Amplifiers of selection

B. Adlam, K. Chatterjee, M. Nowak, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2015) 20150114.

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Journal Article | Published | English
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Abstract
When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement-that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.
Publishing Year
Date Published
2015-09-08
Journal Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Acknowledgement
K.C. gratefully acknowledges support from ERC Start grant no. (279307: Graph Games), Austrian Science Fund (FWF) grant no. P23499-N23, and FWF NFN grant no. S11407-N23 (RiSE).
Volume
471
Issue
2181
Article Number
20150114
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Adlam B, Chatterjee K, Nowak M. Amplifiers of selection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2015;471(2181):20150114. doi:10.1098/rspa.2015.0114
Adlam, B., Chatterjee, K., & Nowak, M. (2015). Amplifiers of selection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2181), 20150114. https://doi.org/10.1098/rspa.2015.0114
Adlam, Ben, Krishnendu Chatterjee, and Martin Nowak. “Amplifiers of Selection.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (2015): 20150114. https://doi.org/10.1098/rspa.2015.0114.
B. Adlam, K. Chatterjee, and M. Nowak, “Amplifiers of selection,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 471, no. 2181, p. 20150114, 2015.
Adlam B, Chatterjee K, Nowak M. 2015. Amplifiers of selection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 471(2181), 20150114.
Adlam, Ben, et al. “Amplifiers of Selection.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 471, no. 2181, Royal Society of London, 2015, p. 20150114, doi:10.1098/rspa.2015.0114.
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