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The shape of a seed bank tree

Part of: Markov processes Combinatorial probability

Published online by Cambridge University Press:  02 June 2022

Adrián González Casanova ,
Lizbeth Peñaloza  and
Arno Siri-Jégousse
Adrián González Casanova*
Affiliation:
Universidad Nacional Autónoma de México
Lizbeth Peñaloza*
Affiliation:
Universidad del Mar
Arno Siri-Jégousse*
Affiliation:
Universidad Nacional Autónoma de México
*
*Postal address: Av. Universidad 3000, Col. UNAM Ciudad Universitaria, Delegación Coyoacán C.P. 04510 Ciudad de México.
***Postal address: Ciudad Universitaria, Santa María Huatulco, Oaxaca, México C.P. 70989.
*Postal address: Av. Universidad 3000, Col. UNAM Ciudad Universitaria, Delegación Coyoacán C.P. 04510 Ciudad de México.
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Abstract

We derive the asymptotic behavior of the total, active, and inactive branch lengths of the seed bank coalescent when the initial sample size grows to infinity. These random variables have important applications for populations evolving under some seed bank effects, such as plants and bacteria, and for some cases of structured populations like metapopulations. The proof relies on the analysis of the tree at a stopping time corresponding to the first time a deactivated lineage is reactivated. We also give conditional sampling formulas for the random partition, and we study the system at the time of the first reactivation of a lineage. All these results provide a good picture of the different regimes and behaviors of the block-counting process of the seed bank coalescent.

Keywords

Seed bankstructured coalescentbranch lengthssampling formula

MSC classification

Secondary: 60C05: Combinatorial probability 60J28: Applications of continuous-time Markov processes on discrete state spaces 92D25: Population dynamics (general)
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 631 - 651
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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