2009/09/22 by Kavita Jain, Abhishek Dasgupta, Gayatri Das
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Social Sciences · #Applied mathematics #Biology #Computer science #Demography #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Extreme value theory #Fitness landscape #Gumbel distribution #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Population #Set (abstract data type) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #q-bio.PE
paper · pdf · doi:10.1088/1742-5468/2009/10/l10001
published as J. Stat. Mech. (2009) L10001
arxiv created 2009/09/22 · openalex publication_date 2009/10/07 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the distribution of the maximum of a set of random fitnesses with a fixed number of mutations in a model of biological evolution. The fitness variables are not independent and the correlations can be varied via a parameter . We present analytical calculations for the following three solvable cases: (i) one-step mutants with arbitrary , (ii) weakly correlated fitnesses with , (iii) strongly correlated fitnesses with . In all these cases, we find that the limit distribution for the maximum fitness is not of the standard Gumbel form.