Exact and limit distributions of the largest fitness on correlated fitness landscapes

Details Exact and limit distributions of the largest fitness on correlated fitness landscapes Exact and limit distributions of the largest fitness on correlated fitness landscapes

2009-09-22

arxiv.org/abs/0909.3933v1

J. Stat. Mech. (2009) L10001

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We study the distribution of the maximum of a set of random fitnesses with 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 $\ell=1,...,L$. We present analytical calculations for the following three solvable cases: (i) one-step mutants with arbitrary $\ell$ (ii) weakly correlated fitnesses with $\ell=L/2$ (iii) strongly correlated fitnesses with $\ell=2$. In all these cases, we find that the limit distribution for the maximum fitness is not of the standard Gumbel form.

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