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Weak convergence of non-neutral genealogies to Kingman’s coalescent

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  • Brown, Suzie
  • Jenkins, Paul A.
  • Johansen, Adam M.
  • Koskela, Jere

Abstract

Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both applications. Under neutrality, when fitnesses of particles are independent from those of their parents, rescaled genealogies are known to converge to Kingman’s coalescent. Recent work has established convergence under non-neutrality, but only for finite-dimensional distributions. We prove weak convergence of non-neutral genealogies on the space of càdlàg paths under standard assumptions, enabling analysis of the whole genealogical tree.

Suggested Citation

  • Brown, Suzie & Jenkins, Paul A. & Johansen, Adam M. & Koskela, Jere, 2023. "Weak convergence of non-neutral genealogies to Kingman’s coalescent," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 76-105.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:76-105
    DOI: 10.1016/j.spa.2023.04.016
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    References listed on IDEAS

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    1. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
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