The fastest evolutionary trajectory

Traulsen, Arne; Iwasa, Yoh; Nowak, Martin A.

doi:10.1016/j.jtbi.2007.08.012

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The fastest evolutionary trajectory

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Traulsen, Arne
Department Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, Max Planck Society;
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Traulsen, A., Iwasa, Y., & Nowak, M. A. (2007). The fastest evolutionary trajectory. Journal of Theoretical Biology, 249(3), 617-623. doi:10.1016/j.jtbi.2007.08.012.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-D730-B

Abstract

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.