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Genealogy of a Wright-Fisher Model with Strong SeedBank Component

  • Jochen Blath
  • Bjarki Eldon
  • Adrián González Casanova
  • Noemi Kurt
Conference paper
Part of the Progress in Probability book series (PRPR, volume 69)

Abstract

We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seedbank effect. More precisely, we consider a simple seedbank age distribution with two atoms, leading to either classical or long genealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power N β of the population size N, thus giving rise to a ‘strong’ seedbank effect. For a certain range of β, we prove that the ancestral process of a sample of n individuals converges under a non-classical time-scaling to Kingman’s n−coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.

Keywords

Seedbanks Wright-Fisher model Kingman’s coalescent 

Mathematics Subject Classification (2000).

Primary 60K35 Secondary 92D15 

Notes

Acknowledgements

JB, BE and NK acknowledge support by the DFG SPP 1590 “Probabilistic structures in evolution”. AGC is supported by the DFG RTG 1845, the Berlin Mathematical School (BMS), and the Mexican Council of Science in collaboration with the German Academic Exchange Service (DAAD). The authors wish to thank Julien Berestycki and Dario Spanò for interesting discussions.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jochen Blath
    • 1
  • Bjarki Eldon
    • 1
  • Adrián González Casanova
    • 1
  • Noemi Kurt
    • 1
  1. 1.Institut für MathematikBerlinGermany

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