multiplier #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical optimization #Mathematics #Population #Representation (politics) #Sequence (biology) #Viral quasispecies #Virus #cond-mat.stat-mech #q-bio.PE
paper · pdf · doi:10.1103/physreve.73.041913
published as Phys. Rev. E 73 (2006) 041913 · 10 pages, 3 figures, 2 tables
openalex publication_date 2006/04/11 · arxiv created 2006/08/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.