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Gene surfing in expanding populations

Author

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  • Hallatschek, Oskar
  • Nelson, David R.

Abstract

Large scale genomic surveys are partly motivated by the idea that the neutral genetic variation of a population may be used to reconstruct its migration history. However, our ability to trace back the colonization pathways of a species from their genetic footprints is limited by our understanding of the genetic consequences of a range expansion. Here, we study, by means of simulations and analytical methods, the neutral dynamics of gene frequencies in an asexual population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a “surfing†mechanism [Edmonds, C.A., Lillie, A.S., Cavalli-Sforza, L.L., 2004. Mutations arising in the wave front of an expanding population. Proc. Natl. Acad. Sci. 101, 975–979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our stochastic simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in the presence of cooperation between individuals (“pushed waves†) than when individuals proliferate independently (“pulled waves†), and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction–diffusion systems, that yields simple predictions for any deterministic population dynamics. Our analytical theory compares well with the simulation results for pushed waves, but is less accurate in the case of pulled waves when stochastic fluctuations in the tip of the wave are important.

Suggested Citation

  • Hallatschek, Oskar & Nelson, David R., 2008. "Gene surfing in expanding populations," Theoretical Population Biology, Elsevier, vol. 73(1), pages 158-170.
  • Handle: RePEc:eee:thpobi:v:73:y:2008:i:1:p:158-170
    DOI: 10.1016/j.tpb.2007.08.008
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    References listed on IDEAS

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    Cited by:

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    2. Louvet, Apolline, 2022. "Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component," Theoretical Population Biology, Elsevier, vol. 145(C), pages 22-37.
    3. Kajántó, Sándor & Néda, Zoltán, 2018. "Universality in the coarse-grained fluctuations for a class of linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 215-220.
    4. Paula Villa Martín & Miguel A Muñoz & Simone Pigolotti, 2019. "Bet-hedging strategies in expanding populations," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-17, April.
    5. Wakano, Joe Y. & Kawasaki, Kohkichi & Shigesada, Nanako & Aoki, Kenichi, 2011. "Coexistence of individual and social learners during range expansion," Theoretical Population Biology, Elsevier, vol. 80(2), pages 132-140.
    6. Máté, Gabriell & Néda, Zoltán, 2016. "The advantage of inhomogeneity — Lessons from a noise driven linearized dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 310-317.
    7. Barton, N.H. & Etheridge, A.M. & Kelleher, J. & Véber, A., 2013. "Genetic hitchhiking in spatially extended populations," Theoretical Population Biology, Elsevier, vol. 87(C), pages 75-89.
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    9. Foutel-Rodier, Félix & Etheridge, Alison M., 2020. "The spatial Muller’s ratchet: Surfing of deleterious mutations during range expansion," Theoretical Population Biology, Elsevier, vol. 135(C), pages 19-31.

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