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arXiv · 0909.3933

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

Kavita Jain·Abhishek Dasgupta·Gayatri Das
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Abstract

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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Kavita Jain, Abhishek Dasgupta, Gayatri Das. 2009-09-22. Exact and limit distributions of the largest fitness on correlated fitness landscapes. https://doi.org/10.1088/1742-5468%2F2009%2F10%2Fl10001

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