Population Genetics with Fluctuating Population Sizes

Abstract

Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is reviewed. We then study a situation such that the competing species are neutral at the equilibrium population size but population size fluctuations nevertheless favor fixation of one species over the other. In this case, a separation of timescales emerges naturally and allows adiabatic elimination of a fast population size variable to deduce the fluctuation-induced selection dynamics near the equilibrium population size. The results highlight the incompleteness of the standard population genetics with a strictly fixed population size.

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Acknowledgements

This work was supported in part by the National Science Foundation (NSF) through Grants Nos. DMR-1608501 and DMR-1306367 and by the Harvard Materials Research Science and Engineering Laboratory, through MRSEC Grant No. DMR-1420570. Portions of this research were conducted during a stay at the Center for Models of Life at the Niels Bohr Institute, the University of Copenhagen. Computations were performed on the Odyssey cluster supported by the FAS Division of Science Research Computing Group at Harvard University.

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Correspondence to Thiparat Chotibut.

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Chotibut, T., Nelson, D.R. Population Genetics with Fluctuating Population Sizes. J Stat Phys 167, 777–791 (2017). https://doi.org/10.1007/s10955-017-1741-y

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Keywords

  • Population genetics
  • Fluctuating population sizes
  • Dynamical system
  • Stochastic process