Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.
K.C. acknowledges support from ERC Start grant no. (279307: Graph Games), ERC Consolidator grant no. (863818: ForM-SMart), Austrian Science Fund (FWF) grant no. P23499-N23 and S11407-N23 (RiSE). M.A.N. acknowledges support from Office of Naval Research grant N00014-16-1-2914 and from the John Templeton Foundation.
Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Fast and strong amplifiers of natural selection. Nature Communications. 2021;12(1). doi:10.1038/s41467-021-24271-w
Tkadlec, J., Pavlogiannis, A., Chatterjee, K., & Nowak, M. A. (2021). Fast and strong amplifiers of natural selection. Nature Communications. Springer Nature. https://doi.org/10.1038/s41467-021-24271-w
Tkadlec, Josef, Andreas Pavlogiannis, Krishnendu Chatterjee, and Martin A. Nowak. “Fast and Strong Amplifiers of Natural Selection.” Nature Communications. Springer Nature, 2021. https://doi.org/10.1038/s41467-021-24271-w.
J. Tkadlec, A. Pavlogiannis, K. Chatterjee, and M. A. Nowak, “Fast and strong amplifiers of natural selection,” Nature Communications, vol. 12, no. 1. Springer Nature, 2021.
Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2021. Fast and strong amplifiers of natural selection. Nature Communications. 12(1), 4009.
Tkadlec, Josef, et al. “Fast and Strong Amplifiers of Natural Selection.” Nature Communications, vol. 12, no. 1, 4009, Springer Nature, 2021, doi:10.1038/s41467-021-24271-w.
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