The optimization and shock waves in evolution dynamics

Details The optimization and shock waves in evolution dynamics The optimization and shock waves in evolution dynamics

2009-08-17

arxiv.org/abs/0908.2290v1

Biology

Quantitative Biology

Populations and Evolution

6 pages

Scientific paper

We consider the optimal dynamics in the infinite population evolution models with general symmetric fitness landscape. The search of optimal evolution trajectories are complicated due to sharp transitions (like shock waves) in evolution dynamics with smooth fitness landscapes, which exist even in case of popular quadratic fitness. We found exact analytical solutions for discontinuous dynamics at the large genome length limit. We found the optimal mutation rates for the fixed fitness landscape. The single peak fitness landscape gives the fastest dynamics to send the vast majority of the population from the initial sequence to the neighborhood of the final sequence.

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